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Math Help - Animation Graph

  1. #1
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    Animation Graph

    Many years ago what I am about to say would have been science fiction, today we have sufficiently advanced computers to do this.

    To help illustrate what I am trying to say, for example, we have a fluid in a container which is moving. Let u(x,y,t) represent the x-th and y-th coordinate of the location of the surface of the fluid at time t. Say the fluid starts at some initial state u(x,y,0)=f(x,y) and given motion by an inital speed u_t(x,y,0)=g(x,y). And say these boundary values satisfy some differencial equation which represents the position of the surface (I have no idea, maybe, Navier-Stokes). But anyway, we manage to solve this equation somehow. And have this unique function u(x,y,t). Is there such a thing when we draw surfaces by keeping "t" fixed and varying continously say from t>=0 till the end of the process. What I am saying at t=0 we have u(x,y,0) a surface, at t=.01 we have u(x,y,.01) a different surface, at t=.02 we have u(x,y,.02) and so one. And we create an animation, that is we create a program which shows all these surfaces as the time is varying continously. Which should produce an animation of exactly the fluid behaves.
    Is there such a program?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker View Post
    Many years ago what I am about to say would have been science fiction, today we have sufficiently advanced computers to do this.

    To help illustrate what I am trying to say, for example, we have a fluid in a container which is moving. Let u(x,y,t) represent the x-th and y-th coordinate of the location of the surface of the fluid at time t. Say the fluid starts at some initial state u(x,y,0)=f(x,y) and given motion by an inital speed u_t(x,y,0)=g(x,y). And say these boundary values satisfy some differencial equation which represents the position of the surface (I have no idea, maybe, Navier-Stokes). But anyway, we manage to solve this equation somehow. And have this unique function u(x,y,t). Is there such a thing when we draw surfaces by keeping "t" fixed and varying continously say from t>=0 till the end of the process. What I am saying at t=0 we have u(x,y,0) a surface, at t=.01 we have u(x,y,.01) a different surface, at t=.02 we have u(x,y,.02) and so one. And we create an animation, that is we create a program which shows all these surfaces as the time is varying continously. Which should produce an animation of exactly the fluid behaves.
    Is there such a program?
    I have had occaision to animate data in this manner, what I do is build
    a movie from plots of u(x,y,t0+n*deltat) for n = 1, 2, ..

    This can be done in Matlab, Euler, and probably in Maple and Mathematica as well.

    RonL
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    Forum Admin topsquark's Avatar
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    I have seen it done using Mathematica, though I've never programmed it myself.

    -Dan
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by topsquark View Post
    I have seen it done using Mathematica, though I've never programmed it myself.

    -Dan
    Well I have, but if I told you what it was I had animated this way I would
    then have to kill you

    Needless to say the audience was gobsmacked to see the data like that

    RonL
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