Smoluchowski-Rotor-Chain

Smoluchowski-Rotor-Chain is a simple C++ program devoted to the diffusive simulation of a chain of hydrodynamically independent 2D rotors interacting with a nearest-neighbour potential. The software solves the Symmetrized Fokker-Planck-Smoluchowski eigenvalue problem by expansion over a basis set.

How to cite this code

This code can be used and modified freely under the GPL-3.0 License. If you use this code please cite the URL of this repository and the paper: Pierpaolo Pravatto et al 2021 New J. Phys. 23 123045

Requirements

• gcc (g++) 9.3
• CBLAS 3.8
• LAPACK 3.8
• gnu-gsl 2.6
• OpenMP (only for parallel version)

Compiling

A Makefile is provided to compile the code. The serial compilation can be linked against the system installation of the CBLAS library:

make serial

or against the CBLAS version provided by GNU-GSL:

make serial-gsl

A parallel (multi-threaded) version of the software can also be compiled linking against the OpenMP library either with the system CBLAS library:

make parallel

or against the one provided by GNU-GSL:

make parallel-gsl

The make clean command can be used to remove the executable file.

Running calculations

In order to perform a calulation an input file must be provided as inline argument to the main.exe executable.

./main.exe input.txt

The program can be executed in background and the output redirected to an output.txt file using the syntax:

./main.exe input.txt > output.txt &

If a parallel version of the program is compiled the number of threads can be selected through the OpenMP environment variable OMP_NUM_THREADS.

Input file syntax

The command syntax for the program must be always structurated as follows:

# KEYWORD
parameters

The line marked by # identify a command line. The line should contain the marker # followed by a single white space and a keyword. The full list of keyword is available in the next section. The first line after the keyword must contain the parameters either as a single number (if only one is required) or as a list of numbers separated by a ,. Floating point numbers can be expressed in exponential form (e.g. 6.02e-23). The . must be used as decimal point.

Every input file should contain the number of rotors to be considered. This can be specified as:

# NROT
number of rotors

Please note how # NROT represent the number of rotors and not the number of dihedral angles.

Input file keywords

Keyword	Description	Number of parameters	Type	Default value
NROT	Number of rotors in the chain	1	integer	-
NUM-MIN	Number of potential minimum	NROT-1	integer list	1
ISOLATED-BASIS	Number of single dihedral basis functions	NROT-1	integer list	100
COUPLED-BASIS	Number of single dihedral eigenfunctions to be used in the multiple rotor expansion	NROT-1	integer list	10
BARRIER	Potential energy barrier for each dihedral	NROT-1	double list	1.
DIFFUSION-COEFF	Diffusion coefficient for each rotor	NROT	double list	1.
NPT-INTEG-SINGLE	Maximum number of integration points for the single dihedral	1	int	10000
ABS-INTEG-SINGLE	Absolute integrator error threshold for the single dihedral	1	double	1e-10
REL-INTEG-SINGLE	Relative integrator error threshold for the single dihedral	1	double	1e-10
QAG-KEY-SINGLE	GSL key for selecting the QAG integrator order for the single dihedral	1	int	6
NPT-INTEG-COUPLED	Maximum number of integration points for the rotor chain	1	int	10000
ABS-INTEG-COUPLED	Absolute integrator error threshold for the rotor chain	1	double	1e-10
REL-INTEG-COUPLED	Relative integrator error threshold for the rotor chain	1	double	1e-10
QAG-KEY-COUPLED	GSL key for selecting the QAG integrator order for the rotor chain	1	int	6
SAVE-VQE	Setting the flag to 1 or 0 activate or deactivate the generation of a file containing the matrix of sFPS operator integrals on the composite basis set	1	bool (as 0 or 1)	0
SAVE-EIGVAL-LIST	Setting the flag to 1 or 0 activate or deactivate the generation of a file containing all the eigenvalues computed for the system	1	bool (as 0 or 1)	0
SINGLE-COUPLED_SCAN	Setup a basis-set dimension scan for a defined dihedral (for more informations see the "Independent coupled basis scan keyword" section)	4	integer list	-
LOCKED-COUPLED_SCAN	Setup a basis-set dimension scan for all dihedral (for more informations see the "Locked coupled basis scan keyword" section)	3	integer list	-

Independent coupled basis scan keyword

The SINGLE-COUPLED-SCAN keyword can be used to set up a scan on the number of basis functions for each dihedral angle. The function varies the basis set cutoff for the selected dihedral and overrides the corresponentSINGLE-COUPLED-BASIS instruction. The following four integer syntax can be used:

# SINGLE-COUPLED-SCAN
<dihedral number>, <initial basis set>, <final basis set>, <step>

For example the instruction:

# SINGLE-COUPLED-SCAN
0, 4, 7, 1

will run a calculation for 4, 5, 6, 7 basis functions for the first rotor of the chain while keeping the number of basis function constant for the remaining rotors. Multiple scan instructions are not implemented at the moment, subsequent calls to SINGLE-COUPLED-SCAN will override all previous instructions except the last one. If the user want to scan all dihedral simultaneousy the keyword LOCKED-COUPLED-SCAN must be used (see next section for more details).

Locked coupled basis scan keyword

The LOCKED-COUPLED-SCAN keyword can be used to set up a scan on the number of basis functions for all the dihedral angles in the chain. The function varies the basis set cutoff for all the dihedrals and overrides the corresponentCOUPLED-BASIS instruction. The following three integer syntax can be used:

# LOCKED-COUPLED-SCAN
<initial basis set>, <final basis set>, <step>

For example the instruction:

# LOCKED-COUPLED-SCAN
4, 7, 1

will run a calculation setting the cutoff for all dihedral basis to 4, 5, 6, 7.