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Evaluate the time average of Mathieu functions

I defined a function composed of Mathieu's periodic functions: ...
ZHENGYAO HUANG's user avatar
2 votes
1 answer
68 views

How to constrain a Mathematica vector to a periodic domain?

Consider a function $F({\bf v})$, where ${\bf v}=(v_x,v_y)$ is a vector in $\mathbb{R}_2$. I would like to define a new function $f({\bf v})$ which is periodic under $f({\bf v})=f({\bf v}+(n_x,n_y))$ ...
Paul Eugenio's user avatar
1 vote
2 answers
133 views

Fundamental matrix solution of a differential equation $x'=A(t)x$

In this question about Floquet theory the author asked about the fundamental matrix solution $X(t)$ of the following $2\pi$-periodic differential equation $${\displaystyle {\dot {x}}=A(t)x}$$ with $$A(...
user50618's user avatar
  • 123
3 votes
2 answers
202 views

FunctionPeriod for functions defined in a Piecewise manner

To create a minimal example, consider a piecewise function: ...
Syed's user avatar
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1 answer
76 views

Non Linear System of Diferential Equations with periodic function

I am programming a system of differential equations consisting of 3 cell populations; Normal cells N, Tumor cells T and chemotherapy treatment Q, when a function q is constant. The system is as ...
Cristian Camilo Espitia's user avatar
4 votes
1 answer
170 views

FEM solution of Helmholtz equation

I'm trying to solve the Helmholtz equation : https://en.wikipedia.org/wiki/Helmholtz_equation in a 3d space, in vacuum, using FEM. I expect the solution to be an function oscillating in the x ...
dnad's user avatar
  • 41
3 votes
1 answer
522 views

How can we plot a step function in Mathematica and make it periodic?

Consider a periodic function of the form $$ f(t) = \left\{ \begin{array}{r} 1, & 0\leq t \leq T/2, \\ 0, & T/2\leq t\leq T, \\ \end{array} \right. $$ with $f(t+T)=f(t)$. How can we define ...
Solidification's user avatar
2 votes
1 answer
93 views

Trouble Finding the period of a function [closed]

I want to use Mathematica to compute the period of the function $F(t)=\cos t - \exp \left( - \sum_{k=1}^{50} \frac{\sin (kt) }{k} \right) -\sum_{k=1}^{50} \frac{\cos (kt)}{k}$, so here's my code ...
user avatar
7 votes
2 answers
156 views

Why does FunctionPeriod give two different results for alternative forms of the given function?

I have a function for the variable $x>0$ and constant $a\in\mathbb{R}$. I write it in its two alternative forms $$f(x)=\cos a\pi-\cos x\pi =-2\sin\frac{(a-x)\pi}{2}\sin\frac{(a+x)\pi}{2} $$ Then, I ...
Phys96's user avatar
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1 vote
0 answers
35 views

Reduce giving seemingly unnecessary conditions

Although is not a problem by itself, I have noticed that when working with periodic functions, Reduce returns sometimes extra conditions that seem unnecessary. I was wondering whether this is a ...
Jorge's user avatar
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-1 votes
1 answer
135 views

Solve A System of Trigonometric Equations

I tried running the following code on Mathematica Cloud, but it didn't because it was taking long of I have the basic plan. Would someone please run this code for me and share with me the results. it'...
Thando 's user avatar
0 votes
2 answers
62 views

Supremum of a complex periodic signal in symbolic form

For complex periodic signal: $-\frac{8 T \left(2 T \omega \sin (2 t \omega )-e^{-\frac{t}{T}}+\cos (2 t \omega )\right)}{\alpha ^2 \left(4 T^2 \omega ^2+1\right)}$ where $T,\alpha,\omega$ - ...
dtn's user avatar
  • 2,404
1 vote
2 answers
154 views

Function decomposition to Fourier series using first impulse function

I have periodic function with certain first impulse function and period value. My task is to decompose it to approximate Fourier series (k_max = 10) using Laplace transform of first impulse function: ...
Cpp Nosavvier's user avatar
2 votes
1 answer
223 views

Is it possible to ask Mathematica to give a table of probability that $f(x)>0$?

