Download MHD1.mw

 

 

System of equations with boundary conditions are moving?

Also, find the values of unknown variables?

I know that, tetrahedron with vertices (0, 0, 0), (3, 0, 0), (0, 5, 0), (0, 0, 14) has center of insphere is  (1, 1, 1) and radius R = 1. How to create a tetrahedron whose coordinates of all vertices are integers, the inscribed spherical center and the inscribed spherical radius are integers?

Dear maple users 

Greetings.

In this code, I am solving the PDEs via perturbation method.

There is some mistake in the boundary condition and pdsolve.

Kindly help me that to get the solution for this PDE via perturbation method.

Wating for your replay.

BC: 

Code: JVB.mw

Hello,

I wanted to substitute exp(a) with p in an expression of the form exp(-a).

subs(exp(a)=p,exp(-a))

This threw back exp(-a) to me. I was expecting 

exp(-a)->1/exp(a)->1/p

Is there a way to do that with subs? (a some mystical option perhaps?)

Thanks in advance.

This integral 

for n integer and n>=0. 

Maple finds it if I tell it this in the assumptions.  But if I remove the assumption that n>=0 and just keep the assumption that n is integer, it hangs. (at least I waited 5 minutes and gave up).

Is this something to be expected?  If I try the same thing in Mathematica, i.e. telling it n is an integer, but not that it is n>=0, it returns result  immediately, with condition that the result is valid for n>=0.

restart;
int(x^n*exp(-x),x=0..infinity) assuming n::integer

seems to hang.

In Mathematica:

My question is  if this behaviour of int hanging is to be expected, since it was not told than n>=0? Should it have returned result of n!  like Mathematica, with the assumption given in the result as well?

Since for n<0 the integral does not converge, and maple knows this

restart;
int(x^(-2)*exp(-x),x=0..infinity)

            infinity

May be this is just a design issue in int and it was stuck trying to evaluate the integral for negative integers, and could not determine if it converges or not?

Any thoughts?

Maple 2020.2

Hello everyone,

My question might be trivial for you but I really could not find any solution online. In an academic assignment, the load function acting on top of a beam contains dirac function and its derivatives. What I want is that the dirac function, Dirac(x-a1), is equal to 1 when x=a1, but all I get is Dirac(0.). 

I solved the same problem with Heaviside function with the NumericEventHandler but did not find anything about Dirac delta function.

My goal is to also plot this load function ("q" in my case) along a beam of 5 meters length. When I tried it looks like the dirac delta function are not considered at all.

restart:
with(plots):
NumericEventHandler(invalid_operation=`Heaviside/EventHandler`(value_at_zero=1/2)):
alias(delta=Dirac):
q:=3-0.2*x+varV1*delta(x-a1)+varV3*delta(x-a3)+EI2*varPhi2*delta(2,(x-a2))+EI2*varW2*delta(3,(x-a3));
            q := 3 - 0.2 x + varV1 delta(-x + a1) + varV3 delta(-x + a3)

   + EI2 varPhi2 delta(2, -x + a2) - EI2 varW2 delta(3, -x + a3)

a1:=1:a2:=3:a3:=2:
x:=a2:q;
                 2.4 + EI2 varPhi2 delta(2, 0)

x:='x':plot(q,x=0..5);
 

Thank you in advance.

