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26) with a fixed spring constant, k, and fixed rest lengths sj since the spherical elastic vesicle is held together by N points connected by Hookean springs. The rest lengths of the springs, sij for point Xi connected to all other points Xj , j = 1, . . , N, are set to be the initial distances between points in a spherical configuration. For example, given a Hookean spring between two points located at X and Y with rest length s, the general form for the force at either end of the Hookean spring is: fspring = ± k X−Y ||X − Y|| −1 .
We model each flagellum as a rigid, rotating helix attached to a wall, and study flows around both a single helix and a small patch of multiple helices. To test our numerical method and gain intuition about flows induced by a single rotating helix, we first perform a numerical timereversibility experiment. , Biophys J 86, 1863–1870, 2004) that a small number of rotating flagella could produce “whirlpools” and “rivers” a small distance above them. Using our model system, we are able to produce “whirlpools” and “rivers” when the helices are rotating out of phase.
25. Therefore the damage levels cannot surpass the death threshold of the cells, and at the end of the simulation period, we are left with a resistant tumor composed entirely of resistant cells. 3 Complete Treatment Failure Consistent with theoretical predictions, when p > 6 × 10−4 , all clones survive treatment with a DNA damaging drug. Simulations further reveal that the tumor grows monotonically in this parameter regime, meaning the drug fails to exhibit any anti-tumor activity (FIG. 4c where p = 10−2 ).