I have a function $$f(x)=(4 \cos 2 a x+3) (\cos a x+2 \cos 300 x),$$ and I want to calculate the probability that $f(x)>0$ for $a=\{1,2,3,...,100\}$ assuming that $x$ has uniform distribution. More ...
charmin's user avatar
  • 1,159
2 votes
2 answers
228 views

Computing periodic points of some function

Given a function h[{x_, y_}, b_, c_] := {x^2 + c - b*y, x} for some parameter values b and c ...
math's user avatar
  • 773
3 votes
2 answers
437 views

Finding the period of a function of an interpolating function

I have two quantities of interest, x and y which are functions of $\theta$ and thus implicitly of time. They also depend on two ...
JamesVR's user avatar
  • 407
13 votes
3 answers
1k views

Finding the Period of a Limit Cycle

I'm interested in the periods of limit cycles of the Wilson-Cowan equations which have the form $$x'(t) = -x + S(ax(t) - by(t) +e)$$ $$y'(t) = -y + S(cx(t) - dy(t) + f)$$ where $$S(x) = 1 + \frac{\...
Cheyne's user avatar
  • 312
3 votes
2 answers
168 views

Error in definition of PeriodicBoundaryCondition?

The documentation for PeriodicBoundaryCondition (https://reference.wolfram.com/language/ref/PeriodicBoundaryCondition.html) has: Where it says $u ( x_{target} ) = a + b\ u ( f ( x_{target} ) )$, I ...
Anthony's user avatar
  • 87
4 votes
1 answer
142 views

Periodic extrapolation out of the domain of the solution of a PDE in two directions

As a prototypic problem ...
Αλέξανδρος Ζεγγ's user avatar
6 votes
1 answer
451 views

FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
SantaP's user avatar
  • 845
2 votes
1 answer
151 views

Constructing and plotting a special periodic function

I need to program and plot the following special function in Mathematica 12.0: $$ a_{1}(t)= \sum_{n\geq 1} \beta_{n}(t), $$ such that, for every $ n \geq 1 $ $$ \beta_{n}(t)= \displaystyle \sum_{...
Kamal Khalil's user avatar
4 votes
2 answers
421 views

FEM: Solving the heat conduction with 2D periodic condition

Suppose you have a region $\Omega = [0,P_1] \times [0,P_2]$ which is composed of, e.g., two materials. One material is distributed as inclusions in an embedding material. We split the region as $\...
Mauricio Fernández's user avatar
5 votes
1 answer
232 views

One dimensional heat exchange on a ring: Periodic solution

Subsequent I consider the transient heat exchange problem of a ring in polar coordinates. The ring is heated in a small range 0<\[CurlyPhi]<20° and cooled ...
Ulrich Neumann's user avatar
16 votes
4 answers
1k views

Understanding PeriodicBoundaryConditions

Every thing works fine in a simple example with periodic boundary condition u[ 2,y]==u[0,y] from documentation of ...
Ulrich Neumann's user avatar
3 votes
1 answer
276 views

Problem with complex eigenvalues in periodic Sturm-Liouville problem

I'm having trouble using NDEigenvalues to obtain the first few eigenvalues for a differential operator on the circle of radius one-half. $\qquad Lf(x) = f''(x)+ (-...
Misha's user avatar
  • 125
2 votes
1 answer
503 views

Why I get negative values on using periodogram after Fourier analysis?

sorry for bothering you with this question today. I am trying to analyze wave data that was produced using a wave tank. The period used for the waves is 1.7s, the waves encountered an obstacle at some ...
mrvladivostok's user avatar
0 votes
1 answer
368 views

Extending periodic piecewise continuous function

I need to plot the piecewise function $$ f(x) = \left\{ \begin{array}{r} x^2, & -2 \leq x \leq 0, \\ 0, & 0 < x \leq 1, \\ 1 - x, & 1 < x \leq 3. \\ \end{array} \right. $$ as a ...
MKA's user avatar
  • 13
3 votes
2 answers
76 views

Interleaving position

How could I proceed to interleave the presented values to obtain the same result obtained by this code? ...
LCarvalho's user avatar
  • 9,233
1 vote
2 answers
4k views

Plot on the surface of a Torus

I'm trying to plot a system with a variable (or field) $\theta(x,t)\in[-\pi,\pi]$ which is an angle at every position $x$. The positional argument $x$ itself is a periodic coordinate $x\in[-\pi,\pi]$. ...
sobol's user avatar
  • 113
1 vote
1 answer
141 views

Mathematica doesn't evaluate my Limit expression

I tried to evaluate the following limit: Limit[Sin[x]^n, n -> Infinity] However, Mathematica doesn't evaluate it, and just reprints the original problem: <...
JohnS's user avatar
  • 21
-1 votes
1 answer
296 views

Solving differential equation with periodic variable (poincare section)

I'm trying to make a Poincare section using the code here: ...
ZufolgeWeierstrass's user avatar
0 votes
1 answer
324 views

How to find max and min values

Need to find max and min values like on pic. I am wondering how I could determine max and min values of oscillations ? How could I find these values: My code: ...
John's user avatar
  • 573
5 votes
1 answer
206 views

How to efficiently implement periodic function to reuse computed values

Assume I have a function f = Function[t, VeryDifficultComputation] But I would like to exploit the fact that the function is periodic to "cache" computations ...
user1747134's user avatar
2 votes
2 answers
1k views

How to make a square wave function with controllable period, phase and duty cycle that can work really fast?

