Updates 4-7-21

Kuramoto.py

@@ -27,6 +27,17 @@
 N = 50      # 50
 width = 0.2
 
+# model_case 1 = complete graph (Kuramoto transition)
+# model_case 2 = Erdos-Renyi
+model_case = int(input('Input Model Case (1-2)'))
+if model_case == 1:
+    facoef = 0.2
+    nodecouple = nx.complete_graph(N)
+elif model_case == 2:
+    facoef = 5
+    nodecouple = nx.erdos_renyi_graph(N,0.1)
+
+
 # function: omegout, yout = coupleN(G)
 def coupleN(G):
 
@@ -110,8 +121,6 @@ def flow_deriv(y,t0):
 omega = omegatemp - meanomega
 sto = np.std(omega)
 
-#nodecouple = nx.complete_graph(N)
-nodecouple = nx.erdos_renyi_graph(N,0.1)
 
 lnk = np.zeros(shape = (N,), dtype=int)
 for loop in range(N):
@@ -128,7 +137,6 @@ def flow_deriv(y,t0):
 xx = np.zeros(shape=(Nfac,))
 for facloop in range(Nfac):
     print(facloop)
-    facoef = 0.2
 
     fac = facoef*(16*facloop/(Nfac))*(1/(N-1))*sto/mnomega
     for nodeloop in range(N):

NetDynamics.py

@@ -26,7 +26,7 @@
 
 
 Nfac = 25   # 25
-N = 36      # 50
+N = 100      # 50
 width = 0.2
 
 # model_case 1 = Complete Graph

caustic.py

@@ -0,0 +1,116 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Feb 16 19:50:54 2021
+
+caustic.py
+
+@author: nolte
+
+D. D. Nolte, Optical Interferometry for Biology and Medicine (Springer,2011)
+"""
+
+import numpy as np
+from matplotlib import pyplot as plt
+from numpy import random as rnd
+from scipy import signal as signal
+
+plt.close('all')
+
+N = 256
+
+def gauss2(sy,sx,wy,wx):
+
+    x = np.arange(-sx/2,sy/2,1)
+    y = np.arange(-sy/2,sy/2,1)
+    y = y[..., None]
+
+    ex = np.ones(shape=(sy,1))
+    x2 = np.kron(ex,x**2/(2*wx**2));
+
+    ey = np.ones(shape=(1,sx));
+    y2 = np.kron(y**2/(2*wy**2),ey);
+
+    rad2 = (x2+y2);
+
+    A = np.exp(-rad2);
+
+    return A
+
+def cauchy(sy,sx,wy,wx):
+
+    x = np.arange(-sx/2,sy/2,1)
+    y = np.arange(-sy/2,sy/2,1)
+    y = y[..., None]
+
+    ex = np.ones(shape=(sy,1))
+    x2 = np.kron(ex,x**2/(2*wx**2))
+
+    ey = np.ones(shape=(1,sx))
+    y2 = np.kron(y**2/(2*wy**2),ey)
+
+    rad2 = (x2+y2)
+
+    A = 1/(1+rad2)
+
+    return A
+
+def speckle2(sy,sx,wy,wx):
+
+    Btemp = 2*np.pi*rnd.rand(sy,sx);
+    B = np.exp(complex(0,1)*Btemp);
+
+    C = gauss2(sy,sx,wy,wx);
+
+    Atemp = signal.convolve2d(B,C,'same');
+
+    Intens = np.mean(np.mean(np.abs(Atemp)**2));
+
+    D = np.real(Atemp/np.sqrt(Intens));
+
+    Dphs = np.arctan2(np.imag(D),np.real(D));
+
+    return D, Dphs
+
+
+Sp, Sphs = speckle2(N,N,N/16,N/16)
+
+#Sp = cauchy(N,N,N/16,N/16)
+
+plt.figure(2)
+plt.matshow(Sp,2,cmap=plt.cm.get_cmap('seismic'))  # hsv, seismic, bwr
+plt.show()
+
+fx, fy = np.gradient(Sp);
+
+fxx,fxy = np.gradient(fx);
+fyx,fyy = np.gradient(fy);
+
+J = fxx*fyy - fxy*fyx;
+
+D = np.abs(1/J)
+
+plt.figure(3)
+plt.matshow(D,3,cmap=plt.cm.get_cmap('gray'))  # hsv, seismic, bwr
+plt.clim(0,0.5e7)
+plt.show()
+
+eps = 1e-7
+cnt = 0
+E = np.zeros(shape=(N,N))
+for yloop in range(0,N-1):
+    for xloop in range(0,N-1):
+
+        d = N/2
+
+        indx = int(N/2 + (d*(fx[yloop,xloop])+(xloop-N/2)/2))
+        indy = int(N/2 + (d*(fy[yloop,xloop])+(yloop-N/2)/2))
+
+        if ((indx > 0) and (indx < N)) and ((indy > 0) and (indy < N)):
+            E[indy,indx] = E[indy,indx] + 1
+
+plt.figure(4)
+plt.imshow(E,interpolation='bicubic',cmap=plt.cm.get_cmap('gray'))
+plt.clim(0,20)
+plt.xlim(N/4, 3*N/4)
+plt.ylim(N/4,3*N/4)

