Swimming via wave propagation

all_external_forces.m

@@ -9,7 +9,8 @@
 
 cross_links_trig = false;
 cross_links_linear = false;
-cross_links_linear_osc = true;
+cross_links_linear_osc = false;
+cross_links_linear_osc_swimming = true;
 cross_links_han_peskin = false;
 
 external_pinch = false;
@@ -44,6 +45,11 @@
     [FX, FY] = cl_forces_variable_al_linear_osc(FX, FY, X_S, Y_S, N_w, cl_el, nt, TOTAL_STEPS);
 end
 
+% Cross linked forces with variable arc length, linear, swimming
+if cross_links_linear_osc_swimming
+    [FX, FY] = cl_forces_variable_al_linear_swimming(FX, FY, X_S, Y_S, N_w, cl_el, nt, TOTAL_STEPS);
+end
+
 if cross_links_han_peskin
     [FX, FY, T] = cl_forces_hanpeskin_new(FX, FY, X_S, Y_S, N_w, N_pairs, dt, T_S);
 end

cl_forces_variable_al_linear_osc.m

@@ -8,16 +8,15 @@
 % Constants for cross links (linear and trig)
 k_a = 1;
 k_b = 1;
-lambda = 3;
+lambda = 5;
 
 % Initialise
 t = nt;
 
 for i=1:(N_w - 1)
         % Parameters for time component
         reps = 6;
-        scale = 2;
-        time_component = scale * sin(reps * pi * t / TOTAL_STEPS);
+        time_component = sin(reps * pi * t / TOTAL_STEPS);
 
         % Equilibrium lengths
         el_a = cl_el + lambda * time_component * ((i - 1) / N_w);

cl_forces_variable_al_linear_swimming.asv

@@ -0,0 +1,53 @@
+function [FX, FY] = cl_forces_variable_al_linear_swimming(FX_IN, FY_IN, X_IN, Y_IN, N_w, cl_el, nt, TOTAL_STEPS)
+
+% This function returns a complete asymmetric crosslinked set of forces
+
+FX = FX_IN;
+FY = FY_IN;
+
+% Constants for cross links (linear and trig)
+k_a = 1;
+k_b = 1;
+lambda = 5;
+
+% Initialise
+t = nt;
+
+% Divisions of filament
+div = 2;
+
+% Segments per division
+spdiv = floor(N_w / div);
+
+for j=1:div
+    seg_start = 1 + (spdiv * (j - 1));
+    seg_end = seg_start + spdiv - 1;
+
+    if seg_end == N_w
+        seg_end = seg_end - 1;
+    end
+
+    for i=seg_start:seg_end
+
+            % Parameters for time component
+            omega = 2 * pi / TOTAL_STEPS        % undulation freq
+            k = w                               % wave number
+            time_component = sin(k*s - omega*t + phi);
+
+            % Equilibrium lengths
+            el_a = cl_el + lambda * ((i - 1) / (div * N_w));
+            el_b = cl_el + lambda * (1 - ((i - 1) / (div * N_w)));
+
+            if j == 1
+                scale = 2 * (1 - ((i - 1) / N_w));
+            else
+                scale = 1;
+            end
+
+            el_a = cl_el + lambda * time_component * scale;
+
+            % Add forces
+            [FX, FY] = add_spring_force_between_segments(FX, FY, X_IN, Y_IN, i, N_w + i + 1, k_a, el_a);    
+            [FX, FY] = add_spring_force_between_segments(FX, FY, X_IN, Y_IN, i + 1, N_w + i, k_b, el_b);    
+    end
+end

cl_forces_variable_al_linear_swimming.m

@@ -0,0 +1,54 @@
+function [FX, FY] = cl_forces_variable_al_linear_swimming(FX_IN, FY_IN, X_IN, Y_IN, N_w, cl_el, nt, TOTAL_STEPS)
+
+% This function returns a complete asymmetric crosslinked set of forces
+
+FX = FX_IN;
+FY = FY_IN;
+
+% Constants for cross links (linear and trig)
+k_a = 1;                              % Young's Constant for Active Cross-Link
+k_b = 1;                              % Young's Constant for Passive Cross-Link
+lambda = 10;                          % Amplitude
+
+% Parameters for time component
+time_div = 1;
+speed = 4;
+omega = 2 * pi * speed / (time_div * TOTAL_STEPS);        % undulation freq
+k = 1;                                                    % wave number
+phi = 0;                                                  % phase
+
+% Initialise
+t = nt;
+
+% Divisions of filament
+div = 2;
+
+% Segments per division
+spdiv = floor(N_w / div);
+
+for j=1:div
+    seg_start = 1 + (spdiv * (j - 1));
+    seg_end = seg_start + spdiv - 1;
+
+    if seg_end == N_w
+        seg_end = seg_end - 1;
+    end
+
+    for i=seg_start:seg_end
+
+            time_component = sin(k*(i - 1) - omega*t + phi);
+
+            if j == 1
+                scale = 2 * (1 - ((i - 1) / N_w));
+            else
+                scale = 1;
+            end
+
+            el_a = cl_el + lambda * time_component * scale;
+            el_b = cl_el;
+
+            % Add forces
+            [FX, FY] = add_spring_force_between_segments(FX, FY, X_IN, Y_IN, i, N_w + i + 1, k_a, el_a);    
+            [FX, FY] = add_spring_force_between_segments(FX, FY, X_IN, Y_IN, i + 1, N_w + i, k_b, el_b);    
+    end
+end

data.m

@@ -12,14 +12,14 @@
 % Filament data
 a = 1;                        % segment 'radius' (half filament width)
 N_sw = 2 * N_pairs;           % number of filaments
-N_w = 15;                     % number of segments in filament (21)
+N_w = 21;                     % number of segments in filament (21)
 Np = N_sw*N_w;                % total number of segments
 N_lam = N_sw*(N_w - 1);       % number of lambdas
 
 B = 1000;                      % dimensionless elasto-gravitational number B
 weight_per_unit_length = 1e0;  % weight per unit length W
 
-DL_factor = 2.2;               
+DL_factor = 2.2;               % 2.2               
 DL = DL_factor*a;              % distance between segment centres, Delta L
 L = N_w*DL;                    % filament length L
 mu = 10;                       % fluid viscosity

set_up_graphics.m

@@ -11,10 +11,10 @@
 
 % Plot centreline and walls of two filaments
 plot_centreline = true;
-plot_walls = true;
+plot_walls = false;
 
 % Line thicknesses
-wdth_centreline = 5;
+wdth_centreline = 10;
 wdth_wall = 5;
 
 % Plot initial conditions