3,744 research outputs found
Molecular Dynamics in a Grand Ensemble: Bergmann-Lebowitz model and Adaptive Resolution Simulation
This article deals with the molecular dynamics simulation of open systems
that can exchange energy and matter with a reservoir; the physics of the
reservoir and its interactions with the system are described by the model
introduced by Bergmann and Lebowitz.Despite its conceptual appeal, the model
did not gain popularity in the field of molecular simulation and, as a
consequence, did not play a role in the development of open system molecular
simulation techniques, even though it can provide the conceptual legitimation
of simulation techniques that mimic open systems. We shall demonstrate that the
model can serve as a tool to devise both numerical procedures and conceptual
definitions of physical quantities that cannot be defined in a straightforward
way by systems with a fixed number of molecules. In particular, we discuss the
utility of the Bergmann-Lebowitz (BL) model for the calculation of equilibrium
time correlation functions within the Grand Canonical Adaptive Resolution
method (GC-AdResS) and report numerical results for the case of liquid water.Comment: 31 pages, 6 figure
Stochastic boundary conditions for molecular dynamics simulations
In this paper we develop a stochastic boundary conditions (SBC) for
event-driven molecular dynamics simulations of a finite volume embedded within
an infinite environment. In this method, we first collect the statistics of
injection/ejection events in periodic boundary conditions (PBC). Once
sufficient statistics are collected, we remove the PBC and turn on the SBC. In
the SBC simulations, we allow particles leaving the system to be truly ejected
from the simulation, and randomly inject particles at the boundaries by
resampling from the injection/ejection statistics collected from the current or
previous simulations. With the SBC, we can measure thermodynamic quantities
within the grand canonical ensemble, based on the particle number and energy
fluctuations. To demonstrate how useful the SBC algorithm is, we simulated a
hard disk gas and measured the pair distribution function, the compressibility
and the specific heat, comparing them against literature values.Comment: 24 pages, 16 figure
Driven lattice gas of dimers coupled to a bulk reservoir
We investigate the non-equilibrium steady state of a one-dimensional (1D)
lattice gas of dimers. The dynamics is described by a totally asymmetric
exclusion process (TASEP) supplemented by attachment and detachment processes,
mimicking chemical equilibrium of the 1D driven transport with the bulk
reservoir. The steady-state phase diagram, current and density profiles are
calculated using both a refined mean-field theory and extensive stochastic
simulations. As a consequence of the on-off kinetics, a new phase coexistence
region arises intervening between low and high density phases such that the
discontinuous transition line of the TASEP splits into two continuous ones. The
results of the mean-field theory and simulations are found to coincide. We show
that the physical picture obtained in the corresponding lattice gas model with
monomers is robust, in the sense that the phase diagram changes quantitatively,
but the topology remains unaltered. The mechanism for phase separation is
identified as generic for a wide class of driven 1D lattice gases.Comment: 15 pages, 10 figures, 1tabl
Generic principles of active transport
Nonequilibrium collective motion is ubiquitous in nature and often results in
a rich collection of intringuing phenomena, such as the formation of shocks or
patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase
transitions. These stochastic many-body features characterize transport
processes in biology, soft condensed matter and, possibly, also in nanoscience.
Inspired by these applications, a wide class of lattice-gas models has recently
been considered. Building on the celebrated {\it totally asymmetric simple
exclusion process} (TASEP) and a generalization accounting for the exchanges
with a reservoir, we discuss the qualitative and quantitative nonequilibrium
properties of these model systems. We specifically analyze the case of a
dimeric lattice gas, the transport in the presence of pointwise disorder and
along coupled tracks.Comment: 21 pages, 10 figures. Pedagogical paper based on a lecture delivered
at the conference on "Stochastic models in biological sciences" (May 29 -
June 2, 2006 in Warsaw). For the Banach Center Publication
Fluctuating hydrodynamic modelling of fluids at the nanoscale
A good representation of mesoscopic fluids is required to combine with
molecular simulations at larger length and time scales (De Fabritiis {\it et.
al}, Phys. Rev. Lett. 97, 134501 (2006)). However, accurate computational
models of the hydrodynamics of nanoscale molecular assemblies are lacking, at
least in part because of the stochastic character of the underlying fluctuating
hydrodynamic equations. Here we derive a finite volume discretization of the
compressible isothermal fluctuating hydrodynamic equations over a regular grid
in the Eulerian reference system. We apply it to fluids such as argon at
arbitrary densities and water under ambient conditions. To that end, molecular
dynamics simulations are used to derive the required fluid properties. The
equilibrium state of the model is shown to be thermodynamically consistent and
correctly reproduces linear hydrodynamics including relaxation of sound and
shear modes. We also consider non-equilibrium states involving diffusion and
convection in cavities with no-slip boundary conditions
Open Boundary Simulations of Proteins and Their Hydration Shells by Hamiltonian Adaptive Resolution Scheme
The recently proposed Hamiltonian Adaptive Resolution Scheme (H-AdResS)
allows to perform molecular simulations in an open boundary framework. It
allows to change on the fly the resolution of specific subset of molecules
(usually the solvent), which are free to diffuse between the atomistic region
and the coarse-grained reservoir. So far, the method has been successfully
applied to pure liquids. Coupling the H-AdResS methodology to hybrid models of
proteins, such as the Molecular Mechanics/Coarse-Grained (MM/CG) scheme, is a
promising approach for rigorous calculations of ligand binding free energies in
low-resolution protein models. Towards this goal, here we apply for the first
time H-AdResS to two atomistic proteins in dual-resolution solvent, proving its
ability to reproduce structural and dynamic properties of both the proteins and
the solvent, as obtained from atomistic simulations.Comment: This document is the Accepted Manuscript version of a Published Work
that appeared in final form in Journal of Chemical Theory and Computation,
copyright \c{opyright} American Chemical Society after peer review and
technical editing by the publishe
Thermal conduction in classical low-dimensional lattices
Deriving macroscopic phenomenological laws of irreversible thermodynamics
from simple microscopic models is one of the tasks of non-equilibrium
statistical mechanics. We consider stationary energy transport in crystals with
reference to simple mathematical models consisting of coupled oscillators on a
lattice. The role of lattice dimensionality on the breakdown of the Fourier's
law is discussed and some universal quantitative aspects are emphasized: the
divergence of the finite-size thermal conductivity is characterized by
universal laws in one and two dimensions. Equilibrium and non-equilibrium
molecular dynamics methods are presented along with a critical survey of
previous numerical results. Analytical results for the non-equilibrium dynamics
can be obtained in the harmonic chain where the role of disorder and
localization can be also understood. The traditional kinetic approach, based on
the Boltzmann-Peierls equation is also briefly sketched with reference to
one-dimensional chains. Simple toy models can be defined in which the
conductivity is finite. Anomalous transport in integrable nonlinear systems is
briefly discussed. Finally, possible future research themes are outlined.Comment: 90 pages, revised versio
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