RationalizeRoots: Software package for the rationalization of square roots

• Publication: Computer Physics Communications
• Author(s): Besier, MarcoWasser, PascalWeinzierl, Stefan
• Bibcode: 2020CoPhC.25307197B

The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to find such transformations. After an introduction to the theoretical background, we explain in detail how to use the program in practice.

Program files doi:http://dx.doi.org/10.17632/gbcc9z9tdb.1

Licensing provisions: GNU General Public License 3

Programming language: Mathematica, Maple

Nature of problem: Analytic solutions for Feynman integrals are critical for accurate theoretical predictions in high energy particle physics. The computation of these integrals often involves square roots that need to be rationalized via suitable variable transformations.

Solution method: Appropriate variable changes for given square roots are constructed by parametrizing algebraic hypersurfaces associated to these square roots by families of lines.

$\texttt{SpaceMath}$ version 1.0. $\$ A $\texttt{Mathematica}$ package for beyond the standard model parameter space searches

• Publication: arXiv e-prints
• Author(s): Arroyo-Ureña, M. A.Gaitán, R.Valencia-Pérez, T. A.
• Bibcode: 2020arXiv200800564A

We present a $\texttt{Mathematica}$ package, called $\texttt{SpaceMath}$, for Beyond the Standard Model (BSM) parameter space searches which be agree with the most up-to-date experimental measurements. The physical observables implemented in $\texttt{SpaceMath}$ are classified in five categories, namely, LHC Higgs boson data (LHC-HBD), Flavor-Violating Processes (FVP), Oblique Parameters (OP), Unitarity and perturbativity (UP) and Meson Physics (MP). Nevertheless, $\texttt{SpaceMath}$ version 1.0 ($\texttt{SpaceMath v1.0}$) works only with LHC-HBD and with extended scalar sector models. Future versions will implement the observables previously mentioned. $\texttt{SpaceMath v1.0}$ is able to find allowed regions for free parameters of extension models by using LHC-HBD within a friendly interface and an intuitive environment in which users enter the couplings, set parameters and execute $\texttt{Mathematica}$ in the traditional way. We present examples, step by step, in order to start new users in a fast and efficient way. To validate $\texttt{SpaceMath v1.0}$, we reproduce results reported in the literature.

QBMMlib: A library of quadrature-based moment methods

• Publication: arXiv e-prints
• Author(s): Bryngelson, Spencer H.Colonius, TimFox, Rodney O.
• Bibcode: 2020arXiv200805063B

QBMMlib is an open source Mathematica package of quadrature-based moment methods and their algorithms. Such methods are commonly used to solve fully-coupled disperse flow and combustion problems, though formulating and closing the corresponding governing equations can be complex. QBMMlib aims to make analyzing these techniques simple and more accessible. Its routines use symbolic manipulation to formulate the moment transport equations for a population balance equation and a prescribed dynamical system. However, the resulting moment transport equations are unclosed. QBMMlib trades the moments for a set of quadrature points and weights via an inversion algorithm, of which several are available. Quadratures then closes the moment transport equations. Embedded code snippets show how to use QBMMlib, with the algorithm initialization and solution spanning just 13 total lines of code. Examples are shown and analyzed for linear harmonic oscillator and bubble dynamics problems.

On Geodesic Congruences and the Raychaudhuri Equations in $\textrm{SAdS}_4$ Spacetime

• Publication: arXiv e-prints
• Author(s): Biswas, DriptoShivottam, Jyotirmaya
• Bibcode: 2020arXiv200805326B

In this article, we look into geodesics in the Schwarzschild-Anti-de Sitter metric in (3+1) spacetime dimensions. We investigate the class of marginally bound geodesics (timelike and null), while comparing their behavior with the normal Schwarzschild metric. Using $\textit{Mathematica}$, we calculate the shear and rotation tensors, along with other components of the Raychaudhuri equation in this metric and we argue that marginally bound timelike geodesics, in the equatorial plane, always have a turning point, while their null analogues have at least one family of geodesics that are unbound. We also present associated plots for the geodesics and geodesic congruences, in the equatorial plane.

QuESTlink[LongDash]Mathematica embiggened by a hardware-optimised quantum emulator

• Publication: Quantum Science and Technology
• Author(s): Jones, TysonBenjamin, Simon
• Bibcode: 2020QS&T....5c4012J

We introduce QuESTlink,pronounced 'quest link', an open-source Mathematicapackage which efficiently emulates quantum computers. By integratingwith the Quantum Exact Simulation Toolkit (QuEST), QuESTlink offers ahigh-level, expressive and usable interface to a high-performance, hardware-accelerated emulator. Requiring no installation, QuESTlink streamlines the powerful analysis capabilities of Mathematica into the study of quantum systems, even utilising remote multi-core and GPU hardware. We demonstrate the use of QuESTlink to concisely and efficiently simulate several quantum algorithms, and present some comparative benchmarking against core QuEST. *with additional support from Quantum Motion Technologies Ltd United Kingdom.

Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN order for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting

• Publication: Physical Review D
• Author(s): Munna, ChristopherEvans, Charles R.Hopper, SethForseth, Erik
• Bibcode: 2020PhRvD.102b4047M

We present an extension of work in an earlier paper showing high precision comparisons between black hole perturbation theory and post-Newtonian (PN) theory in their region of overlapping validity for bound, eccentric-orbit, Schwarzschild extreme-mass-ratio inspirals. As before we apply a numerical fitting scheme to extract eccentricity coefficients in the PN expansion of the gravitational wave fluxes, which are then converted to exact analytic form using an integer-relation algorithm. In this work, however, we fit to individual l m n modes to exploit simplifying factorizations that lie therein. Since the previous paper focused solely on the energy flux, here we concentrate initially on analyzing the angular momentum flux to infinity. A first step involves finding convenient forms for hereditary contributions to the flux at low-PN order, analogous to similar terms worked out previously for the energy flux. We then apply the upgraded techniques to find new PN terms through 9PN order and (at many PN orders) to e³⁰ in the power series in eccentricity. With the new approach applied to angular momentum fluxes, we return to the energy fluxes at infinity to extend those previous results. Like before, the underlying method uses a Mathematica code based on use of the Mano-Suzuki-Takasugi (MST) function expansion formalism to represent gravitational perturbations and spectral source integration (SSI) to find numerical results at arbitrarily high precision.

Calculation of IR absorption intensities for hydrogen bond from exactly solvable Schrödinger equation

• Publication: arXiv e-prints
• Author(s): Sitnitsky, A. E.
• Bibcode: 2020arXiv200712410S

A theoretical description of IR spectroscopy data for a hydrogen bond (HB) is constructed on the base of trigonometric double-well potential for which an exact analytic solution of the one-dimensional Schrödinger equation (SE) is available. The wave functions (full orthogonal basis) are expressed via the spheroidal function while its spectrum of eigenvalues yields the corresponding energy levels (both special functions are implemented in {\sl {Mathematica}}). Then an approximate solution of two-dimensional SE taking into account the excitation state of heavy atoms stretching mode in HB is obtained. It is constructed by decomposing over the above mentioned basis within the framework of standard adiabatic separating the proton motion from that of the heavy atoms. We exemplify the general theory by calculating the IR relative absorption intensities for HB in the Zundel ion ${\rm{H_5O_2^{+}}}$ (oxonium hydrate).

Bell, Bohm, and qubit: EPR remixed

• Publication: American Journal of Physics
• Author(s): Press, William H.
• Bibcode: 2020AmJPh..88..558P

This article reviews the predictions of quantum mechanics (QM) for one- and two-particle Stern-Gerlach experiments and then frames Bell's results, which rule out hidden-variable alternatives to QM, as attempts by a skeptical Eve to fool Alice and Bob with (first example) classical probability mixtures of non-entangled quantum states and (second example) a classical hidden-variable theory. With hidden variables, Eve can succeed when Alice and Bob limit themselves to two Stern-Gerlach directions, but always fails for some choices of three directions. For three random directions, hidden-variable theories are impossible (we show) exactly 2/3 of the time. All the calculations in this article are available in uc(Mathematica) and uc(Python) files in the supplementary material, allowing readers to experiment with their own variants.

Basis Decompositions and a Mathematica Package for Modular Graph Forms

• Publication: arXiv e-prints
• Author(s): Gerken, Jan E.
• Bibcode: 2020arXiv200705476G

Modular graph forms (MGFs) are a class of non-holomorphic modular forms which naturally appear in the low-energy expansion of closed-string genus-one amplitudes and have generated considerable interest from pure mathematicians. MGFs satisfy numerous non-trivial algebraic- and differential relations which have been studied extensively in the literature and lead to significant simplifications. In this paper, we systematically combine these relations to obtain basis decompositions of all two- and three-point MGFs of total modular weight $w+\bar{w}\leq12$, starting from just two well-known identities for banana graphs. Furthermore, we study previously known relations in the integral representation of MGFs, leading to a new understanding of holomorphic subgraph reduction as Fay identities of Kronecker--Eisenstein series and opening the door towards decomposing divergent graphs. We provide a computer implementation for the manipulation of MGFs in the form of the $\texttt{Mathematica}$ package $\texttt{ModularGraphForms}$ which includes the basis decompositions obtained.

Factorization of the Riesz-Feller fractional quantum harmonic oscillators

• Publication: arXiv e-prints
• Author(s): Rosu, Haret C.Mancas, Stefan C.
• Bibcode: 2020arXiv200610872R

Using the Riesz-Feller fractional derivative, we apply the factorization algorithm to the fractional quantum harmonic oscillator along the lines previously proposed by Olivar-Romero and Rosas-Ortiz, extending their results. We solve the non-Hermitian fractional eigenvalue problem in the k space by introducing in that space a new class of Hermite polynomials' that we call Riesz-Feller Hermite polynomials'. Using the inverse Fourier transform in Mathematica, interesting analytic results for the same eigenvalue problem in the x space are also obtained. Additionally, a more general factorization with two different Levy indices is briefly introduced

Quasinormal modes of Kerr-de Sitter black holes via the Heun function

• Publication: arXiv e-prints
• Author(s): Hatsuda, Yasuyuki
• Bibcode: 2020arXiv200608957H

This note addresses quasinormal mode frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky's equations for Kerr-de Sitter black holes are mapped to Heun's equations, we are able to compute their quasinormal mode frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating black holes.

The method of numerical and analytical solution of linear differential equations with non-integer derivatives in Caputo order and with variable coefficients

• Publication: arXiv e-prints
• Author(s): Vasyliev, Oleksii V.
• Bibcode: 2020arXiv200602206V

The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential equations of both fractional and mixed orders. Computational experiments performed in a Mathematica (TM) software environment

xAct Implementation of the Theory of Cosmological Perturbation in Bianchi I Spacetimes

• Publication: arXiv e-prints
• Author(s): Agullo, IvanOlmedo, JavierSreenath, V.
• Bibcode: 2020arXiv200603397A

This paper presents a computational algorithm to derive the theory of linear gauge invariant perturbations on anisotropic cosmological spacetimes of the Bianchi I type. Our code is based on the tensor algebra packages xTensor and xPert, within the computational infrastructure of xAct written in Mathematica. The algorithm is based on a Hamiltonian, or phase space formulation, and it provides an efficient and transparent way of isolating the gauge invariant degrees of freedom in the perturbation fields and to obtain the Hamiltonian generating their dynamics. The restriction to Friedmann--Lemaître--Robertson--Walker spacetimes is straightforward.

