Related papers: Planar polycrystals with extremal bulk and shear m…
A strategy is developed for generating equilibrated high molecular-weight polymer melts described with microscopic detail by sequentially backmapping coarse-grained (CG) configurations. The microscopic test model is generic but retains…
In this paper, maximum principles for Euclidean and hyperbolic discrete conformal structures on polyhedral surfaces are established. These maximum principles unify and generalize the maximum principles for vertex scalings and different…
The mechanism by which a patterned state accommodates the breaking of translational symmetry by a phase boundary or a sample wall has been addressed in the context of Landau branching in type-I superconductors, refinement of magnetic…
Packing problems have been of great interest in many diverse contexts for many centuries. The optimal packing of identical objects has been often invoked to understand the nature of low temperature phases of matter. In celebrated work,…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
We study the two-dimensional hierarchical rectangle packing problem, motivated by applications in analog integrated circuit layout, facility layout, and logistics. Unlike classical strip or bin packing, the dimensions of the container are…
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
A layer of monodisperse circular steel disks in a nearly square horizontal cell forms, for shear amplitudes SA $\le$ 0.08, hexagonal close-packed crystallites that grow and merge until a single crystal fills the container. Increasing the…
Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…
Sheared multi-component bulk metallic glasses are characterized by both chemical and structural disorder that define their properties. We investigate the behavior of the local, microstructural elastic modulus across the plastic yielding…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
The clean surfaces of quasicrystals, orthogonal to the directions of the main symmetry axes, have a terrace-like appearance. We extend the Bravais' rule for crystals to quasicrystals, allowing that instead of a single atomic plane a layer…
Manipulating the way in which colloidal particles self-organise is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly…
Paradigmatic model systems, which are used to study the mechanical response of matter, are random networks of point-atoms, random sphere packings, or simple crystal lattices, all of these models assume central-force interactions between…
We consider the isoperimetric problem for clusters in the plane with a double density, that is, perimeter and volume depend on two weights. In this paper we consider the isotropic case, in the parallel paper "On the Steiner property for…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Conical surfaces pose an interesting challenge to crystal growth: a crystal growing on a cone can wrap around and meet itself at different radii. We use a disk-packing algorithm to investigate how this closure constraint can geometrically…
We provide upper and lower bounds on the least-perimeter way to enclose and separate n regions of equal area in the plane. Along the way, inside the hexagonal honeycomb, we provide minimizers for each n .
The self-gravitating, spherically symmetric thin shells built of orbiting particles are sstudied. Two new features are found. One is the minimal possible value for an angular momentum of particles, above which elleptic orbits become…