%
%  w01drift.m - drift (djm: 07 jan 10)
%

%  clear everything & set parameters
clear;  close all
a = 0.8

%  coordinates & drift speed plot
xx = 0:pi/100:4*pi;
uu = 1 ./ (1 + a*sin(xx));

subplot(2,1,1)
plot(xx,uu,'k-')
axis([0 4*pi 0 1.1*(max(uu))])

title(['\bf drift speed (a=' num2str(a) ')'])
xlabel('\bf x-axis')
ylabel('\bf u(x)')
text(  pi/2-0.4,3,'\bf slow')
text(3*pi/2-0.4,1,'\bf fast')

%  three drift paths (x_0 = 0,pi/2,pi)
subplot(2,1,2);  hold on

x_0 = 0;  x = x_0:pi/20:4*pi;  
t = (x - a*cos(x)) - (x_0 - a*cos(x_0));
plot(x,t)

x_0 = pi/2;  x = x_0:pi/20:4*pi;  
t = (x - a*cos(x)) - (x_0 - a*cos(x_0));
plot(x,t)

x_0 = pi;  x = x_0:pi/20:4*pi;  
t = (x - a*cos(x)) - (x_0 - a*cos(x_0));
plot(x,t)

%  always label plot & axes
axis([0 4*pi 0 4*pi])
title('\bf drift paths')
xlabel('\bf X-axis')
ylabel('\bf t(X) for 3 IVs')
text(1,8,'\bf slope = 1/speed')

%  lines at time = 3 & 6
plot([0 4*pi],[3 3],'r--')
plot([0 4*pi],[6 6],'r--')