Related papers: Directed polymers on a disordered tree with a defe…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
We introduce a new disorder regime for directed polymers with one space and one time dimension that is accessed by scaling the inverse temperature parameter \beta with the length of the polymer n. We scale \beta_n := \beta n^{-\alpha} for…
We show that the weak disorder phase for the directed polymer model in a bounded random environment is characterized by the integrability of the running supremum $\sup_{n\in \mathbb N}W_n^\beta$ of the associated martingale…
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…
A microscopic theory of the free energy barriers and folding routes for minimally frustrated proteins is presented, greatly expanding on the presentation of the variational approach outlined previously [J. J. Portman, S. Takada, P. G.…
The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey a multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario…
The effects of two types of randomness on the behaviour of directed polymers are discussed in this chapter. The first part deals with the effect of randomness in medium so that a directed polymer feels a random external potential. The…
In this paper we look at the pinning of a directed polymer by a one-dimensional linear interface carrying random charges. There are two phases, localized and delocalized, depending on the inverse temperature and on the disorder bias. Using…
The impact of polymer-polymer interactions of various types on the thermodynamics, structure, and accommodation of topological constraints is addressed for systems comprising many directed polymers in two spatial dimensions. The approach is…
Directed paths have been used extensively in the scientific literature as a model of a linear polymer. Such paths models in particular the conformational entropy of a linear polymer and the effects it has on the free energy. These directed…
We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in presence of disorder, equivalent to the KPZ equation on the half space with droplet initial conditions. From a Bethe Ansatz solution of the…
We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in [5,6,7]. Given a fixed realization of a random walk Y$ on Z^d with jump rate rho (that plays the role of the random medium), we modify the law of a…
A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization.…
We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at…
We study the conformational properties of polymers in presence of extended columnar defects of parallel orientation. Two classes of macromolecules are considered: the so-called partially directed polymers with preferred orientation along…
We consider the drift of a polymer chain in a disordered medium, which is caused by a constant force applied to the one end of the polymer, under neglecting the thermal fluctuations. In the lowest order of the perturbation theory we have…
Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two…
We introduce a new disorder regime for directed polymers in dimension $1+1$ that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter…
We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \mathbb{N}$ and a segment number $s\in \mathbb{N}$. When $b\leq…
The phase behavior of a cross-linked polymer blend made of two incompatible species, $A$ and $B$, of different chemical nature is analyzed. Besides a homogeneous phase, this system also exhibits two microphases and a phase of total…