938 research outputs found
Efficient algorithms for rigid body integration using optimized splitting methods and exact free rotational motion
Hamiltonian splitting methods are an established technique to derive stable
and accurate integration schemes in molecular dynamics, in which additional
accuracy can be gained using force gradients. For rigid bodies, a tradition
exists in the literature to further split up the kinetic part of the
Hamiltonian, which lowers the accuracy. The goal of this note is to comment on
the best combination of optimized splitting and gradient methods that avoids
splitting the kinetic energy. These schemes are generally applicable, but the
optimal scheme depends on the desired level of accuracy. For simulations of
liquid water it is found that the velocity Verlet scheme is only optimal for
crude simulations with accuracies larger than 1.5%, while surprisingly a
modified Verlet scheme (HOA) is optimal up to accuracies of 0.4% and a fourth
order gradient scheme (GIER4) is optimal for even higher accuracies.Comment: 2 pages, 1 figure. Added clarifying comments. Accepted for
publication in the Journal of Chemical Physic
A method for molecular dynamics on curved surfaces
Dynamics simulations of constrained particles can greatly aid in
understanding the temporal and spatial evolution of biological processes such
as lateral transport along membranes and self-assembly of viruses. Most
theoretical efforts in the field of diffusive transport have focussed on
solving the diffusion equation on curved surfaces, for which it is not
tractable to incorporate particle interactions even though these play a crucial
role in crowded systems. We show here that it is possible to combine standard
constraint algorithms with the classical velocity Verlet scheme to perform
molecular dynamics simulations of particles constrained to an arbitrarily
curved surface, in which such interactions can be taken into account.
Furthermore, unlike Brownian dynamics schemes in local coordinates, our method
is based on Cartesian coordinates allowing for the reuse of many other standard
tools without modifications, including parallelisation through domain
decomposition. We show that by applying the schemes to the Langevin equation
for various surfaces, confined Brownian motion is obtained, which has direct
applications to many biological and physical problems. Finally we present two
practical examples that highlight the applicability of the method: (i) the
influence of crowding and shape on the lateral diffusion of proteins in curved
membranes and (ii) the self-assembly of a coarse-grained virus capsid protein
model.Comment: 30 pages, 5 figure
Towards Better Integrators for Dissipative Particle Dynamics Simulations
Coarse-grained models that preserve hydrodynamics provide a natural approach
to study collective properties of soft-matter systems. Here, we demonstrate
that commonly used integration schemes in dissipative particle dynamics give
rise to pronounced artifacts in physical quantities such as the compressibility
and the diffusion coefficient. We assess the quality of these integration
schemes, including variants based on a recently suggested self-consistent
approach, and examine their relative performance. Implications of
integrator-induced effects are discussed.Comment: 4 pages, 3 figures, 2 tables, accepted for publication in Phys. Rev.
E (Rapid Communication), tentative publication issue: 01 Dec 200
Numerical Methods for the Nonlocal Wave Equation of the Peridynamics
In this paper we will consider the peridynamic equation of motion which is
described by a second order in time partial integro-differential equation. This
equation has recently received great attention in several fields of Engineering
because seems to provide an effective approach to modeling mechanical systems
avoiding spatial discontinuous derivatives and body singularities. In
particular, we will consider the linear model of peridynamics in a
one-dimensional spatial domain. Here we will review some numerical techniques
to solve this equation and propose some new computational methods of higher
order in space; moreover we will see how to apply the methods studied for the
linear model to the nonlinear one. Also a spectral method for the spatial
discretization of the linear problem will be discussed. Several numerical tests
will be given in order to validate our results
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