## Top new questions this week:

### How can I find a functional square root in Mathematica?

A functional square root of a function $g$ is another function $f$ such that $g=f\circ f$. According to that article, there is a systematic approach to finding a functional square root that involves ...

equation-solving calculus-and-analysis

### The numerics of FresnelS[]

Bug introduced in 12.1 or earlier and persisting through 12.1.1 or later [CASE:4615361] Note: A worse problem existed in 12.0 for inputs greater than 8 and of precisions less than 43.66; 12.1 fixed ...

bugs numerics special-functions

### How to enter a nuclear reaction?

Sometimes the simplest things are the most difficult, I need to make a presentation, and I thought to do it in Mathematica, I wanted to do a demonstration too, well...this is the Rutherford's equation ...

formatting physics writing

### How to find a numerical antiderivative with NIntegrate methods?

@JimBelk asked in Interpolating an Antiderivative how to find a numerical antiderivative. I gave an answer that uses NDSolve with the default method for integrating $y'=f(x,y)$. However for ...

calculus-and-analysis numerical-integration approximation

### How to draw one-line Venn diagram?

This is the a list of set. data = {{"A"}, {"J"}, {"Q"}, {"G", "H"}, {"I", "O"}, {"B", "C", "E", ...

graphics visualization

### How to get the progressive application of list of rules?

all. I need some suggestion on this problem. I have a very long list of rules, using this list of rules I want to see how some elements evolve as I successively apply the next rules on the previous ...

function-construction replacement

### How to express permutation as the least number of exchanges

If there are grammatical or terminological errors in the following description, please help correct: In some problems, it is necessary to find out what minimum number of exchanges can change a list ...

combinatorics permutation

## Greatest hits from previous weeks:

### Skip header lines on import

When importing a data file what are the comment symbols for Mathematica? That is, given a file like this blabla bulbul 1 2 6 54 7 ... .. what symbol do I have to put in front of header lines so ...

import text

### Calculate the 2D Fourier transform of an Image

I am new to Mathematica, and using version 8.0. I would like to calculate the 2D Fourier Transform of an Image with Mathematica and plot the magnitude and phase spectrum, as well as reconstruct the ...

image-processing image fourier-analysis

### How do I plot a plane EM wave?

I would like to display an electromagnetic (EM) wave. I have written code that works, but it does not "shade" the area between the graph and the axes. Both the Filling and EdgeForm commands are ...

graphics physics visualization

### How to make the digits of π go around in a spiral like this?

Here is a start. MapIndexed[Text[Reverse[First[RealDigits[Pi,10,252]]][[Tr@#2]],#]&, Table[{t Cos[t],t Sin[t]},{t,0,16Pi,0.2}]]//Graphics

graphics formatting generative-art

### How to create effect like Van Gogh's stroke brush?

I need to apply Van Gogh's stroke brush effect to a random image Take the following image as an example: Thank you so much if you could help!

image-processing code-request generative-art

### Cutting bagels into linked halves

I recently came across this video: Mathematically correct breakfast, which shows how a bagel can be neatly sliced into two identical linked halves. I'd like to try this with Mathematica. Here's a ...

graphics graphics3d

### QR Code in shopping cart handle

This week, the market people from my work wanted to put QR codes in shopping cart handles, but when they tested it, the QR code did not work. I noted that the cylindrical curvature (even small) ...

image-processing

## Can you answer these questions?

### Import OVF 2.0 Vector field files

I'm using a simulation software (mumax3) which outputs OVF_2.0 files. It can either export binary or text files. The binary files are usually much smaller than the text files. I would like to use the ...

import vector binary
 asked by Walter Lars Lee 1 vote

### Solving system of coupled PDEs with method of lines

I'm trying to solve: $\partial _{z} U(z,t) = i \sqrt{d} P(z,t)$ $\partial _{t} P(z,t) = -P(z, t) + i \sqrt{d} U(z,t) + i \Omega_{c}(t)S(z, t)$ $\partial _{t} S(z,t) = i \Omega_{c}(t)P(z, t)$ For the ...

differential-equations numerical-integration

### Trouble verifying a solution to a differential equation

I am reading a physics book which has discussed one approach towards solving the differential equation $$\frac{d^2 x(t)}{dt^2} = Cx(t)$$ as follows: Using Mathematica to solve the equation. I ...

differential-equations simplifying-expressions symbolic physics algebraic-manipulation