%Script to integrate charge depletion model
%B. Kay 2/15/2016 et seq.
%B. De Bari 12/2016 et seq.

h_inc = 0.1; %integration step
t0 = h_inc;
tfinal = 100; 

tspan = t0:h_inc:tfinal;
lts = length(tspan);

%Set up noise, which is a force on the bead:
noise_amp = 0.4;
rng(1445834248); %Fixed seed for random number generator
%rng('shuffle'); %New seed every time, based on system clock
noise_func = noise_amp*randn(lts,1);

% parameters for charge-distribution function & bead
c1 = 1; %Conductance of bead
c2 = 1; %Charge depletion denominator parameter
sigma = 1.5; %Rate of charge saturation
% cbase = 31; %baseline charge distribution over x
q = -1; %charge carried by the bead
b = 6; %damping parameter 
mu = 1; %dipole moment of bead

nx = 1000; %Number of x (location) values
xlimit_right = 10;
xlimit_left = -10;
incr = (xlimit_right-xlimit_left)/(nx-1);
x = (xlimit_left:incr:xlimit_right);

% magnet parameters
global  mp ton toff mon moff;
mp = 0; %position of magnet in x-space
ton = 0; %time magnet turns on 
toff = 400; %time magnet turns off
mon = 0; %magnet strength when on
moff = 0; %magnet strength when off
mbase = 5;
mmax_x = 1./(c2 + (x - mp).^2) + mbase; %magnet strength at each location in x.




volt = (10:1:18);

ampl = zeros(length(volt),2);
ampl(:,1) = volt;

volt_bif = zeros(1,3);

for i = 1:length(volt)
    
    cbase = volt(i);
cmax_x = 1./(0.5 + (x).^2) + cbase; %inverse-square steady-state charge distribution 
                        
charge0 = cmax_x'; %Initial charge distribution
indx = find(x>0,1,'first');
bead0 = [x(indx) 0 0]'; %Initial bead state (position, velocity, current)
y0 = [charge0; bead0]; 

%Integrate:
[t,y] = rk4(@charge_depletion_model,t0,tfinal,y0,h_inc,noise_func,x,c1,c2,sigma,cmax_x,b,mu, mmax_x, q);

% envelope = abs(hilbert(y(:,nx+1)));
% tmp_amp = mean(envelope);

% tmp_amp = max(y(:,nx+1));
% ampl(i,2) = tmp_amp;
tmp = horzcat(y(:,nx+1), t);
v = zeros(1000,1);
v(:,1) = volt(i);
tmp = horzcat(tmp, v);

volt_bif = vertcat(volt_bif, tmp);
end

plot(ampl(:,1),ampl(:,2));
% 
% current = [((diff(y(:,nx+3))).*h_inc)' 0]; %current through ground
% pos = y(:,nx+1); %position of the bead
% v = y(:,nx+2); %velocity of the bead
% 
% tpos = tspan;
% tcur = [0 (tspan(1:end-1) - h_inc/4)];
% 
% amp = max(abs(pos));
% 
% figure(1); % bead position and current through ground
% clf;
% % hold on;
% % plot(tcur, (abs(current)))
% % plot(tpos, (normalize(abs(pos(:,1)))));
% % legend('Current (Normalized)','Bead Displacement (Normalized)')
% % title('CDM Normalized Bead Displacement and Current')
% plot(pos)
% ylim([-10, 10])
% cdm_dat = [tpos', pos, tcur',current'];
% 
% figure(2);
% plot(current)
%% Relative Phase of Position and Current

pos_cdm = abs(current); %absolute value - more negative values for current = higher current
cur_cdm = abs(pos); %position is now displacement from source 

pos_cdm = pos_cdm-mean(pos_cdm); %mean-centering time-series for Hilbert transform
cur_cdm = cur_cdm-mean(cur_cdm);

pos_cdm_wrapped = (angle(hilbert(pos_cdm)));
cur_cdm_wrapped = (angle(hilbert(cur_cdm)));

relphase_cdm = pos_cdm_wrapped - cur_cdm_wrapped;

figure(4);
clf;
hold on;
plot(relphase_cdm)
title('CDM Wrapped Relative Phase Pos - Current');
xlabel('Time');
ylabel('Relative Phase (Radians)');

mean_relphase = mean(abs(relphase_cdm));