restart; _local(D); A := [-L, 0]; B := [L, 0]; C := [x, y]; D := [-x, y]; Dist := proc (X, Y) options operator, arrow; sqrt((X[1]-Y[1])^2+(X[2]-Y[2])^2) end proc; Eq := (Dist(C, D) = Dist(C, B))^2; centre := [solve(diff(Eq, x), x), solve(diff(Eq, y), y)]; with(geometry); `assuming`([conic(p, Eq, [x, y])], [L > 0]); detail(p); asymptotes(p); y_acymp := `~`[solve](`~`[Equation](asymptotes(p)), y); y := solve(Eq, y)[1] P := proc (X, L0) local Curve, Asymptote, Trapezoid, T, pt, Ip; Curve := plot(eval([y, -y], L = L0), x = -(1/3)*L0 .. 15, color = red, thickness = 3); Asymptote := plot(eval([-sqrt(3)*x-(1/3)*sqrt(3)*L, sqrt(3)*x+(1/3)*sqrt(3)*L], L = L0), x = -(1/3)*L0 .. 15, linestyle = 3, color = black, thickness = 0); Trapezoid := plottools:-polygon(eval([A, B, C, D], [L = L0, x = X]), color = "LightGreen"); Ip := (1/3)*(eval(C, [x = X-(1/3)*L0, L = L0])); #centre of gravity of ABC T := plots:-textplot([[(eval(A, [x = X, L = L0]))[], "A"], [(eval(B, [x = X, L = L0]))[], "B"], [(eval(C, [x = X, L = L0]))[], "C"], [(eval(D, [x = X, L = L0]))[], "D"], [Ip[], "I"]], align = {above, left}, font = [TIMES, 16]); pt := plot([A, B, C, Ip], style = plottools:-point, color = blue, symbolsize = 15); plots:-display(Curve, Asymptote, Trapezoid, T, pt, scaling = constrained, size = [400, 800]) end proc; a := 7; P((1/2)*a, 6) I would like of location of centre of gravity of ABC. Thank you.

Hi

I am trying to implement normally distributed noise into a maplesim simulation. I thought this would be done most easily thru adding a modelica custom component. There are some examples to go on on the web however Modelica are not really good at explaining there implementation. 

The code for my implemented block can be seen below. 

 

model Noise2
    import MBI = Modelica.Blocks.Interfaces;
    import MBN = Modelica.Blocks.Noise;
    import MMD = Modelica.Math.Distributions.Uniform;
    
    output MBI.RealOutput out annotation (Placement(transformation(extent={{100,-10},{120,10}}))); 

    inner Modelica.Blocks.Noise.GlobalSeed globalSeed(fixedSeed=42);
    
    MBN.NormalNoise generator(samplePeriod=0.1,distribution=MMD.density(0, -1, 1));

    
    Real y(useGlobalSeed=true, useAutomaticLocalSeed = false, fixedLocalSeed=false, startTime = 0);
    
equation
    out = generator.y;
end Noise2;

 

However this results in the following error

Argument 1 must have integer[4] data type

 

Due to my inexperience with Modelica, I don't even know were to start searching for the error. So I turn to this wonderful community in my hour of need, How do I implement normal distributed noise in maplesim?

Mvh

Eric Ragnarsson

This  is a question from https://mathematica.stackexchange.com/questions/239055/how-to-reduce-the-time-to-solve-this-system-of-equations. How to reduce the time in Maple?
 

  {x, y, z, a, b, m, n} /. Solve[{1/x + 1/y == 1/z, a/x  + b/y == m/n, 2 <= x <= 30, 2 <= y <= 30, 1 <= z <= 30, 2 <= a <= 10, 2 <= b <= 10, a > b, 2 <= m <= 10, 2 <= n <= 10, x > y, GCD[m, n] == 1, GCD[a, b, m] == 1, m <= n}, {x, y, z, a, b, m, n}, Integers]

Hello there, 

The equations described below are third-order equations. Therefore, the number of solutions would be 3. 

However, when I tried to solve them using the 'solve' command, only two solutions came out. 

Is there any chance to find the last one?

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Q20210201.mw .
 

Download Q20210201.mw

Hey there,

After updating from Maple 15 to 18 and installing Maple Add-In to my Office 2016 version I still have some problems:

I'm trying to catch the data from the Excel. It is so simple at this stage. Import a number from an excel file, just this.

If I do:

Import();

Then a dialog opens and lets me select the Excel file and then the cell range. Everything works well.

But if I do:

Import("Libro1", "Hoja1", "A1");

Then it can't open the document.

