## 119 Reputation

17 years, 22 days

## How best to convert a Maple worksheet in...

Maple 2020

I have a large Maple 2020 worksheet which contains images and text.  I have been asked to publish a paper on the worksheet, in which I need to include LaTeX format. I have attempted to make the Maple => LaTeX conversion, but have the resulting file is very cluttered and takes much time to clean.  Can anyone offer advice on the best way to get clean LaTeX document from a worksheet?

Melvin Brown

sympl55@gmail.com

## Can points in a graph each be an active ...

Maple

I have a plot of points in a graphical plot on the domain (x,y).  At each point xi (i=1..N) , there is a numerical value yi = S(xi) from which I plot a series of points (xi, S(xi)) in the (x,y) domain.

Each point (xi,yi) represents a transient plot of two variables u(x,t) and v(x,t) in a plot file.  Is it possible to define a graph of the points (xi, S(xi)), such that clicking on any such point in the graph opens up a graphical file which is parameterised by (xi, S(xi))?

Would welcome help on this...

Melvin

## Maple 2018 recently become sluggish to ...

Maple 2018

Maple 2018  has recently has  become sluggish to start up  -and very slow to respond to input. Can anyone suggest remedies?  I have plenty of space and CPU. Other apps seem to start fine.  Can any suggest a diagnosis and/or solution?

Melvin

## Coupled PDEs:Error, (in pdsolve/numeric/...

Maple 2018

Analysis of the semiclassical (SC) momentum rate equations

Plotting the ICs and BCs and examining sensitivity to the Re and Im forces

MRB: 24/2/2020, 27/2/2020, 2/3/2020.

We examine solution of the SC version of the momentum rate equations, in which O terms for are removed. A high level of sensitivity to ICs and BCs makes solution finding difficult.

 > restart;
 > with(PDETools): with(CodeTools):with(plots):

We set up the initial conditions:

 > ICu := {u(x, 0) = .1*sin(2*Pi*x)}; ICv := {v(x, 0) = .2*sin(Pi*x)};  (1)
 > plot([0.1*sin(2*Pi*x),0.2*sin(Pi*x)],x = 0..2, title="ICs:\n u(x,0) (red), v(x,0) (blue)",color=[red,blue],gridlines=true); The above initial conditions represent a positive velocity field (blue) and a colliding momentum field (red).

Here are the BCs

 > BCu := {u(0,t) = 0.5*(1-cos(2*Pi*t))}; (2)
 > BCv := {v(0,t) = 0.5*sin(2*Pi*t),v(2,t)=-0.5*sin(2*Pi*t)}; (3)
 > plot([0.5*(1-cos(2*Pi*t)),0.5*sin(2*Pi*t),-0.5*sin(2*Pi*t)],t=0..1,color=[red,blue,blue],linestyle=[dash,dash,dot],title="BCs:\n u(0,t) (red-dash),\n v(0,t) (blue-dash), v(1,t) (blue-dot)",gridlines=true);
 > We can now set up the PDEs for the semiclassical case.

 > hBar:= 1:m:= 1:Fu:= 0.2:Fv:= 0.1:#1.0,0.2
 > pdeu := diff(u(x,t),t)+u(x,t)/m*(diff(u(x,t),x)) = Fu; (4)
 > pdev := diff(v(x,t),t)+u(x,t)/m*(diff(v(x,t),x))-hBar*(diff(u(x,t),x\$2))/(2*m)+v(x,t)*(diff(u(x,t),x))/m = Fv; (5)
 > ICu:={u(x,0) = 0.1*sin(2*Pi*x)}; (6)
 > ICv:={v(x,0) = 0.2*sin(Pi*x/2)}; (7)
 > IC := ICu union ICv; (8)
 > BCu := {u(0,t) = 0.5*(1-cos(2*Pi*t)), D(u)(2,t) = 0.1*cos(2*Pi*t)}; (9)
 > BCv := {v(0,t) = 0.2*(1-cos(2*Pi*t))}; (10)
 > BC := BCu union BCv; (11)

We now set up the PDE solver:

 > pds := pdsolve({pdeu,pdev},{BC[],IC[]},time = t,range = 0..2,numeric);#'numeric' solution (12)
 > Cp:=pds:-animate({[u, color = red, linestyle = dash],[v,color = blue,linestyle = dash]},t = 30,frames = 400,numpoints = 400,title="Semiclassical momentum equations solution for Re and Im momenta u(x,t) (red) and v(x,t) (blue) \n under respective constant positive forces [0.2, 0.1] \n with sinusoidal boundary conditions at x = 0, 1 and sinusoidal initial conditions: \n time = %f ", gridlines = true,linestyle=solid):Cp; (13)

Observations on the quantum case:

The classical equation for is independent of the equation for . (red) is a solution of the classical Burgers equation subject to a force 0.2, but is NOT influenced by .  On the otherhand, (blue) is a solution of the quantum dynamics equation subject to force 0.1 and is influenced by .   This one way causality (u )  is a feature of the semiclassical case, and it emphasises the controlling influence of the classical , which modulates the quantum solution for .  Causally, we have u .

The initial conditions are of low momentum amplitude: 0.1 for the classical (red) field and .2 for (blue)  but their influence is soon washed out by the boundary conditions and that drive the momentum dynamics.

The temporal frequency of the boundary condition on the -field is twice that of the classical -field. This is evident in the above blue transient plot. Moreover, the boundary condition on the classical -momentum (red), drives that field in the positive direction, initially overtaking the quantum field, as consistent with the applied forces [0.2, 0.1]. Although initially of greater amplitude than the classical field, the momentum field is asymptotically of the same amplitude as the field, but has greater spatial and temporal frequency, owing to the boundary conditions.

Referring to the semiclassical momentum rate equations, we note that the classical field (red) modulates the quantum momentum rate equation for .

 > I am having difficulty getting solutions to a pair of PDEs.  Would anyone like to cast an eye over the attached file, incase I am missing something.

Thanks

Melvin

## 2 coupled PDEs...can't get solution: not...

Can anyone help get solution to a coupled pair of PDEs

Error, (in pdsolve/numeric/plot3d) unable to compute solution for t>HFloat(0.0):
Newton iteration is not converging..

I attach file: SemiclassicalTestfile.mw

Melvin

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