626 research outputs found
Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer
The number of solid partitions of a positive integer is an unsolved problem
in combinatorial number theory. In this paper, solid partitions are studied
numerically by the method of exact enumeration for integers up to 50 and by
Monte Carlo simulations using Wang-Landau sampling method for integers up to
8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where
p(n) is the number of solid partitions of the integer n. This result strongly
suggests that the MacMahon conjecture for solid partitions, though not exact,
could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex
Topological entropy of a stiff ring polymer and its connection to DNA knots
We discuss the entropy of a circular polymer under a topological constraint.
We call it the {\it topological entropy} of the polymer, in short. A ring
polymer does not change its topology (knot type) under any thermal
fluctuations. Through numerical simulations using some knot invariants, we show
that the topological entropy of a stiff ring polymer with a fixed knot is
described by a scaling formula as a function of the thickness and length of the
circular chain. The result is consistent with the viewpoint that for stiff
polymers such as DNAs, the length and diameter of the chains should play a
central role in their statistical and dynamical properties. Furthermore, we
show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure
Critical exponents for random knots
The size of a zero thickness (no excluded volume) polymer ring is shown to
scale with chain length in the same way as the size of the excluded volume
(self-avoiding) linear polymer, as , where . The
consequences of that fact are examined, including sizes of trivial and
non-trivial knots.Comment: 4 pages, 0 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
On directed interacting animals and directed percolation
We study the phase diagram of fully directed lattice animals with
nearest-neighbour interactions on the square lattice. This model comprises
several interesting ensembles (directed site and bond trees, bond animals,
strongly embeddable animals) as special cases and its collapse transition is
equivalent to a directed bond percolation threshold. Precise estimates for the
animal size exponents in the different phases and for the critical fugacities
of these special ensembles are obtained from a phenomenological renormalization
group analysis of the correlation lengths for strips of width up to n=17. The
crossover region in the vicinity of the collapse transition is analyzed in
detail and the crossover exponent is determined directly from the
singular part of the free energy. We show using scaling arguments and an exact
relation due to Dhar that is equal to the Fisher exponent
governing the size distribution of large directed percolation clusters.Comment: 23 pages, 3 figures; J. Phys. A 35 (2002) 272
The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for
nonequilibrium dynamics, in particular driven diffusive processes. It is
usually considered in a canonical ensemble in which the number of sites is
fixed. We observe that the grand-canonical partition function for the ASEP is
remarkably simple. It allows a simple direct derivation of the asymptotics of
the canonical normalization in various phases and of the correspondence with
One-Transit Walks recently observed by Brak et.al.Comment: Published versio
Area distribution of the planar random loop boundary
We numerically investigate the area statistics of the outer boundary of
planar random loops, on the square and triangular lattices. Our Monte Carlo
simulations suggest that the underlying limit distribution is the Airy
distribution, which was recently found to appear also as area distribution in
the model of self-avoiding loops.Comment: 10 pages, 2 figures. v2: minor changes, version as publishe
Relaxation of a Single Knotted Ring Polymer
The relaxation of a single knotted ring polymer is studied by Brownian
dynamics simulations. The relaxation rate lambda_q for the wave number q is
estimated by the least square fit of the equilibrium time-displaced correlation
function to a double exponential decay at long times. The relaxation rate
distribution of a single ring polymer with the trefoil knot appears to behave
as lambda_q=A(1/N^)x for q=1 and lambda_q=A'(q/N)^x' for q=2 and 3, where
x=2.61, x'=2.02 and A>A'. The wave number q of the slowest relaxation rate for
each N is given by q=2 for small values of N, while it is given by q=1 for
large values of N. This crossover corresponds to the change of the structure of
the ring polymer caused by the localization of the knotted part to a part of
the ring polymer.Comment: 13 pages, 5 figures, uses jpsj2.cl
Task shifting and integration of HIV care into primary care in South Africa: The development and content of the streamlining tasks and roles to expand treatment and care for HIV (STRETCH) intervention
Background: Task shifting and the integration of human immunodeficiency virus (HIV) care into primary care services have been identified as possible strategies for improving access to antiretroviral treatment (ART). This paper describes the development and content of an intervention involving these two strategies, as part of the Streamlining Tasks and Roles to Expand Treatment and Care for HIV (STRETCH) pragmatic randomised controlled trial. Methods: Developing the intervention: The intervention was developed following discussions with senior management, clinicians, and clinic staff. These discussions revealed that the establishment of separate antiretroviral treatment services for HIV had resulted in problems in accessing care due to the large number of patients at ART clinics. The intervention developed therefore combined the shifting from doctors to nurses of prescriptions of antiretrovirals (ARVs) for uncomplicated patients and the stepwise integration of HIV care into primary care services. Results: Components of the intervention: The intervention consisted of regulatory changes, training, and guidelines to support nurse ART prescription, local management teams, an implementation toolkit, and a flexible, phased introduction. Nurse supervisors were equipped to train intervention clinic nurses in ART prescription using outreach education and an integrated primary care guideline. Management teams were set up and a STRETCH coordinator was appointed to oversee the implementation process. Discussion: Three important processes were used in developing and implementing this intervention: active participation of clinic staff and local and provincial management, educational outreach to train nurses in intervention sites, and an external facilitator to support all stages of the intervention rollout
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