One-loop Jet Functions by Geometric Subtraction

• Publication: arXiv e-prints
• Author(s): Basdew-Sharma, AvanishHerzog, FranzSchrijnder van Velzen, SolangeWaalewijn, Wouter J.
• Bibcode: 2020arXiv200614627B

In factorization formulae for cross sections of scattering processes, final-state jets are described by jet functions, which are a crucial ingredient in the resummation of large logarithms. We present an approach to calculate generic one-loop jet functions, by using the geometric subtraction scheme. This method leads to local counterterms generated from a slicing procedure; and whose analytic integration is particularly simple. The poles are obtained analytically, up to an integration over the azimuthal angle for the observable-dependent soft counterterm. The poles depend only on the soft limit of the observable, characterized by a power law, and the finite term is written as a numerical integral. We illustrate our method by reproducing the known expressions for the jet function for angularities, the jet shape, and jets defined through a cone or $k_T$ algorithm. As a new result, we obtain the one-loop jet function for an angularity measurement in $e^+e^-$ collisions, that accounts for the formally power-suppressed but potentially large effect of recoil. An implementation of our approach is made available as the GOJet Mathematica package accompanying this paper.

MasterTwo: A Mathematica Package for the Automated Calculation of Two Loop Diagrams in the Standard Model and Beyond

• Publication: arXiv e-prints
• Author(s): Schilling, Sabine
• Bibcode: 2020arXiv200604137S

The calculation of rare loop decays in the Standard Model of Particle Physics and its extensions is an extremely tedious work. The Mathematica package MasterTwo facilitates this task. It automatically calculates all loop integrals reducible to scalar integrals depending on up to two different masses independent of external momenta. MasterTwo consists of two sub packages, Fermions and Integrals. Whereas Fermions covers the standard Dirac Algebra, Integrals performs the Taylor expansion, partial fraction, tensor reduction and the integration of the thus achieved scalar integrals. The package works completely inside Mathematica and can be easily customised for both educational and research purposes.

FeynOnium: Using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories

• Publication: arXiv e-prints
• Author(s): Brambilla, NoraSok Chung, HeeShtabovenko, VladyslavVairo, Antonio
• Bibcode: 2020arXiv200615451B

We present new results on FeynOnium, an ongoing project to develop a general purpose software toolkit for semi-automatic symbolic calculations in nonrelativistic Effective Field Theories (EFTs). Building upon FeynCalc, an existing Mathematica package for symbolic evaluation of Feynman diagrams, we have created a powerful framework for automatizing calculations in nonrelativistic EFTs (NREFTs) at tree- and 1-loop level. This is achieved by exploiting the novel features of FeynCalc that support manipulations of Cartesian tensors, Pauli matrices and nonstandard loop integrals. Additional operations that are common in nonrelativistic EFT calculations are implemented in a dedicated add-on called FeynOnium. While our current focus is on EFTs for strong interactions of heavy quarks, extensions to other systems that admit a nonrelativistic EFT description are planned for the future. All our codes are open-source and publicly available. Furthermore, we provide several example calculations that demonstrate how FeynOnium can be employed to reproduce known results from the literature.

Emulate the chaotic flows of fractional jerk system to scramble the sound and image memo with circuit execution

• Publication: Physica Scripta
• Author(s): Khan, Najeeb AlamHameed, ToobaQureshi, Muhammad AliAkbar, SaeedAlzahrani, Abdullah Khamis
• Bibcode: 2020PhyS...95f5217K

The purpose of this paper is to investigate the chaotic influence of the fractional order jerk system with the theoretical execution of circuit and practical consequent on cryptography. The Caputo fractional derivative (CFD) has been used for the commensurate order and obtains the necessary condition to appear chaos using Lyapunov exponent (LE). The existence, uniqueness of the system is analyzed, and the stabilities of the equilibrium points are explored. The output of the electronic circuit equations has been inspected graphically and the values of passive components resistor, capacitor and voltage are tabulated. The scrambling protocol is designed in multiple paradigmatic language Python for various aspects of information security such as sound and image for confidentiality. The analog and numerical simulations carry out in Multisim and Mathematica respectively, to see the effects of physical parameters on phase portraits which are incorporated through graphs and tables. The significance level of occur fluctuation is also measured by a statistical package the NIST test suite to ensure the stream of generating numbers for a particular cryptographic application. Furthermore, originality of the system also tested with the help of error measuring tool named mean absolute error (MAE) and found that the performance index of the designed system is in good agreement.

New traveling wave solutions for the higher Sharma-Tasso-Olver equation by using extension exponential rational function method

• Publication: Results in Physics
• Author(s): El-Rashidy, K.
• Bibcode: 2020ResPh..1703066E

A new and general wave traveling solutions for Sharma-Tasso-Olver and (2 + 1)-dimensional Sharma-Tasso-Olver equation are deduced by using the extension exponential rational function method. The solution's graphics described the physical phenomena of the Sharma-Tasso-Olver dynamical system. The Wolfram Mathematica program used to compute the solutions and the graphics plots in this study.

Riemann-Hilbert approach and nonlinear dynamics in the nonlocal defocusing nonlinear Schrödinger equation

• Publication: European Physical Journal Plus
• Author(s): Wu, Jianping
• Bibcode: 2020EPJP..135..523W

The nonlocal defocusing nonlinear Schrödinger (ND-NLS) equation is comparatively studied via the Riemann-Hilbert approach. Firstly, via spectral analysis, the spectral structure of the ND-NLS equation is investigated, which is different to those of the other three NLS-type equations, i.e., the local focusing nonlinear Schrödinger (LF-NLS) equation, the local defocusing nonlinear Schrödinger (LD-NLS) equation and the nonlocal focusing nonlinear Schrödinger (NF-NLS) equation. Secondly, by solving the Riemann-Hilbert problem corresponding to the reflectionless cases, multi-soliton solutions are obtained for the ND-NLS equation. Thirdly, we prove that, if parameters are suitably chosen, the multi-soliton solutions of the ND-NLS equation can be reduced to those of the LF-NLS equation and the LD-NLS equation, respectively. Fourthly, the multi-soliton solutions of the ND-NLS equation are demonstrated to possess repeated singularities generally, but they can also remain analytic for appropriate soliton parameters. Moreover, the multi-soliton dynamics are graphically illustrated using Mathematica symbolic computations. These results show that the solution structure and the nonlinear dynamics in the ND-NLS equation are rather different from those of the LF-NLS equation, the LD-NLS equation and the NF-NLS equation.

Improved perturbed nonlinear Schrödinger dynamical equation with type of Kerr law nonlinearity with optical soliton solutions

• Publication: Physica Scripta
• Author(s): Seadawy, Aly R.Cheemaa, Nadia
• Bibcode: 2020PhyS...95f5209S

In this paper we have presented the analytical treatment of integrable improved perturbed nonlinear Schrödinger equation with type of Kerr law nonlinearity by using a newly proposed technique extended modified auxiliary equation mapping method. By the implementation of this method we have obtained a variety of some new and quite general form of exact traveling wave solutions in which we are including periodic, doubly periodic, combined, dark, bright, half dark, half bright, using three parameters which is the main key difference of our newly proposed method. For detailed dynamical physical description of our newly found results we have presented them with graphical representation using Mathematica 10.4 to explain in a more efficient manner the behavior of different physical structures of solutions.

Propagation of isolated waves of coupled nonlinear (2 + 1)-dimensional Maccari System in plasma physics

• Publication: Results in Physics
• Author(s): Cheemaa, NadiaChen, ShengSeadawy, Aly R.
• Bibcode: 2020ResPh..1702987C

In this article we have presented the analytical analysis of coupled integrable (2 + 1)-dimensional Maccari System with the aid of newly developed technique named as an extended modified auxiliary equation mapping method. As a result we have found a variety of new families of exact traveling wave solutions including triangular-type solutions, periodic and doubly periodic like solutions, combined soliton like solutions, kink and anti kink type soliton like solutions with the help of three parameters which is the key importance of this method. Maccari System is a well known model to define the dynamics of isolated waves, localized in a very small part of space in different fields of physics such as quantum mechanics, hydrodynamics, plasma physics, quantum field theory to study the dynamics of Langmuir solitons which are appearing in the nonlinear optics. For physical description of our newly obtained solutions we have expressed them graphically using Mathematica 10.4 to explain more efficiently the behavior of different shapes of solutions. Also the computational work and efficiency of the method demonstrates the reliability, straightforwardness, and simplicity of the method for solving other nonlinear complicated partial differential equations.

Creating and Transforming a Second-Rank Antisymmetric Field- Strength Tensor F[Alpha][Beta] in Minkowski Space using MATHEMATICA

• Publication: Journal of Astronomy and Space Sciences
• Author(s): Kim, BogyeongYun, Hee-Joong
• Bibcode: 2020JASS...37..131K

As the laws of physics are expressed in a manner that makes their invariance under coordinate transformations manifest, they should be written in terms of tensors. Furthermore, tensors make manifest the characteristics and behaviors of electromagnetic fields through inhomogeneous, anisotropic, and compressible media. Electromagnetic fields are expressed completely in tensor form, F[Alpha][Beta], which implies both electric field E [RightArrow] and magnetic field B [RightArrow] rather than separately in the vector fields. This study presents the Mathematica platform that generates and transforms a second-rank antisymmetric field-strength tensor F[Alpha][Beta] and whiskbroom pattern in Minkowski space. The platforms enhance the capabilities of students and researchers in tensor analysis and improves comprehension of the elegant features of complete structure in physics.

$q-$spherical surfaces in Euclidean space

• Publication: arXiv e-prints
• Author(s): Gorjanc, SonjaJurkin, Ema
• Bibcode: 2020arXiv200614878G

In this paper we define $q$-spherical surfaces as the surfaces that contain the absolute conic of the Euclidean space as a $q-$fold curve. Particular attention is paid to the surfaces with singular points of the highest order. Two classes of such surfaces, with one and two $n-$fold points, are discussed in detail. We study their properties, give their algebraic equations and visualize them with the program {\it Mathematica}.

DiffExp, a Mathematica package for computing Feynman integrals in terms of one-dimensional series expansions

• Publication: arXiv e-prints
• Author(s): Hidding, Martijn
• Bibcode: 2020arXiv200605510H

DiffExp is a Mathematica package for integrating families of Feynman integrals order-by-order in the dimensional regulator from their systems of differential equations, in terms of one-dimensional series expansions along lines in phase-space, which are truncated at a given order in the line parameter. DiffExp is based on the series expansion strategies that were explored in recent literature for the computation of families of Feynman integrals relevant for Higgs plus jet production with full heavy quark mass dependence at next-to-leading order. The main contribution of this paper, and its associated package, is to provide a public implementation of these series expansion methods, which works for any family of integrals for which the user provides a set of differential equations and boundary conditions (and for which the program is not computationally constrained.) The main functions of the DiffExp package are discussed, and its use is illustrated by applying it to the three loop equal-mass and unequal-mass banana graph families.

Learning selection strategies in Buchberger's algorithm

• Publication: arXiv e-prints
• Author(s): Peifer, DylanStillman, MichaelHalpern-Leistner, Daniel
• Bibcode: 2020arXiv200501917P

Studying the set of exact solutions of a system of polynomial equations largely depends on a single iterative algorithm, known as Buchberger's algorithm. Optimized versions of this algorithm are crucial for many computer algebra systems (e.g., Mathematica, Maple, Sage). We introduce a new approach to Buchberger's algorithm that uses reinforcement learning agents to perform S-pair selection, a key step in the algorithm. We then study how the difficulty of the problem depends on the choices of domain and distribution of polynomials, about which little is known. Finally, we train a policy model using proximal policy optimization (PPO) to learn S-pair selection strategies for random systems of binomial equations. In certain domains, the trained model outperforms state-of-the-art selection heuristics in total number of polynomial additions performed, which provides a proof-of-concept that recent developments in machine learning have the potential to improve performance of algorithms in symbolic computation.

Packing of spanning mixed arborescences

• Publication: arXiv e-prints
• Author(s): Gao, HuiYang, Daqing
• Bibcode: 2020arXiv200503218G

In this paper, we characterize a mixed graph $F$ which contains $k$ edge and arc disjoint spanning mixed arborescences $F_{1}, \ldots, F_{k}$, such that for each $v \in V(F)$, the cardinality of ${i \in [k]: v \text{ is the root of } F_{i}}$ lies in some prescribed interval. This generalizes both Nash-Williams and Tutte's theorem on spanning tree packing for undirected graphs and the previous characterization on digraphs which was given by Cai [in: Arc-disjoint arborescences of digraphs, J. Graph Theory 7(2) (1983), 235-240] and Frank [in: On disjoint trees and arborescences, Algebraic Methods in Graph Theory, Colloquia Mathematica Soc. J. Bolyai, Vol. 25 (North-Holland, Amsterdam) (1978), 159-169].

Precision early universe thermodynamics made simple: N_eff and neutrino decoupling in the Standard Model and beyond

• Publication: Journal of Cosmology and Astroparticle Physics
• Author(s): Escudero Abenza, Miguel
• Bibcode: 2020JCAP...05..048E

Precision measurements of the number of effective relativistic neutrino species and the primordial element abundances require accurate theoretical predictions for early Universe observables in the Standard Model and beyond. Given the complexity of accurately modelling the thermal history of the early Universe, in this work, we extend a previous method presented by the author in [1] to obtain simple, fast and accurate early Universe thermodynamics. The method is based upon the approximation that all relevant species can be described by thermal equilibrium distribution functions characterized by a temperature and a chemical potential. We apply the method to neutrino decoupling in the Standard Model and find N_eff^SM = 3.045[LongDash]a result in excellent agreement with previous state-of-the-art calculations. We apply the method to study the thermal history of the Universe in the presence of a very light (1 eV<m_phi < 1 MeV) and weakly coupled ([Lambda] lesssim 10^[Minus]9) neutrinophilic scalar. We find our results to be in excellent agreement with the solution to the exact Liouville equation. Finally, we release a code: NUDEC_BSM (available in both Mathematica and Python formats), with which neutrino decoupling can be accurately and efficiently solved in the Standard Model and beyond: https://github.com/MiguelEA/nudec_BSM.

Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data

• Publication: arXiv e-prints
• Author(s): Anand, NikhilFitzpatrick, A. LiamKatz, EmanuelKhandker, Zuhair U.Walters, Matthew T.Xin, Yuan
• Bibcode: 2020arXiv200513544A

We both review and augment the lightcone conformal truncation (LCT) method. LCT is a Hamiltonian truncation method for calculating dynamical quantities in QFT in infinite volume. This document is a self-contained, pedagogical introduction and "how-to" manual for LCT. We focus on 2D QFTs which have UV descriptions as free CFTs containing scalars, fermions, and gauge fields, providing a rich starting arena for LCT applications. Along our way, we develop several new techniques and innovations that greatly enhance the efficiency and applicability of LCT. These include the development of CFT radial quantization methods for computing Hamiltonian matrix elements and a new SUSY-inspired way of avoiding state-dependent counterterms and maintaining chiral symmetry. We walk readers through the construction of their own basic LCT code, sufficient for small truncation cutoffs. We also provide a more sophisticated and comprehensive set of Mathematica packages and demonstrations that can be used to study a variety of 2D models. We guide the reader through these packages with several examples and illustrate how to obtain QFT observables, such as spectral densities and the Zamolodchikov $C$-function. Specific models considered are finite $N_c$ QCD, scalar $\phi^4$ theory, and Yukawa theory.

TripleK: A Mathematica package for evaluating triple-K integrals and conformal correlation functions

• Publication: arXiv e-prints
• Author(s): Bzowski, Adam
• Bibcode: 2020arXiv200510841B

I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and 3-point massless multi-loop Feynman integrals with generalized propagators. The package is accompanied by five Mathematica notebooks containing detailed calculations of numerous conformal 3-point functions in momentum space.

Efficient Calculation of Crossing Symmetric BCJ Tree Numerators

• Publication: arXiv e-prints
• Author(s): Edison, AlexTeng, Fei
• Bibcode: 2020arXiv200503638E

In this paper, we propose an improved method for directly calculating double-copy-compatible tree numerators in (super-)Yang-Mills and Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence on reference orderings, restoring a form of crossing symmetry to the numerators. This in turn improves the computational efficiency of the algorithm, allowing us to go well beyond the number of external particles accessible with the reference order based methods. Motivated by a parallel study of one-loop BCJ numerators from forward limits, we explore the generalization to include a pair of fermions. To improve the accessiblity of the new algorithm, we provide a Mathematica package that implements the numerator construction. The structure of the computation also provides for a straightforward introduction of minimally-coupled massive particles potentially useful for future computations in both classical and quantum gravity.

Analytical and numerical solutions for the current and voltage model on an electrical transmission line with time and distance

• Publication: Physica Scripta
• Author(s): Khater, Mostafa M. A.Alzaidi, J. F.Attia, Raghda A. M.Inc, MustafaLu, Dianchen
• Bibcode: 2020PhyS...95e5206K

This research paper employs three different techniques on the fractional nonlinear space-time telegraph equation to get the solitary traveling wave solutions, semi-analytical wave solution, and numerical solutions. We implement a modified Khater method, Adomian decomposition method, and B-spline techniques (cubic, quantic, and septic) on the fractional telegraph equation. This model is one of the fundamental equations in an electrical transmission and electromagnetic waves that describes the current and voltage on an electrical transmission line with time and distance. It derived by Oliver Heaviside in the 1880s and used to discuss the mirror phenomena of the electromagnetic waves and wave patterns through along line. New structure forms of solitary traveling wave solutions are obtained, and the comparison between the three kinds of solutions is given. The obtained solutions verified with Maple 16 & Mathematica 12 by placing them back into the original equations. The performance of these methods shows the power and effectiveness of them for applying to many different forms of the nonlinear partial differential equation with integer order and fractional order.

Quadratic Sieve Factorization Quantum Algorithm and its Simulation

• Publication: arXiv e-prints
• Author(s): Singh Bhatia, AmandeepKumar, Ajay
• Bibcode: 2020arXiv200511668S

Quantum computing is a winsome field that concerns with the behaviour and nature of energy at the quantum level to improve the efficiency of computations. In recent years, quantum computation is receiving much attention for its capability to solve difficult problems efficiently in contrast to classical computers. Specifically, some well-known public-key cryptosystems depend on the difficulty of factoring large numbers, which takes a very long time. It is expected that the emergence of a quantum computer has the potential to break such cryptosystems by 2020 due to the discovery of powerful quantum algorithms (Shor's factoring, Grover's search algorithm and many more). In this paper, we have designed a quantum variant of the second fastest classical factorization algorithm named "Quadratic Sieve". We have constructed the simulation framework of quantized quadratic sieve algorithm using high-level programming language Mathematica. Further, the simulation results are performed on a classical computer to get a feel of the quantum system and proved that it is more efficient than its classical variants from computational complexity point of view.

Two meshless methods for solving nonlinear ordinary differential equations in engineering and applied sciences

• Publication: Nonlinear Engineering
• Author(s): Al-Jawary, Majeed A.Ibraheem, Ghada H.
• Bibcode: 2020NLE.....9..244A

In this paper, two meshless methods have been introduced to solve some nonlinear problems arising in engineering and applied sciences. These two methods include the operational matrix Bernstein polynomials and the operational matrix with Chebyshev polynomials. They provide an approximate solution by converting the nonlinear differential equation into a system of nonlinear algebraic equations, which is solved by using Mathematica® 10. Four applications, which are the well-known nonlinear problems: the magnetohydrodynamic squeezing fluid, the Jeffery-Hamel flow, the straight fin problem and the Falkner-Skan equation are presented and solved using the proposed methods. To illustrate the accuracy and efficiency of the proposed methods, the maximum error remainder is calculated. The results shown that the proposed methods are accurate, reliable, time saving and effective. In addition, the approximate solutions are compared with the fourth order Runge-Kutta method (RK4) achieving good agreements.

Scanner data in inflation measurement: from raw data to price indices

• Publication: arXiv e-prints
• Author(s): Białek, JacekBeręsewicz, Maciej
• Bibcode: 2020arXiv200511233B

Scanner data offer new opportunities for CPI or HICP calculation. They can be obtained from awide variety ofretailers (supermarkets, home electronics, Internet shops, etc.) and provide information at the level ofthe barcode. One ofadvantages ofusing scanner data is the fact that they contain complete transaction information, i.e. prices and quantities for every sold item. To use scanner data, it must be carefully processed. After clearing data and unifying product names, products should be carefully classified (e.g. into COICOP 5 or below), matched, filtered and aggregated. These procedures often require creating new IT or writing custom scripts (R, Python, Mathematica, SAS, others). One ofnew challenges connected with scanner data is the appropriate choice ofthe index formula. In this article we present aproposal for the implementation ofindividual stages ofhandling scanner data. We also point out potential problems during scanner data processing and their solutions. Finally, we compare alarge number ofprice index methods based on real scanner datasets and we verify their sensitivity on adopted data filtering and aggregating methods.

Entropy analysis for the peristaltic flow of third grade fluid with variable thermal conductivity

• Publication: European Physical Journal Plus
• Author(s): Hayat, TasawarNawaz, SadafAlsaedi, AhmedAhmad, Bashir
• Bibcode: 2020EPJP..135..421H

Recently there is a need to enhance the cooling capabilities required in many industrial applications. Therefore it is important to know the factors for system's disorderliness. This work is based on the study of entropy analysis in fluid transport phenomenon by peristalsis. Mixed convective flow in compliant wall channel is considered. Here third grade fluid is considered. Effect of gravity is also encountered. Magnetohydrodynamic and Joule heating are part of flow modeling. Energy equation is addressed subject to viscous dissipation and variable thermal conductivity. Resulting system is solved with the help of NDSolve command in Mathematica. Proper attention is given to the study of velocity, temperature and entropy analysis. This analysis is carried out via graphical results for different embedded parameters. Graphs for heat transfer coefficient are also plotted and analyzed.

Charge relaxation rates in insulating straight capillaries

• Publication: Physical Review A
• Author(s): Giglio, Eric
• Bibcode: 2020PhRvA.101e2707G

The charge relaxation of accumulated charge patches in insulating straight capillaries is investigated theoretically. The model assumes that charges accumulate only at the inner and outer insulator-vacuum interface of the capillary but not in the bulk. We give an analytical solution to the coupled equations that describe the surface charge dynamics at both interfaces. We provide a tool to calculate easily the characteristic relaxation times in a straight capillary of any dimension, possibly surrounded by a conducting cylinder. The latter allows for different scenarios found in experimental setups, and is applicable to both nanocapillaries and macrocapillaries. We propose an original experimental technique to monitor the charge relaxation in a straight glass capillary and show how to use the presented model to extract the bulk and surface conductivity of the insulator from the measured data. In the Supplemental Material, we provide a script in uc(mathematica) that allows the reader to compute comfortably the decay rates for all straight insulating capillaries the reader is interested in.

Large deformations description of the continuum, shells and thin-wall structures and their visualisation with Mathematica

• Publication: American Institute of Physics Conference Series
• Author(s): Walentyński, Ryszard
• Bibcode: 2020AIPC.2239b0048W

Proper description of large deformation of the continuum or the shell requires dealing with curved spaces and application of tensor analysis and distinguishing of covariant and contravariant basis.

Thanks to symbolic computations and visualization capabilities of the Mathematica system, this task can be carried out straightfor- ward. It has been already discussed in [1] and [2]. This paper is a further extension of them.

First it will be shown that the deformation is indeed changing of curvature of the considered space. Next, there will be shown how Cartesian basis of the flat undeformed space splits to the covariant and contravariant ones and that this basis changes in the space. It makes possible to explain why we have to introduce covariant derivatives and Christoffel symbols, for example. It is important in case of the optical analysis of large deformations of thin wall structures.

