210 research outputs found
Reply to: Comment on `Long-range electrostatic interactions between like-charged colloids: steric and confinement effects'
In his Comment (cond-mat/0104060) to [Phys. Rev. E 60, 6530 (1999)], Mateescu
shows that while the effective interactions remain repulsive when the specific
size of the micro-ions is taken into account via a Modified Poisson-Boltzmann
equation, a similar conclusion cannot be reached for the situation of complete
lateral confinement. This point is correct but has already been considered in a
more general study [Phys. Rev. E 62, R1465 (2000), where repulsion is
generically obtained]; moreover, we argue that it illustrates the irrelevancy
of the notion of pair potential in completely confined configurations, as shown
on a simple example
Kovacs-like memory effect in driven granular gases
While memory effects have been reported for dense enough disordered systems
such as glasses, we show here by a combination of analytical and simulation
techniques that they are also intrinsic to the dynamics of dilute granular
gases. By means of a certain driving protocol, we prepare the gas in a state
where the granular temperature coincides with its long time limit. However,
does not subsequently remain constant, but exhibits a non-monotonic
evolution before reaching its non-equilibrium steady value. The corresponding
so-called Kovacs hump displays a normal behavior for weak dissipation (as
observed in molecular systems), but is reversed under strong dissipation, where
it thus becomes anomalous.Comment: 5 pages, to appear in Physical Review Letter
Lack of energy equipartition in homogeneous heated binary granular mixtures
We consider the problem of determining the granular temperatures of the
components of a homogeneous binary heated mixture of inelastic hard spheres, in
the framework of Enskog kinetic theory. Equations are derived for the
temperatures of each species and their ratio, which is different from unity, as
may be expected since the system is out of equilibrium. We focus on the
particular heating mechanism where the inelastic energy loss is compensated by
an injection through a random external force (``stochastic thermostat''). The
influence of various parameters and their possible experimental relevance is
discussed.Comment: 8 pages, 9 eps figures, to be published in Granular Matte
Effective charge of cylindrical and spherical colloids immersed in an electrolyte: the quasi-planar limit
We consider the non-linear Poisson-Boltzmann theory for a single cylindrical
or spherical macro-ion in symmetric 1:1, together with asymmetric 1:2 and 2:1
electrolytes. We focus on the regime where , the ratio of the
macro-ion radius over the inverse Debye length in the bulk electrolyte, is
large. Analyzing the structure of the analytical expansion emerging from a
multiple scale analysis, we uncover a hidden structure for the electrostatic
potential. This structure, which appears after a heuristic resummation,
suggests a new and convenient expansion scheme that we present and work out in
detail. We show that novel exact results can thereby be obtained, in particular
pertaining to effective charge properties, in complete agreement with the
direct numerical solution to the problem
Free cooling and inelastic collapse of granular gases in high dimensions
The connection between granular gases and sticky gases has recently been
considered, leading to the conjecture that inelastic collapse is avoided for
space dimensions higher than 4. We report Molecular Dynamics simulations of
hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular
medium is monitored throughout the cooling process. The behaviour is found to
be very similar to that of a two-dimensional system, with a shearing-like
instability of the velocity field and inelastic collapse when collisions are
inelastic enough, showing that the connection with sticky gases needs to be
revised.Comment: 6 pages, 6 figures (7 postscript files), submitted to EPJ
Poisson-Boltzmann thermodynamics of counter-ions confined by curved hard walls
We consider a set of identical mobile point-like charges (counter-ions)
confined to a domain with curved hard walls carrying a uniform fixed surface
charge density, the system as a whole being electroneutral. Three domain
geometries are considered: a pair of parallel plates, the cylinder and the
sphere. The particle system in thermal equilibrium is assumed to be described
by the nonlinear Poisson-Boltzmann theory. While the effectively 1D plates and
the 2D cylinder have already been solved, the 3D sphere problem is not
integrable. It is shown that the contact density of particles at the charged
surface is determined by a first-order Abel differential equation of the second
kind which is a counterpart of Enig's equation in the critical theory of
gravitation and combustion/explosion. This equation enables us to construct the
exact series solutions of the contact density in the regions of small and large
surface charge densities. The formalism provides, within the mean-field
Poisson-Boltzmann framework, the complete thermodynamics of counter-ions inside
a charged sphere (salt-free system)
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