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A STOCHASTIC IMMERSED BOUNDARY METHOD FOR FLUID-STRUCTURE DYNAMICS AT MICROSCOPIC LENGTH
 

Summary: A STOCHASTIC IMMERSED BOUNDARY METHOD FOR
FLUID-STRUCTURE DYNAMICS AT MICROSCOPIC LENGTH
SCALES
PAUL J. ATZBERGER , PETER R. KRAMER , AND CHARLES S. PESKIN
Abstract. In modeling many biological systems, it is important to take into account the in-
teraction of flexible structures with a fluid. At the length scale of cells and cell organelles, thermal
fluctuations of the aqueous environment become significant. In this work it is shown how the im-
mersed boundary method of (64) for modeling flexible structures immersed in a fluid can be extended
to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiff-
ness in the system of equations by handling systematically the statistical contributions of the fastest
dynamics of the fluid and immersed structures over long time steps. An important feature of the
numerical method is that time steps can be taken in which the degrees of freedom of the fluid are
completely underresolved, partially resolved, or fully resolved while retaining a good level of accu-
racy. Error estimates in each of these regimes are given for the method. A number of theoretical and
numerical checks are furthermore performed to assess its physical fidelity. For a conservative force,
the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is
shown in three dimensions that the diffusion of immersed particles simulated with the method has
the correct scaling in the physical parameters. The method is also shown to reproduce a well-known
hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits
an algebraic (-3/2) decay for long times (6; 16; 20; 23; 37; 38; 54; 67; 78). A few preliminary results

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics