Related papers: Tilings With Very Elastic Dimers
This note sharpens the smoothing inequality of Giacomin and Toninelli for disordered polymers. This inequality is shown to be valid for any disorder distribution with locally finite exponential moments, and to provide an asymptotically…
The entropic pressure in the vicinity of a cubic lattice knot is examined as a model of the entropic pressure near a knotted ring polymer in a good solvent. A model for the scaling of the pressure is developed and this is tested numerically…
A \emph{surface of translation} is a sum $(u,v)\mapsto\gt\alpha(u)+\gt\beta(v)$ of two space curves: a \emph{path} $\gt\alpha$ and a \emph{profile} $\gt\beta$. A fundamental problem of differential geometry and shell theory is to determine…
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
A self-interacting polymer can undergo an orientational ordering transition, depending on the magnitude of the nematic interaction. The effect of embedding such a polymer into a flexible surface on this transition is studied on the…
Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively…
The usefulness of glasses, and particularly of metallic glasses, in technological applications is often limited by their toughness, which is defined as the area under the stress vs. strain curve before plastic yielding. Recently toughness…
By taking advantage of the molecular weight dependence of the glass transition of polymers and their ability to form perfectly miscible blends, we propose a way to modify the fragility of a system, from fragile to strong, keeping the same…
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two…
Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…
We introduce a new symmetry class of both boxed plane partitions and lozenge tilings of a hexagon, called the $\mathbf{r}$-block diagonal symmetry class, where $\mathbf{r}$ is an $n$-tuple of non-negative integers. We prove that the tiling…
Flows of suspensions are often affected by wall slip, that is the fluid velocity $v_{f}$ in the vicinity of a boundary differs from the wall velocity $v_{w}$ due to the presence of a lubrication layer. While the slip velocity $v_s=\vert…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
A well known result by Lagarias and Ziegler states that there are finitely many equivalence classes of d-dimensional lattice polytopes having volume at most K, for fixed constants d and K. We describe an algorithm for the complete…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
Solids deform and fluids flow, but soft glassy materials, such as emulsions, foams, suspensions, and pastes, exhibit an intricate mix of solid and liquid-like behavior. While much progress has been made to understand their elastic (small…
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments under such loading have found this to be accompanied by a striking dip in the segmental relaxation time.…
The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In…
A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…