相关论文: Self-dual solutions of a field theory model of two…
We consider the statistical mechanics of a system of topologically linked polymers, such as for instance a dense solution of polymer rings. If the possible topological states of the system are distinguished using the Gauss linking number as…
The field theory approach to the statistical mechanics of a system of N polymer rings linked together is generalized to the case of links that have a fixed number $2s$ of maxima and minima. Such kind of links are called plats and appear for…
Anyon systems are studied in connection with several interesting applications including high $T_C$ superconductivity and topological quantum computing. In this work we show that these systems can be realized starting from directed polymers…
Spaces with a Weyl-type connection and torsion of a special type induced by the structure of the differentiability conditions in the algebra of complex quaternions are considered. The consistency of these conditions implies the self-duality…
The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of…
Polymer rings in solution are either permanently entangled or not. Permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume. Conversely,…
We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited…
Self-duality plays a very important role in many applications in field theories possessing topological solitons. In general, the self-duality equations are first order partial differential equations such that their solutions satisfy the…
Bounded interactions are particularly important in soft-matter systems, such as colloids, microemulsions, and polymers. We derive new duality relations for a class of soft potentials, including three-body and higher-order functions, that…
The statistical mechanics of [2]catenanes in a solution with constrained number of maxima and minima along a special direction (the height) is discussed. The interest in this system comes from the fact that, in the homopolymer case, it has…
A general method for the construction of solutions of the d'Alambertian and double d'Alambertian (harmonic and bi-harmonic) equations with local dependence of arbitrary functions upon two independent arguments is proposed. The connection…
In this work a field theoretical model is constructed to describe the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. As an application, the effects of the…
Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance,…
We construct static and time-dependent exact soliton solutions with non-trivial Hopf topological charge for a field theory in 3+1 dimensions with the target space being the two dimensional sphere S**2. The model considered is a reduction of…
Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first…
We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then…
We show that the self-dual Yang-Mills equations afford supersymmetrisation to systems of equations invariant under global N-extended super-Poincar\'e transformations for arbitrary values of N, without the limitation (N\le 4) applicable to…
Analytical treatments of polymer dynamics have mostly been restricted to linear response theory around some steady state obtained via perturbative field theory. Here, I derive an analytical framework that yields unified access to the…
Polymer self-consistent field theory techniques are used to find radial electron densities and total binding energies for isolated atoms. Quantum particles are modelled as Gaussian threads with ring-polymer architecture in a four…
Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and,…