Moreover it is possible to easily explain that strain tensor is defined with change of metric tensor. It also helps to show the idea of material (Lagrangian) and spatial (Eulerian) description of the deformation and the motion and avoid misunderstandings in this matter.

Everything is visualised with 3D graphical capabilities and interactive maniputation of the plots provided within the Mathematica system.

This paper can be also usefull inspiration both in teaching and learning of the Continuum Mechanics, the Theory of Shells and Thin-Wall Structures.

The work has been presented at the conference Polish Congress of Mechanics, Computer Methods in Mechanics PCM-CMM-2019 in Krakow.

One Package For All Multi-Harmonic Cumulants

• Publication: arXiv e-prints
• Author(s): Farid Taghavi, Seyed
• Bibcode: 2020arXiv200504742F

The cumulants of flow harmonic fluctuations are considered as one of the main observables for testing the collectivity in heavy-ion physics. Using a multi-dimensional generating function, we propose a method to extract all possible cumulants of multi-harmonic flow fluctuations. The procedure is implemented in a Mathematica package that can be employed to obtain cumulants for any combinations of flow harmonics. Using iEBE-VISHNU event generator, we study all cumulants with order $2,3,4,5$ for harmonics $2,3,4,5$. Introducing normalized cumulants, we compare the eccentricity fluctuations with flow fluctuations. We show that the sign difference between some initial and final state cumulants containing symmetry plane correlations can be explained by adding a phase to the hydrodynamic linear response coefficient. Finally, we introduce a general method to obtain multi-particle correlation functions. The latter set of observables can be employed to investigate the flow and non-flow effects in large and small systems. We specifically study the flow-induced three-particle correlation function in Pb--Pb collisions by using iEBE-VISHNU.

First Integral Method for Constructing New Exact Solutions of The important Nonlinear Evolution Equations in Physics

• Publication: Journal of Physics Conference Series
• Author(s): Hasan, Faeza L.
• Bibcode: 2020JPhCS1530a2109H

In this paper, some new exact solutions of the important nonlinear partial differential equations in physics as Gardener's equation and Sharma-Tasso-Over equation are formally derived by utilizing the first integral method, where it is equipment us with many exact solutions by using the travelling wave transform, then deduce a system of ordinary differential equations which is solved by depending on theorem in commutative algebra and with helping the mathematical software like Maple and Wolfram Mathematica.

Two Reliable Iterative Methods for Solving Chaos synchronization

• Publication: Journal of Physics Conference Series
• Author(s): Gani, Sayl
• Bibcode: 2020JPhCS1530a2082G

In this article we proposed two reliable iterative methods for solving Chaos synchronization. The iterative methods are the Adomain Decompustion method (ADM) and Variational Iteration Method (VIM). The ADM and VIM are solved several problems in different areas which accuracy and efficiency in the results. The solution which get is an approximate solution is accuracy as we well show that in figures and tables for the analysis of maximum error reminder various. The software which used in the study for the calculations was MATHEMATICA 11.

Analytical and approximate solutions of (2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

• Publication: Communications in Theoretical Physics
• Author(s): Senol, Mehmet
• Bibcode: 2020CoTPh..72e5003S

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely Burgers-Kadomtsev-Petviashvili equation (Burgers-K-P) that arises in shallow water waves. Furthermore, using the residual power series method (RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.

CoSMoS v2.0: Making Time Series Generation Simple

• Publication: EGU General Assembly Conference Abstracts
• Author(s): Papalexiou, Simon MichaelStrnad, FilipMarkonis, YannisSerinaldi, FrancescoRupa Rajulapati, ChandraHobbi, SalmaHanel, Martin
• Bibcode: 2020EGUGA..2222357P

Many physically based models aiming to quantify the vulnerability and risk of hydrologic and geomorphic hazards need as input or forcing time series of processes such as precipitation, temperature, humidity, etc. The reliability of their output depends on how realistic the inputs are. CoSMoS is a multi-platform software that generates reliable time series from hydroclimatic variables (precipitation, temperature, wind, relative humidity, streamflow, etc.). It is developed in R (version 2.0) as well as in other platforms (Matlab, Mathematica, Excel). It can be used to generate univariate and multivariate time series at any time scale by reproducing the marginal distributions and the linear correlation structures (including intermittency) of the process under investigation. CoSMoS implements a unified stochastic modelling scheme that expands and enhances a generic modelling approach based on the transformation of "parent" Gaussian time series. By design it aims to offer a simple and easy-to-apply solution to the user requesting minimal information, such as the target marginal distribution and the correlation structure. The software is accompanied by a complete users' manual.

Effect of Endometriosis to fallopian tube of the peristaltic-ciliary flow of third grade fluid in a finite narrow tube

• Publication: Journal of Physics Conference Series
• Author(s): Mawlood, Pro. . Ahmad, Dr.Sagban Abied, Malath
• Bibcode: 2020JPhCS1530a2035M

The present prospective theoretical investigation deals with analysis of the peristaltic-ciliary transport of a developing embryo within the fallopian tubal fluid in the human fallopian tube under the effect6 of Endometriosis. This disease make the peristalsis ciliary flow become to peristalsis flow. A mathematical model induced flow of viscoelastic fluid characterized by the third grade fluid in a finite two dimensional narrow tube. That research is study the effect of couple stress to peristaltic [HorizontalLine]ciliary flow to Non-Newtonian fluids. Non-linear partial differential equations are solved by perturbation method. Flow variables like axial and radial velocities, appropriate residue time over tube length, pressure difference over have been derived under the assumption of long wavelength and low Reynolds number approximation and the expression for pressure rise is obtained by using wavelength and stream function are analysed for embedded parameter. This study is done through by the "MATHEMATICA"

Deriving canonical differential equations for Feynman integrals from a single uniform weight integral

• Publication: Journal of High Energy Physics
• Author(s): Dlapa, ChristophHenn, JohannesYan, Kai
• Bibcode: 2020JHEP...05..025D

Differential equations are a powerful tool for evaluating Feynman integrals. Their solution is straightforward if a transformation to a canonical form is found. In this paper, we present an algorithm for finding such a transformation. This novel technique is based on a method due to Höschele et al. and relies only on the knowledge of a single integral of uniform transcendental weight. As a corollary, the algorithm can also be used to test the uniform transcendentality of a given integral. We discuss the application to several cutting-edge examples, including non-planar four-loop HQET and non-planar two-loop five-point integrals. A Mathematica implementation of our algorithm is made available together with this paper.

A universal framework for t-channel dark matter models

• Publication: European Physical Journal C
• Author(s): Arina, ChiaraFuks, BenjaminMantani, Luca
• Bibcode: 2020EPJC...80..409A

We present the DMSimpt model implementation in uc(FeynRules), which aims to offer a unique general framework allowing for all simulations relevant for simplified t-channel dark matter models at colliders and for the complementary cosmology calculations. We describe how to match next-to-leading-order QCD fixed-order calculations with parton showers to derive robust bounds and predictions in the context of LHC dark matter searches, and moreover validate two model restrictions (relevant for Dirac and Majorana fermionic dark matter respectively) to exemplify how to evaluate dark matter observables to constrain the model parameter space. More importantly, we emphasise how to achieve these results by using a combination of publicly available automated tools, and discuss how dark matter predictions are sensitive to the model file and software setup. All files, together with illustrative uc(Mathematica) notebooks, are available from the URL http://feynrules.irmp.ucl.ac.be/wiki/DMsimpt.

The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field

• Publication: arXiv e-prints
• Author(s): Serino, Mirko
• Bibcode: 2020arXiv200408668S

We present an explicit momentum space computation of the four-point function of the energy-momentum tensor in 4 spacetime dimensions for the free and conformally invariant theory of a scalar field. The result is obtained by explicit evaluation of the Feynman diagrams by tensor reduction. We work by embedding the scalar field theory in a gravitational background consistently with conformal invariance in order to derive all the terms the correlator consists of and all the Ward identities implied by the requirements of general covariance and anomalous Weyl symmetry. We test all these identities numerically in several kinematic configurations. Mathematica notebooks detailing the step-by-step computation are made publicly available through a GitHub repository. To the best of our knowledge, this is the first explicit result for the four-point correlation function of the energy-momentum tensor in a conformal and non supersymmetric field theory which is readily numerically evaluable in any kinematic configuration.

On the Computation of Identities Relating Partition Numbers in Arithmetic Progressions with Eta Quotients: An Implementation of Radu's Algorithm

• Publication: arXiv e-prints
• Author(s): Smoot, Nicolas Allen
• Bibcode: 2020arXiv200403949S

In 2015 Cristian-Silviu Radu designed an algorithm to detect identities of a class studied by Ramanujan and Kolberg. This class includes the famous identities by Ramanujan which provide a witness to the divisibility properties of $p(5n+4),$ $p(7n+5)$. We give an implementation of this algorithm using Mathematica. The basic theory is first described, and an outline of the algorithm is briefly given, in order to describe the functionality and utility of our package. We thereafter give multiple examples of applications to recent work in partition theory. In many cases we have used our package to derive alternate proofs of various identities or congruences; in other cases we have improved previously established identities, and in at least one case we have confirmed a standing conjecture.

Differential operators for superconformal correlation functions

• Publication: Journal of High Energy Physics
• Author(s): Manenti, Andrea
• Bibcode: 2020JHEP...04..145M

We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible N = 1 multiplets and some cases of interest for N = 2. As an application of the formalism we prove that certain N = 2 spinning chiral operators (also known as "exotic" chiral primaries) do not admit a consistent three-point function with the stress tensor and therefore cannot be present in any local SCFT. This extends a previous proof in the literature which only applies to certain classes of theories. To each superdescendant we associate a superconformally covariant differential operator, which can then be applied to any correlator in superspace. In the case of three- point functions, we introduce a convenient representation of the differential operators that considerably simplifies their action. As a consequence it is possible to efficiently obtain the linear relations between the OPE coefficients of the operators in the same superconformal multiplet and in turn streamline the computation of superconformal blocks. We also introduce a Mathematica package to work with four dimensional superspace.

Variability regions for the second derivative of bounded analytic functions

• Publication: arXiv e-prints
• Author(s): Chen, GangqiangYanagihara, Hiroshi
• Bibcode: 2020arXiv200402405C

Let $z_0$ and $w_0$ be given points in the open unit disk $\mathbb{D}$ with $|w_0| &lt; |z_0|$. Let $\mathcal{H}_0$ be the class of all analytic self-maps $f$ of $\mathbb{D}$ normalized by $f(0)=0$, and $\mathcal{H}_0 (z_0,w_0) = { f \in \mathcal{H}_0 : f(z_0) =w_0}$. In this paper, we explicitly determine the variability region of $f''(z_0)$ when $f$ ranges over $\mathcal{H}_0 (z_0,w_0)$. We also show a geometric view of our main result by Mathematica.

Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg-de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma

• Publication: Physica A Statistical Mechanics and its Applications
• Author(s): Seadawy, Aly R.Iqbal, MujahidLu, Dianchen
• Bibcode: 2020PhyA..54423560S

In this research work, we investigate the dust ion-acoustic solitary wave in an unmagnetized collisional dusty plasma, which consists on ions having positive charge, dust fluid with negative charge, q nonextensive electrons and background neutral particles. We formulated nonlinear model by the damped modified Korteweg-de Vries (D-mKdV) equation by applying reductive perturbation technique. We also constructed the new solitary wave solutions for nonlinear D-mKdV equation with the help of two techniques. The obtained solutions are new and general and having the structure in the form of solitons, kink and antikink wave solitons, traveling waves, periodic solitary wave and we also show the structure of obtained solutions by two-dim and three-dim graphical by using the Mathematica to know the physical interpretation of different structure of DIASWs. These obtained solutions are more useful in the development of quantum plasma, dynamics of solitons, dynamics of fluid, problems of biomedical, dynamics of adiabatic parameters, industrial phenomena and many other branches. The calculations show that these techniques are more effective, fruitfulness and powerful to investigate analytical other nonlinear physical models of PDEs involves in Mathematical physics, plasma physics, Geo physics, fluid mechanics, hydrodynamics, mathematical biology, field of engineering and many other physical sciences.