gravcaustic.py

@@ -0,0 +1,134 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Feb 16 19:50:54 2021
+
+caustic.py
+
+@author: nolte
+
+D. D. Nolte, Optical Interferometry for Biology and Medicine (Springer,2011)
+"""
+
+import numpy as np
+from matplotlib import pyplot as plt
+from numpy import random as rnd
+from scipy import signal as signal
+
+plt.close('all')
+
+N = 256
+
+def grav(sy,sx,w):
+
+    x = np.arange(-sx/2,sy/2,1)
+    y = np.arange(-sy/2,sy/2,1)
+    y = y[..., None]
+
+    ex = np.ones(shape=(sy,1))
+    x2 = np.kron(ex,x**2);
+
+    ey = np.ones(shape=(1,sx));
+    y2 = np.kron(y**2,ey);
+
+    rad2 = (x2+y2);
+
+    A = np.positive(1.0/np.sqrt((1.0 - w/np.sqrt(rad2)))**2 + 1e-10) ;
+
+    return A
+
+def gauss2(sy,sx,wy,wx):
+
+    x = np.arange(-sx/2,sy/2,1)
+    y = np.arange(-sy/2,sy/2,1)
+    y = y[..., None]
+
+    ex = np.ones(shape=(sy,1))
+    x2 = np.kron(ex,x**2/(2*wx**2));
+
+    ey = np.ones(shape=(1,sx));
+    y2 = np.kron(y**2/(2*wy**2),ey);
+
+    rad2 = (x2+y2);
+
+    A = np.exp(-rad2);
+
+    return A
+
+def cauchy(sy,sx,wy,wx):
+
+    x = np.arange(-sx/2,sy/2,1)
+    y = np.arange(-sy/2,sy/2,1)
+    y = y[..., None]
+
+    ex = np.ones(shape=(sy,1))
+    x2 = np.kron(ex,x**2/(2*wx**2))
+
+    ey = np.ones(shape=(1,sx))
+    y2 = np.kron(y**2/(2*wy**2),ey)
+
+    rad2 = (x2+y2)
+
+    A = 1/(1+rad2)
+
+    return A
+
+def speckle2(sy,sx,wy,wx):
+
+    Btemp = 2*np.pi*rnd.rand(sy,sx);
+    B = np.exp(complex(0,1)*Btemp);
+
+    C = gauss2(sy,sx,wy,wx);
+
+    Atemp = signal.convolve2d(B,C,'same');
+
+    Intens = np.mean(np.mean(np.abs(Atemp)**2));
+
+    D = np.real(Atemp/np.sqrt(Intens));
+
+    Dphs = np.arctan2(np.imag(D),np.real(D));
+
+    return D, Dphs
+
+
+#Sp = grav(N,N,N/8)
+
+Sp = cauchy(N,N,N/8,N/8)
+
+plt.figure(2)
+plt.matshow(Sp,2,cmap=plt.cm.get_cmap('seismic'))  # hsv, seismic, bwr
+plt.show()
+
+fx, fy = np.gradient(Sp);
+
+fxx,fxy = np.gradient(fx);
+fyx,fyy = np.gradient(fy);
+
+J = fxx*fyy - fxy*fyx;
+
+D = np.abs(1/J)
+
+plt.figure(3)
+plt.matshow(D,3,cmap=plt.cm.get_cmap('gray'))  # hsv, seismic, bwr
+plt.clim(0,0.5e7)
+plt.show()
+
+eps = 1e-7
+cnt = 0
+E = np.zeros(shape=(N,N))
+for yloop in range(0,N-1):
+    for xloop in range(0,N-1):
+
+        d = 5*N/2
+
+        indx = int(N/2 + (d*(fx[yloop,xloop])+(xloop-N/2)/2))
+        indy = int(N/2 + (d*(fy[yloop,xloop])+(yloop-N/2)/2))
+
+        if ((indx > 0) and (indx < N)) and ((indy > 0) and (indy < N)):
+            E[indy,indx] = E[indy,indx] + 1
+
+plt.figure(4)
+plt.imshow(E,interpolation='bicubic',cmap=plt.cm.get_cmap('gray'))
+plt.clim(0,20)
+plt.xlim(N/4, 3*N/4)
+plt.ylim(N/4,3*N/4)

