Added way to match TF radii by matching atom number in addition to scaling magnification
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Data-Analyzer/matchTFRadiiAtomNumber.m
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163
Data-Analyzer/matchTFRadiiAtomNumber.m
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% ----------------------------
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% Experimental data
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% ----------------------------
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PixelSize = 4.6; % microns
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TF_Radii_X_pixels = [48.44308968, 46.01326593, 46.45950681, 46.41644117, 45.56176919, ...
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46.60816438, 46.85307478, 47.61086543, 46.66687703, 46.17986721, ...
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46.67877165, 46.07789481, 46.42285497, 46.22167708, 45.95144492, ...
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47.05400117, 49.03005788, 45.84588659, 46.85742777, 45.9824117 , ...
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47.14731188, 47.4984484 , 45.9055646 , 47.31804553, 47.52321888, ...
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47.76823968, 46.459749 , 45.4498851 , 45.38339308, 46.68736642, ...
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45.76607233, 48.1796053 , 46.94291541, 47.54092708, 48.26130406, ...
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47.44092616, 48.73463214, 46.39356452, 48.74120217, 45.57014182, ...
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47.56467835, 46.62867035, 46.62322802, 46.03032919, 44.78559832, ...
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46.31282562, 46.83537518, 47.68015029, 47.71093571, 47.34079816];
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TF_Radii_Y_pixels = [113.52610841, 113.68862761, 112.84031747, 114.22062324, ...
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112.45378285, 114.53863928, 111.39181472, 112.67024271, ...
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113.65387448, 113.57576769, 110.22576589, 110.45091803, ...
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109.97966067, 112.84785553, 109.3836049 , 111.22290862, ...
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111.17028727, 110.71088554, 111.72973603, 112.39623635, ...
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113.18160954, 112.00016346, 109.66542778, 111.98705097, ...
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112.35983901, 110.21703075, 112.14565939, 111.2029942 , ...
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110.74296 , 112.56607054, 112.58015318, 111.93031032, ...
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111.59774288, 112.30723266, 112.79543793, 111.08288891, ...
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113.85269603, 111.77349741, 113.58639434, 111.28694353, ...
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112.1993445 , 111.72215918, 111.93271101, 112.17593036, ...
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110.82246602, 113.61806907, 114.13693144, 114.27245731, ...
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114.24223538, 112.61704196];
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% ----------------------------
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% Load simulation data for fitting
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% ----------------------------
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% baseDir = 'D:\Results - Numerics\Data_Full3D\PhaseDiagram\TFRadii\LowN';
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baseDir = 'C:\Users\Karthik\Documents\GitRepositories\Calculations\Estimations\ThomasFermiRadius';
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refData = load(fullfile(baseDir, 'TFFermi_Theta0.mat'));
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% ----------------------------
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% Set fixed magnification and convert experimental TF radii to real units
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% ----------------------------
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Magnification = 24; % Set your desired fixed magnification here
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fprintf('Using fixed magnification: %.2f\n', Magnification);
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TF_Radii_X_Real = TF_Radii_X_pixels * PixelSize / Magnification;
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TF_Radii_Y_Real = TF_Radii_Y_pixels * PixelSize / Magnification;
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Avg_X = mean(TF_Radii_X_Real);
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Avg_Y = mean(TF_Radii_Y_Real);
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Std_X = std(TF_Radii_X_Real);
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Std_Y = std(TF_Radii_Y_Real);
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fprintf('Experimental TF Radius X = %.2f ± %.2f µm\n', Avg_X, Std_X);
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fprintf('Experimental TF Radius Y = %.2f ± %.2f µm\n', Avg_Y, Std_Y);
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% ----------------------------
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% Fit atom number to match experimental radii
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% ----------------------------
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if ndims(refData.TF_Radii) > 2
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TF_Radii = squeeze(refData.TF_Radii);
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else
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TF_Radii = refData.TF_Radii;
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end
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NUM_ATOMS_LIST = refData.NUM_ATOMS_LIST;
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errorFunc = @(N) ...
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(interp1(NUM_ATOMS_LIST, TF_Radii(:,1), N) - Avg_X)^2 + ...
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(interp1(NUM_ATOMS_LIST, TF_Radii(:,2), N) - Avg_Y)^2;
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AtomNumberFit = fminbnd(errorFunc, min(NUM_ATOMS_LIST), max(NUM_ATOMS_LIST));
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fprintf('Best-fit atom number (fixed magnification): %.0f\n', AtomNumberFit);
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TF_X_target = interp1(NUM_ATOMS_LIST, TF_Radii(:,1), AtomNumberFit);
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TF_Y_target = interp1(NUM_ATOMS_LIST, TF_Radii(:,2), AtomNumberFit);
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fprintf('TF_X_target = %.2f µm\n', TF_X_target);
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fprintf('TF_Y_target = %.2f µm\n', TF_Y_target);
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% ----------------------------
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% Convert to real space and get stats
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% ----------------------------
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TF_Radii_X_Real = TF_Radii_X_pixels * PixelSize / Magnification;
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TF_Radii_Y_Real = TF_Radii_Y_pixels * PixelSize / Magnification;
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Avg_X = mean(TF_Radii_X_Real);
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Avg_Y = mean(TF_Radii_Y_Real);
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Std_X = std(TF_Radii_X_Real);
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Std_Y = std(TF_Radii_Y_Real);
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fprintf('TF Radius X = %.2f ± %.2f µm\n', Avg_X, Std_X);
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fprintf('TF Radius Y = %.2f ± %.2f µm\n', Avg_Y, Std_Y);
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% ----------------------------
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% Plotting
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% ----------------------------
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fileList = {'TFFermi_Theta0.mat'};
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thetaLabels = {'\theta = 0^\circ', '\theta = 20^\circ', '\theta = 40^\circ'};
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fig = figure(1); clf;
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set(gcf,'Position', [100, 100, 1200, 500])
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t = tiledlayout(1, 2, 'TileSpacing', 'compact', 'Padding', 'compact');
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colors = lines(length(fileList));
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legendEntries = cell(1, length(fileList));
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for j = 1:length(fileList)
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data = load(fullfile(baseDir, fileList{j}));
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aS = data.SCATTERING_LENGTH_RANGE;
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NUM_ATOMS_LIST = data.NUM_ATOMS_LIST;
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if ndims(data.TF_Radii) > 2
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TF_Radii = squeeze(data.TF_Radii);
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else
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TF_Radii = data.TF_Radii;
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end
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legendEntries{j} = sprintf('%s, a_s = %.2f a_0', thetaLabels{j}, aS);
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% Rx
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nexttile(1);
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plot(NUM_ATOMS_LIST, TF_Radii(:,1), '-', ...
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'Color', colors(j,:), 'LineWidth', 1.5, ...
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'DisplayName', legendEntries{j}); hold on;
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% Ry
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nexttile(2);
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plot(NUM_ATOMS_LIST, TF_Radii(:,2), '-', ...
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'Color', colors(j,:), 'LineWidth', 1.5, ...
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'DisplayName', legendEntries{j}); hold on;
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end
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% ----------------------------
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% Add experimental point w/ error bars and annotation
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% ----------------------------
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% TF Radius X
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nexttile(1);
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errorbar(AtomNumberFit, Avg_X, Std_X, ...
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'd', 'MarkerSize', 8, 'MarkerFaceColor', [0.2 0.2 0.8], ...
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'MarkerEdgeColor', 'k', 'Color', 'k', 'LineWidth', 1.2, ...
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'DisplayName', '\theta = 0^\circ, Experimental Value');
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% TF Radius Y
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nexttile(2);
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errorbar(AtomNumberFit, Avg_Y, Std_Y, ...
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'd', 'MarkerSize', 8, 'MarkerFaceColor', [0.2 0.2 0.8], ...
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'MarkerEdgeColor', 'k', 'Color', 'k', 'LineWidth', 1.2, ...
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'DisplayName', '\theta = 0^\circ, Experimental Value');
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% ----------------------------
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% Finalize
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% ----------------------------
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nexttile(1);
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xlabel('Number of Atoms', 'FontSize', 16);
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ylabel('TF Radius - X ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 16);
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legend('FontSize', 12, 'Interpreter', 'tex', 'Location', 'bestoutside');
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axis square; grid on;
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nexttile(2);
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xlabel('Number of Atoms', 'FontSize', 16);
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ylabel('TF Radius - Y ($\mu$m)', 'Interpreter', 'latex', 'FontSize', 16);
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legend('FontSize', 12, 'Interpreter', 'tex', 'Location', 'bestoutside');
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axis square; grid on;
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sgtitle('[ \omega_x, \omega_y, \omega_z ] = 2 \pi \times [ 50, 20, 150 ] Hz', ...
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'Interpreter', 'tex', 'FontSize', 18);
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