Plot dispersion curves using Bloch theorem

Hi,

I am trying to reproduce below dispersion curves. (dashed lines, not red)

Dispersion relation equation is as follow with mr = 0.125 and omegar=1

I used fimplicit function to plot this, but it seems it only gives me similar graph for the real portion as below.(with code)

m=0.125;

r=1;

syms x y

f=2*(1-cos(x))-(y)^2*(1+(m)/(1-((y)^2/(r)^2)))

fimplicit(f,[-2 2 0 2])

Any wisdom to plot this?

Answer 1

[Alan Stevens]

Like this?

OmegaR = 1;
mR = 0.125;

Omega = 0:0.01:2.5;
mu = acos(1 - Omega.^2.*(1+mR./(1-Omega.^2/OmegaR^2))/2);

plot(imag(mu),Omega,'k--',real(mu),Omega,'k--')

[Jungyun Lim]

Thank you so much!

Do you happen to know why fimplicit does not result the same way?

[Alan Stevens]

fimplicit only deals with real numbers. Compare the folowing for example

fimplicit(@(x,y) x.^2+y.^2-1, [-1,1])

with

fimplicit(@(x,y) x.^2+y.^2+1, [-1,1])