plot stream over two spheres

Question

Shreen El-Sapa 2021-11-19

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1591129-plot-stream-over-two-spheres

评论： Shreen El-Sapa 2021-11-20

A  =[       -4.7107
    0.0012
    -0.0056
    0.0132
    -0.0253
    0.0435
    -0.0689
    0.1031
    -0.1473
    0.2040
    -0.2737
    0.3607
    -0.4647
    0.5927
    -0.7425
    0.9265
    -1.1387
    1.4014
    -1.7014
    2.0810
    -2.5114
    3.0805
    -3.7224
    4.6475
    -5.6872
    7.5039
    -9.5388
    16.4146
    -25.4535
    14.3236];
B=[      -3.3794
    0.0005
    -0.0009
    0.0006
    -0.0003
    0.0001
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000];
C=[        6.8417
    -0.0007
    0.0007
    -0.0003
    0.0001
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000];
D=[      -4.7100
    -0.0012
    0.0058
    -0.0132
    0.0253
    -0.0435
    0.0689
    -0.1032
    0.1473
    -0.2040
    0.2737
    -0.3608
    0.4648
    -0.5928
    0.7426
    -0.9266
    1.1388
    -1.4016
    1.7016
    -2.0813
    2.5118
    -3.0810
    3.7230
    -4.6482
    5.6881
    -7.5050
    9.5403
    -16.4171
    25.4574
    -14.3258];
E=[       -3.3789
    -0.0005
    0.0009
    -0.0006
    0.0003
    -0.0001
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000];
F=[       6.8407
    0.0007
    -0.0008
    0.0003
    -0.0001
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000
    0.0000];
a = 1 ;   %RADIUS
L=.1;
dd=4;
kappa=1;gam=0.3;arh=1;  %a2=1;u2=1;beta1=beta2=1
al=kappa.*(2+kappa)./(gam.*(1+kappa));
alpha1=real(((al.^2+arh.^2)./2+((al.^2+arh.^2).^2-(2.*kappa.*arh.^2./gam).^(1./2))./2).^(1./2));
alpha2=real(((al.^2+arh.^2)./2-((al.^2+arh.^2).^2-(2.*kappa.*arh.^2./gam).^(1./2))./2).^(1./2));
c =-a/L;
b =a/L;
m =a*100; % NUMBER OF INTERVALS
[x,y]=meshgrid([c+dd:(b-c)/m:b],[c:(b-c)/m:b]);
[I, J]=find(sqrt(x.^2+y.^2)<(a-.1));
if ~isempty(I)
    x(I,J) = 0; y(I,J) = 0;
end
r=sqrt(x.^2+y.^2);
t=atan2(y,x);
r2=sqrt(r.^2+dd.^2-2.*r.*dd.*cos(t));
zet=(r.^2-r2.^2-dd.^2)./(2.*r2.*dd);
%for i1=1:length(x);
%  for k1=1:length(x);
%    if sqrt(x(i1,k1).^2+y(i1,k1).^2)>1./L;
%        r(i1,k1)=0;r2(i1,k1)=0;
%     end
%  end
%end
warning off
qr1=0;
for i=2:7
    Ai=A(i-1);Bi=B(i-1);Ci=C(i-1);Di=D(i-1);Ei=E(i-1);Fi=F(i-1);
    qr1=qr1-(Ai.*r.^(-i-1)+r.^(-3./2).*besselk(i-1./2,r.*alpha1).*Bi+r.^(-3./2).*besselk(i-1./2,r.*alpha2).*Ci).*legendreP(i-1,cos(t))-(Di.*r2.^(-i-1)+r2.^(-3./2).*besselk(i-1./2,r2.*alpha1).*Ei+r2.^(-3./2).*besselk(i-1./2,r2.*alpha2).*Fi).*legendreP(i-1,zet);
end
hold on
[DH1,h1]=contour(x,y,qr1,3,'-k');
%axis square;
title('$(a)$ $\ell=0.1,\;\alpha=1.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')
%%%%%%%%%%%%%%%%  $\frac{\textstyle a_1+a_2}{\textstyle h}=6.0,\;
hold on
t3 = linspace(0,2*pi,1000);
h2=0;
k2=0;
rr2=1;
x2 = rr2*cos(t3)+h2;                   
y2 = rr2*sin(t3)+k2;
set(plot(x2,y2,'-k'),'LineWidth',1.1);
fill(x2,y2,'w')
%axis square;
hold on
t2 = linspace(0,2*pi,1000);
h=dd;
k=0;
rr=2;
x1 = rr*cos(t2)+h;                   
y1 = rr*sin(t2)+k;
set(plot(x1,y1,'-k'),'LineWidth',1.1);
fill(x1,y1,'w')
%axis square;
axis off

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Adam Danz 2021-11-20

Shreen El-Sapa's answer moved here

I can not get the streamlines

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Answer 1

Cris LaPierre 2021-11-20

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1591129-plot-stream-over-two-spheres#answer_836264

qr1 is all NaNs. Assuming the countours are supposed to be your streamlines, you should check your equation. I'm not sure your for loop is doing what you intended. At the least, there is an issue with your calculation.