The nonlinear diffusion reaction dynamical system with quadratic and cubic nonlinearities with analytical investigations

• Publication: International Journal of Modern Physics B
• Author(s): Seadawy, Aly R.Iqbal, MujahidLu, Dianchen
• Bibcode: 2020IJMPB..3450085S

Our aim in this research work is to formulate the exact traveling and solitary wave solutions of nonlinear diffusion reaction (DR) equation with quadratic and cubic nonlinearities by implementing the new technique which is a modified mathematical method. We have investigated the density independent nonlinear diffusion equation with convective flux term. As a result, we have found a variety of new exact traveling and solitary wave solutions in the form of dark solitons, bright solitons, combined dark-bright solitons, traveling wave, periodic wave solutions and we also represent the physical structure of the obtained solutions by two- and three-dimensional graphics by using the Mathematica software. This work proves the power, reliability and fruitfulness of this new technique.

Perturbed nonlinear Schrödinger dynamical wave equation with Kerr media in nonlinear optics via optical solitons

• Publication: International Journal of Modern Physics B
• Author(s): Seadawy, Aly R.Cheemaa, Nadia
• Bibcode: 2020IJMPB..3450089S

In this paper, we have presented the analytical analysis of integrable perturbed nonlinear Schrödinger (PNLSE) equation with third-order dispersion (TOD) in Kerr media using our newly proposed technique, extended modified auxiliary equation mapping method. By the implementation of this technique, we have obtained a variety of some new families and more general form of exact traveling wave solutions including triangular-type solutions, periodic and doubly periodic-like solutions, combined soliton-like solutions, kink and anti-kink type soliton-like solutions using three parameters which is the key difference of our newly proposed method. PNLSE is a well-known governing model to study the propagation of optical solitons in nonlinear optical fibers and other telecommunication networks with a type of Kerr law nonlinearity. This particular type of nonlinearity originates when a light wave in an optical fiber is subjected to nonlinear responses. For graphical representation of our newly found results, we have presented them with detailed dynamical physical representation using Mathematica 10.4 to explain in a more efficient manner the behavior of different physical structures of solutions. Also, the computational work and efficiency of the method demonstrate the reliability, straightforwardness, and simplicity of the technique for solving other nonlinear complicated partial differential equations.

Limit cycles and their period detection via numeric and symbolic hybrid computations

• Publication: Communications in Nonlinear Science and Numerical Simulations
• Author(s): Moniri, MojtabaMoniri, Saman
• Bibcode: 2020CNSNS..8305107M

Computing the attracting cycles via iterations near bifurcation parameters for the logistic map could be misleading for the beginner. The matter is the recognition of numerical convergence when it is not ultimately monotone, thereby the true length of the limiting cycle as opposed to the impression of a double length. Among the tools used are Gröbner basis, Mathematica calculations, and symbolic dynamics (word-lifting). We compute all the 209 superstable points of period length <= 11. We also obtain the degree of these algebraic integers. Such computer-assisted proofs are of philosophical interest too. The realization of a 5-periodicity as covered in this paper may resemble the discovery of quasicrystals, a topic we briefly mention. Both share the symbolic dynamics aspect of self-similarity. Finally, for the antisymmetric cubic map we calculate some singly and some doubly superstable parameters.

A Simple Method for Computing Some Pseudo-Elliptic Integrals in Terms of Elementary Functions

• Publication: arXiv e-prints
• Author(s): Blake, Sam
• Bibcode: 2020arXiv200404910B

We introduce a method for computing some pseudo-elliptic integrals in terms of elementary functions. The method is simple and fast in comparison to the algebraic case of the Risch-Trager-Bronstein algorithm. This method can quickly solve many pseudo-elliptic integrals which other well-known computer algebra systems (CAS) either fail, return an answer in terms of special functions, or require more than 20 seconds of computing time. Unlike the symbolic integration algorithms of Risch, Davenport, Trager, Bronstein and Miller; our method is not a decision process. The implementation of this method is less than 200 lines of Mathematica code and can be easily ported to other CAS that can solve systems of linear equations.

Characters and Group Invariant Polynomials of (Super)fields: Road to "Lagrangian"

• Publication: arXiv e-prints
• Author(s): Banerjee, UpalaparnaChakrabortty, JoydeepPrakash, SurajRahaman, Shakeel Ur
• Bibcode: 2020arXiv200412830B

The dynamics of the subatomic fundamental particles, represented by quantum fields, and their interactions are determined uniquely by the assigned transformation properties, i.e., the quantum numbers associated with the underlying symmetry of the model. These fields constitute a finite number of group invariant operators which are assembled to build a polynomial, known as the Lagrangian. The order of the polynomial is determined by the mass dimension. In this paper, we have introduced a Mathematica package, GrIP, that computes the complete set of operators that form a basis at each such order for a model containing any number of fields transforming under connected compact groups. The spacetime symmetry is restricted to the Lorentz group. The first part of the paper is dedicated to formulating the algorithm of GrIP. In this context, the detailed and explicit construction of the characters of different representations corresponding to connected compact groups and respective Haar measures have been discussed in terms of the coordinates of their respective maximal torus. In the second part, we have documented the user manual of GrIP that captures the generic features and guides to prepare the input file. This program works very efficiently to find out the higher mass (non-supersymmetric) and canonical (supersymmetric) dimensional operators relevant to the Effective Field Theory. We have demonstrated the working principles with two examples:- the SM and the MSSM. We have further highlighted important features of GrIP, e.g., identification of effective operators leading to specific rare processes linked with the violation of baryon and lepton numbers, using several BSM scenarios. We have also tabulated a complete set of dimension-6 operators for each such model. Some of the operators possess rich flavour structures which are discussed in detail. This work paves the way towards BSM-EFT.

ProteinLogic: Protein Logic Paper Code

• Publication: Zenodo
• Author(s): Chen, Zibo
• Bibcode: 2020zndo...3697264C

Mathematica code to simulate the cooperative binding scheme in Fig. 1c.

Restricted Irreducible Representations for the Non-graded Hamiltonian $H(2; (1,1); \Phi(1))$

• Publication: arXiv e-prints
• Author(s): Guerra, Horacio
• Bibcode: 2020arXiv200304233G

We classify the simple restricted modules for the minimal $p$-envelope of the non-graded, non-restricted Hamiltonian Lie algebra $H(2; (1,1); \Phi(1))$ over an algebraically closed field $k$ of characteristic $p \geq 5$. We also give the restrictions of these modules to a subalgebra isomorphic to the first Witt Algebra, a result stated in [S. Herpel and D. Stewart, \emph{Selecta Mathematica} 22:2 (2016) 765--799] with an incomplete proof.

New exact solutions for the doubly dispersive equation using the improved Bernoulli sub-equation function method

• Publication: Indian Journal of Physics
• Author(s): Dusunceli, FarukCelik, ErcanAskin, MuzafferBulut, Hasan
• Bibcode: 2020InJPh.tmp...52D

In this study, the doubly dispersive equation is presented by the application of the improved Bernoulli sub-equation function method (IBSEFM). The doubly dispersive equation which is a nonlinear partial differential equation is transformed into nonlinear ordinary differential equation using a wave transformation and then is solved by IBSEFM. Some new solutions are successfully constructed. All the obtained solutions in this study have been satisfied the doubly dispersive equation. In the present study, we have used Wolfram Mathematica 9 software for all of the computations and graphic plottings.

A Study of Secular Perturbations of Translational-Rotational Motion in a Nonstationary Two-Body Problem Using Computer Algebra

• Publication: Computational Mathematics and Mathematical Physics
• Author(s): Bizhanova, S. B.Minglibayev, M. Zh.Prokopenya, A. N.
• Bibcode: 2020CMMPh..60...26B

A nonstationary two-body problem is considered such that one of the bodies has a spherically symmetric density distribution and is central, while the other one is a satellite with axisymmetric dynamical structure, shape, and variable oblateness. Newton's interaction force is characterized by an approximate expression of the force function up to the second harmonic. The body masses vary isotropically at different rates. Equations of motion of the satellite in a relative system of coordinates are derived. The problem is studied by the methods of perturbation theory. Equations of secular perturbations of the translational-rotational motion of the satellite in analogues of Delaunay-Andoyer osculating elements are deduced. All necessary symbolic computations are performed using the Wolfram Mathematica computer algebra system.

The Use of Computational Mathematics Teaching Materials aided Mathematica Software in Vector Algebra Course

• Publication: Journal of Physics Conference Series
• Author(s): Baist, AbdulAmarullah, AhmadTirta Safitri, PrahestiEnawar
• Bibcode: 2020JPhCS1477b2013B

This study aims to get a picture of the effect of the use of computational mathematics teaching materials aided Mathematica software on student learning outcomes. The problem commonly faced by students in vector algebra courses is the understanding of concepts in the lecture material so that it impacts on the low student learning outcomes. The method used in this study is a quasi-experimental with pretest-posttest non-equivalent control group design. The results obtained in this study are the differences in learning outcomes between groups of students who use these teaching materials and those who do not. A significant increase in student learning outcomes by an average of 5% was found after the use of computational mathematics teaching materials aided Mathematica software in the Vector Algebra course. Therefore, it can be concluded that the use of teaching materials influences student learning outcomes.

Error correction schemes for fully correlated quantum channels protecting both quantum and classical information

• Publication: Quantum Information Processing
• Author(s): Li, Chi-KwongLyles, SethPoon, Yiu-Tung
• Bibcode: 2020QuIP...19..153L

We study efficient quantum error correction schemes for the fully correlated channel on an n-qubit system with error operators that assume the form [Sigma]_x^{[CircleTimes]n}, [Sigma]_y^{[CircleTimes]n}, [Sigma]_z^{[CircleTimes]n}. Previous schemes are improved to facilitate implementation. In particular, when n is odd and equals 2 k +1 , we describe a quantum error correction scheme using one arbitrary qubit [Sigma] to protect the data state [Rho] in a 2k-qubit system. The encoding operation [Sigma] [CircleTimes][Rho] [RightTeeArrow][CapitalPhi] ([Sigma] [CircleTimes][Rho] ) only requires 3k CNOT gates (each with one control bit and one target bit). After the encoded state [CapitalPhi] ([Sigma] [CircleTimes][Rho] ) goes through the channel, we can apply the inverse operation [CapitalPhi]^-1 to produce [Sigma] ~[CircleTimes][Rho] so that a partial trace operation can recover [Rho] . When n is even and equals 2 k +2 , we describe a hybrid quantum error correction scheme using any one of the two classical bits [Sigma] [Element]{|i j ⟩⟨i j |:i ,j [Element]{0 ,1 }} to protect a 2k-qubit state [Rho] and two classical bits. The encoding operation [Sigma] [CircleTimes][Rho] [RightTeeArrow][CapitalPhi] ([Sigma] [CircleTimes][Rho] ) can be done by 3 k +2 CNOT gates and a single-qubit Hadamard gate. After the encoded state [CapitalPhi] ([Sigma] [CircleTimes][Rho] ) goes through the channel, we can apply the inverse operation [CapitalPhi]^-1 to produce [Sigma] [CircleTimes][Rho] so that a perfect protection of the two classical bits [Sigma] and the 2k-qubit state is achieved. If one uses an arbitrary two-qubit state [Sigma] , the same scheme will protect 2k-qubit states. The scheme was implemented using MATLAB, Mathematica, Python and the IBM's quantum computing framework qiskit.

