172 research outputs found
Warm Asymmetric Nuclear Matter and Proto-Neutron Star
Asymmetric nuclear matter equation of state at finite temperature is studied
in SU(2) chiral sigma model using mean field approximation. The effect of
temperature on effective mass, entropy, and binding energy is discussed.
Treating the system as one with two conserved charges the liquid-gas phase
transition is investigated. We have also discussed the effect of proton
fraction on critical temperature with and without -meson contribution. We
have extended our work to study the structure of proto-neutron star with
neutron free charge-neutral matter in beta-equilibrium. We found that the mass
and radius of the star decreases as it cools from the entropy per baryon S = 2
to S = 0 and the maximum temperature of the core of the star is about 62 MeV
for S = 2.Comment: 25 pages, 16 figure
Nonequilibrium stationary states and equilibrium models with long range interactions
It was recently suggested by Blythe and Evans that a properly defined steady
state normalisation factor can be seen as a partition function of a fictitious
statistical ensemble in which the transition rates of the stochastic process
play the role of fugacities. In analogy with the Lee-Yang description of phase
transition of equilibrium systems, they studied the zeroes in the complex plane
of the normalisation factor in order to find phase transitions in
nonequilibrium steady states. We show that like for equilibrium systems, the
``densities'' associated to the rates are non-decreasing functions of the rates
and therefore one can obtain the location and nature of phase transitions
directly from the analytical properties of the ``densities''. We illustrate
this phenomenon for the asymmetric exclusion process. We actually show that its
normalisation factor coincides with an equilibrium partition function of a walk
model in which the ``densities'' have a simple physical interpretation.Comment: LaTeX, 23 pages, 3 EPS figure
Exact solution of a model of a vesicle attached to a wall subject to mechanical deformation
Area-weighted Dyck-paths are a two-dimensional model for vesicles attached to
a wall. We model the mechanical response of a vesicle to a pulling force by
extending this model.
We obtain an exact solution using two different approaches, leading to a
q-deformation of an algebraic functional equation, and a q-deformation of a
linear functional equation with a catalytic variable, respectively. While the
non-deformed linear functional equation is solved by substitution of special
values of the catalytic variable (the so-called "kernel method"), the
q-deformed case is solved by iterative substitution of the catalytic variable.
Our model shows a non-trivial phase transition when a pulling force is
applied. As soon as the area is weighted with non-unity weight, this transition
vanishes.Comment: extended revision, 12 pages, 6 figure
Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter
We study the inflated phase of two dimensional lattice polygons, both convex
and column-convex, with fixed area A and variable perimeter, when a weight
\mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The
mean perimeter is calculated as a function of the fugacity \mu and the bending
rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic
behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) .
The constant K(J) is found to be the same for both types of polygons,
suggesting that self-avoiding polygons should also exhibit the same asymptotic
behaviour.Comment: 10 pages, 3 figure
Quantum cohomology via vicious and osculating walkers
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra
On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures
We study the interaction problem of a linear polymer chain, floating in
fractal containers that belong to the three-dimensional Sierpinski gasket (3D
SG) family of fractals, with a surface-adsorbed linear polymer chain. Each
member of the 3D SG fractal family has a fractal impenetrable 2D adsorbing
surface, which appears to be 2D SG fractal. The two-polymer system is modelled
by two mutually crossing self-avoiding walks. By applying the Monte Carlo
Renormalization Group (MCRG) method, we calculate the critical exponents
, associated with the number of contacts of the 3D SG floating polymer
chain, and the 2D SG adsorbed polymer chain, for a sequence of SG fractals with
. Besides, we propose the codimension additivity (CA) argument
formula for , and compare its predictions with our reliable set of the
MCRG data. We find that monotonically decreases with increasing ,
that is, with increase of the container fractal dimension. Finally, we discuss
the relations between different contact exponents, and analyze their possible
behaviour in the fractal-to-Euclidean crossover region .Comment: 15 pages, 3 figure
Exact Scaling Functions for Self-Avoiding Loops and Branched Polymers
It is shown that a recently conjectured form for the critical scaling
function for planar self-avoiding polygons weighted by their perimeter and area
also follows from an exact renormalization group flow into the branched polymer
problem, combined with the dimensional reduction arguments of Parisi and
Sourlas. The result is generalized to higher-order multicritical points,
yielding exact values for all their critical exponents and exact forms for the
associated scaling functions.Comment: 5 pages; v2: factors of 2 corrected; v.3: relation with existing
theta-point results clarified, some references added/update
Osculating and neighbour-avoiding polygons on the square lattice
We study two simple modifications of self-avoiding polygons. Osculating
polygons are a super-set in which we allow the perimeter of the polygon to
touch at a vertex. Neighbour-avoiding polygons are only allowed to have nearest
neighbour vertices provided these are joined by the associated edge and thus
form a sub-set of self-avoiding polygons. We use the finite lattice method to
count the number of osculating polygons and neighbour-avoiding polygons on the
square lattice. We also calculate their radius of gyration and the first
area-weighted moment. Analysis of the series confirms exact predictions for the
critical exponents and the universality of various amplitude combinations. For
both cases we have found exact solutions for the number of convex and
almost-convex polygons.Comment: 14 pages, 5 figure
Dyck Paths, Motzkin Paths and Traffic Jams
It has recently been observed that the normalization of a one-dimensional
out-of-equilibrium model, the Asymmetric Exclusion Process (ASEP) with random
sequential dynamics, is exactly equivalent to the partition function of a
two-dimensional lattice path model of one-transit walks, or equivalently Dyck
paths. This explains the applicability of the Lee-Yang theory of partition
function zeros to the ASEP normalization.
In this paper we consider the exact solution of the parallel-update ASEP, a
special case of the Nagel-Schreckenberg model for traffic flow, in which the
ASEP phase transitions can be intepreted as jamming transitions, and find that
Lee-Yang theory still applies. We show that the parallel-update ASEP
normalization can be expressed as one of several equivalent two-dimensional
lattice path problems involving weighted Dyck or Motzkin paths. We introduce
the notion of thermodynamic equivalence for such paths and show that the
robustness of the general form of the ASEP phase diagram under various update
dynamics is a consequence of this thermodynamic equivalence.Comment: Version accepted for publicatio
Relaxation time in a non-conserving driven-diffusive system with parallel dynamics
We introduce a two-state non-conserving driven-diffusive system in
one-dimension under a discrete-time updating scheme. We show that the
steady-state of the system can be obtained using a matrix product approach. On
the other hand, the steady-state of the system can be expressed in terms of a
linear superposition Bernoulli shock measures with random walk dynamics. The
dynamics of a shock position is studied in detail. The spectrum of the transfer
matrix and the relaxation times to the steady-state have also been studied in
the large-system-size limit.Comment: 10 page
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