All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 44

Showing per page

Large deviations for partition functions of directed polymers in an IID field

Iddo Ben-Ari (2009)

Annales de l'I.H.P. Probabilités et statistiques

Consider the partition function of a directed polymer in ℤd, d≥1, in an IID field. We assume that both tails of the negative and the positive part of the field are at least as light as exponential. It is well known that the free energy of the polymer is equal to a deterministic constant for almost every realization of the field and that the upper tail of the large deviations is exponential. The lower tail of the large deviations is typically lighter than exponential. In this paper we obtain sharp...

Large scale behavior of semiflexible heteropolymers

Francesco Caravenna, Giambattista Giacomin, Massimiliano Gubinelli (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...

Limit laws for the energy of a charged polymer

Xia Chen (2008)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j<k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j<k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest,...

Mathematically Modelling The Dissolution Of Solid Dispersions

Meere, Martin, McGinty, Sean, Pontrelli, Giuseppe (2017)

Proceedings of Equadiff 14

A solid dispersion is a dosage form in which an active ingredient (a drug) is mixed with at least one inert solid component. The purpose of the inert component is usually to improve the bioavailability of the drug. In particular, the inert component is frequently chosen to improve the dissolution rate of a drug that is poorly soluble in water. The construction of reliable mathematical models that accurately describe the dissolution of solid dispersions would clearly assist with their rational design....

On a mathematical model for the crystallization of polymers

Maria Pia Gualdani (2003)

Bollettino dell'Unione Matematica Italiana

We consider a mathematical model proposed in [1] for the cristallization of polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. The model includes a constraint W e ⁢ q on the crystal volume fraction. Essentially, the model is a system of both second order and first order evolutionary partial differential equations with nonlinear terms which are Lipschitz continuous, as in [1], or Hölder continuous, as in [3]. The main novelty here is the...

Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift

David J. Knezevic, Endre Süli (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential U that is equal to + ∞ along the boundary ∂ D of the computational domain D . Using a symmetrization...

Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift

David J. Knezevic, Endre Süli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential U that is equal to +∞ along the boundary ∂D of the computational domain D. Using a symmetrization...

Strong disorder in semidirected random polymers

N. Zygouras (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.

Superdiffusive bounds on self-repellent precesses in d = 2 — extended abstract

Bálint Tóth, Benedek Valkó (2010)

Actes des rencontres du CIRM

We prove superdiffusivity with multiplicative logarithmic corrections for a class of models of random walks and diffusions with long memory. The family of models includes the “true” (or “myopic”) self-avoiding random walk, self-repelling Durrett-Rogers polymer model and diffusion in the curl-field of (mollified) massless free Gaussian field in 2D. We adapt methods developed in the context of bulk diffusion of ASEP by Landim-Quastel-Salmhofer-Yau (2004).

Superdiffusivity for brownian motion in a poissonian potential with long range correlation I: Lower bound on the volume exponent

Hubert Lacoin (2012)

Annales de l'I.H.P. Probabilités et statistiques

We study trajectories of d -dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V is constructed from a field of traps whose centers location is given by a Poisson Point Process and whose radii are IID distributed with a common distribution that has unbounded support; it has the particularity of having long-range correlation. We focus on the case where the law of the trap radii ν has power-law decay and prove that superdiffusivity...

Superdiffusivity for brownian motion in a poissonian potential with long range correlation II: Upper bound on the volume exponent

Hubert Lacoin (2012)

Annales de l'I.H.P. Probabilités et statistiques

This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here that for both point-to-point and point-to-plane model the volume exponent (the exponent associated to transversal fluctuation of the trajectories) ξ is strictly less than 1 and give an explicit upper bound that depends on the parameters of the problem. In some specific cases, this upper bound matches the lower bound proved in the first part of this work and...

Currently displaying 21 – 40 of 44