The nonlinear integro-differential Ito dynamical equation via three modified mathematical methods and its analytical solutions

• Publication: Open Physics
• Author(s): Seadawy, AlyAli, AsgharAljahdaly, Noufe
• Bibcode: 2020OPhy...18....4S

In this work, we construct traveling wave solutions of (1+1) - dimensional Ito integro-differential equation via three analytical modified mathematical methods. We have also compared our achieved results with other different articles. Portrayed of some 2D and 3D figures via Mathematica software demonstrates to understand the physical phenomena of the nonlinear wave model. These methods are powerful mathematical tools for obtaining exact solutions of nonlinear evolution equations and can be also applied to non-integrable equations as well as integrable ones. Hence worked-out results ascertained suggested that employed techniques best to deal NLEEs.

Solar panels for the lunar base

• Publication: Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series
• Author(s): Maskal, LeulayeSingleton, ChristianAboudiwan, AhmedTaha, AliMarciniak, Malgorzata
• Bibcode: 2020SPIE11275E..18M

The motivation behind this research lies in the well-spread news about USA and China's plans to build bases on the moon within the next 10 years. In this research, we create a mathematical model of efficiency for geometrical solar panels, as well as discuss which locations on the moon may be suitable for placing a non-tracing solar power plant. We consider the North Pole, the Equator and additional locations; and analyze the accumulation of illumination over an 18.6-year period that represents the lunar cycle. The simulation for geometrical panels is based on the etendue, with the panel being the diaphragm and a selected segment of the sky being the source. However, the etendue needs to be modified due to the properties of solar energy. The selected segment of the sky is crafted with careful analysis of the motion of the moon. The difficulty of the model comes from the fact that the motion of the sun on the moon's sky is subject to change in its speed and direction, which is created by the moon's libration. In addition, we discuss the change of luminosity of the sun's light due to the varied distance between the moon and the sun. The simulation was performed using MATLAB and Mathematica.

Propagation of long internal waves in density stratified ocean for the (2+1)-dimensional nonlinear Nizhnik-Novikov-Vesselov dynamical equation

• Publication: Results in Physics
• Author(s): Iqbal, MujahidSeadawy, Aly R.Khalil, Omar H.Lu, Dianchen
• Bibcode: 2020ResPh..1602838I

Our aim in this article to constructed the new solitary wave solutions of (2+1)-dim nonlinear Nizhnik-Novikov-Vesselov equation by novel approach which is extended modified rational expansion method. The new solitary wave solutions are rational, trigonometric, hyperbolic, elliptic functions including dark, bright, singular, combined, optical solitons, kink wave, anti-kink wave, periodic wave, travelling wave and we also represent the physical interpretation of new solutions by 2D and 3D graphical by using the Mathematica. These constructed solutions may play vital role in the areas of Mathematical physics, plasma physics, nonlinear optics, quantum mechanics, fluid dynamics and many different fields of applied sciences. The complete calculations show that this new technique is more powerful, effective, straightforward and we can also apply on other nonlinear PDEs involves in Mathematical physics and many other physical sciences.

Entropy analysis for the peristalsis flow with homogeneous-heterogeneous reaction

• Publication: European Physical Journal Plus
• Author(s): Hayat, TasawarNawaz, SadafAlsaedi, Ahmed
• Bibcode: 2020EPJP..135..296H

Our major focus in this analysis is to study the peristaltic motion of fluid by considering the homogeneous-heterogeneous reaction aspect. Prandtl nanofluid has been carried out for this purpose. Magnetic field is applied in the perpendicular direction to the flow. Joule heating effect is also considered in this analysis. Buongiorno nanofluid model has been used which incorporates two prominent slip mechanisms, i.e., Brownian motion and thermophoresis. The second law of thermodynamics has been utilized for entropy generation analysis. No-slip boundary conditions are employed for the considered analysis. NdSolve command of Mathematica 9.0 is employed for the solution of problem. Graphs for pertinent parameters are plotted and analyzed. These graphs contain velocity, temperature, homogeneous-heterogeneous reaction, entropy, and heat transfer coefficient. Key points of the investigation are collected in the conclusion.

Quantifying of quantum entanglement in Schrödinger cat states with the trapped ion-coherent system for the deep Lamb-Dick regime

• Publication: Indian Journal of Physics
• Author(s): Dermez, Rasim
• Bibcode: 2020InJPh.tmp...41D

The entangled qudits of three-level trapped ion and two phonons (in coherent state) in [CapitalLambda] configuration forming a Hilbert space of 12-D are investigated. The quantum entropy is analyzed "such as an elaborated measure" in trapped ion-coherent state system. Four values of Lamb-Dicke parameter (LDP), [Eta] =0.005 ,0.07 ,0.08 and 0.09 are probed for deep Lamb-Dick regime. We elucidate that as [Eta] is increased, sudden death of entangled state in the trapped ion-coherent state system is decreased or vice versa. By this way, sudden birth of entangled state can be tuned by LDP. All graphs in this study are plotted with aid of the Wolfram Mathematica 9.

Multimedia and special computer facilities used in teaching differential geometry, general relativity and cosmology

• Publication: American Institute of Physics Conference Series
• Author(s): Vulcanov, Dumitru N.
• Bibcode: 2020AIPC.2218f0005V

This article is dedicated to recent developments and facts produced by the advance of computer integrated platforms as MAPLE, MATHEMATICA or MathLab. We have at our disposal today a complete multimedia environment with computer algebra, numerical computing, graphical simulations and animations and many more in one single computer procedure/program.

Erratum to: Leading higher-derivative corrections to Kerr geometry

• Publication: Journal of High Energy Physics
• Author(s): Cano, Pablo A.Ruipérez, Alejandro
• Bibcode: 2020JHEP...03..187C

There was an error when copying eqs. (4.41), (4.42) and (4.43) from the Mathematica file. The error does not propagate and, in particular, the figures are not affected.

On finite series solutions of conformable time-fractional Cahn-Allen equation

• Publication: Nonlinear Engineering
• Author(s): Zafar, AsimRezazadeh, HadiAli, Khalid K.
• Bibcode: 2020NLE.....9..194Z

The aim of this article is to derive new exact solutions of conformable time-fractional Cahn-Allen equation. We have achieved this aim by hyperbolic function and expa function methods with the aid of symbolic computation using Mathematica. This idea seems to be very easy to employ with reliable results. The time fractional Cahn-Allen equation is reduced to respective nonlinear ordinary differential equation of fractional order. Also, we have depicted graphically the constructed solutions.

DoFun 3.0: Functional equations in mathematica

• Publication: Computer Physics Communications
• Author(s): Huber, Markus Q.Cyrol, Anton K.Pawlowski, Jan M.
• Bibcode: 2020CoPhC.24807058H

We present version 3.0 of the Mathematica package DoFun for the derivation of functional equations. In this version, the derivation of equations for correlation functions of composite operators was added. In the update, the general workflow was slightly modified taking into account experience with the previous version. In addition, various tools were included to improve the usage experience and the code was partially restructured for easier maintenance.

Feasible solution of the time table assignment problem to faculty

• Publication: American Institute of Physics Conference Series
• Author(s): Sharma, SunitaTuli, Renu
• Bibcode: 2020AIPC.2214b0031S

An algorithm has been developed to find feasible solution of the time table assignment problem to faculty. A 0-1 linear programming model in developed, considering the priorities of the teacher and the workload. This process of assigning the tasks by developing a model and finding a feasible solution is difficult because of its size and the various conflicting objectives of the problem. Use of LINGO18 and MATHEMATICA 9 softwares have been made to achieve the desired results.

Image based Particle Shape Analysis Toolbox (IPSAT)

• Publication: Computers and Geosciences
• Author(s): Tunwal, MohitMulchrone, Kieran F.Meere, Patrick A.
• Bibcode: 2020CG....13504391T

Shape analysis can provide vital information regarding the origin, transport and deposition history of grains. Particle shape measurement has been an active area of research for sedimentologists since the 20th century. With advancement in the field of computation and image analysis, shape analysis can be done in a faster and much more accurate way compared to manual measurements. The results obtained are reproducible as compared to visual qualitative analysis. However, there is a lack of image analysis software tools aimed at the field of sedimentology where the fine details of a particle boundaries are required. Image based Particle Shape Analysis Toolbox (IPSAT) developed in the Mathematica environment for the quantitative characterisation of sedimentary grains in 2-dimensions is presented here. This image analysis toolbox can be used to analyse consolidated as well as loose sediment samples. A total of 12 parameters are available for shape measurement comprising conventional shape parameters (roundness, angularity, circularity and irregularity), mathematically complex shape parameters (fractal dimension and Fourier descriptors) and common geometrical shape parameters (aspect ratio, convexity, solidity, mod ratio, rectangularity and compactness). Additionally, IPSAT offers to compute 6 particle size measurement parameters. Furthermore, 2-D particle size distribution can be transformed to a 3-D size distribution for thin section analysis. Example analyses have been carried out on a sandstone and a loose sediment sample. The toolbox presented here aims to establish a textural analysis methodology to be used by geologists and sedimentologists in particular. It will allow users to quantitatively characterise a large set of grains with a fast, cheap and robust methodology.

Factorization of denominators in integration-by-parts reductions

• Publication: arXiv e-prints
• Author(s): Usovitsch, Johann
• Bibcode: 2020arXiv200208173U

We present a Mathematica package which finds a basis of master integrals for the Feynman integral reduction. In this basis the dependence on the dimensional regularization in the denominators factorizes in kinematic independent polynomials.

Compression with wildcards: All spanning trees

• Publication: arXiv e-prints
• Author(s): Wild, Marcel
• Bibcode: 2020arXiv200209707W

By processing all minimal cutsets of a graph G, and by using novel wildcards, all spanning trees of G can be compactly encoded. Thus, different from all previous enumeration schemes, the spanning trees are not generated one-by-one. The Mathematica implementation of one of our algorithms generated for a random (11,50)-graph its 819'603'181 spanning trees, in bundles of size about 400, within 52 seconds.

bimEX: A Mathematica package for exact computations in 3 + 1 bimetric relativity

• Publication: Computer Physics Communications
• Author(s): Torsello, Francesco
• Bibcode: 2020CoPhC.24706948T

We present bimEX, a Mathematica package for exact computations in 3 + 1 bimetric relativity. It is based on the xAct bundle, which can handle computations involving both abstract tensors and their components. In this communication, we refer to the latter case as concrete computations. The package consists of two main parts. The first part involves the abstract tensors, and focuses on how to deal with multiple metrics in xAct. The second part takes an ansatz for the primary variables in a chart as the input, and returns the covariant BSSN bimetric equations in components in that chart. Several functions are implemented to make this process as fast and user-friendly as possible. The package has been used and tested extensively in spherical symmetry and was the workhorse in obtaining the bimetric covariant BSSN equations and reproducing the bimetric 3 + 1 equations in the spherical polar chart.

Newton's discrete dynamics

• Publication: European Physical Journal Plus
• Author(s): Toxvaerd, Søren
• Bibcode: 2020EPJP..135..267T

In 1687, Isaac Newton published PHILOSOPHIÆ NATURALIS PRINCIPIA MATHEMATICA, where the classical analytic dynamics was formulated. But Newton also formulated a discrete dynamics, which is the central difference algorithm, known as the Verlet algorithm. In fact, Newton used the central difference to derive his second law. The central difference algorithm is used in computer simulations, where almost all Molecular Dynamics simulations are performed with the Verlet algorithm or other reformulations of the central difference algorithm. Here, we show that the discrete dynamics obtained by Newton's algorithm for Kepler's equation has the same solutions as the analytic dynamics. The discrete positions of a celestial body are located on an ellipse, which is the exact solution for a shadow Hamiltonian nearby the Hamiltonian for the analytic solution.