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Shreen El-Sapa 2021-11-20

编辑：Cris LaPierre 2021-11-20

在 MATLAB Online 中打开

edited code to make it more readable

A=[-4.7107 0.0012 -0.0056 0.0132 -0.0253 0.0435 -0.0689 0.1031 -0.1473 0.2040 -0.2737 0.3607 -0.4647 0.5927 -0.7425 0.9265 -1.1387 1.4014 -1.7014 2.0810 -2.5114 3.0805 -3.7224 4.6475 -5.6872 7.5039 -9.5388 16.4146 -25.4535 14.3236];

B=[-3.3794 0.0005 -0.0009 0.0006 -0.0003 0.0001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

C=[6.8417 -0.0007 0.0007 -0.0003 0.0001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

AA=[-4.7100 -0.0012 0.0058 -0.0132 0.0253 -0.0435 0.0689 -0.1032 0.1473 -0.2040 0.2737 -0.3608 0.4648 -0.5928 0.7426 -0.9266 1.1388 -1.4016 1.7016 -2.0813 2.5118 -3.0810 3.7230 -4.6482 5.6881 -7.5050 9.5403 -16.4171 25.4574 -14.3258];

BB=[-3.3789 -0.0005 0.0009 -0.0006 0.0003 -0.0001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

CC=[6.8407 0.0007 -0.0008 0.0003 -0.0001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

a = 1 ; %RADIUS

L=.13;

akm=1;gamma=0.3;arh=0.1;

alphaa=sqrt(((2+akm).*(akm./gamma)).^2+arh.^2);

betaa=(2.*akm.*arh.^2./gamma).^(0.25);

alpha1=sqrt((alphaa.^2+sqrt(alphaa.^4-4.*betaa.^4))./2);

alpha2=sqrt((alphaa.^2-sqrt(alphaa.^4-4.*betaa.^4))./2);

dd=5;

c =-a/L;

b =a/L;

m =a*50; % NUMBER OF INTERVALS

[x,y]=meshgrid([c+dd:(b-c)/m:b],[c:(b-c)/m:b]');

[I J]=find(sqrt(x.^2+y.^2)<(a-.1));

if ~isempty(I);

x(I,J) = 0; y(I,J) = 0;

end

r=sqrt(x.^2+y.^2);

t=atan2(y,x);

r2=sqrt(r.^2+dd.^2-2.*r.*dd.*cos(t));

zet=(r.^2-r2.^2-dd.^2)./(2.*r2.*dd);

warning on

psi1=0;

for i=2:3;

Ai=A(i-1);

Bi=B(i-1);

Ci=C(i-1);

AAi=AA(i-1);

BBi=BB(i-1);

CCi=C(i-1);

psi1=-psi1-(Ai.*r.^(-i-1)+r.^(-3./2).*besselk(i-1./2,r.*alpha1).*Bi+r.^(-3./2).*besselk(i-1./2,r.*alpha2).*Ci).*legendreP(i-1,cos(t))-(AAi.*r2.^(-i-1)+r2.^(-3./2).*besselk(i-1./2,r2.*alpha1).*BBi+r2.^(1./2).*besselk(i-1./2,r2.*alpha2).*CCi).*legendreP(i-1,zet);

end

[DH1,h1]=contour(x,y,psi1,20,'-k');

title('$(a)$ $\ell=0.1,\;\alpha=1.0$','Interpreter','latex','FontSize',10,'FontName','Times New Roman','FontWeight','Normal')

hold on

t3 = linspace(0,2*pi,1000);

h2=0;

k2=0;

rr2=1;

x2 = rr2*cos(t3)+h2;

y2 = rr2*sin(t3)+k2;

set(plot(x2,y2,'-k'),'LineWidth',1.1);

fill(x2,y2,'w')

t2 = linspace(0,2*pi,1000);

h=dd;

k=0;

rr=2;

x1 = rr*cos(t2)+h;

y1 = rr*sin(t2)+k;

set(plot(x1,y1,'-k'),'LineWidth',1.1);

fill(x1,y1,'w')

axis off

hold off

Cris LaPierre 2021-11-20

Personally, I use the streamlines function to create streamlines, not contour. However, even with streamlines, you will need to calculate and input the vector field components u and v.

Shreen El-Sapa 2021-11-20

Capture.GIF

I used the equations below. Can I used it to plot the streamlines? as you say?

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plot stream over two spheres

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plot stream over two spheres

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