223 research outputs found
Thermodynamically admissible form for discrete hydrodynamics
We construct a discrete model of fluid particles according to the GENERIC
formalism. The model has the form of Smoothed Particle Hydrodynamics including
correct thermal fluctuations. A slight variation of the model reproduces the
Dissipative Particle Dynamics model with any desired thermodynamic behavior.
The resulting algorithm has the following properties: mass, momentum and energy
are conserved, entropy is a non-decreasing function of time and the thermal
fluctuations produce the correct Einstein distribution function at equilibrium.Comment: 4 page
Static and Dynamic Properties of Dissipative Particle Dynamics
The algorithm for the DPD fluid, the dynamics of which is conceptually a
combination of molecular dynamics, Brownian dynamics and lattice gas automata,
is designed for simulating rheological properties of complex fluids on
hydrodynamic time scales. This paper calculates the equilibrium and transport
properties (viscosity, self-diffusion) of the thermostated DPD fluid explicitly
in terms of the system parameters. It is demonstrated that temperature
gradients cannot exist, and that there is therefore no heat conductivity.
Starting from the N-particle Fokker-Planck, or Kramers' equation, we prove an
H-theorem for the free energy, obtain hydrodynamic equations, and derive a
non-linear kinetic equation (the Fokker-Planck-Boltzmann equation) for the
single particle distribution function. This kinetic equation is solved by the
Chapman-Enskog method. The analytic results are compared with numerical
simulations.Comment: 22 pages, LaTeX, 3 Postscript figure
Dissipative Particle Dynamics with energy conservation
Dissipative particle dynamics (DPD) does not conserve energy and this
precludes its use in the study of thermal processes in complex fluids. We
present here a generalization of DPD that incorporates an internal energy and a
temperature variable for each particle. The dissipation induced by the
dissipative forces between particles is invested in raising the internal energy
of the particles. Thermal conduction occurs by means of (inverse) temperature
differences. The model can be viewed as a simplified solver of the fluctuating
hydrodynamic equations and opens up the possibility of studying thermal
processes in complex fluids with a mesoscopic simulation technique.Comment: 5 page
Spinodal decomposition of off-critical quenches with a viscous phase using dissipative particle dynamics in two and three spatial dimensions
We investigate the domain growth and phase separation of
hydrodynamically-correct binary immiscible fluids of differing viscosity as a
function of minority phase concentration in both two and three spatial
dimensions using dissipative particle dynamics. We also examine the behavior of
equal-viscosity fluids and compare our results to similar lattice-gas
simulations in two dimensions.Comment: 34 pages (11 figures); accepted for publication in Phys. Rev.
Computer simulations of domain growth and phase separation in two-dimensional binary immiscible fluids using dissipative particle dynamics
We investigate the dynamical behavior of binary fluid systems in two
dimensions using dissipative particle dynamics. We find that following a
symmetric quench the domain size R(t) grows with time t according to two
distinct algebraic laws R(t) = t^n: at early times n = 1/2, while for later
times n = 2/3. Following an asymmetric quench we observe only n = 1/2, and if
momentum conservation is violated we see n = 1/3 at early times. Bubble
simulations confirm the existence of a finite surface tension and the validity
of Laplace's law. Our results are compared with similar simulations which have
been performed previously using molecular dynamics, lattice-gas and
lattice-Boltzmann automata, and Langevin dynamics. We conclude that dissipative
particle dynamics is a promising method for simulating fluid properties in such
systems.Comment: RevTeX; 22 pages, 5 low-resolution figures. For full-resolution
figures, connect to http://www.tcm.phy.cam.ac.uk/~ken21/tension/tension.htm
Particle-Based Mesoscale Hydrodynamic Techniques
Dissipative particle dynamics (DPD) and multi-particle collision (MPC)
dynamics are powerful tools to study mesoscale hydrodynamic phenomena
accompanied by thermal fluctuations. To understand the advantages of these
types of mesoscale simulation techniques in more detail, we propose new two
methods, which are intermediate between DPD and MPC -- DPD with a multibody
thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are
applying a Langevin thermostat to the relative velocities of pairs of particles
or multi-particle collisions, and whether or not to employ collision cells. The
viscosity of MPC-LD is derived analytically, in very good agreement with the
results of numerical simulations.Comment: 7 pages, 2 figures, 1 tabl
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
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
A discretized integral hydrodynamics
Using an interpolant form for the gradient of a function of position, we
write an integral version of the conservation equations for a fluid. In the
appropriate limit, these become the usual conservation laws of mass, momentum
and energy. We also discuss the special cases of the Navier-Stokes equations
for viscous flow and the Fourier law for thermal conduction in the presence of
hydrodynamic fluctuations. By means of a discretization procedure, we show how
these equations can give rise to the so-called "particle dynamics" of Smoothed
Particle Hydrodynamics and Dissipative Particle Dynamics.Comment: 10 pages, RevTex, submitted to Phys. Rev.
A reduced model for shock and detonation waves. II. The reactive case
We present a mesoscopic model for reactive shock waves, which extends a
previous model proposed in [G. Stoltz, Europhys. Lett. 76 (2006), 849]. A
complex molecule (or a group of molecules) is replaced by a single
mesoparticle, evolving according to some Dissipative Particle Dynamics.
Chemical reactions can be handled in a mean way by considering an additional
variable per particle describing a rate of reaction. The evolution of this rate
is governed by the kinetics of a reversible exothermic reaction. Numerical
results give profiles in qualitative agreement with all-atom studies
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