Related papers: Directed Polymers on Hierarchical Lattices with si…
We consider a directed variant of the negative-weight percolation model in a two-dimensional, periodic, square lattice. The problem exhibits edge weights which are taken from a distribution that allows for both positive and negative values.…
We have developed a thorough and accurate method of determining anharmonic free energies, the temperature dependent effective potential technique (TDEP). It is based on \emph{ab initio} molecular dynamics followed by a mapping onto a model…
In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which allows to compute the scaling exponent $\theta$ of the free energy…
A common approach to study nucleation rates is the estimation of free-energy barriers. This usually requires knowledge about the shape of the forming droplet, a task that becomes notoriously difficult in macromolecular setups starting with…
We present results for a lattice model of bio-polymers where the type of $\beta$-sheet formation can be controlled by different types of hydrogen bonds depending on the relative orientation of close segments of the polymer. Tuning these…
This report deals with phase transition in Bond Fluctuation Model (BFM) of a linear homo polymer on a two dimensional square lattice. Each monomer occupies a unit cell of four lattice sites. The condition that a lattice site can at best be…
In lattice models local pressure on a surface is derived from the change in the free energy of the system due to the exclusion of a certain boundary site, while the total force on the surface can be obtained by a similar exclusion of all…
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. We construct weak solutions of the two-phase model by performing the…
We construct a phenomenological theory of self-localization of directed polymers in d+1 dimensions. In d=1 we show that the polymer is always self-localized, whereas in d=2 there is a phase transition between localized and free states. We…
Joint ground states of two directed polymers in a random medium are investigated. Using exact min-cost flow optimization the true two-line ground-state is compared with the single line ground state plus its first excited state. It is found…
We study the stability of the glassy equilibrium state of a directed polymer in random media against weak perturbations including the intriguing problem of temperature-chaos. The statistical correlation of two real replica systems under…
We study a two-dimensional tight-binding lattice for excitons with on-site disorder, coupled to a thermal environment at infinite temperature. The disorder acts to localise an exciton spatially, while the environment generates dynamics…
We consider a directed random walk model of a random heterogeneous polymer in the proximity of an interface separating two selective solvents. This model exhibits a localization/delocalization transition. A positive value of the free energy…
We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…
The mosaic Wannier Stark lattice has gained increasing prominence as a disorder free system exhibiting unconventional localization behavior induced by spatially periodic Stark potentials. In the infinite size limit, exact spectral analysis…
We prove a phase transition for the law of large numbers and fluctuations of $\mathsf F_N$, the maximum of the free energy of the log-gamma directed polymer with parameter $\theta$, maximized over all possible starting and ending points in…
We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our focus is on scaling schemes in which a size parameter $n$,…
We show that choosing appropriate distributions of the randomness, the search for optimal paths links diverse problems of disordered media like directed percolation, invasion percolation, directed and non-directed spanning polymers. We also…
We study analytically a model of a two dimensional, partially directed, flexible or semiflexible polymer, attached to an attractive wall which is perpendicular to the preferred direction. In addition, the polymer is stretched by an…
A two-dimensional lattice model with bond disorder is used to investigate the fracture behaviour under stress-controlled conditions. Although the cumulative energy of precursors does not diverge at the critical point, its derivative with…