gravfront.py

@@ -0,0 +1,74 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Tue Mar 30 19:47:31 2021
+
+gravfront.py
+
+@author: David Nolte
+Introduction to Modern Dynamics, 2nd edition (Oxford University Press, 2019)
+
+Gravitational Lensing
+"""
+
+import numpy as np
+from matplotlib import pyplot as plt
+
+plt.close('all')
+
+def refindex(x):
+    n = n0/(1 + abs(x)**expon)**(1/expon);
+    return n
+
+
+delt = 0.001
+Ly = 10
+Lx = 5
+n0 = 1
+expon = 2   # adjust this from 1 to 10
+
+
+delx = 0.01
+rng = np.int(Lx/delx)
+x = delx*np.linspace(-rng,rng)
+
+n = refindex(x)
+
+dndx = np.diff(n)/np.diff(x)
+
+plt.figure(1)
+lines = plt.plot(x,n)
+
+plt.figure(2)
+lines2 = plt.plot(dndx)
+
+plt.figure(3)
+plt.xlim(-Lx, Lx)
+plt.ylim(-Ly, 2)
+Nloop = 160;
+xd = np.zeros((Nloop,3))
+yd = np.zeros((Nloop,3))
+for loop in range(0,Nloop):
+    xp = -Lx + 2*Lx*(loop/Nloop)
+    plt.plot([xp, xp],[2, 0],'b',linewidth = 0.25)
+
+    thet = (refindex(xp+delt) - refindex(xp-delt))/(2*delt)
+    xb = xp + np.tan(thet)*Ly
+    plt.plot([xp, xb],[0, -Ly],'b',linewidth = 0.25)
+
+    for sloop in range(0,3):
+        delay = n0/(1 + abs(xp)**expon)**(1/expon) - n0
+        dis = 0.75*(sloop+1)**2 - delay
+        xfront = xp + np.sin(thet)*dis
+        yfront = -dis*np.cos(thet)
+
+        xd[loop,sloop] = xfront
+        yd[loop,sloop] = yfront
+
+for sloop in range(0,3):
+    plt.plot(xd[:,sloop],yd[:,sloop],'r',linewidth = 0.5)
+
+
+
+
+