1,169 research outputs found
Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules
Detailed calculations of the transport coefficients of a recently introduced
particle-based model for fluid dynamics with a non-ideal equation of state are
presented. Excluded volume interactions are modeled by means of biased
stochastic multiparticle collisions which depend on the local velocities and
densities. Momentum and energy are exactly conserved locally. A general scheme
to derive transport coefficients for such biased, velocity dependent collision
rules is developed. Analytic expressions for the self-diffusion coefficient and
the shear viscosity are obtained, and very good agreement is found with
numerical results at small and large mean free paths. The viscosity turns out
to be proportional to the square root of temperature, as in a real gas. In
addition, the theoretical framework is applied to a two-component version of
the model, and expressions for the viscosity and the difference in diffusion of
the two species are given.Comment: 31 pages, 8 figures, accepted by J. Phys. Cond. Matte
Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures
A recently introduced particle-based model for fluid dynamics with continuous
velocities is generalized to model immiscible binary mixtures. Excluded volume
interactions between the two components are modeled by stochastic multiparticle
collisions which depend on the local velocities and densities. Momentum and
energy are conserved locally, and entropically driven phase separation occurs
for high collision rates. An explicit expression for the equation of state is
derived, and the concentration dependence of the bulk free energy is shown to
be the same as that of the Widom-Rowlinson model. Analytic results for the
phase diagram are in excellent agreement with simulation data. Results for the
line tension obtained from the analysis of the capillary wave spectrum of a
droplet agree with measurements based on the Laplace's equation. The
introduction of "amphiphilic" dimers makes it possible to model the phase
behavior and dynamics of ternary surfactant mixtures.Comment: 7 pages including 6 figure
Resummed Green-Kubo relations for a fluctuating fluid-particle model
A recently introduced stochastic model for fluid flow can be made Galilean
invariant by introducing a random shift of the computational grid before
collisions. This grid shifting procedure accelerates momentum transfer between
cells and leads to a collisional contribution to transport coefficients. By
resumming the Green-Kubo relations derived in a previous paper, it is shown
that this collisional contribution to the transport coefficients can be
determined exactly. The resummed Green-Kubo relations also show that there are
no mixed kinetic-collisional contributions to the transport coefficients. The
leading correlation corrections to the transport coefficients are discussed,
and explicit expressions for the transport coefficients are presented and
compared with simulation data.Comment: 4 pages including 4 figures, submitted to PRE Rapid Com
Comment on ``Solidification of a Supercooled Liquid in a Narrow Channel''
Comment on PRL v. 86, p. 5084 (2001) [cond-mat/0101016]. We point out that
the authors' simulations are consistent with the known theory of steady-state
solutions in this system
Characteristic Functions for Cosmological Cross-Correlations
We introduce a novel unbiased, cross-correlation estimator for the one-point
statistics of cosmological random fields. One-point statistics are a useful
tool for analysis of highly non-Gaussian density fields, while
cross-correlations provide a powerful method for combining information from
pairs of fields and separating them from noise and systematics. We derive a new
Deconvolved Distribution Estimator that combines the useful properties of these
two methods into one statistic. Using two example models of a toy Gaussian
random field and a line intensity mapping survey, we demonstrate these
properties quantitatively and show that the DDE can be used for inference. This
new estimator can be applied to any pair of overlapping, non-Gaussian
cosmological observations, including large-scale structure, the
Sunyaev-Zeldovich effect, weak lensing, and many others.Comment: 13 pages, 13 figures, for submission to MNRA
Consistent particle-based algorithm with a non-ideal equation of state
A thermodynamically consistent particle-based model for fluid dynamics with
continuous velocities and a non-ideal equation of state is presented. Excluded
volume interactions are modeled by means of biased stochastic multiparticle
collisions which depend on the local velocities and densities. Momentum and
energy are exactly conserved locally. The equation of state is derived and
compared to independent measurements of the pressure. Results for the kinematic
shear viscosity and self-diffusion constants are presented. A caging and
order/disorder transition is observed at high densities and large collision
frequency.Comment: 7 pages including 4 figure
Multi-particle-collision dynamics: Flow around a circular and a square cylinder
A particle-based model for mesoscopic fluid dynamics is used to simulate
steady and unsteady flows around a circular and a square cylinder in a
two-dimensional channel for a range of Reynolds number between 10 and 130.
Numerical results for the recirculation length, the drag coefficient, and the
Strouhal number are reported and compared with previous experimental
measurements and computational fluid dynamics data. The good agreement
demonstrates the potential of this method for the investigation of complex
flows.Comment: 6 pages, separated figures in .jpg format, to be published in
Europhysics Letter
Quasiperiodic Tip Splitting in Directional Solidification
We report experimental results on the tip splitting dynamics of seaweed
growth in directional solidification of succinonitrile alloys with
poly(ethylene oxide) or acetone as solutes. The seaweed or dense branching
morphology was selected by solidifying grains which are oriented close to the
{111} plane. Despite the random appearance of the growth, a quasiperiodic tip
splitting morphology was observed in which the tip alternately splits to the
left and to the right. The tip splitting frequency f was found to be related to
the growth velocity V as a power law f V^{1.5}. This finding
is consistent with the predictions of a tip splitting model that is also
presented. Small anisotropies are shown to lead to different kinds of seaweed
morphologies.Comment: 4 pages, 7 figures, submitted to Physical Review Letter
Dynamic correlations in stochastic rotation dynamics
The dynamic structure factor, vorticity and entropy density dynamic
correlation functions are measured for Stochastic Rotation Dynamics (SRD), a
particle based algorithm for fluctuating fluids. This allows us to obtain
unbiased values for the longitudinal transport coefficients such as thermal
diffusivity and bulk viscosity. The results are in good agreement with earlier
numerical and theoretical results, and it is shown for the first time that the
bulk viscosity is indeed zero for this algorithm. In addition, corrections to
the self-diffusion coefficient and shear viscosity arising from the breakdown
of the molecular chaos approximation at small mean free paths are analyzed. In
addition to deriving the form of the leading correlation corrections to these
transport coefficients, the probabilities that two and three particles remain
collision partners for consecutive time steps are derived analytically in the
limit of small mean free path. The results of this paper verify that we have an
excellent understanding of the SRD algorithm at the kinetic level and that
analytic expressions for the transport coefficients derived elsewhere do indeed
provide a very accurate description of the SRD fluid.Comment: 33 pages including 16 figure
Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth
We propose a mean-field model for describing the averaged properties of a
class of stochastic diffusion-limited growth systems. We then show that this
model exhibits a morphology transition from a dense-branching structure with a
convex envelope to a dendritic one with an overall concave morphology. We have
also constructed an order parameter which describes the transition
quantitatively. The transition is shown to be continuous, which can be verified
by noting the non-existence of any hysteresis.Comment: 16 pages, 5 figure
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