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RSS Feed for Wolfram Community showing any discussions in tag Graphics and Visualization sorted by active[WSS22] Topological invariants in discrete lattice via graph rewriting
https://community.wolfram.com/groups/-/m/t/2575438
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[1]: https://www.wolframcloud.com/obj/4cb404ed-c97b-4eb8-9d07-7881255095c6Sinuhe Perea2022-07-19T22:26:30ZYield curve animation
https://community.wolfram.com/groups/-/m/t/2860277
&[YieldCurveAnimation][1]
[1]: https://www.wolframcloud.com/obj/9c2167cc-2dee-4591-8947-fbaa965b3431Robert Rimmer2023-03-27T19:43:51ZBrachistochrone Problem: shortest time to slide on a curve
https://community.wolfram.com/groups/-/m/t/2859015
![enter image description here][1]
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[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fall.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/fe054a06-4dd1-43ef-8712-403b1ecbf790Yaosheng Zhang2023-03-25T16:01:29ZHat tilings via HTPF equivalence
https://community.wolfram.com/groups/-/m/t/2858759
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=HattilingsviaHTPFequivalence.png&userId=20103
[2]: https://www.wolframcloud.com/obj/8834ec94-ab97-4b06-9446-1654c806e062Brad Klee2023-03-24T23:19:15ZHappy Harmonic 2017 !
https://community.wolfram.com/groups/-/m/t/987658
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[1]: https://www.wolframcloud.com/obj/a399625a-4884-493f-a1e7-210f67fb2a8cMichael Trott2016-12-29T15:23:34ZDifferent results when solving a DE using symbolic and numerical methods
https://community.wolfram.com/groups/-/m/t/2858283
I'm getting different results when solving a differential equation using symbolic and numerical methods. Attached is a notebook for the community to evaluate.
Sincerely,
SinvalSinval Santos2023-03-24T16:30:46ZParts of Graphics Frame disappears depending of ImageSize
https://community.wolfram.com/groups/-/m/t/2857532
The Frame around a Graphics part like ArrayPlot is not always complete. The Right and/of Bottom part are missing depending on the Image Size.
Is there some explanation for this behavior? Can this be prevented?
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[1]: https://www.wolframcloud.com/obj/bc2e642d-4bab-41ca-8ab5-aa707f7a329fChris Van Damme2023-03-23T13:34:10ZTool for graphing images of transformations: trnsfrm
https://community.wolfram.com/groups/-/m/t/2857472
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=trnsfrmatoolforgraphingimagesoftransformations.png&userId=20103
[2]: https://www.wolframcloud.com/obj/5379f2ef-eabd-4b3f-b592-4d7b01fe7b73Alan Horwitz2023-03-23T00:14:00ZThree-dimensional model of a split-crystal X-ray and neutron interferometer
https://community.wolfram.com/groups/-/m/t/2848320
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2967Three-dimensionalmodelofasplit-crystalX-rayandneutroninterferometer.png&userId=20103
[2]: https://www.wolframcloud.com/obj/3e7a42e5-efe5-40d1-8442-ad340e9b3dd8Giovanni Mana2023-03-09T19:08:18Z1D HeatTransfer problem reformulation
https://community.wolfram.com/groups/-/m/t/2850551
Hi, I would like to solve the 1D Heat Transfer problem for $ T(x,t) $ on a rod of length $ L $
that has a sinus temperature at one end and is isolated at the other end:
(IBVP 1): $ T_t - a^2 T_xx = 0 $ with
BC: $ T(x=0,t) = T_1 sin(wt), T_x(x=L,t) = 0, $ and IC: $T(x,t=0) = T_0 $
This is easily solved using the NDSolveValue command (see below).
As I am finally interested in an analytic solution of (IBVP 1),
in a frist step I reformulated the initial boundary value problem using
$T(x,t) = U(x,t) + f(t),$ with $ f(t) = T_1 sin(wt) $
arriving at the inhomogeneous (IBVP 2) with homogeneous BCs for $ U(x,t):$
(IBVP 2): $ U_t - a^2 U_xx = Q $ with $ Q=- df(t)/dt,$
BC: $U(x=0,t) = 0, U_x(x=L,t) = 0, $ IC: $ U(x,t=0) = T_0$
To confirm the identity of (IBVP 1) with (IBVP 2), I implemented both with the NDSolve command (see below).
Surprisingly, the solutions are clearly different.
