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Monolayers of growing bacteria, confined within channel geometries, exhibit self-organization into a highly aligned laminar state along the axis of the channel. Although this phenomenon has been observed in experiments and simulations under…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
When a thin sheet is crushed into a small three-dimensional volume, it invariably forms a structure with a low volume fraction but high resistance to further compression. Being a far-from-equilibrium process, forced crumpling is not…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
Using transfer operator and fundamental measure theories, we examine the structural and thermodynamic properties of hard rectangles confined between two parallel hard walls. The side lengths of the rectangle ($L$ and $D$, $L>D$) and the…
We report numerical simulation of the deposition of spherical particles on a planar surface, by ballistic, straight-line trajectory transport, and assuming irreversible adhesion on contact with the surface or previously deposited particles.…
We present an alternative derivation of upper-bounds for the bulk modulus of both two-dimensional and three-dimensional cellular materials. For two-dimensional materials, we recover exactly the expression of the Hashin-Shtrikman (HS)…
Detection of crystal structures from particle positions of crystalline assemblies formed in computer simulations is an unsolved problem. The standard protocol, formulated in the reciprocal space, for structure determination from…
One of the essential questions in the area of granular matter is, how to obtain macroscopic tensorial quantities like stress and strain from ``microscopic'' quantities like the contact forces in a granular assembly. Different averaging…
We use circle-packing methods to generate quadrilateral meshes for polygonal domains, with guaranteed bounds both on the quality and the number of elements. We show that these methods can generate meshes of several types: (1) the elements…
Crystal growth processes produce a diverse array of surface formations, primarily distinguished by their geometric shapes. While some structures strictly adhere to the underlying crystal symmetry, others exhibit universal circular or oval…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Fully-nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A new formulation of the optimization is…
Crystalline order in dense packings of long polymers with a definite handedness is difficult to reconcile with the tendency of these chiral objects to twist and braid about each other. If the chirality is weak, the state of lowest energy is…
Hierarchical matrix computations have attracted significant attention in the science and engineering community as exploiting data-sparse structures can significantly reduce the computational complexity of many important kernels. One…
This note presents a new, self-contained proof of Shahgholian's geometric theorem on quadrature surfaces using the thickness function and level set methods. By relying on a radial parametrisation and fundamental maximum principles, the…
The problem of imaging materials with circular polarization properties is discussed within the framework of vectorial ptychography. We demonstrate, both theoretically and numerically, that using linear polarizations to investigate such…
We study the optimal packing of short, hard spherocylinders confined to lie tangential to a spherical surface, using simulated annealing and molecular dynamics simulations. For clusters of up to twelve particles, we map out the changes in…
We consider compact connected minimal surfaces, with a pair of boundary curves (not necessarily convex) in distinct planes, that have least-area amongst all orientable surfaces with the same boundary. When the planes containing these two…