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Knots, links, anyons and statistical mechanics of entangled polymer rings
The field theory approach to the statistical mechanics of a system of N polymer rings linked together is extended to the case of links whose paths in space are characterized by a fixed number 2s of maxima and minima. Such kind of links are called 2s-plats and appear for instance in the DNA of living organisms or in the wordlines of quasiparticles associated with vortices nucleated in a quasi-two-dimensional superfluid. The path integral theory describing the statistical mechanics of polymers subjected to topological constraints is mapped here into a field theory of quasiparticles (anyons). In the particular case of s=2, it is shown that this field theory admits vortex solutions with special self-dual points in which the interactions between the vortices vanish identically. The topological states of the link are distinguished using two topological invariants, namely the Gauss linking number and the so-called bridge number which is related to s. The Gauss linking number is a topological invariant that is relatively weak in distinguishing the different topological configurations of a general link. The addition of topological constraints based on the bridge number allows to get a glimpse into the non-abelian world of quasiparticles, which is relevant for important applications like topological quantum computing and high-TC superconductivity. At the end an useful connection with the cosh-Gordon equation is shown in the case s=2. © 201
Dynamics of self-organized driven particles with competing range interaction
Non-equilibrium self-organized patterns formed by particles interacting
through competing range interaction are driven over a substrate by an external
force. We show that, with increasing driving force, the pre-existed static
patterns evolve into dynamic patterns either via disordered phase or depinned
patterns, or via the formation of non-equilibrium stripes. Strikingly, the
stripes are formed either in the direction of the driving force or in the
transverse direction, depending on the pinning strength. The revealed dynamical
patterns are summarized in a dynamical phase diagram.Comment: 8 pages, 11 figure
Number of states for nucleons in a single- shell
In this paper we obtain number of states with a given spin and a given
isospin for systems with three and four nucleons in a single- orbit, by
using sum rules of six- and nine- symbols obtained in earlier works.Comment: to be published in Physical Review
Existence theorems for a nonlinear second-order distributional differential equation
In this work, we are concerned with existence of solutions for a nonlinear
second-order distributional differential equation, which contains measure
differential equations and stochastic differential equations as special cases.
The proof is based on the Leray--Schauder nonlinear alternative and
Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to
demonstrate that the main results are sharp.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of King Saud University - Science', ISSN 1018-3647. Submitted
05-March-2017; revised 24-April-2017; accepted for publication 26-April-201
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