56 research outputs found
Granular Collapse as a Percolation Transition
Inelastic collapse is found in a two-dimensional system of inelastic hard
disks confined between two walls which act as an energy source. As the
coefficient of restitution is lowered, there is a transition between a state
containing small collapsed clusters and a state dominated by a large collapsed
cluster. The transition is analogous to that of a percolation transition. At
the transition the number of clusters n_s of size s scales as with .Comment: 10 pages revtex, 5 figures, accepted by Phys Rev E many changes and
corrections from previous submissio
Effective Interactions and Volume Energies in Charge-Stabilized Colloidal Suspensions
Charge-stabilized colloidal suspensions can be conveniently described by
formally reducing the macroion-microion mixture to an equivalent one-component
system of pseudo-particles. Within this scheme, the utility of a linear
response approximation for deriving effective interparticle interactions has
been demonstrated [M. J. Grimson and M. Silbert, Mol. Phys. 74, 397 (1991)].
Here the response approach is extended to suspensions of finite-sized macroions
and used to derive explicit expressions for (1) an effective electrostatic pair
interaction between pseudo-macroions and (2) an associated volume energy that
contributes to the total free energy. The derivation recovers precisely the
form of the DLVO screened-Coulomb effective pair interaction for spherical
macroions and makes manifest the important influence of the volume energy on
thermodynamic properties of deionized suspensions. Excluded volume corrections
are implicitly incorporated through a natural modification of the inverse
screening length. By including nonlinear response of counterions to macroions,
the theory may be generalized to systematically investigate effective many-body
interactions.Comment: 13 pages (J. Phys.: Condensed Matter, in press
A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
We study a symmetry property of momentum distribution functions in the steady
state of heat conduction. When the equation of motion is symmetric under change
of signs for all dynamical variables, the distribution function is also
symmetric. This symmetry can be broken by introduction of an asymmetric term in
the interaction potential or the on-site potential, or employing the thermal
walls as heat reservoirs. We numerically find differences of behavior of the
models with and without the on-site potential.Comment: 13 pages. submitted to JPS
Phase Changes in an Inelastic Hard Disk System with a Heat Bath under Weak Gravity for Granular Fluidization
We performed numerical simulations on a two-dimensional inelastic hard disk
system under gravity with a heat bath to study the dynamics of granular
fluidization. Upon increasing the temperature of the heat bath, we found that
three phases, namely, the condensed phase, locally fluidized phase, and
granular turbulent phase, can be distinguished using the maximum packing
fraction and the excitation ratio, or the ratio of the kinetic energy to the
potential energy.It is shown that the system behavior in each phase is very
different from that of an ordinary vibrating bed.Comment: 4 pages, including 5 figure
Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory
Interparticle interactions in charge-stabilized colloidal suspensions, of
arbitrary salt concentration, are described at the level of effective
interactions in an equivalent one-component system. Integrating out from the
partition function the degrees of freedom of all microions, and assuming linear
response to the macroion charges, general expressions are obtained for both an
effective electrostatic pair interaction and an associated microion volume
energy. For macroions with hard-sphere cores, the effective interaction is of
the DLVO screened-Coulomb form, but with a modified screening constant that
incorporates excluded volume effects. The volume energy -- a natural
consequence of the one-component reduction -- contributes to the total free
energy and can significantly influence thermodynamic properties in the limit of
low-salt concentration. As illustrations, the osmotic pressure and bulk modulus
are computed and compared with recent experimental measurements for deionized
suspensions. For macroions of sufficient charge and concentration, it is shown
that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure
Phase behaviour of a model of colloidal particles with a fluctuating internal state
Colloidal particles are not simple rigid particles, in general an isolated
particle is a system with many degrees of freedom in its own right, e.g., the
counterions around a charged colloidal particle.The behaviour of model
colloidal particles, with a simple phenomenological model to account for these
degrees of freedom, is studied. It is found that the interaction between the
particles is not pairwise additive. It is even possible that the interaction
between a triplet of particles is attractive while the pair interaction is
repulsive. When this is so the liquid phase is either stable only in a small
region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure
Capturing the essence of folding and functions of biomolecules using Coarse-Grained Models
The distances over which biological molecules and their complexes can
function range from a few nanometres, in the case of folded structures, to
millimetres, for example during chromosome organization. Describing phenomena
that cover such diverse length, and also time scales, requires models that
capture the underlying physics for the particular length scale of interest.
Theoretical ideas, in particular, concepts from polymer physics, have guided
the development of coarse-grained models to study folding of DNA, RNA, and
proteins. More recently, such models and their variants have been applied to
the functions of biological nanomachines. Simulations using coarse-grained
models are now poised to address a wide range of problems in biology.Comment: 37 pages, 8 figure
Segregation and Phase Inversion in a Simple Granular System
The segregation and the phase inversion are investigated through a simple
granular system which consists of only two inelastic hard spheres in a square
box with an energy source. With the variation of the coefficient of
restitution, the mass ratio between two spheres or the box size, we show that
two types of segregated states and crossover between them are realized in such
a small simple system.Comment: 7 pages, 3 figure
Nonequilibrium Molecular Dynamics Simulation of Interacting Many Electrons Scattered by Lattice Vibrations
We propose a new model suitable for a nonequilibrium molecular dynamics (MD)
simulation of electrical conductors. The model consists of classical electrons
and atoms. The atoms compose a lattice vibration system. The electrons are
scattered by electron-electron and electron-atom interactions. Since the
scattering cross section is physically more important than the functional form
of a scattering potential, we propose to devise the electron-atom interaction
potential in such a way that its scattering cross section agrees with that of
quantum-mechanical one. To demonstrate advantages of the proposed model, we
perform a nonequilibrium MD simulation assuming a doped semiconductor at room
or higher temperature. In the linear response regime, we confirm Ohm's law, the
dispersion relations and the fluctuation-dissipation relation. Furthermore, we
obtain reasonable dependence of the electrical conductivity on temperature,
despite the fact that our model is a classical model.Comment: 21 pages, 11 figure
Non-Newtonian Couette-Poiseuille flow of a dilute gas
The steady state of a dilute gas enclosed between two infinite parallel
plates in relative motion and under the action of a uniform body force parallel
to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation
is analytically solved for this Couette-Poiseuille flow to first order in the
force and for arbitrary values of the Knudsen number associated with the shear
rate. This allows us to investigate the influence of the external force on the
non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille
flow is analyzed when the shear-rate Knudsen number and the scaled force are of
the same order and terms up to second order are retained. In this way, the
transition from the bimodal temperature profile characteristic of the pure
force-driven Poiseuille flow to the parabolic profile characteristic of the
pure Couette flow through several intermediate stages in the Couette-Poiseuille
flow are described. A critical comparison with the Navier-Stokes solution of
the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10
additional references. Published in a special issue of the journal "Kinetic
and Related Models" dedicated to the memory of Carlo Cercignan
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