Skip to main content

differential equations - Changing a wave simulation


I want to adjust some code that I found on this Wolfram Demonstration: http://demonstrations.wolfram.com/WaterRipplesPassingThroughASlit/


Basically it shows a wave passing through a single slit. I want to change the code so that there is no longer any slit, so the wave just bounces off the walls. It's that bit I'm having trouble with. I'll put the code I have now then explain what I think it's doing and what I've tried:


Manipulate[
With[{ripple = iter[tf]},

Show[ListPlot3D[ripple, Mesh -> False, PlotRange -> {-1, 1},
ImageSize -> 450, ColorFunction -> "PearlColors", Axes -> False]]],
{{tf, .45, Style["t", Italic]}, 0.05, 1., 0.001, ImageSize -> Tiny},

ControlPlacement -> Left,
SynchronousInitialization -> False,
SynchronousUpdating -> False,
Initialization :> (
n = 64; dx = 1.0/(n - 1.);
Courant = 1/Sqrt[2];
dt = (Courant dx)/c; c = 1.;
iter = Compile[{{tf, _Real}},
Module[{z1 = ConstantArray[0., {64, 64}],
z2 = ConstantArray[0., {64, 64}]},

Do[{z1, z2} = {z2, z1}; z1[[32, 16]] = Sin[16. \[Pi] t];
Do[If[0.45 < i/n < 0.55 || ! 0.48 < j/n < 0.52,
z2[[i, j]] =
1/(1. + 5. dt) (Courant^2 (z1[[i - 1, j]] + z1[[i + 1, j]] +
z1[[i, j - 1]] + z1[[i, j + 1]])) - z2[[i, j]]], {i,
2, 63}, {j, 2, 63}], {t, 0., tf, dt}]; z1]];)]

I don't think anything before 'Initialization' needs to be changed. The second half sets up two 64X64 grids z1 and z2. They get updated by the Do command. The part that seems to be directly about the slit is


       Do[If[0.45 < i/n < 0.55 || ! 0.48 < j/n < 0.52, 
z2[[i, j]] =

1/(1. + 5. dt) (Courant^2 (z1[[i - 1, j]] + z1[[i + 1, j]] +
z1[[i, j - 1]] + z1[[i, j + 1]])) - z2[[i, j]]], {i,
2, 63}, {j, 2, 63}], {t, 0., tf, dt}]

Because it is telling the program to do something if the grid in question is where the slit should be. The issue is that I can't just delete that part, because then the wave doesn't evolve over time! It's like the instructions for how the other parts of the grid should act are also in that line, but I don't understand it.


Any hints at all would be so useful, I've been stuck for a day!



Answer



As I wrote earlier you just have to delete the condition. To explain a little bit:


n = 64;
arr = Array[Boole[0.45 < #/n < 0.55 || ! 0.48 < #2/n < 0.52] &, {64, 64}];


ArrayPlot[arr, ImageSize -> 300]

enter image description here


Black area is the area where condition inside If allows the wave to propagate.


So if the wave is comming from the left and face the "wall" it just stops. And the part that manage to get through the slit can propagate again in all directions as there is all in Black.


By removing this condidtion we are leaving whole area Black.


enter image description here


Comments

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...