1,259 research outputs found
Pathologies in the sticky limit of hard-sphere-Yukawa models for colloidal fluids. A possible correction
A known `sticky-hard-sphere' model, defined starting from a
hard-sphere-Yukawa potential and taking the limit of infinite amplitude and
vanishing range with their product remaining constant, is shown to be
ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an
{\it exact}second virial coefficient which {\it diverges}, unlike that of
Baxter's original model (SHS1). This deficiency has never been observed so far,
since the linearization implicit in the `mean spherical approximation' (MSA),
within which the model is analytically solvable, partly {\it masks} such a
pathology. To overcome this drawback and retain some useful features of SHS2,
we propose both a new model (SHS3) and a new closure (`modified MSA'), whose
combination yields an analytic solution formally identical with the SHS2-MSA
one. This mapping allows to recover many results derived from SHS2, after a
re-interpretation within a correct framework. Possible developments are finally
indicated.Comment: 21 pages, 1 figure, accepted in Molecular Physics (2003
A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
The one-dimensional penetrable-square-well fluid is studied using both
analytical tools and specialized Monte Carlo simulations. The model consists of
a penetrable core characterized by a finite repulsive energy combined with a
short-range attractive well. This is a many-body one-dimensional problem,
lacking an exact analytical solution, for which the usual van Hove theorem on
the absence of phase transition does not apply. We determine a
high-penetrability approximation complementing a similar low-penetrability
approximation presented in previous work. This is shown to be equivalent to the
usual Debye-H\"{u}ckel theory for simple charged fluids for which the virial
and energy routes are identical. The internal thermodynamic consistency with
the compressibility route and the validity of the approximation in describing
the radial distribution function is assessed by a comparison against numerical
simulations. The Fisher-Widom line separating the oscillatory and monotonic
large-distance behavior of the radial distribution function is computed within
the high-penetrability approximation and compared with the opposite regime,
thus providing a strong indication of the location of the line in all possible
regimes. The high-penetrability approximation predicts the existence of a
critical point and a spinodal line, but this occurs outside the applicability
domain of the theory. We investigate the possibility of a fluid-fluid
transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence
of such a transition. Additional analytical arguments are given to support this
claim. Finally, we find a clustering transition when Ruelle's stability
criterion is not fulfilled. The consequences of these findings on the
three-dimensional phase diagrams are also discussed.Comment: 17 pages, 12 figures; to be published in JC
Exact clesed form of the return probability on the Bethe lattice
An exact closed form solution for the return probability of a random walk on
the Bethe lattice is given. The long-time asymptotic form confirms a previously
known expression. It is however shown that this exact result reduces to the
proper expression when the Bethe lattice degenerates on a line, unlike the
asymptotic result which is singular. This is shown to be an artefact of the
asymptotic expansion. The density of states is also calculated.Comment: 7 pages, RevTex 3.0, 2 figures available upon request from
[email protected], to be published in J.Phys.A Let
Thermodynamic consistency of energy and virial routes: An exact proof within the linearized Debye-H\"uckel theory
The linearized Debye-H\"uckel theory for liquid state is shown to provide
thermodynamically consistent virial and energy routes for any potential and for
any dimensionality. The importance of this result for bounded potentials is
discussed.Comment: 4 pages, 1 figure; v2: minor change
Diffusion and Trapping on a one-dimensional lattice
The properties of a particle diffusing on a one-dimensional lattice where at
each site a random barrier and a random trap act simultaneously on the particle
are investigated by numerical and analytical techniques. The combined effect of
disorder and traps yields a decreasing survival probability with broad
distribution (log-normal). Exact enumerations, effective-medium approximation
and spectral analysis are employed. This one-dimensional model shows rather
rich behaviours which were previously believed to exist only in higher
dimensionality. The possibility of a trapping-dominated super universal class
is suggested.Comment: 20 pages, Revtex 3.0, 13 figures in compressed format using uufiles
command, to appear in Phys. Rev. E, for an hard copy or problems e-mail to:
[email protected]
Diffusion with critically correlated traps and the slow relaxation of the longest wavelength mode
We study diffusion on a substrate with permanent traps distributed with
critical positional correlation, modeled by their placement on the perimeters
of a critical percolation cluster. We perform a numerical analysis of the
vibrational density of states and the largest eigenvalue of the equivalent
scalar elasticity problem using the method of Arnoldi and Saad. We show that
the critical trap correlation increases the exponent appearing in the stretched
exponential behavior of the low frequency density of states by approximately a
factor of two as compared to the case of no correlations. A finite size scaling
hypothesis of the largest eigenvalue is proposed and its relation to the
density of states is given. The numerical analysis of this scaling postulate
leads to the estimation of the stretch exponent in good agreement with the
density of states result.Comment: 15 pages, LaTeX (RevTeX
A pseudo-spectral approach to inverse problems in interface dynamics
An improved scheme for computing coupling parameters of the
Kardar-Parisi-Zhang equation from a collection of successive interface
profiles, is presented. The approach hinges on a spectral representation of
this equation. An appropriate discretization based on a Fourier representation,
is discussed as a by-product of the above scheme. Our method is first tested on
profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it
is shown to reproduce the input parameters very accurately. When applied to
microscopic models of growth, it provides the values of the coupling parameters
associated with the corresponding continuum equations. This technique favorably
compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys.
Rev.
Models of Fractal River Basins
Two distinct models for self-similar and self-affine river basins are
numerically investigated. They yield fractal aggregation patterns following
non-trivial power laws in experimentally relevant distributions. Previous
numerical estimates on the critical exponents, when existing, are confirmed and
superseded. A physical motivation for both models in the present framework is
also discussed.Comment: 16 pages, latex, 9 figures included using uufiles command (for any
problem: [email protected]), to be publishes in J. Stat. Phys. (1998
Diffusion on non exactly decimable tree-like fractals
We calculate the spectral dimension of a wide class of tree-like fractals by
solving the random walk problem through a new analytical technique, based on
invariance under generalized cutting-decimation transformations. These fractals
are generalizations of the NTD lattices and they are characterized by non
integer spectral dimension equal or greater then 2, non anomalous diffusion
laws, dynamical dimension splitting and absence of phase transitions for spin
models.Comment: 5 pages Latex, 3 figures (figures are poscript files
Phase diagram of the penetrable square well-model
We study a system formed by soft colloidal spheres attracting each other via
a square-well potential, using extensive Monte Carlo simulations of various
nature. The softness is implemented through a reduction of the infinite part of
the repulsive potential to a finite one. For sufficiently low values of the
penetrability parameter we find the system to be Ruelle stable with square-well
like behavior. For high values of the penetrability the system is
thermodynamically unstable and collapses into an isolated blob formed by a few
clusters each containing many overlapping particles. For intermediate values of
the penetrability the system has a rich phase diagram with a partial lack of
thermodynamic consistency.Comment: 6 pages and 5 figure
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