Related papers: Statistical Mechanical Model for a closed loop ple…
It is common to study polymer physics through the use of idealized single-chain models, and the most popular of these is the freely jointed chain model. In certain thermodynamic ensembles, statistical mechanical treatment of this model is…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
We consider a linearly elastic body consisting of two equal symmetrically arranged layers (or half-planes) connected by a structured interface as a prospective crack path. The interface is comprised by periodic discrete system of bonds. In…
A conformal restriction system is a commutative, associative, unital algebra equipped with a representation of the groupoid of univalent conformal maps on connected open sets of the Riemann sphere, and a family of linear functionals on…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
The statistical mechanics of a long knotted collapsed polymer is determined by a free-energy with a knot-dependent subleading term, which is linked to the length of the shortest polymer that can hold such knot. The only other parameter…
In this paper we study Maxwell lattices with non-rectilinear constraints, where the elastic energy is determined by the collective motion of three or more particles, in contrast to a rectilinear spring whose elastic energy only relies on…
We study a class of models for brittle fracture: elastic theory models which allow for cracks but not for plastic flow. We show that these models exhibit, at all finite temperatures, a transition to fracture under applied load similar to…
Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set-point. This phenomenon is often referred to as mechanical homeostasis. In contradiction…
We introduce the strict-weak polymer model, and show the KPZ universality of the free energy fluctuation of this model for a certain range of parameters. Our proof relies on the observation that the discrete time geometric q-TASEP model,…
An $hp$-adaptive continuous Galerkin finite element method is developed to analyze a static anti-plane shear crack embedded in a nonlinear, strain-limiting elastic body. The geometrically linear material is described by a constitutive law…
This contribution relates to the simulation of the flow around the tip of a helicopter rotor blade in hovering flight conditions. We here propose a new methodology of framework adaptation, using a comprehensive rotor code and high-fidelity…
Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously…
Using a two dimensional lattice model we investigate the crack growth under the influence of remote tensile forces as well as due to an internally applied pressure (hydraulic fracturing). For homogeneous elastic properties we present…
We study the effects of thermal fluctuations on a small elastic ring. We derive analytical expressions for the correlation functions of the Euler angles, for the real space two--point correlation functions and for the probability…
This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack…
The buckling and twisting of slender, elastic fibers is a deep and well-studied field. A slender elastic rod that is twisted with respect to a fixed end will spontaneously form a loop, or hockle, to relieve the torsional stress that builds.…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
The superfluid weight is an important observable of superconducting materials since it is related to the London penetration depth of the Meissner effect. It can be computed from the change in the grand potential (or free energy) in response…
In this paper we look at a class of random optimization problems that arise in the forms typically known in statistical physics as Little models. In \cite{BruParRit92} the Little models were studied by means of the well known tool from the…