Final Project Enrique

[ealopez]

No description provided.

[ealopez]

Dear Instructors,

I am submiting my final project. Any feedback will be really appreciated, I am giving in this notebook a quite extensive introduction to scanning probe microscopy simulations and two bonus schemes are provided: Verlet and Runge Kutta 4.
Thank you.

[labarba]

Very interesting and well laid out notebook. Substantial piece of work! It was an excellent idea to start with the simple harmonic motion to test your code, before adding tip forces. This is the way to develop numerical codes! I'm also very pleased to see the error analysis, and of course the new integrators.

Why do you have section headings preceded by "3"? (3.1, 3.2, 3.3, etc.)
Did you prepare the illustrations yourself? (If not, you would need to add a credit line.)

You forgot to say what Q is, when you first use it (Equation 1). At the end of this section of text (and before the code starts), you mention "quality factor," but your reader likely does not know what this is. In fact, all symbols should be defined, even if most of them are familiar to many readers.

Yay for loading NumPy like you did! :-)
(It's the way we like it, but certainly not the mainstream on the internets)

In [20]: seems to have an extra space before t=, which won't work!
(you may have introduced a space after running the code?)

Error analysis:
You say that RK4 converges faster than Verlet, but what I see in the plot is that the two methods reduce the error by 3 orders of magnitude in the range of dt from 1e-6 to 1e-9.
And what would you expect? What is the order of convergence of each method?

RK4 gives smaller errors, as you mention, by one order of magnitude. Here's an interesting question: how does the time-to-solution compare for the same error? (RK4 presumably takes longer to compute for a given dt).

I would be happy to merge this pull request to add your notebook to the NumericalMOOC "knowledge base," but there are so many typos! If you have time, it would be great if you could fix these.

Typos & style
Inn this Ipython notebook —> In this IPython notebook, (note the comma)
the mainly used nowadays —> the most frequently used nowadays
due to the significant advantages —> due to its advantages (or you can add "important," but save "significant" for statistically significant in technical writing)
computanionally —> computationally
more about thi —> this
So, the equation —> do you really need "so" here? (slangy, idiomatic)
that is besides —> remove "besides" (or remove all 3 words)

–use a backslash before functions in LaTeX mode to get roman type: \cos, \arctan
(there are a bunch of missing commas, but it would be cumbersome to list)
–add a semicolon to the end of your plotting statements to suppress the ugly Matplotlib output (like <matplotlib.lines.Line2D at 0x7e29550>)

as most self-contained as possible—>just say "self-contained"
This previous coupled equations—> These coupled equations
big with relation to—> big with respect to (or: in relation to)
we have set intentionally ONLY—>we have intentionally set it to ONLY
can't cath up the physics—>can't capture the physics
can catch the physics—>can capture the physics

(Verlet) ... around $z_i$—>should be $z_n$
... solving for $z_{i_1}$—> should be {n+1} in the subscript
ending up being—ending up with
is mainly used —>it's mainly used
equation to integrated—>equation to be integrated
is mainly used —>it's mainly used
substracting—> subtracting
(and the big-O terms is \Delta t^2, because you divided over by \Delta t)
neglest—> neglect
more about this soon after—> more about this later
cath up the physics—>to capture the physics
composed by—>composed of

(RK4) ... However, we have—> delete "However"
both depend in—>depend on
values are intercalated—>values are used sequentially (?)
(intercalate doesn't have the meaning you intend here)
making a different job quality—>giving different quality
is hard to—>it's hard to
make an error analysis—>do (or perform) an error analysis
made the model—>developed the model
with regards of the separation—>with respect to the separation
arisen —>arising
is arisen —>arises
a emerging—>an emerging
tip does deeper—>tip goes deeper
the higher the contact area—>the larger the contact area(?)
half-sapace—> half-space
analitically—> analytically
straigthforward approachable—> remove "approachable"
tha Young's modulus—>the
to sinusoidals—>two
high position enough—>high-enough position
the phase can give relative about—> ??
interested on—>interested in

– There are many, many missing commas!
– Many instances of compound adjectives with missing hyphen. E.g.:
second-order ODE
1st-order differential equations
steady-state oscillation
more-efficient scheme
etc.

[ealopez]

Dear Professor Barba and instructors,

I have made the changes suggested, and I think it is ready to be merged. I have checked the text in a text editor in order to check spelling error and typos, besides correcting all the typos that you kindly pointed out.
The last version to be merged would be the one marked as: "with readme". Please do not pay attention to the version: "test". If you need me to change something else please let me know.

Thank you!

Enrique