Article

# A stochastic Trotter integration scheme for dissipative particle dynamics.

Departamento de Física Fundamental, UNED, Avda. Senda del Rey 9, 28040 Madrid, Spain; Centre for Computational Science, Department of Chemistry, University College London, 20 Gordon Street, WC1H 0AJ London, UK

Mathematics and Computers in Simulation 01/2006; 72:190-194. DOI: 10.1016/j.matcom.2006.05.019 Source: DBLP

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**ABSTRACT:**This paper invites the reader to experiment with an easy-to-use MATLAB implementation of Metropolis integrators for Molecular Dynamics (MD) simulation. These integrators are analysis-based, in the sense that they can rigorously simulate dynamics along an infinitely long MD trajectory. Among explicit integrators for MD, they seem to be the only ones that satisfy the fundamental requirement of stability. The schemes can handle stiff or hard-core potentials, and are straightforward to set up, apply and extend to new situations. Potential pitfalls in high dimension are discussed, and tricks for mitigation are given.09/2013; - [Show abstract] [Hide abstract]

**ABSTRACT:**We consider the problem of time-stepping/sampling for molecular and meso-scale particle dynamics. The aim of the work is to derive numerical time-stepping methods that generate samples exactly from the desired target temperature distribution. The numerical methods proposed in this paper rely on the well-known splitting of stochastic thermostat equations into conservative and fluctuation-dissipation parts. We propose a methodology to derive numerical approximation to the fluctuation-dissipation part that exactly samples from the underlying Boltzmann distribution.Our methodology applies to Langevin dynamics as well as Dissipative Particle Dynamics and, more generally, to arbitrary position dependent fluctuation-dissipation terms. A Metropolis criterion is introduced to correct for numerical inconsistency in the conservative dynamics part of the model. Shadow energies are used to increase the acceptance rate under the Metropolis criterion. We call the newly proposed method meso-GSHMC.Procedia CS. 01/2011; 4:1353-1362. - [Show abstract] [Hide abstract]

**ABSTRACT:**A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order time-accurate schemes for the immersed boundary method, viscous force coupling and external boundary force are derived. Furthermore, a modified formulation of the external boundary force is introduced that leads to a more accurate no-slip boundary condition. The derivation also reveals that the coupling methods can be cast into a unified form, and that the immersed boundary method can be interpreted as the limit of force coupling for vanishing particle mass. In practice, the ratio between fluid and particle mass determines the strength of the force transfer in the coupling. The integration schemes formally improve the accuracy of first-order algorithms that are commonly employed when coupling immersed objects to a lattice Boltzmann fluid. It is anticipated that they will also lead to superior long-time stability in simulations of complex fluids with multiple scales.Computer Physics Communications. 06/2014;

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