Related papers: Two-dimensional polymer networks at a mixed bounda…
A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form…
A convergence criterion of cluster expansion is presented in the case of an abstract polymer system with general pair interactions (i.e. not necessarily hard core or repulsive). As a concrete example, the low temperature disordered phase of…
We present a direct and fairly simple proof of the following incidence bound: Let $P$ be a set of $m$ points and $L$ a set of $n$ lines in ${\mathbb R}^d$, for $d\ge 3$, which lie in a common algebraic two-dimensional surface of degree $D$…
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…
This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. The…
Bounds are obtained on the volume fraction in a two-dimensional body containing two elastically isotropic materials with known bulk and shear moduli. These bounds use information about the average stress and strain fields, energy,…
Based on the $H^2$ existence of the solution, we investigate weighted estimates for a mixed boundary elliptic system in a two-dimensional corner domain, when the contact angle $\om\in(0,\pi/2)$. This system is closely related to the…
Polymer chains decorated with a fraction of monomers capable of forming reversible bonds form transient polymer networks that are important in soft and biological systems. If chains are flexible and the attractive monomers are all of the…
The density profile and surface tension for the interface of phase-separated colloid-polymer mixtures have been studied in the framework of the square gradient approximation for both ideal and interacting polymers in good solvent. The…
The properties of semiflexible polymers tethered by one end to an impenetrable wall and exposed to oscillatory shear flow are investigated by mesoscale simulations. A polymer, confined in two dimensions, is described by a linear bead-spring…
In this paper, we analyze the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The…
We consider the scaling limit of a generic ferromagnetic system with a continuous phase transition, on the half plane with boundary conditions leading to the equilibrium of two different phases below criticality. We use general properties…
In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between the layers, while close packing of the layers…
We perform a Monte Carlo study of $N$-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions ($d=2$), or the tip of an impenetrable cone in $d=3$, of sizes ranging up to $N=10^6$ steps. We find that the…
The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consider vector bundles over the boundary together with general…
We study the combinatorial properties of 2-dimensional tropical complexes. In particular, we prove tropical analogues of the Hodge index theorem and Noether's formula. In addition, we introduce algebraic equivalence for divisors on tropical…
A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In…
We give a solution to the Poincar\'e Problem, in the formulation of Cerveau and Lins Neto. We obtain a bound on the degree of general leaves of foliations of general type, which is linear in $g$. To achieve this we study the birational…
We consider the moduli space of bordered Riemann surfaces with boundary and marked points. Such spaces appear in open-closed string theory, particularly with respect to holomorphic curves with Lagrangian submanifolds. We consider a…
We observe that the proof of the Bogomolov stable restriction theorem can be adapted to give an ampleness criterion for globally generated rank 2 vector bundles on certain surfaces. This applies to the Lazarsfeld-Mukai bundles, to…