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gyacomo/matlab/evolve_tracers.m
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evolve_tracers.m
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% Options
SHOW_FILM = 0;
field2plot ='Ni00';
INIT = 'lin'; % lin (for a line)/ round (for a small round)/ gauss for random
U_TIME = 200; % >0 for frozen velocity at a given time, -1 for evolving field
Evolve_U = 1; % 0 for frozen velocity at a given time, 1 for evolving field
Tfin = 200;
dt_ = 0.1;
Nstep = ceil(Tfin/dt_);
% Init tracers
Np = 20; %number of tracers
% color = tcolors;
color = jet(Np);
tcolors = distinguishable_colors(Np); %Their colors
Na = 1/dt_; %length of trace
Traj_x = zeros(Np,Nstep);
Traj_y = zeros(Np,Nstep);
Disp_x = zeros(Np,Nstep);
Disp_y = zeros(Np,Nstep);
xmax = max(data.x); xmin = min(data.x);
ymax = max(data.y); ymin = min(data.y);
switch INIT
case 'lin'
% Evenly distributed initial positions
dp_ = (xmax-xmin)/(Np-1);
Xp = linspace(xmin+dp_/2,xmax-dp_/2,Np);
Yp = zeros(1,Np);
Zp = zeros(Np);
case 'round'
% All particles arround a same point
xc = 0; yc = 0;
theta = rand(1,Np)*2*pi; r = 0.1;
Xp = xc + r*cos(theta);
Yp = yc + r*sin(theta);
Zp = zeros(Np);
case 'gauss'
% normal distribution arround a point
xc = 0; yc = 0; sgm = 1.0;
dx = normrnd(0,sgm,[1,Np]); dx = dx - mean(dx);
Xp = xc + dx;
dy = normrnd(0,sgm,[1,Np]); dy = dy - mean(dy);
Yp = yc + dy;
Zp = zeros(Np);
end
% position grid and velocity field
[YY_, XX_ ,ZZ_] = meshgrid(data.y,data.x,data.z);
[KX,KY] = meshgrid(data.kx,data.ky);
Ux = zeros(size(XX_));
Uy = zeros(size(XX_));
Uz = zeros(size(XX_));
ni = zeros(size(XX_));
[~,itu_] = min(abs(U_TIME-data.Ts3D));
% computing the frozen velocity field
for iz = 1:data.Nz
% Ux(:,:,iz) = real(ifft2( 1i*KY.*(data.PHI(:,:,iz,itu_)),data.Nx,data.Ny));
% Uy(:,:,iz) = real(ifft2(-1i*KX.*(data.PHI(:,:,iz,itu_)),data.Nx,data.Ny));
% ni(:,:,iz) = real(ifft2(data.DENS_I(:,:,iz,itu_),data.Nx,data.Ny));
Ux(:,:,iz) = ifourier_GENE( 1i*KY.*(data.PHI(:,:,iz,itu_)))';
Uy(:,:,iz) = ifourier_GENE(-1i*KX.*(data.PHI(:,:,iz,itu_)))';
ni(:,:,iz) = ifourier_GENE(data.DENS_I(:,:,iz,itu_))';
end
%% FILM options
FPS = 30; DELAY = 1/FPS;
FORMAT = '.gif';
if SHOW_FILM
FILENAME = [data.localdir,'tracer_evolution',FORMAT];
switch FORMAT
case '.avi'
vidfile = VideoWriter(FILENAME,'Uncompressed AVI');
vidfile.FrameRate = FPS;
open(vidfile);
end
fig = figure;
end
%
%Time loop
t_ = 0;
it = 1;
itu_old = 0;
nbytes = fprintf(2,'frame %d/%d',it,Nstep);
while(t_<Tfin && it <= Nstep)
if Evolve_U
[~,itu_] = min(abs(U_TIME+t_-data.Ts3D));
end
if Evolve_U && (itu_old ~= itu_)
% updating the velocity field and density field
for iz = 1:data.Nz
Ux(:,:,iz) = ifourier_GENE( 1i*KY.*(data.PHI(:,:,iz,itu_)))';
Uy(:,:,iz) = ifourier_GENE(-1i*KX.*(data.PHI(:,:,iz,itu_)))';
% ni(:,:,iz) = ifourier_GENE(data.DENS_I(:,:,iz,itu_))';
ni(:,:,iz) = ifourier_GENE(data.Ni00(:,:,iz,itu_))';
end
end
