Related papers: One dimensional directed polymer "memory model"
This review is devoted to the detailed consideration of the universal statistical properties of one-dimensional directed polymers in a random potential. In terms of the replica Bethe ansatz technique we derive several exact results for…
Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results for this model continue to hold for a more general reference…
We consider a one-dimensional directed polymer in a random potential which is characterized by the Gaussian statistics with the finite size local correlations. It is shown that the well-known Kardar's solution obtained originally for a…
The mechanical behavior of disordered materials such as dense suspensions, glasses or granular materials depends on their thermal and mechanical past. Here we report the memory behavior of a quenched mesoscopic elasto-plastic (QMEP) model.…
Predicting the macroscopic mechanical behavior of polymeric materials from the micro-structural features has remained a challenge for decades. Existing theoretical models often fail to accurately capture the experimental data, due to…
Directed polymers in random media are studied using results of the asymptotic theory of extreme statistics. Despite the strong correlation, one can recover the behavior of independent random variables for high dimensions, using a result…
We consider $(1+1)$-dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, and for polymers started…
Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…
In these lecture notes, which are based on the mini-course given at 2013 Prague School on Mathematical Statistical Physics, we discuss ballistic phase of quenched and annealed stretched polymers in random environment on ${\mathbb Z}^d$ with…
We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between…
We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain…
In this note we give upper bounds for the free energy of discrete polymers in random media. The bounds are given by the so-called generalized multiplicative cascades from the statistical theory of turbulence. For the polymer model, we…
We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…
The relaxational dynamics of 1+1 dimensional directed polymer in random potential is studied by Monte Carlo simulation. A series of temperature quench experiments is performed changing waiting times. Clear crossover from quasi-equilibrium…
Motivated by the observation of the storage of excess elastic free energy - (prestress) -- in cross linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random…
Evaluating accessible conformational space is computationally expensive and thermal motions are partly neglected in computer models of molecular interactions. This produces error into the estimates of binding strength. We introduce a method…
We study the depinning transition of the $1+1$ dimensional directed polymer in a random environment with a defect line. The random environment consists of i.i.d. potential values assigned to each site of $\mathbb{Z}^2$; sites on the…
We have developed a theory of polymer entanglement using an extended Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive term, operating over mesoscales, which is interpreted as giving rise to entanglement, and the…
In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the…
The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly…