Related papers: Exact free energy distribution function of a rando…
We consider the fluctuations of the free energy of positive temperature directed polymers in thin rectangles (N,N^{\alpha}), \alpha < 3/14. For general weight distributions with finite fourth moment we prove that the distribution of these…
In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of…
We derive the partition function of a non-relativistic quantum string which its ends are allowed to freely slide on the two angled straight solid rods. We first derive the classical solution of the model and then use it to derive the…
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 probability distribution $F(u)$ of the maximum of smooth Gaussian fields defined on compact subsets of $\R^d$ having some geometric regularity. Our main result is a general formula for the density of $F$. Even though this is an…
Let f:=(f^1,\...,f^n) be a sparse random polynomial system. This means that each f^i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussian probability distribution of arbitrary variance. We express…
We study the statistics of the dissipated energy in the two-dimensional random fuse model for fracture under different imposed strain conditions. By means of extensive numerical simulations we compare different ways to compute the…
In this chapter we review the rich behavior of polymer chains embedded in a quenched random environment. We first consider the problem of a Gaussian chain free to move in a random potential with short-ranged correlations. We derive the…
Recent experiments have established negative energetic elasticity, the negative contribution of energy to the elastic modulus, as a universal property of polymer gels. To reveal the microscopic origin of this phenomenon, Shirai and…
Loops undergoing thermal fluctuations are prevalent in nature. Ring-like or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated…
The conformational properties of a semi-flexible polymer chain, anchored at one end in a uniform force field, are studied in a simple two-dimensional model. Recursion relations are derived for the partition function and then iterated…
We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative…
The statistics of power fluctuations are studied in simulations of two-dimensional turbulence in both inverse (energy) and direct (enstrophy) cascade regimes from both Lagrangian and Eulerian perspectives. The probability density function…
We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…
The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive…
The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain ends is investigated. We perform our study in the "fixed height" statistical ensemble where one…
In this article, we try to give a rather complete picture of the behavior of the free energy for a model of directed polymer in a random environment, in which the polymer is a simple symmetric random walk on the lattice $\Z^d$, and the…
Free electron approximation for electron states in poly($p$-phenylene vinylene) and other conjugated systems is developed. It provides simple and clear analytical expressions for energies of electron states and for wave functions. The…