% evolve each tracer
for ip = 1:Np
% locate the tracer
% find corners of the cell
x_ = Xp(ip);
[e_x,ixC] = min(abs(x_-data.x));
if e_x == 0 % on the face
ix0 = ixC;
ix1 = ixC;
elseif x_ > data.x(ixC) % right from grid point
ix0 = ixC;
ix1 = ixC+1;
else % left
ix0 = ixC-1;
ix1 = ixC;
end
y_ = Yp(ip);
[e_y,iyC] = min(abs(y_-data.y));
if e_y == 0 % on the face
iy0 = iyC;
iy1 = iyC;
elseif y_ > data.y(iyC) % above
iy0 = iyC;
iy1 = iyC+1;
else % under
iy0 = iyC-1;
iy1 = iyC;
end
z_ = Zp(ip,1);
[e_z,izC] = min(abs(z_-data.z));
if e_z == 0 % on the face
iz0 = izC;
iz1 = izC;
elseif z_ > data.z(izC) % before
iz0 = izC;
iz1 = izC+1;
else % behind
iz0 = izC-1;
iz1 = izC;
end
x0 = data.x(ix0); x1 = data.x(ix1); %left right
y0 = data.y(iy0); y1 = data.y(iy1); %down top
z0 = data.z(iz0); z1 = data.z(iz1); %back front
if(e_x > 0)
ai__ = (x_ - x0)/(x1-x0); % interp coeff x
else
ai__ = 0;
end
if(e_y > 0)
a_i_ = (y_ - y0)/(y0-y1); % interp coeff y
else
a_i_ = 0;
end
if(e_z > 0)
a__i = (z_ - z0)/(z1-z0); % interp coeff z
else
a__i = 0;
end
% interp velocity and density
%velocity values
u000 = [Ux(ix0,iy0,iz0) Uy(ix0,iy0,iz0) ni(ix0,iy0,iz0)];
u001 = [Ux(ix0,iy0,iz1) Uy(ix0,iy0,iz1) ni(ix0,iy0,iz1)];
u010 = [Ux(ix0,iy1,iz0) Uy(ix0,iy1,iz0) ni(ix0,iy1,iz0)];
u011 = [Ux(ix0,iy1,iz1) Uy(ix0,iy1,iz1) ni(ix0,iy1,iz1)];
u100 = [Ux(ix1,iy0,iz0) Uy(ix1,iy0,iz0) ni(ix1,iy0,iz0)];
u101 = [Ux(ix1,iy0,iz1) Uy(ix1,iy0,iz1) ni(ix1,iy0,iz1)];
u110 = [Ux(ix1,iy1,iz0) Uy(ix1,iy1,iz0) ni(ix1,iy1,iz0)];
u111 = [Ux(ix1,iy1,iz1) Uy(ix1,iy1,iz1) ni(ix1,iy1,iz1)];
%linear interpolation
linterp = @(x1,x2,a) (1-a)*x1 + a*x2;
u_00 = linterp(u000,u100,ai__);
u_10 = linterp(u010,u110,ai__);
u__0 = linterp(u_00,u_10,a_i_);
u_01 = linterp(u001,u101,ai__);
u_11 = linterp(u011,u111,ai__);
u__1 = linterp(u_01,u_11,a_i_);
u___ = linterp(u__0,u__1,a__i);
% push the particle
% q = sign(-u___(3));
q = -u___(3);
% q =1;
x_ = x_ + dt_*u___(1)*q;
y_ = y_ + dt_*u___(2)*q;
% apply periodic boundary conditions
if(x_ > xmax)
x_ = xmin + (x_ - xmax);
elseif(x_ < xmin)
x_ = xmax + (x_ - xmin);
end
if(y_ > ymax)
y_ = ymin + (y_ - ymax);
elseif(y_ < ymin)
y_ = ymax + (y_ - ymin);
end
% store data
% Trajectory
Traj_x(ip,it) = x_;
Traj_y(ip,it) = y_;
% Displacement
Disp_x(ip,it) = Disp_x(ip,it) + dt_*u___(1)*q;
Disp_y(ip,it) = Disp_y(ip,it) + dt_*u___(2)*q;
% update position
Xp(ip) = x_; Yp(ip) = y_;
end
%% Movie
if SHOW_FILM && (~Evolve_U || (itu_old ~= itu_))
% updating the velocity field
clf(fig);
switch field2plot
case 'phi'
F2P = ifourier_GENE(data.PHI(:,:,iz,itu_))';
case 'ni'
F2P = ifourier_GENE(data.DENS_I(:,:,iz,itu_))';
case 'Ni00'
F2P = ifourier_GENE(data.Ni00(:,:,iz,itu_))';
case 'none'
F2P = 0*XX_;
end
scale = max(max(abs(F2P))); % Scaling to normalize
pclr = pcolor(XX_,YY_,F2P/scale);
colormap(bluewhitered); caxis([-1 1]);
set(pclr, 'edgecolor','none'); hold on; caxis([-2,2]); shading interp
for ip = 1:Np
ia0 = max(1,it-Na);
plot(Traj_x(ip,ia0:it),Traj_y(ip,ia0:it),'.','Color',color(ip,:)); hold on
end
for ip = 1:Np
plot(Traj_x(ip, 1),Traj_y(ip, 1),'xk'); hold on
plot(Traj_x(ip,it),Traj_y(ip,it),'ok','MarkerFaceColor',color(ip,:)); hold on
end
title(['$t \approx$', sprintf('%.3d',ceil(data.Ts3D(itu_)))]);
axis equal
xlim([xmin xmax]); ylim([ymin ymax]);
drawnow
% Capture the plot as an image
frame = getframe(fig);
switch FORMAT
case '.gif'
im = frame2im(frame);
[imind,cm] = rgb2ind(im,32);
% Write to the GIF File
if it == 1
imwrite(imind,cm,FILENAME,'gif', 'Loopcount',inf);
else
imwrite(imind,cm,FILENAME,'gif','WriteMode','append', 'DelayTime',DELAY);
end
case '.avi'
writeVideo(vidfile,frame);
otherwise
disp('Unknown format');
break
end
end
t_ = t_ + dt_; it = it + 1; itu_old = itu_;
% terminal info
while nbytes > 0
fprintf('\b')
nbytes = nbytes - 1;
end
nbytes = fprintf(2,'frame %d/%d',it,Nstep);
end
disp(' ')
switch FORMAT
case '.gif'
disp(['Gif saved @ : ',FILENAME])
case '.avi'
disp(['Video saved @ : ',FILENAME])
close(vidfile);
end
Nt = it;
%% Plot trajectories and statistics
xtot = Disp_x;
ytot = Disp_y;
% aggregate the displacements
for iq = 1:Np
x_ = 0; y_ = 0;
for iu = 1:Nt-1
x_ = x_ + Disp_x(iq,iu);
y_ = y_ + Disp_y(iq,iu);
xtot(iq,iu) = x_;
ytot(iq,iu) = y_;
end
end
ma = @(x) x;%movmean(x,100);
time_ = linspace(U_TIME,U_TIME+Tfin,it-1);
figure;
subplot(221);
for ip = 1:Np
% plot(ma(time_),ma(Traj_x(ip,:)),'-','Color',tcolors(ip,:)); hold on
plot(ma(time_),xtot(ip,:),'-','Color',tcolors(ip,:)); hold on
% plot(ma(time_),ma(Disp_x(ip,:)),'-','Color',tcolors(ip,:)); hold on
end
ylabel('$x_p$');
xlim(U_TIME + [0 Tfin]);
subplot(222);
itf = floor(Nt/2); %fit end time
% x^2 displacement
plot(time_,mean(xtot.^2,1),'DisplayName','$\langle x.^2\rangle_p$'); hold on
fit = polyfit(time_(1:itf),mean(xtot(:,1:itf).^2,1),1);
plot(time_,fit(1)*time_+fit(2),'--k'); hold on
ylabel('$\langle x^2 \rangle_p$');
% % y^2 displacement
% fit = polyfit(time_(1:itf),mean(ytot(:,1:itf).^2,1),1);
% plot(time_,fit(1)*time_+fit(2),'--k','DisplayName',['$\alpha=',num2str(fit(1)),'$']); hold on
% plot(time_,mean(ytot.^2,1),'DisplayName','$\langle y.^2\rangle_p$');
%
% % r^2 displacement
% fit = polyfit(time_(1:itf),mean(xtot(:,1:itf).^2+ytot(:,1:itf).^2,1),1);
% plot(time_,fit(1)*time_+fit(2),'--k','DisplayName',['$\alpha=',num2str(fit(1)),'$']); hold on
% plot(time_,mean(xtot.^2+ytot.^2,1),'DisplayName','$\langle r.^2\rangle_p$');
% ylabel('$\langle x^2 \rangle_p$');
% xlim(U_TIME + [0 Tfin]);
subplot(223);
for ip = 1:Np
% plot(ma(time_),ma(Traj_y(ip,:)),'-','Color',tcolors(ip,:)); hold on
plot(ma(time_),ytot(ip,:),'-','Color',tcolors(ip,:)); hold on
% plot(ma(time_),ma(Disp_y(ip,:)),'-','Color',tcolors(ip,:)); hold on
end
xlabel('time');
ylabel('$y_p$');
xlim(U_TIME + [0 Tfin]);
subplot(224);
histogram(xtot(:,1),20); hold on
histogram(xtot(:,end),20)
xlabel('position');
ylabel('$n$');
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