Related papers: Copolymers at selective interfaces: settled issues…
This paper deals with transportation polytopes in the probability simplex (that is, sets of categorical bivariate probability distributions with prescribed marginals). Information projections between such polytopes are studied, and a…
The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…
We propose a novel characterization method of randomly branched polymers based on the geometrical property of such objects in confined spaces. The central idea is that randomly branched polymers exhibit passing/clogging transition across…
We study cohomological obstructions to the existence of global conserved quantities. In particular, we show that, if a given local variational problem is supposed to admit global solutions, certain cohomology classes cannot appear as…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple…
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 novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents, the local compromisers, to every…
Block copolymer melts self-assemble in the bulk into a variety of nanostructures, making them perfect candidates to template the position of nanoparticles. The morphological changes of block copolymers are studied in the presence of a…
In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of minimisers and shocks forming interlacing…
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…
A polymer repelled by unfavorable interactions with a uniform flat surface may still be pinned to attractive edges and corners. This is demonstrated by considering adsorption of a two-dimensional ideal polymer to an attractive corner of a…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
We consider a problem concerning tilings of rectangular regions by a finite library of polyominoes. We specifically look at rectangular regions of dimension $n\times m$ and ask whether or not a tiling of this region can be rearranged so…
In this paper we study a two-dimensional directed self-avoiding walk model of a random copolymer in a random emulsion. The copolymer is a random concatenation of monomers of two types, $A$ and $B$, each occurring with density 1/2. The…
The impact of impenetrable obstacles on the energetics and equilibrium structure of strongly repulsive directed polymers is investigated. As a result of the strong interactions, regions of severe polymer depletion and excess are found in…
The existence, stability properties, and bifurcation diagrams of localized patterns and hole solutions in one-dimensional extended systems is studied from the point of view of front interactions. An adequate envelope equation is derived…
Colloidal particles trapped at an interface between two fluids can form a wide range of different structures. Replacing one of the fluid with a liquid crystal increases the complexity of interactions and results in a greater range of…
Over the past two decades polymer nanocomposites have received tremendous interest from industry and academia due to their advanced properties comparative to polymer blends. Many computational studies have revealed that the macroscopic…
We argue that Kantor and Kardar's assertion that their simulation results contradict our criterion for the localization of a softly constrainted ideal polymer is incorrect. Our criterion is inapplicable to the model used in these…