122 research outputs found
Aging and response properties in the parking-lot model
An adsorption-desorption (or parking-lot) model can reproduce qualitatively
the densification kinetics and other features of a weakly vibrated granular
material. Here we study the the two-time correlation and response functions of
the model and demonstrate that their behavior is consistent with recently
observed memory effects in granular materials. Although the densification
kinetics and hysteresis are robust properties, we show that the aging behavior
of the adsorption-desorption model is different from other models of granular
compaction. We propose an experimental test to distinguish the possible aging
behaviors.Comment: 9 pages, 7 figures, to appear in Eur. Phys. Jour.
Optimizing the Throughput of Particulate Streams Subject to Blocking
Filtration, flow in narrow channels and traffic flow are examples of
processes subject to blocking when the channel conveying the particles becomes
too crowded. If the blockage is temporary, which means that after a finite time
the channel is flushed and reopened, one expects to observe a maximum
throughput for a finite intensity of entering particles. We investigate this
phenomenon by introducing a queueing theory inspired, circular Markov model.
Particles enter a channel with intensity and exit at a rate . If
particles are present at the same time in the channel, the system becomes
blocked and no more particles can enter until the blockage is cleared after an
exponentially distributed time with rate . We obtain an exact expression
for the steady state throughput (including the exiting blocked particles) for
all values of . For we show that the throughput assumes a maximum
value for finite if . The time-dependent throughput
either monotonically approaches the steady state value, or reaches a maximum
value at finite time. We demonstrate that, in the steady state, this model can
be mapped to a previously introduced non-Markovian model with fixed transit and
blockage times.
We also examine an irreversible, non-Markovian blockage process with constant
transit time exposed to an entering flux of fixed intensity for a finite time
and we show that the first and second moments of the number of exiting
particles are maximized for a finite intensity.Comment: 20 pages, 13 figure
From Car Parking to Protein Adsorption: An Overview of Sequential Adsorption Processes
The adsorption or adhesion of large particles (proteins, colloids, cells,
>...) at the liquid-solid interface plays an important role in many diverse
applications. Despite the apparent complexity of the process, two features are
particularly important: 1) the adsorption is often irreversible on experimental
time scales and 2) the adsorption rate is limited by geometric blockage from
previously adsorbed particles. A coarse-grained description that encompasses
these two properties is provided by sequential adsorption models whose simplest
example is the random sequential adsorption (RSA) process. In this article, we
review the theoretical formalism and tools that allow the systematic study of
kinetic and structural aspects of these sequential adsorption models. We also
show how the reference RSA model may be generalized to account for a variety of
experimental features including particle anisotropy, polydispersity, bulk
diffusive transport, gravitational effects, surface-induced conformational and
orientational change, desorption, and multilayer formation. In all cases, the
significant theoretical results are presented and their accuracy (compared to
computer simulation) and applicability (compared to experiment) are discussed.Comment: 51 pages, 18 Figures, to appear in a special volume entitled
"Adhesion of Submicron Particles on Solid Surfaces" of Colloids and Surfaces
A, guest-edited by V. Privman.to appear in a special volume entitle
Microphase Separation and modulated phases in a Coulomb frustrated Ising ferromagnet
We study a 3-dimensional Ising model in which the tendency to order due to
short-range ferromagnetic interactions is frustrated by competing long-range
(Coulombic) interactions. Complete ferromagnetic ordering is impossible for any
nonzero value of the frustration parameter, but the system displays a variety
of phases characterized by periodically modulated structures. We have performed
extensive Monte-Carlo simulations which provide strong evidence that the
microphase separation transition between paramagnetic and modulated phases is a
fluctuation-induced first-order transition. Additional transitions to various
commensurate phases may also occur when further lowering the temperature.Comment: 6 pages, 4 figures, accepted in Europhys. Letter
The viscous slowing down of supercooled liquids as a temperature-controlled superArrhenius activated process: a description in terms of frustration-limited domains
We propose that the salient feature to be explained about the glass
transition of supercooled liquids is the temperature-controlled superArrhenius
activated nature of the viscous slowing down, more strikingly seen in
weakly-bonded, fragile systems. In the light of this observation, the relevance
of simple models of spherically interacting particles and that of models based
on free-volume congested dynamics are questioned. Finally, we discuss how the
main aspects of the phenomenology of supercooled liquids, including the
crossover from Arrhenius to superArrhenius activated behavior and the
heterogeneous character of the relaxation, can be described by an
approach based on frustration-limited domains.Comment: 13 pages, 4 figures, accepted in J. Phys.: Condensed Matter,
proceedings of the Trieste workshop on "Unifying Concepts in Glass Physics
Angular velocity distribution of a granular planar rotator in a thermalized bath
The kinetics of a granular planar rotator with a fixed center undergoing
inelastic collisions with bath particles is analyzed both numerically and
analytically by means of the Boltzmann equation. The angular velocity
distribution evolves from quasi-gaussian in the Brownian limit to an algebraic
decay in the limit of an infinitely light particle. In addition, we compare
this model with a planar rotator with a free center. We propose experimental
tests that might confirm the predicted behaviors.Comment: 10 Pages, 9 Figure
Application of the Gillespie algorithm to a granular intruder particle
We show how the Gillespie algorithm, originally developed to describe coupled
chemical reactions, can be used to perform numerical simulations of a granular
intruder particle colliding with thermalized bath particles. The algorithm
generates a sequence of collision ``events'' separated by variable time
intervals. As input, it requires the position-dependent flux of bath particles
at each point on the surface of the intruder particle. We validate the method
by applying it to a one-dimensional system for which the exact solution of the
homogeneous Boltzmann equation is known and investigate the case where the bath
particle velocity distribution has algebraic tails. We also present an
application to a granular needle in bath of point particles where we
demonstrate the presence of correlations between the translational and
rotational degrees of freedom of the intruder particle. The relationship
between the Gillespie algorithm and the commonly used Direct Simulation Monte
Carlo (DSMC) method is also discussed.Comment: 13 pages, 8 figures, to be published in J. Phys. A Math. Ge
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