Modeling the thermoviscoelasticity of transversely isotropic shape memory polymer composites

• Publication: Smart Material Structures
• Author(s): Zeng, HaoPan, NingGu, JianpingSun, Huiyu
• Bibcode: 2020SMaS...29b5012Z

Shape memory polymer composites (SMPCs) are emerging smart materials of great application potential due to high deformability and good shape memory properties, with improved mechanical properties compared to pure polymers. In the paper, a micromechanical model is developed to predict the thermoviscoelastic and shape memory properties of such composite systems. First of all, we extend the Mori-Tanaka method into Carson domain based on the Correspondence Principle in viscoelasticity. Thus, the relaxation moduli of SMPCs at different temperatures can be obtained by the thermoviscoelastic properties of the matrix and the reinforcement in the transformed Carson domain. Next the inversion of the relaxation moduli from the Carson domain to the time (physical) domain is accomplished numerically by a multi-precision algorithm. Then, the three-element fractional Zener model is employed to describe the temperature-dependent relaxation modulus and the constitutive relations of SMPCs, and the analytical solutions to the partially constrained shape recovery behaviors are obtained, as well as the stress-strain relations of the material at different temperatures. The overall micromechanical model is then implemented into Mathematica, and the simulation results are compared to and agree well with the experimental results of two different kinds of SMPCs. The paper provides an efficient method on predicting the complex behaviors of transversely isotropic SMPCs.

The coupled nonlinear Schrödinger-type equations

• Publication: Modern Physics Letters B
• Author(s): Abdelrahman, Mahmoud A. E.Hassan, S. Z.Inc, Mustafa
• Bibcode: 2020MPLB...3450078A

Nonlinear Schrodinger equations can model nonlinear waves in plasma physics, optics, fluid and atmospheric theory of profound water waves and so on. In this work, the exp([Minus][CurlyPhi]([Xi]))-expansion, the sine-cosine and Riccati-Bernoulli sub-ODE techniques have been utilized to establish solitons, periodic waves and several types of solutions for the coupled nonlinear Schrödinger equations. These methods with the help of symbolic computations via Mathematica 10 are robust and adequate to solve partial differential nonlinear equations in mathematical physics. Finally, 3D figures for some selected solutions have been depicted.

Boundaries of the Amplituhedron with amplituhedronBoundaries

• Publication: arXiv e-prints
• Author(s): Lukowski, TomaszMoerman, Robert
• Bibcode: 2020arXiv200207146L

Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called ``amplituhedronBoundaries'' for calculating the boundary structures of three positive geometries: the amplituhedron $\mathcal{A}{n,k}^{(m)}$, the momentum amplituhedron $\mathcal{M}{n,k}^{(m)}$ and the hypersimplex $\Delta_{k,n}$. The first two geometries are relevant for scattering amplitudes in planar $\mathcal{N}=4$ SYM, while the last one is a well-studied polytope appearing in many contexts in mathematics, and is closely related to $\mathcal{M}_{n,k}^{(2)}$. The package includes an array of useful tools for the study of these positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians.

SmeftFR - Feynman rules generator for the Standard Model Effective Field Theory

• Publication: Computer Physics Communications
• Author(s): Dedes, A.Paraskevas, M.Rosiek, J.Suxho, K.Trifyllis, L.
• Bibcode: 2020CoPhC.24706931D

We present SmeftFR, a Mathematica package designed to generate the Feynman rules for the Standard Model Effective Field Theory (SMEFT) including the complete set of gauge invariant operators up to dimension 6. Feynman rules are generated with the use of FeynRules package, directly in the physical (mass eigenstates) basis for all fields. The complete set of interaction vertices can be derived including all or any chosen subset of SMEFT operators. As an option, the user can also choose preferred gauge fixing, generating Feynman rules in unitary or R_[Xi]-gauges (the latter include generation of ghost vertices). Further options allow to treat neutrino fields as massless Weyl or massive Majorana fermions. The derived Lagrangian in the mass basis can be exported in various formats supported by FeynRules, such as UFO and FeynArts. Initialisation of numerical values of d = 6 Wilson coefficients used by SmeftFR is interfaced to WCxf format. The package also includes dedicated Latex generator allowing to print the result in clear human-readable form. SmeftFR can be downloaded from the address www.fuw.edu.pl/smeft.

El experimento de Cavendish

• Publication: arXiv e-prints
• Author(s): Taborda Hernández, Jonathan
• Bibcode: 2020arXiv200204082T

In this article, we present a description of the \textit{apparatus} employed by Henry Cavendish, which in turn is actually a compendium of 17 complex experiments, to try to experimentally measure the universal gravitation constant, theoretically posed by the divine Sir Isaac Newton, in his monumental \textit{Principia Mathematica}.\ Since the gravitational force is very small, gravitational experiments in the laboratory are highly susceptible to strange disturbances. Measuring gravitation in the laboratory is then that problematic and today such difficulties persist.

Quark Contraction Tool - QCT

• Publication: Computer Physics Communications
• Author(s): Djukanovic, D.
• Bibcode: 2020CoPhC.24706950D

We present a Mathematica package for the calculation of Wick contractions in quantum field theories - QCT. The package aims at automatically generating code for the calculation of physical matrix elements, suitable for numerical evaluation in a C++ program. To that end commonly used algebraic manipulations for the calculation of matrix elements in lattice QCD are implemented.

Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method

• Publication: Chaos Solitons and Fractals
• Author(s): Naik, Parvaiz AhmadZu, JianGhoreishi, Mohammad
• Bibcode: 2020CSF...13109500N

Viruses have different mechanisms in causing a disease in an organism, which largely depend on the viral species. The recent advancement, through coupling data analysis and mathematical modeling, has allowed the identification and characterization of the nature of the virus. In the present paper, the homotopy analysis method is applied to provide an approximate solution of the basic HIV viral dynamic model describing the viral dynamics in a susceptible population. The proposed method allows for the solution of the governing system of differential equations to be calculated in the form of an infinite series with components which can be easily calculated. The homotopy analysis method utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. By using the homotopy series solutions, firstly, several [Beta] - curves using an appropriate ratio are plotted to demonstrate the regions of convergence and the optimum value of [HBar], then the residual and absolute errors are obtained for different values of these regions. Secondly, the residual error functions are applied to show the accuracy of the applied homotopy analysis method. Also, the convergence theorem of homotopy analysis method for the HIV viral dynamic model is proved. Mathematica software is used for the calculations and numerical results. The results obtained show the effectiveness and strength of the homotopy analysis method.

Propagation of shock wave in a rotational axisymmetric ideal gas with density varying exponentially and azimuthal magnetic field: isothermal flow

• Publication: Indian Journal of Physics
• Author(s): Nath, G.
• Bibcode: 2020InJPh.tmp...30N

In the present paper, the non-similarity solution for unsteady isothermal flow behind the cylindrical shock wave in a rotational axisymmetric perfect gas in the presence of azimuthal magnetic field is investigated. The ambient medium is assumed to have axial, azimuthal and radial components of fluid velocity. Solutions are obtained for MHD shock in a rotating medium with the vorticity vector and its components in one-dimensional flow case. The numerical solutions are obtained using Mathematica software and Runge-Kutta method of the fourth order. The Alfven Mach number, time and adiabatic exponent effects are worked out in detail. It is obtained that in the presence of magnetic field at the piston (inner expanding surface), the pressure and density vanish and hence a vacuum is formed at the line of symmetry, which is an excellent conformity with conditions to produce the shock wave in laboratory. Also, without magnetic field, the shock strength increases with an increase in time, whereas time has reverse affects on the shock strength in the presence of magnetic field. Our solutions are valid for arbitrary values of time. A comparison is also made between the behavior of non-rotating and rotating medium solutions in the presence or absence of magnetic field.

Mathematical Modeling of Failure Process of AlMg2.5 Alloy in High and Very High Cycle Fatigue

• Publication: Journal of Applied Mechanics and Technical Physics
• Author(s): Bilalov, D. A.Bayandin, Yu. V.Naimark, O. B.
• Bibcode: 2020JAMTP..60.1209B

Prediction of the endurance limit in the high and very high cycle loading range (10²-10¹⁰) is an important problem in aircraft engine construction and high-speed rail transport. It involves the development of models and their experimental verification taking into account damage evolution stages and fatigue crack growth in a damaged medium. A damage evolution model that takes into account the kinetics of defects and microplasticity effects was proposed. The model was used to study the process of fatigue failure of an AlMg2.5 structural alloy. The model parameters were identified and verified using experimental data on static, dynamic, and fatigue loading, as well as tests at various temperatures. The numerical results were used to construct the Wöhler curve, which was found to agree well with experimental data in the range of high cycle fatigue. The duality effect of the S-N curve was described. A computational experiment was performed to study the effect of dynamic loading on the fatigue strength. It was found that the fatigue limit depends weakly on the preliminary dynamic strain, which was confirmed by experimental data. Various mathematical packages and numerical methods for solving the constructed system of differential equations were compared. The Adams method and its modifications were shown to be optimal for the numerical integration of the problem under consideration. Wolfram Mathematica was found to be a preferred software package for numerical solution. The convergence of the numerical solution was investigated.

FindBounce: package for multi-field bounce actions

• Publication: arXiv e-prints
• Author(s): Guada, VictorNemevšek, MihaPintar, Matevž
• Bibcode: 2020arXiv200200881G

We are launching FindBounce, a Mathematica package for the evaluation of the Euclidean bounce action that enters the decay rate of metastable states in quantum and thermal field theories. It is based on the idea of polygonal bounces, which is a semi-analytical approach to solving the bounce equation by discretizing the potential into piecewise linear segments. This allows for a fast and robust evaluation of arbitrary potentials with specified precision and any number of scalar fields. Time cost grows linearly with the number of fields and/or the number of segments. Computation with 20 fields takes $\sim 2$ seconds with $0.5%$ accuracy of the action. The FindBounce function is simple to use with the native Mathematica look and feel, it is easy to install, and comes with detailed documentation and physical examples, such as the calculation of the nucleation temperature. We also provide timing benchmarks with comparisons to existing tools, where applicable.

An approximate analytical solution of non linear partial differential equation for water infiltration in unsaturated soils by combined Elzaki Transform and Adomian Decomposition Method

• Publication: Journal of Physics Conference Series
• Author(s): Varsoliwala, A. C.Singh, T. R., Dr.
• Bibcode: 2020JPhCS1473a2009V

The aim of the concerned paper is to describe the behaviour of the water infiltration problems in unsaturated soils. Governing equation of this phenomenon is known as Richards' equation. The solution of the Richards' equation has been found by Elzaki Adomian Decomposition Method. This method gives a solution in terms of convergent series. Comparison of the approximate solutions and exact solutions have been found here. MATLAB and MATHEMATICA are used to obtain numerical and graphical representation.

Investigation of entropy generation in stratified MHD Carreau nanofluid with gyrotactic microorganisms under Von Neumann similarity transformations

• Publication: European Physical Journal Plus
• Author(s): Naz, RahilaTariq, SanaSohail, MuhammadShah, Zahir
• Bibcode: 2020EPJP..135..178N

In this article Carreau nanofluid over a flat cylinder in the presence of suspended gyrotactic microorganisms and an inclined magnetic field is premeditated. The conversion of physical representation to mathematical form results in coupled partial differential equations which are compact to higher-order coupled ordinary differential equations using Von Neumann similarity transformations. Since the arising system of equations are coupled and highly nonlinear and cannot be solved for the exact solution. The system of nonlinear transformed differential equations are solved by using optimal homotopic scheme. The mathematical scheme is explained numerically through the software Mathematica. Influence of involved parameters is noted on the silhouettes of velocity, temperature, concentration and density number of motile microorganisms and fluxes using different forms of graphical representations. Moreover, the entropy generation is premeditated through contour portraits. Important observations are made that the bioconvection parameters and curvature augment the mass transfer rate of microorganisms. Also, the temperature difference parameter ([Chi] ) can be used to uplift the system's efficiency.