I actually need two things: A square wave function that allows me to control its duty cycle, period and phase. It must work fast enough to be evaluated at least a million times per second. For the ...
Helyrk's user avatar
  • 23
1 vote
2 answers
261 views

Using Nearest with periodic boundary conditions of a list

Take the list e = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} I want to get the nearest points but with a wraparound condition. So lets say I want to find the 5 nearest ...
Luca Pontiggia's user avatar
1 vote
1 answer
98 views

How to pad periodically a cube to be compatible with ListInterpolation?

Context I would like to define a periodic interpolation function on a cube. It seems mathematica's ListInterpolation and the option ...
chris's user avatar
  • 23k
8 votes
2 answers
435 views

Periodic Orbits of the MacKay Map

For the MacKay (Henon action-angle transformation) Map (Mackay 1983): $x_{n+1}=q-\alpha x_n-x_n^2-y_n \\ y_{n+1}=x_n$ with $q, \alpha \in \mathbb{R}$ real parameters I would like to calculate the ...
Bazinga's user avatar
  • 737
0 votes
1 answer
297 views

Using Fourier for periodicity and spike analysis

I am trying to look for significant peaks/spikes and periodic changes or fluctuations in about 60 time series of synthetic data. For example, in data1 below, there ...
user3769181's user avatar
1 vote
0 answers
73 views

Definition of periodic conditions

I want to define some periodic conditions, for example, describing an ellipse in 2D with periods $p_1$ in $x_1$ direction and $p_2$ in $x_2$ direction. I am frying my brain trying to implement this, ...
Mauricio Fernández's user avatar
5 votes
2 answers
529 views

Using EventLocator to detect periodic solutions in NDSolve

I loop over some systems of DAEs with NDSolve; some solutions are periodic, some are not. When integrating with NDSolve, I ...
anderstood's user avatar
  • 14.3k
0 votes
1 answer
88 views

Periodic function Iteration limit [closed]

I have two main issues. The first concerns Mathematica interpreting the same definition differently based on what I call the function, even though the name never occurs in any other part of the ...
Marek's user avatar
  • 3
2 votes
0 answers
143 views

FunctionPeriod returns 0 if input trigonometric function have a real phase

I am using Mathematica 10, FunctionPeriod which is supposed to return period of a given function returns 0 if the input trigonometric function have a Real phase <...
Neel Basu's user avatar
  • 961
2 votes
1 answer
385 views

How to find period from graph

Code is: ...
John's user avatar
  • 573
1 vote
1 answer
1k views

finding fourier coefficient of a parametric curve [closed]

There is a function in mathematica FourierCoefficient for finding fourier coefficients of a periodic function, but it requires the mathematical expression as input. ...
Physicist's user avatar
  • 987
16 votes
2 answers
764 views

Solution diverges in periodic PDE

Problem introduced in 11.0.1 and persisting through 11.3 Mathematica version 11 introduces PeriodicBoundaryCondition which is very useful in solving periodic PDE ...
xslittlegrass's user avatar
1 vote
0 answers
464 views

Periodic boundary condition trick

I'm plotting a curve on a compact space which is having periodic boundaries on the left and right parts. Currently, the code I'm using is working great, but I'm wondering if there's a simpler and ...
Cham's user avatar
  • 4,093
2 votes
1 answer
1k views

How to find period of a discrete sequence?

For example, {1,2,3,4,5,6,7,8} has period 1, the base is {1} {1,2,4,5,7,8,10,11} has period 3, the base is {1,2} I ...
matheorem's user avatar
  • 17.2k
10 votes
2 answers
934 views

How to locate the position of a periodic orbit

These are the equations of the dynamical system ...
Vaggelis_Z's user avatar
  • 8,790
3 votes
1 answer
270 views

Computing planet conjunctions with 2D circular orbits still hard?

All methods I've seen for computing planetary/stellar conjuctions (when two planets or a planet and a star appear close together in the sky because their angular separation, as measured from Earth, ...
user avatar
4 votes
3 answers
317 views

Periodically tiling a function

I have a function which creates a hole of varying radius, depth and would like to tile it in x and y. ...
daFireman's user avatar