Dear Users!
Hope everyone fine here. I tried (as given bellow) to find the solution of nonlinear system of PDEs via FDM. To solve system of nonlinear equations I used newton raphson method and for higher value of like Mx > 8 the matrix G and G1 (mentioned as red) take alot of time. Can anyone help me to reduce the computational time? Becuase I have to evealuate the solution for Mx = 50.

restart; Digits := 30; with(LinearAlgebra);
T := 1; L := 3; N := 30; Mx := 5; `&Delta;x` := L/(1.*Mx); `&Delta;t` := T/(1.*N);
for i from 0 while i <= Mx do
u[i, 0] := 0.; u[i, -1] := u[i, 1]; tau[i, 0] := 0.; theta[i, 0] := 0.; theta[i, -1] := theta[i, 1]
end do;
for n from 0 while n <= N do u[0, n] := 0.; u[Mx, n] := 0.; theta[0, n] := 1.; theta[Mx, n] := 0.
end do;
for n from 0 while n <= N-1 do
print("Simulation in proccess at time-level n", n+1);
for i while i <= Mx-1 do
Ru[i, n] := simplify((u[i+1, n+1]-u[i+1, n])/`&Delta;t`+(u[i+1, n+1]-2*u[i+1, n]+u[i+1, n-1])/`&Delta;t`^2-(u[i+1, n+1]-2*u[i, n+1]+u[i-1, n+1])/`&Delta;x`^2+25.*(u[i+1, n+1]+(u[i+1, n+1]-u[i+1, n])/`&Delta;t`)-1.5*(theta[i, n]+(theta[i, n+1]-theta[i, n])/`&Delta;t`));
`R&theta;`[i, n] := simplify((theta[i+1, n+1]-theta[i+1, n])/`&Delta;t`+(theta[i+1, n+1]-2*theta[i+1, n]+theta[i+1, n-1])/`&Delta;t`^2-(theta[i+1, n+1]-2*theta[i, n+1]+theta[i-1, n+1])/((15.)*`&Delta;x`^2)-((u[i, n+1]-u[i-1, n+1])/`&Delta;x`)^2/(3.)) end do;
for i while i <= Mx-1 do
`R&tau;`[i, n] := simplify(tau[i+1, n+1]+(tau[i+1, n+1]-tau[i+1, n])/`&Delta;t`-1.5^(-1/4)*(u[i+1, n+1]-u[i, n+1])/`&Delta;x`)
end do;
Sys := `<,>`(seq(Ru[i, n], i = 1 .. Mx-1), seq(`R&tau;`[i, n], i = 1 .. Mx-1), seq(`R&theta;`[i, n], i = 1 .. Mx-1));
V := `<,>`(seq(u[i, n+1], i = 1 .. Mx-1), seq(theta[i, n+1], i = 1 .. Mx-1), seq(tau[i, n+1], i = 2 .. Mx));
G := Matrix(3*(Mx-1), proc (i, j) options operator, arrow; diff(Sys[i], V[j]) end proc); G1 := MatrixInverse(G);
X[n, 0] := Vector(1 .. 3*(Mx-1), 1);
for k1 from 0 to r do
X[n, k1+1] := eval(V-G1 . Sys, Equate(V, X[n, k1]))
end do;
Sol[n] := Equate(V, X[n, r+1]); assign(op(Sol[n]));
if n > 0 then
U := eval(`<,>`(seq(u[i1, n+1], i1 = 1 .. Mx)-seq(u[i1, n], i1 = 1 .. Mx))); Noru[n+1] := Norm(%, 2); print("L[&infin;] norm of &tau;(x,y,t) at time level = ", %);
Theta := eval(`<,>`(seq(theta[i1, n+1], i1 = 0 .. Mx)-seq(theta[i1, n], i1 = 0 .. Mx))); `Nor&theta;`[n+1] := Norm(%, 2); print("L[&infin;] norm of &theta;(x,y,t) at time level = ", %) else print("n < 0")
end if end do

Special request to:
@acer @Carl Love @Kitonum @Preben Alsholm

Hey, im new to maple and have a few questions.

1. Sometimes, when i type e.g. a:=10 the blue evaluate line shows "a = 10" and sometimes it just shows "10"

is there a way to get that straight?