Is there an error in my arguments? Is there a problem with my implementation of the numerical solution in NDSolve?
I noticed that an additional factor of 1000 to the souce term $ Q $ makes both solutions more similar.
This brings me to the question of why the source term (as the time derivative of $f(t)$) is so very small .......?
Analytically, (IBVP 2) could be further analysed by Fourier sin transformation.
If there is a known analytical solution of IBVP 1, I would be very happy for a hint to a reference.
I would be very grateful for any suggestions. Thank you!
Here is my implementation in Mathematica:
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/c732dc56-3d36-4d25-8ab9-3b36a95ad643Uwe Schlink2023-03-13T15:17:40ZEmpty plot in Manipulate applied at ParametricPlot?
https://community.wolfram.com/groups/-/m/t/2855316
Hello,
I'm new to Mathematica and trying to plot a parametric equation as a solution of a system of differential equations with a parameter "a". I used ParametricNDSolve and then tried using Manipulate to change the parameter "a" with a slider. Nothing shows up on the graph.
I have successfully plotted the graph using a value for "a" and getting rid of Manipulate.
Any advice would be great!
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/19448b1a-1b43-4bde-9594-7920e1d2822fJonathan Baker2023-03-20T01:44:40ZWhy is my iPad output blurred?
https://community.wolfram.com/groups/-/m/t/2857460
ArrayPlot[CellularAutomaton[250, {{1}, 0}, 10]]
When I input the code line above on my iPad Pro, using either the Wolfram Cloud app or the Browser, the output is blurred as previously shown in the OP. However, if I input it using my iMac the output is very crisp and as it should be. What is causing this blurring?John Bird2023-03-22T23:15:33ZEinstein problem solved (aperiodic monotile discovery)
https://community.wolfram.com/groups/-/m/t/2856178
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Einsteinproblem.gif&userId=20103
[2]: https://www.wolframcloud.com/obj/453006ec-e6a1-4bef-af88-fd13f606fa56Ed Pegg2023-03-21T13:59:14ZHow to plot the result of NDEigensystem
https://community.wolfram.com/groups/-/m/t/2857124
Given the following problem
$-\frac{1}{2}y''(x)+-\frac{1}{2}[x^2+\sin^2{(\frac{2 k \pi x}{L}})]y(x)=E y(x), \quad x \in [-L,L]$
$y(-L)=y(L)=0$ where L=30 and k=2.
We want to calculate the first ten eigenvalues and the 5 first eigenfunctions. Using the command NDEigensystem.
As the following notebook shows, I have defined my equation and my Dirichlet conditions.
Then I used the NDEigensystem command and calculate the first ten eigenvalues. But I cannot figure out how I could plot only the first five eigenfunctions. Any suggestions
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/34cbdfa5-c811-4c46-9448-0bebc3707580Athanasios Paraskevopoulos2023-03-22T09:42:42ZIssue using RegionFunction with ListContourPlot
https://community.wolfram.com/groups/-/m/t/2856114
I've hit a problem using RegionFunction with ListContourPlot and am hoping someone can help.
I'm trying to use RegionFunction with ListContourPlot to suppress the rendering of contours outside a prescribed polygon.
The first example in the attached notebook works as I'd expect. The second does not, in that the contours are drawn outside the specified polygon.
Any suggestions/advice would be much appreciated.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/9c092eba-ea0c-4aad-b729-1c918de9e221Ian Williams2023-03-20T22:09:26Z[WSS22] Linguistic leaps: effective pedagogy in computational communication
https://community.wolfram.com/groups/-/m/t/2575163
![Wolfram Notebook][1]
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[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2022-07-19at4.37.43PM.png&userId=2575145
[2]: https://www.wolframcloud.com/obj/e4f23711-2803-4c7e-8ce8-8b94df791b12Lybrya Kebreab2022-07-19T21:40:16ZAnalytical and numerical solution of the normalized heat equation problem
https://community.wolfram.com/groups/-/m/t/2856871
My question is the following.
Is the procedure I am following correct?
