Platelet simulations

git clone https://github.com/sonwell/ib.cu.git

Results

The table below summarizes the results of platelet simulations using RBF interpolants to compute forces within the immersed boundary (IB) method. The renders column lists two kinds of renders: those that color platelets by computing forces using RBFs (rbf) or a piecewise linear interpolant (ldsm).

The domain is a 16 μm × 16 μm × 16 μm cube. The initial flow is a (mock) shear flow. IDs beginning with "l" (for lightspeed) have Dirichlet boundaries in the z direction which maintain the shear flow. IDs beginning with "c" (for cleopatra) are triply periodic, and a background force is added to maintain the mock shear flow.

id W ɣ̇
s-1		 G
dyn/cm		 K
dyn/cm		 κ
erg		 k Tend frames renders
l8 WnH 50 1×10-1 0 0 1 μs 300 μs 31 rbf ldsm
c12 WnH 50 1×10-1 0 0 1 μs 300 μs 31 rbf ldsm
l9 WnH 50 1×10-1 0 0 100 ns 1.2 ms 13 rbf ldsm
c13 WnH 50 1×10-1 0 0 100 ns 1.2 ms 13 rbf ldsm
l10 WnH -50 1×10-1 0 0 1 μs 300 μs 31 rbf ldsm
c14 WnH -50 1×10-1 0 0 1 μs 300 μs 31 rbf ldsm
l11 WnH 50 1×10-3 0 0 1 μs 10 ms 101 rbf ldsm
l12 WnH 50 1×10-3 1×10-2 0 1 μs 5.4 ms 55 rbf ldsm
l13 WnH+Wb 50 1×10-3 0 2×10-13 1 μs 10 ms 101 rbf ldsm
l14 WnH+Wʹb 50 1×10-3 0 2×10-13 1 μs 10 ms 101 rbf ldsm
l15 WnH+Wb 50 1×10-3 0 2×10-13 1 μs 10 ms 101 rbf ldsm

Abridged Methods

$$ W_\text{nH} = G\left(\frac{I_1}{\sqrt{I_2}}-2\right) + K\left(\sqrt{I_2}-1\right)^2 $$ Let \(\Phi = 2\partial W/\partial I_1\) and \(\Psi = 2\partial W/\partial I_2\). $$ \pmb{F}\Big|_{\pmb{X}_\alpha} = - \frac{\partial \mathcal{E}}{\partial \pmb{X}_\alpha} = -\sum_{\triangle\ni\pmb{X}_\alpha} \int_\triangle \left(\frac{1}{2} \left[\Phi \hat{g}^{ij} + I_2 \Psi g^{ij}\right]\frac{\partial g_{ij}}{\partial \pmb{X}_\alpha}\right) d\hat{A} $$ $$ \pmb{F} = - \frac{\delta \mathcal{E}}{\delta \pmb{X}} = \frac{1}{\sqrt{\hat{g}}}\frac{\partial}{\partial\theta^j}\left(\sqrt{\hat{g}}\left[\Phi \hat{g}^{ij} + I_2 \Psi g^{ij}\right]\frac{\partial \pmb{X}}{\partial \theta^i}\right)d\hat{A} $$