Related papers: Randomly Branched Polymers and Conformal Invarianc…
Randomly branching polymers with {\em annealed} connectivity are model systems for ring polymers and chromosomes. In this context, the branched structure represents transient folding induced by topological constraints. Here we present…
There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + \epsilon$ dimensions, but the naive extension has a small loophole, which…
We investigate the statistical properties of a randomly branched 3--functional $N$--link polymer chain without excluded volume, whose one point is fixed at the distance $d$ from the impenetrable surface in a 3--dimensional space. Exactly…
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size…
Topologically constrained genome-like polymers often double-fold into tree-like configurations. Here we calculate the exact number of tightly double-folded configurations available to a ring polymer in ideal conditions. For this purpose, we…
In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static…
The miscibility of polymer blends, a classical problem in polymer science, may be altered, if one or both of the component do not have chain ends. Based on the idea of {\it topological volume}, we propose a mean-field theory to clarify how…
We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several…
We study the statistics of branching polymers with excluded-volume interactions, by modeling them as single self-avoiding trees on a generic regular periodic lattice with coordination number $q$. Each lattice site can be occupied at most by…
This work examines a field theory for RNA-like molecules in a good solvent. The field theory is based on a lattice model for single- and double-strand RNA with a periodic base sequence, and otherwise contains all known relevant details…
A cornerstone of modern polymer physics is the `Flory ideality hypothesis' which states that a chain in a polymer melt adopts `ideal' random-walk-like conformations. Here we revisit theoretically and numerically this pivotal assumption and…
We use the method of dimensional reduction to show that a branching polymer with excluded volume interaction confined between two flat plates has, in the thermodynamic limit, a confinement free energy and density profile that is the same as…
By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory.…
We find that 2-dimensional (2-D) critical branched polymers with no impurities conclusively belong to the same universality class as 2-D random percolation clusters, although pure critical 3-D branched polymers do not belong to the 3-D…
We establish an exact relation between self-avoiding branched polymers in D+2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D+2 = 2,3,4…
The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore…
We study the aggregation transition of a finite theta-polymer system in dependence on the bending stiffness $\kappa$ with the help of parallel multicanonical simulations. In order to distinguish amorphous aggregates from polymer bundles we…
We consider polymers formed from a (quenched) random sequence of charged monomers of opposite signs. Such polymers, known as polyampholytes (PAs), are compact when completely neutral and expanded when highly charged. We examine the…
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: \textit{uniform} stretching by external forces and \textit{non-uniform} stretching by external fields. Many…
The unfolding of a polymer below the $\theta$ point when pulled by an external force is studied both in d=2 on the lattice and in $d=3$ off lattice. A ground state analysis of finite length chains shows that the globule unfolds via multiple…