Because I want to compare the numerical and analytical solutions for a project I am running.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/4f2d33ae-5ce9-44ec-ad06-e55775754625Athanasios Paraskevopoulos2023-03-21T23:37:13ZFramework for liquid crystal based particle models
https://community.wolfram.com/groups/-/m/t/2856493
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Frameworkforliquidcrystalbasedparticlemodels.png&userId=20103
[2]: https://www.wolframcloud.com/obj/343d5a1b-bee7-4a4f-a6bd-6a94bb03d924Jarek Duda2023-03-21T18:14:22Z⭐ [R&DL] Wolfram R&D Developers on LIVE Stream
https://community.wolfram.com/groups/-/m/t/2593151
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[41]: https://community.wolfram.com/web/alecsCharles Pooh2022-08-05T21:37:19ZSolving Generalized Heat Equation by separation of variables
https://community.wolfram.com/groups/-/m/t/2854987
Given the following problem
$$u_{t}-\frac{v}{2}\cdot u_{xx}+\frac{v}{2}\cdot x^2 \cdot u(x)=0 $$
$$u(x,0)=f(x)$$
Where $ f(x)=y_1(x)+0.2y_4(x)+0.01y_6 (x) $
$y_n$ are the Eigenfunctions that defined as $ y_n(x)=\exp\left(\displaystyle{\frac{-x^2}{2}}\right)H_n(x) $
By separation we assume $$u(x,t)=X(x)T(x)$$
I have found that the general solution of $T$ is
$T(x)=c_1e^{-\lambda v t}$
and the general solution of $X$ is
$ X_n(x)=\exp\left(\displaystyle{\frac{-x^2}{2}}\right)H_n(x) $
So the general solution to our initial problem is
$u_n(x,t)=\sum_{n=1}^{\infty}A_n \exp\left(\displaystyle{\frac{-x^2}{2}}\right)H_n(x) c_1e^{-\lambda v t}$
Using the I.C we got $$ u(x,0)=\sum_{n=1}^{\infty}A_n \exp\left(\displaystyle{\frac{-x^2}{2}}\right)H_n(x)=f(x) $$
I have the following two questions
1. How many terms does the expansion of the solution have? Use the Manipulate command, in conjunction with Plot, to construct animated graphics for the evolution of the solution. For the first case
2. With appropriate snapshots at 3 different moments of your choice (or even using Manipulate), compare the analytical and numerical solutions. Plot using Plot3D the solution u( x, t ).
I have tried this code but it does not seem right to me.
Any suggestions?
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/9e4e7f84-d635-4dd4-b331-5e3f25481667Athanasios Paraskevopoulos2023-03-19T22:40:18ZSolving a Boundary Value Problem--Sturm-Liouville
https://community.wolfram.com/groups/-/m/t/2852682
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/d9bcd4b9-45b7-4f08-974b-a6c057d51f19Athanasios Paraskevopoulos2023-03-15T23:49:25ZHow can I extract line segments from a BooleanRegion
https://community.wolfram.com/groups/-/m/t/2853837
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/777c8dbb-61d5-4b0a-bb74-73ddc0ddcebdNicholas Walton2023-03-17T09:58:17ZEmpty output from an old 3DParametricPlot3D code
https://community.wolfram.com/groups/-/m/t/2855895
I am a new user of Mathematica. Currently, I am using version 13.2. I recently purchased a book titled "GRAPHICS with *MATHEMATICA* FRACTALS, JULIA SETS, PATTERNS and NATURAL FORMS". I did this because of the work that I have done previously on Fractals and Chaos Theory. One of the ParametricPlot3D examples that was provided is shown below:
ParametricPlot3D[
Evaluate[
Table[{Sin[2 (t + \[Pi])] Cos[(t + \[Pi])] Sin[n 36 °],
Sin[2 (t + \[Pi])] Cos[(t + \[Pi])] Cos[n 36 °],
Sin[(t + \[Pi])] Sin[t + \[Pi]], {Thickness[
0.1 Sin[\[Pi] t/(\[Pi] - 2)]],
RGBColor[(0.34 + t/(3 (\[Pi] - 2))), (
0.55 + t/(3.5 (\[Pi] - 2))), (0.12 + t/(
3.5 (\[Pi] - 2)))]}}, {n, 0, 10}], {t, 0, \[Pi] - 2}],
Axes -> False, Boxed -> False, PlotPoints -> 200,
BoxRatios -> {1, 1, 1}, ViewPoint -> {0.862, -2.214, 2.409}]
When I evaluated this expression, I received a blank output cell. In the book it showed a specific image. I am wondering what the problem is with the above syntax. The book was published in 2004 so I imagine that the version it uses is version 5 or 6 of Mathematica.Paul Swanson2023-03-20T20:12:39Z