Code updates today

LMI.m

@@ -0,0 +1,43 @@
+clear all;
+close all;
+clc;
+
+syms a [9,1];
+laminar_state=[1,0,0,0,0,0,0,0,0];
+Re_R = [200, 300, 400, 500, 600, 700, 800, 900, 1000, 1500, 2000];  
+
+
+for Re_ind=1:length(Re_R)
+     Re=Re_R(Re_ind);
+     Lx = 1.75*pi;
+     Lz = 1.2*pi;
+     alpha = (2*pi)/Lx;
+     Beta = pi/2;
+     Gamma = 2*pi/Lz;
+     KBG = sqrt(Beta^2+Gamma^2);
+     KAG = sqrt(alpha^2+Gamma^2);
+     KABG = (alpha^2+Beta^2+Gamma^2)^(1/2);
+
+     adot(1,1) = Beta^2/Re - Beta^2 * a(1)/Re - sqrt(3/2)*Beta*Gamma*a(6)*a(8)/KABG + sqrt(3/2)*Beta*Gamma*a(2)*a(3)/KBG;
+     adot(2,1) = -(4*Beta^2/3 + Gamma^2)*a(2)/Re + (5/3)*sqrt(2/3)*Gamma^2*a(4)*a(6)/KAG - Gamma^2*a(5)*a(7)/(sqrt(6)*KAG) ...
+               - alpha*Beta*Gamma*a(5)*a(8)/(sqrt(6)*KAG*KABG) - sqrt(3/2)*Beta*Gamma*a(1)*a(3)/KBG - sqrt(3/2)*Beta*Gamma*a(3)*a(9)/KBG;
+     adot(3,1) = -(Beta^2+Gamma^2)*a(3)/Re + 2*alpha*Beta*Gamma*(a(4)*a(7)+a(5)*a(6))/(sqrt(6)*KAG*KBG) + (Beta^2*(3*alpha^2 + Gamma^2) - 3*Gamma^2*(alpha^2 + Gamma^2))*a(4)*a(8)/(sqrt(6)*KAG*KBG*KABG);
+     adot(4,1) = -(3*alpha^2+4*Beta^2)*a(4)/(3*Re) - alpha*a(1)*a(5)/sqrt(6) - 10*alpha^2*a(2)*a(6)/(3*sqrt(6)*KAG)  ...
+               - sqrt(3/2)*alpha*Beta*Gamma*a(3)*a(7)/KAG*KBG - sqrt(3/2)*alpha^2*Beta^2*a(3)*a(8)/KAG*KBG*KABG - alpha*a(5)*a(9)/sqrt(6);
+
+     adot(5,1) = -(alpha^2+Beta^2)*a(5)/Re + alpha*a(1)*a(4)/sqrt(6) + alpha^2*a(2)*a(7)/(sqrt(6)*KAG) - alpha*Beta*Gamma*a(2)*a(8)/(sqrt(6)*KAG*KABG) + alpha*a(4)*a(9)/sqrt(6) + 2*alpha*Beta*Gamma*a(3)*a(6)/(sqrt(6)*KAG*KBG);
+
+     adot(6,1) = -(3*alpha^2+4*Beta^2+3*Gamma^2)*a(6)/(3*Re) + alpha*a(1)*a(7)/sqrt(6) + sqrt(3/2)*Beta*Gamma*a(1)*a(8)/KABG  ...
+                + 10*(alpha^2-Gamma^2)*a(2)*a(4)/(KAG*3*sqrt(6)) - 2*sqrt(2/3)*a(3)*a(5)*alpha*Beta*Gamma/(KAG*KBG) + alpha*a(7)*a(9)/sqrt(6) + sqrt(3/2)*Beta*Gamma*a(8)*a(9)/KABG ;
+
+     adot(7,1) = -(alpha^2+Beta^2+Gamma^2)*a(7)/Re - alpha*(a(1)*a(6)+ a(6)*a(9))/sqrt(6) + (Gamma^2- alpha^2)*a(2)*a(5)/(sqrt(6)*KAG) + alpha*Beta*Gamma*a(3)*a(4)/(sqrt(6)*KAG*KBG);
+
+     adot(8,1) = -(alpha^2+Beta^2+Gamma^2)*a(8)/Re + 2*alpha*Beta*Gamma*a(2)*a(5)/(sqrt(6)*KAG*KABG) + Gamma^2*(3*alpha^2-Beta^2+3*Gamma^2)*a(3)*a(4)/(sqrt(6)*KAG*KBG*KABG);
+
+     adot(9,1) = -9*Beta^2*a(9)/Re +sqrt(3/2)*Beta*Gamma*a(2)*a(3)/KBG -sqrt(3/2)*Beta*Gamma*a(6)*a(8)/KABG;
+
+
+end
+adot_jacobian=jacobian(adot);
+% adot_hessian=hessian(adot,a);
+

ODE45_9D_model.m

@@ -1,15 +1,17 @@
 
 %y0 = [0,0,0,0,0,0,0,0,0];  % 9d model %
-num_vectors = 10000; %should be large enough
+num_vectors = 10; %should be large enough
 Re_R = [200, 300, 400, 500, 600, 700, 800, 900, 1000, 1500, 2000];  
 min_distances = zeros(size(Re_R));
 laminar_state=[1,0,0,0,0,0,0,0,0];
-delta_list=logspace(-5,-1,100); %the last value of logspace means spacing should also be large enough
-parfor i = 1:length(Re_R)
+delta_list=logspace(-5,-1,128); %the last value of logspace means spacing should also be large enough
+delete(gcp('nocreate'));
+parpool(64); 
+for i = 1:length(Re_R)
     Re = Re_R(i);
-    distances = zeros(1, num_vectors);
     laminar_delta_ind=zeros(size(delta_list));
-    for delta_ind=1:length(delta_list)
+    parfor delta_ind=1:length(delta_list)
+        distances = zeros(1, num_vectors);
         delta=delta_list(delta_ind);
         for j = 1:num_vectors  
             perturbation=randn(1,9);
@@ -26,11 +28,14 @@
     min_distances(i) = max(laminar_delta_ind.*delta_list);
 end
 
+save('ODE45_9D_model.mat');
+
 loglog(Re_R, min_distances, '-o')
 xlabel('Re')
 ylabel('Minimum boundary distance')
 title('Minimum boundary distance vs Reynolds number')
 grid on
+saveas(gcf,'figure.fig');
 
 
 

submit_matlab_uconn

@@ -0,0 +1,21 @@
+#!/bin/bash -l
+#SBATCH --job-name=matlab
+#SBATCH --time=01:00:00
+#SBATCH --partition=general 
+#SBATCH --nodes=1
+#SBATCH --ntasks-per-node=64
+#SBATCH --output=matlab_history_%j
+
+#---------------------------------------------------------------------
+# SLURM job script to run serial MATLAB
+#---------------------------------------------------------------------
+
+SUBMITDIR=$SLURM_SUBMIT_DIR
+WORKDIR=/scratch/chl23026/chl23026/matlab_$SLURM_JOB_ID
+mkdir -p "$WORKDIR" && cp -r *.m "$WORKDIR" && cp submit_* "$WORKDIR" && cd "$WORKDIR" || exit -1
+
+module load matlab/R2022b
+
+matlab -nodisplay -nosplash -nodesktop -r "ODE45_9D_model"
+
+echo "matlab exit code: $?"