293 research outputs found
Shear-induced quench of long-range correlations in a liquid mixture
A static correlation function of concentration fluctuations in a (dilute)
binary liquid mixture subjected to both a concentration gradient and uniform
shear flow is investigated within the framework of fluctuating hydrodynamics.
It is shown that a well-known long-range correlation at
large wave numbers crosses over to a weaker divergent one for wave numbers
satisfying , while an asymptotic shear-controlled
power-law dependence is confirmed at much smaller wave numbers given by , where , , and are the
mass concentration, the rate of the shear, the mass diffusivity and the
kinematic viscosity of the mixture, respectively. The result will provide for
the first time the possibility to observe the shear-induced suppression of a
long-range correlation experimentally by using, for example, a low-angle light
scattering technique.Comment: 8pages, 2figure
A Molecular Hydrodynamic Theory of Supercooled Liquids and Colloidal Suspensions under Shear
We extend the conventional mode-coupling theory of supercooled liquids to
systems under stationary shear flow. Starting from generalized fluctuating
hydrodynamics, a nonlinear equation for the intermediate scattering function is
constructed. We evaluate the solution numerically for a model of a two
dimensional colloidal suspension and find that the structural relaxation time
decreases as with an exponent , where
is the shear rate. The results are in qualitative agreement with
recent molecular dynamics simulations. We discuss the physical implications of
the results.Comment: 5 pages, 1 figur
Long-range correlations in non-equilibrium systems: Lattice gas automaton approach
In systems removed from equilibrium, intrinsic microscopic fluctuations
become correlated over distances comparable to the characteristic macroscopic
length over which the external constraint is exerted. In order to investigate
this phenomenon, we construct a microscopic model with simple stochastic
dynamics using lattice gas automaton rules that satisfy local detailed balance.
Because of the simplicity of the automaton dynamics, analytical theory can be
developed to describe the space and time evolution of the density fluctuations.
The exact equations for the pair correlations are solved explicitly in the
hydrodynamic limit. In this limit, we rigorously derive the results obtained
phenomenologically by fluctuating hydrodynamics. In particular, the spatial
algebraic decay of the equal-time fluctuation correlations predicted by this
theory is found to be in excellent agreement with the results of our lattice
gas automaton simulations for two different types of boundary conditions.
Long-range correlations of the type described here appear generically in
dynamical systems that exhibit large scale anisotropy and lack detailed
balance.Comment: 23 pages, RevTeX; to appear in Phys. Rev.
Multiple-Point and Multiple-Time Correlations Functions in a Hard-Sphere Fluid
A recent mode coupling theory of higher-order correlation functions is tested
on a simple hard-sphere fluid system at intermediate densities. Multi-point and
multi-time correlation functions of the densities of conserved variables are
calculated in the hydrodynamic limit and compared to results obtained from
event-based molecular dynamics simulations. It is demonstrated that the mode
coupling theory results are in excellent agreement with the simulation results
provided that dissipative couplings are included in the vertices appearing in
the theory. In contrast, simplified mode coupling theories in which the
densities obey Gaussian statistics neglect important contributions to both the
multi-point and multi-time correlation functions on all time scales.Comment: Second one in a sequence of two (in the first, the formalism was
developed). 12 pages REVTeX. 5 figures (eps). Submitted to Phys.Rev.
Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime
The Landau-Lifshitz fluctuating hydrodynamics is used to study the
statistical properties of the linearized Kolmogorov flow. The relative
simplicity of this flow allows a detailed analysis of the fluctuation spectrum
from near equilibrium regime up to the vicinity of the first convective
instability threshold. It is shown that in the long time limit the flow behaves
as an incompressible fluid, regardless of the value of the Reynolds number.
This is not the case for the short time behavior where the incompressibility
assumption leads in general to a wrong form of the static correlation
functions, except near the instability threshold. The theoretical predictions
are confirmed by numerical simulations of the full nonlinear fluctuating
hydrodynamic equations.Comment: 20 pages, 4 figure
Stability of scaling regimes in developed turbulence with weak anisotropy
The fully developed turbulence with weak anisotropy is investigated by means
of renormalization group approach (RG) and double expansion regularization for
dimensions . Some modification of the standard minimal substraction
scheme has been used to analyze stability of the Kolmogorov scaling regime
which is governed by the renormalization group fixed point. This fixed point is
unstable at ; thus, the infinitesimally weak anisotropy destroyes above
scaling regime in two-dimensional space. The restoration of the stability of
this fixed point, under transition from to has been demonstrated
at borderline dimension . The results are in qualitative agreement
with ones obtained recently in the framework of the usual analytical
regularization scheme.Comment: 23 pages, 2 figure
Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection
We present a systematic way to compute the scaling exponents of the structure
functions of the Kraichnan model of turbulent advection in a series of powers
of , adimensional coupling constant measuring the degree of roughness of
the advecting velocity field. We also investigate the relation between standard
and renormalization group improved perturbation theory. The aim is to shed
light on the relation between renormalization group methods and the statistical
conservation laws of the Kraichnan model, also known as zero modes.Comment: Latex (11pt) 43 pages, 22 figures (Feynman diagrams). The reader
interested in the technical details of the calculations presented in the
paper may want to visit:
http://www.math.helsinki.fi/mathphys/paolo_files/passive_scalar/passcal.htm
A model for the atomic-scale structure of a dense, nonequilibrium fluid: the homogeneous cooling state of granular fluids
It is shown that the equilibrium Generalized Mean Spherical Model of fluid
structure may be extended to nonequilibrium states with equation of state
information used in equilibrium replaced by an exact condition on the two-body
distribution function. The model is applied to the homogeneous cooling state of
granular fluids and upon comparison to molecular dynamics simulations is found
to provide an accurate picture of the pair distribution function.Comment: 29 pages, 11 figures Revision corrects formatting of the figure
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