78 research outputs found
Third and fourth degree collisional moments for inelastic Maxwell models
The third and fourth degree collisional moments for -dimensional inelastic
Maxwell models are exactly evaluated in terms of the velocity moments, with
explicit expressions for the associated eigenvalues and cross coefficients as
functions of the coefficient of normal restitution. The results are applied to
the analysis of the time evolution of the moments (scaled with the thermal
speed) in the free cooling problem. It is observed that the characteristic
relaxation time toward the homogeneous cooling state decreases as the
anisotropy of the corresponding moment increases. In particular, in contrast to
what happens in the one-dimensional case, all the anisotropic moments of degree
equal to or less than four vanish in the homogeneous cooling state for .Comment: 15 pages, 3 figures; v2: addition of two new reference
Hydrodynamics of driven granular gases
Hydrodynamic equations for granular gases driven by the Fokker-Planck
operator are derived. Transport coefficients appeared in Navier-Stokes order
change from the values of a free cooling state to those of a steady state.Comment: 5 pages, 3 figure
Polydisperse Adsorption: Pattern Formation Kinetics, Fractal Properties, and Transition to Order
We investigate the process of random sequential adsorption of polydisperse
particles whose size distribution exhibits a power-law dependence in the small
size limit, . We reveal a relation between pattern
formation kinetics and structural properties of arising patterns. We propose a
mean-field theory which provides a fair description for sufficiently small
. When , highly ordered structures locally identical
to the Apollonian packing are formed. We introduce a quantitative criterion of
the regularity of the pattern formation process. When , a sharp
transition from irregular to regular pattern formation regime is found to occur
near the jamming coverage of standard random sequential adsorption with
monodisperse size distribution.Comment: 8 pages, LaTeX, 5 figures, to appear in Phys.Rev.
Atomistic mechanism of friction force independence on the normal load and other friction laws for dynamic structural superlubricity
We explore dynamic structural superlubricity for the case of a relatively
large contact area, where the friction force is proportional to the area
(exceeding ) experimentally, numerically, and theoretically. We
use a setup comprised of two molecular smooth incommensurate surfaces --
graphene-covered tip and substrate. The experiments and MD simulations
demonstrate independence of the friction force on the normal load, for a wide
range of normal loads and relative surface velocities. We propose an atomistic
mechanism of this phenomenon, associated with synchronic out-of-plane surface
fluctuations of thermal origin, and confirm it by numerical experiments. Based
on this mechanism, we develop a theory for this type of superlubricity and show
that friction force increases linearly with increasing temperature and relative
velocity, for velocities, larger than a threshold velocity. The MD results are
in a fair agreement with predictions of the theory.Comment: Accepted to Physical Review Letters on November 14, 202
Generalized Smoluchowski equation with correlation between clusters
In this paper we compute new reaction rates of the Smoluchowski equation
which takes into account correlations. The new rate K = KMF + KC is the sum of
two terms. The first term is the known Smoluchowski rate with the mean-field
approximation. The second takes into account a correlation between clusters.
For this purpose we introduce the average path of a cluster. We relate the
length of this path to the reaction rate of the Smoluchowski equation. We solve
the implicit dependence between the average path and the density of clusters.
We show that this correlation length is the same for all clusters. Our result
depends strongly on the spatial dimension d. The mean-field term KMFi,j = (Di +
Dj)(rj + ri)d-2, which vanishes for d = 1 and is valid up to logarithmic
correction for d = 2, is the usual rate found with the Smoluchowski model
without correlation (where ri is the radius and Di is the diffusion constant of
the cluster). We compute a new rate: the correlation rate K_{i,j}^{C}
(D_i+D_j)(r_j+r_i)^{d-1}M{\big(\frac{d-1}{d_f}}\big) is valid for d \leq
1(where M(\alpha) = \sum+\infty i=1i\alphaNi is the moment of the density of
clusters and df is the fractal dimension of the cluster). The result is valid
for a large class of diffusion processes and mass radius relations. This
approach confirms some analytical solutions in d 1 found with other methods. We
also show Monte Carlo simulations which illustrate some exact new solvable
models
Coefficient of normal restitution of viscous particles and cooling rate of granular gases
We investigate the cooling rate of a gas of inelastically interacting
particles. When we assume velocity dependent coefficients of restitution the
material cools down slower than with constant restitution. This behavior might
have large influence to clustering and structure formation processes.Comment: 3 figures, Phys. Rev. E (in press
Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic
hard spheres can be identified, and calculated in the long wavelength limit.
Assuming they dominate at long times, formal expressions for the Navier-Stokes
transport coefficients are derived. They can be expressed in a form that
generalizes the Green-Kubo relations for molecular systems, and it is shown
that they can also be evaluated by means of -particle simulation methods.
The form of the hydrodynamic modes to zeroth order in the gradients is used to
detect the presence of inherent velocity correlations in the homogeneous
cooling state, even in the low density limit. They manifest themselves in the
fluctuations of the total energy of the system. The theoretical predictions are
shown to be in agreement with molecular dynamics simulations. Relevant related
questions deserving further attention are pointed out
Scaling of Transport Coefficients of Porous Media under Compaction
Porous sediments in geological systems are exposed to stress by the
above-laying mass and consequent compaction, which may be significantly
nonuniform across the massif. We derive scaling laws for the compaction of
sediments of similar geological origin. With these laws, we evaluate the
dependence of the transport properties of a fluid-saturated porous medium
(permeability, effective molecular diffusivity, hydrodynamic dispersion,
electrical and thermal conductivities) on its porosity. In particular, we
demonstrate that the assumption of a uniform geothermal gradient is not
adequate for systems with nonuniform compaction and show the importance of the
derived scaling laws for mathematical modelling of methane hydrate deposits;
these deposits are believed to have potential for impact on global climate
change and Glacial-Interglacial cycles.Comment: 6 pages, 2 figure
Fractal dimension and degree of order in sequential deposition of mixture
We present a number models describing the sequential deposition of a mixture
of particles whose size distribution is determined by the power-law , . We explicitly obtain the scaling function in
the case of random sequential adsorption (RSA) and show that the pattern
created in the long time limit becomes scale invariant. This pattern can be
described by an unique exponent, the fractal dimension. In addition, we
introduce an external tuning parameter beta to describe the correlated
sequential deposition of a mixture of particles where the degree of correlation
is determined by beta, while beta=0 corresponds to random sequential deposition
of mixture. We show that the fractal dimension of the resulting pattern
increases as beta increases and reaches a constant non-zero value in the limit
when the pattern becomes perfectly ordered or non-random
fractals.Comment: 16 pages Latex, Submitted to Phys. Rev.
Cooling dynamics of a dilute gas of inelastic rods: a many particle simulation
We present results of simulations for a dilute gas of inelastically colliding
particles. Collisions are modelled as a stochastic process, which on average
decreases the translational energy (cooling), but allows for fluctuations in
the transfer of energy to internal vibrations. We show that these fluctuations
are strong enough to suppress inelastic collapse. This allows us to study large
systems for long times in the truely inelastic regime. During the cooling stage
we observe complex cluster dynamics, as large clusters of particles form,
collide and merge or dissolve. Typical clusters are found to survive long
enough to establish local equilibrium within a cluster, but not among different
clusters. We extend the model to include net dissipation of energy by damping
of the internal vibrations. Inelatic collapse is avoided also in this case but
in contrast to the conservative system the translational energy decays
according to the mean field scaling law, E(t)\propto t^{-2}, for asymptotically
long times.Comment: 10 pages, 12 figures, Latex; extended discussion, accepted for
publication in Phys. Rev.
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