Unified computational approach to nilpotent algebra classification problems

• Publication: arXiv e-prints
• Author(s): Kadyrov, ShiraliMashurov, Farukh
• Bibcode: 2020arXiv200107498K

In this article, we provide an algorithm with Wolfram Mathematica code that gives a unified computational power in classification of finite dimensional nilpotent algebras using Skjelbred-Sund method. To illustrate the code, we obtain new finite dimensional Moufang algebras.

Bell Polynomials in the Mathematica System and Asymptotic Solutions of Integral Equations

• Publication: Theoretical and Mathematical Physics
• Author(s): Marichev, O. I.Slavyanov, S. Yu.Brychkov, Yu. A.
• Bibcode: 2020TMP...201.1798M

We consider the possibility of solving functional equations that arise when integrating homogeneous integral Fredholm equations of the second kind with a highly oscillatory kernel by using Bell polynomials. We review different types and properties of Bell polynomials. The focus of this paper is to promote using tools in the Bell polynomial package in the Mathematica system to solve certain problems in electrodynamics.

Water dynamics in deuterated gypsum, CaSO₄⋅2D₂O, investigated by solid state deuterium NMR

• Publication: Journal of Magnetic Resonance
• Author(s): Tobar, CelesteCordova, ReginaSolomon, TriciaPalombo, KristineOlivares, GladysHelston, JoshuaLuo, WenbinCizmeciyan, DenizBenesi, Alan
• Bibcode: 2020JMagR.31006640T

NMR relaxation theory and NMR lineshape calculations were used to characterize the rates of C₂ symmetry jumps of deuterium nuclei in partly deuterated gypsum powder. The experimental data consisted of variable temperature deuterium NMR powder line shapes and deuterium T₁ relaxation times. All of the Mathematica© notebooks used to simulate the spectra and match the experimental T₁ values are included as supplementary material, and are suitable templates for similar calculations on other systems. Our simulations show that the deuterium nuclei of D₂O in Gypsum undergo a two-site C₂ 180[Degree] jump about the D-O-D bisector angle of 54.8[Degree]. The jump rate stays in the fast motion regime down to about 218 K. Below 193 K the powder lineshapes change, the spectral intensities drop significantly, and the motion slows into the intermediate motion regime. The best fit quadrupole coupling constants (QCC's) vary between 216 kHz at the highest temperatures to 235 kHz at the lowest temperatures. The asymmetry parameters (ɳ) vary between 0.11 at the highest temperatures to 0.15 at the lowest temperatures. Knowledge of the C₂ jump rates allowed us to calculate activation parameters for the jumps, namely [Laplacian]H^{[DoubleDagger]} = 22 kJ/mol, and [Laplacian]S^{[DoubleDagger]} = -10 J/mol[CenterDot]K which indicate a non-spontaneous activation process, an activation energy of E_a = 23 kJ/mol, and a pre-exponential factor of A = 3.6 * 10¹². As expected, there was no evidence of quantum tunneling.

Towards an automation of the circle method

• Publication: arXiv e-prints
• Author(s): Sills, Andrew V.
• Bibcode: 2020arXiv200109568S

The derivation of the Hardy-Ramanujan-Rademacher formula for the number of partitions of $n$ is reviewed. Next, the steps for finding analogous formulas for certain restricted classes of partitions or overpartiitons is examined, bearing in mind how these calculations can be automated in a CAS. Finally, a number of new formulas of this type which were conjectured with the aid of \emph{Mathematica} are presented along with results of a test for their numerical accuracy.

Bions and Instantons in Triple-well and Multi-well Potentials

• Publication: arXiv e-prints
• Author(s): Dunne, Gerald V.Sulejmanpasic, TinUnsal, Mithat
• Bibcode: 2020arXiv200110128D

Quantum systems with multiple degenerate classical harmonic minima exhibit new non-perturbative phenomena which are not present for the double-well and periodic potentials. The simplest characteristic example of this family is the triple-well potential. Despite the fact that instantons are exact semiclassical solutions with finite and minimal action, they do not contribute to the energy spectrum at leading order in the semiclassical analysis. This is because the instanton fluctuation prefactor vanishes, which can be interpreted as the action becoming infinite quantum mechanically. Instead, the non-perturbative physics is governed by different types of {\it bion} configurations. A generalization to supersymmetric and quasi-exactly soluble models is also discussed. An interesting pattern of interference between topological and neutral bions, depending on the hidden topological angle, the discrete theta angle and the perturbative level number, leads to an intricate pattern of divergent/convergent expansions for low lying states, and provides criteria for the exact solvability of some of the states. We confirm these semiclassical bion predictions using the Bender-Wu Mathematica package to study the structure of the associated perturbative expansions. It also turns out that all the systems we study have a curious exact one-to-one relationship between the perturbative coefficients of the three wells, which we check using the BenderWu package.

Calculation and Properties of Zonal Polynomials

• Publication: arXiv e-prints
• Author(s): Jiu, LinKoutschan, Christoph
• Bibcode: 2020arXiv200111599J

We investigate the zonal polynomials, a family of symmetric polynomials that appear in many mathematical contexts, such as multivariate statistics, differential geometry, representation theory, and combinatorics. We present two computer algebra packages, in SageMath and in Mathematica, for their computation. With the help of these software packages, we carry out an experimental mathematics study of some properties of zonal polynomials. Moreover, we derive and prove closed forms for several infinite families of zonal polynomial coefficients.

A Mathematica code for calculating massless spectrum of (0,2) Landau-Ginzburg orbifold

• Publication: arXiv e-prints
• Author(s): Parsian, HadiFeng, He
• Bibcode: 2020arXiv200108738P

In this short paper, we try to explain how to use our program which has been written in Wolfram Mathematica to get the massless spectrum of any Landau-Ginzburg orbifold. The technique has been developed by Witten-Kachru theoretically, but calculating it for an explicit Landau-Ginzburg model is exhausting and in general, beyond human ability to calculate using pen and paper.

Bases of Quantum Group Algebras in Terms of Lyndon Words

• Publication: arXiv e-prints
• Author(s): Valetov, Eremey
• Bibcode: 2020arXiv200110435V

We have reviewed some results on quantized shuffling, and in particular, the grading and structure of this algebra. In parallel, we have summarized certain details about classical shuffle algebras, including Lyndon words (primes) and the construction of bases of classical shuffle algebras in terms of Lyndon words. We have explained how to adapt this theory to the construction of bases of quantum group algebras in terms of Lyndon words. This method has a limited application to the specific case of the quantum group parameter being a root of unity, with the requirement that specialization to the root of unity is non-restricted. As an additional, applied part of this work, we have implemented a Wolfram Mathematica package with functions for quantum shuffle multiplication and constructions of bases in terms of Lyndon words.

Spin Dynamics Investigation of Quasi-Frozen Spin Lattice for EDM Searches

• Publication: arXiv e-prints
• Author(s): Valetov, EremeySenichev, YurijBerz, Martin
• Bibcode: 2020arXiv200107062V

The Quasi-Frozen Spin (QFS) method was proposed by Yu. Senichev et al. in [1] as an alternative to the Frozen Spin (FS) method [2] for the search of deuteron electric dipole moment (dEDM). The QFS approach simplifies the design of the lattice. In particular, small changes to the currently operating COSY storage ring will satisfy the QFS condition. Spin decoherence and systematic errors fundamentally limit EDM signal detection and measurement. Our QFS implementation method includes measurement of spin precession in (1) the horizontal plane to calibrate the magnetic field when changing field polarity and (2) the vertical plane to search for EDM. To address systematic errors due to element misalignments, we track particle bunches in forward and reverse directions. We modeled and tracked two QFS and one FS lattice in COSY INFINITY. The models include normally distributed random variate spin kicks in magnetic dipoles and combined electrostatic and magnetic field elements. We used Wolfram Mathematica programs to partially automate lattice input file generation and tracking output data analysis. We observed indications that the QFS method is a viable alternative to the FS method. [1] Y. Senichev, A. Lehrach, B. Lorentz, R. Maier, S. Andrianov, A. Ivanov, S. Chekmenev, M. Berz, and E. Valetov (on behalf of the JEDI Collaboration), in Proceedings of IPAC 2015, Richmond, VA (2015) MOPWA044. [2] D. Anastassopoulos et al., AGS Proposal: Search for a Permanent Electric Dipole Moment of the Deuteron Nucleus at the $10^{-29}:e\cdot\mathrm{cm}$ Level, BNL Report, Brookhaven National Laboratory, Upton, NY (2008).

Complete form factors in Yang-Mills from unitarity and spinor helicity in six dimensions

• Publication: Physical Review D
• Author(s): Accettulli Huber, ManuelBrandhuber, AndreasDe Angelis, StefanoTravaglini, Gabriele
• Bibcode: 2020PhRvD.101b6004A

We present a systematic procedure to compute complete, analytic form factors of gauge-invariant operators at loop level in pure Yang-Mills. We consider applications to operators of the form Tr Fⁿ where F is the gluon field strength. Our approach is based on an extension to form factors of the dimensional reconstruction technique, in conjunction with the six-dimensional spinor-helicity formalism and generalized unitarity. For form factors this technique requires the introduction of additional scalar operators, for which we provide a systematic prescription. We also discuss a generalization of dimensional reconstruction to any number of loops, both for amplitudes and form factors. Several novel results for one-loop minimal and nonminimal form factors of Tr Fⁿ with n >2 are presented. Finally, we describe the Mathematica package uc(s)pinoruc(h)elicity6uc(d), which is tailored to handle six-dimensional quantities written in the spinor-helicity formalism.

Optimization of parameters of integrated optical waveguides based on thin-film Sol-gel structures by using mathematical modelling

• Publication: Journal of Physics Conference Series
• Author(s): Aliev, S. A.Pakhlavonova, K. D.Ravin, A. R.Trofimov, N. S.Chekhlova, T. K.
• Bibcode: 2020JPhCS1439a2024A

An algorithm for calculating optical waveguide film parameters was proposed, the use of which makes it possible to reduce the time for processing experimental data. The developed algorithm was tested using experimental data of waveguides samples with a wave-guiding layer of zirconium dioxide sol-gel films. A comparison of the developed algorithm and the Wolfram Mathematica program showed a good agreement of the results, as well as the developed method advantage in terms of using ease and timesaving spent on processing the results.

Entropy analysis of EMHD non-Newtonian fluid flow induced by Riga plate with slip and convective boundary phenomena

• Publication: International Journal of Modern Physics C
• Author(s): El-Aziz, Mohamed AbdAfify, Ahmed A.
• Bibcode: 2020IJMPC..3150066E

Our paper is consecrated to show the influence of variable fluid properties in EMHD non-Newtonian power-law fluid along a moving Riga plate. Slip velocity phenomenon is considered at the surface which is convectively heated. Entropy analysis is elaborated employing thermodynamic second relation. The governing nonlinear PDEs are altered into ODEs through adequate propinquity transformations which have been solved numerically via the shooting method with the fourth-order Runge-Kutta algorithm through Mathematica software (bvp4c). Characteristics of different basic parameters on velocity, temperature, entropy generation and Bejan number are highlighted through graphs. The outcomes exhibit that the minimum entropy rate in the flow system can be obtained either with rising viscosity parameter and slip parameter or declining dimensionless parameter and thermal conductivity parameter. The entropy rate is minimal for dilatant fluid when compared to pseudo plastic fluid with the most governing parameters. Contrast behavior on the thermal field is noticed for larger values of viscosity parameter and thermal conductivity parameter.