Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
The Journal of Supercomputing - Special issue on supercomputing in medicine
Long-Time-Step Methods for Oscillatory Differential Equations
SIAM Journal on Scientific Computing
Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
SIAM Journal on Numerical Analysis
Numerical Methods for Stochastic Systems Preserving Symplectic Structure
SIAM Journal on Numerical Analysis
A computational model of flow through porous media at the microscale
A computational model of flow through porous media at the microscale
Fourth-Order Time-Stepping for Stiff PDEs
SIAM Journal on Scientific Computing
Journal of Computational Physics
Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations
Mathematics and Computers in Simulation
DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method
Journal of Computational Physics
A phase field model for vesicle-substrate adhesion
Journal of Computational Physics
Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method
Journal of Computational Physics
A lattice Boltzmann based implicit immersed boundary method for fluid-structure interaction
Computers & Mathematics with Applications
Journal of Computational Physics
A multirate time integrator for regularized Stokeslets
Journal of Computational Physics
Stochastic Eulerian Lagrangian methods for fluid-structure interactions with thermal fluctuations
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
A stochastic finite element model for the dynamics of globular macromolecules
Journal of Computational Physics
Electric load forecasting using support vector machines for robust regression
Proceedings of the Emerging M&S Applications in Industry & Academia / Modeling and Humanities Symposium
Journal of Computational Physics
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In modeling many biological systems, it is important to take into account flexible structures which interact 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 immersed boundary method of [C.S. Peskin, The immersed boundary method, Acta Num. 11 (2002) 1-39.] for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness 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 accuracy. 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 (@t^-^3^/^2) decay for long times [B.J. Alder, T.E. Wainwright, Decay of the Velocity Autocorrelation Function, Phys. Rev. A 1(1) (1970) 18-21]. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method. Specifically, we present simulations of osmotic effects of molecular dimers, worm-like chain polymer knots, and a basic model of a molecular motor immersed in fluid subject to a hydrodynamic load force. The theoretical analysis and numerical results show that the immersed boundary method with thermal fluctuations captures many important features of small length scale hydrodynamic systems and holds promise as an effective method for simulating biological phenomena on the cellular and subcellular length scales.