Related papers: Copolymers at selective interfaces: settled issues…
In this paper we investigate the conformation statistics of a Gaussian chain embedded in a medium of finite size, in the presence of quenched random obstacles. The similarities and differences between the case of random obstacles and 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…
These notes are devoted to the statistical mechanics of directed polymers interacting with one-dimensional spatial defects. We are interested in particular in the situation where frozen disorder is present. These polymer models undergo a…
These lecture notes are a guided tour through the fascinating world of polymer chains interacting with themselves and/or with their environment. The focus is on the mathematical description of a number of physical and chemical phenomena,…
In this review we provide an organized summary of the theoretical and computational results which are available for polymers subject to spatial or topological constraints. Because of the interdisciplinary character of the topic, we provide…
We study the depinning phase transition of a directed polymer in a $d$-dimensional space by a periodic potential localized on a straight line. We give exact formulas in all dimensions for the critical pinning we need to localize the…
We study the localization of a random heteropolymer onto an homogeneous surface, the problem which is equivalent to the wetting of an interface at disordered substrate in two dimensions, via replica trick by using the Green's function…
We investigate the phase diagram of disordered copolymers at the interface between two selective solvents, and in particular its weak-coupling behavior, encoded in the slope $m_c$ of the critical line at the origin. In mathematical terms,…
We investigate the localization of a hydrophobic - polar (HP) - regular copolymer at a selective solvent-solvent interface with emphasis on the impact of block length $M$ on the copolymer behavior. The considerations are based on simple…
In this paper we consider a two-dimensional copolymer consisting of a random concatenation of hydrophobic and hydrophilic monomers near a linear interface separating oil and water acting as solvents. The configurations of the copolymer are…
Using the results of the recently studied problem of adsorption of a Gaussian polymer in a weak periodic surface potential we study the influence of a single rod like defect on the polymer being localized in the periodic surface potential.…
In this article, I study the localization transition of an hydrophobic homopolymer in interaction with an interface between oil and water. To that aim I consider a model in which the trajectories of a simple random walk play the role of the…
We give a selection of major open problems involving selective properties, diagonalizations, and covering properties for sets of real numbers. This is a revision of the version published as a chapter in the book \textbf{Open Problems in…
We study theoretically situations where competition arises between an interdiffusion process and a cross-linking chemical reaction at interfaces between pieces of the same polymer material. An example of such a situation is observable in…
Configurational fluctuations of conducting polymers in solution can bring into proximity monomers which are distant from each other along the backbone. Electrons can hop between these monomers across the "bridges" so formed. We show how…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
This paper presents an alternative approach to simplify the proofs of some important results related to polynomial mappings in Computational Algebraic Geometry such as Polynomial Implicitization, Image Closure and some properties of the…
We consider the adsorption of a random heteropolymer onto an interface within the model by Garel et al. [1] by taking into account self-interactions between the monomers. Within the replica trick and by using a self-consistent preaveraging…
In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer…
We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive…