1,754 research outputs found
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
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]
Colour analysis of degraded parchment
Multispectral imaging was employed to collect data on the degradation of an 18th century parchment by a series of physical and chemical treatments. Each sample was photographed before and after treatment by a monochrome digital camera with 21 narrow-band filters. A template-matching technique was used to detect the circular holes in each sample and a four-point projective transform to register the 21 images. Colour accuracy was verified by comparison of reconstructed spectra with measurements by spectrophotometer
Risk Factor Analysis and Portfolio Immunization in the Corporate Bond Market
In this paper we develop a multi-factor model for the yields of corporate bonds. The model allows the analysis of factors which influence the changes in the term structure of corporate bonds. More than 98% of the variability in the corporate bond market is captured by the model, which is then used to develop credit risk immunization strategies. Empirical results are given for the U.S. market using data for the period 1992-1999.
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.
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
Patchy sticky hard spheres: analytical study and Monte Carlo simulations
We consider a fluid of hard spheres bearing one or two uniform circular
adhesive patches, distributed so as not to overlap. Two spheres interact via a
``sticky'' Baxter potential if the line joining the centers of the two spheres
intersects a patch on each sphere, and via a hard sphere potential otherwise.
We analyze the location of the fluid-fluid transition and of the percolation
line as a function of the size of the patch (the fractional coverage of the
sphere's surface) and of the number of patches within a virial expansion up to
third order and within the first two terms (C0 and C1) of a class of closures
Cn hinging on a density expansion of the direct correlation function. We find
that the locations of the two lines depend sensitively on both the total
adhesive coverage and its distribution. The treatment is almost fully
analytical within the chosen approximate theory. We test our findings by means
of specialized Monte Carlo (MC) simulations and find the main qualitative
features of the critical behaviour to be well captured in spite of the low
density perturbative nature of the closure. The introduction of anisotropic
attractions into a model suspension of spherical particles is a first step
towards a more realistic description of globular proteins in solution.Comment: 47 pages, 18 figures, to appear on J. Chem. Phy
Structure and phase behavior of colloidal dumbbells with tunable attractive interactions
We investigate thermodynamic and structural properties of colloidal dumbbells
in the framework provided by the Reference Interaction Site Model (RISM) theory
of molecular fluids and Monte Carlo simulations. We consider two different
models: in the first one we set identical square-well attractions on the two
tangent spheres composing the molecule (SW-SW model); in the second scheme, one
of square-well interactions is switched off (HS-SW model). Appreciable
differences emerge between the physical properties of the two models.
Specifically, the behavior of SW-SW structure factors points
to the presence of a gas-liquid coexistence, as confirmed by subsequent fluid
phase equilibria calculations. Conversely, the HS-SW develops a low-
peak, signaling the presence of aggregates; such a process destabilizes the
gas-liquid phase separation, promoting at low temperatures the formation of a
cluster phase, whose structure depends on the system density. We further
investigate such differences by studying the phase behavior of a series of
intermediate models, obtained from the original SW-SW by progressively reducing
the depth of one square-well interaction. RISM structural predictions
positively reproduce the simulation data, including the rise of ) in
the SW-SW model and the low- peak in the HS-SW structure factor. As for the
phase behavior, RISM agrees with Monte Carlo simulations in predicting a
gas-liquid coexistence for the SW-SW model (though the critical parameters
appears overestimated by the theory) and its progressive disappearance moving
toward the HS-SW model.Comment: 12 pages, 13 figures, 1 table, 78 reference
- …