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We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set $P$ of $n$ points in the…
The presence of current singularities in a quasisymmetric magnetic field is explored. Quasisymmetry is shown effective in isolating Pfirsch-Schl\"{u}ter singularities, to leading order, to a single magnetic surface resonant with the…
We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell confined between two parallel surfaces: a planar surface and a spatially modulated one. The relief of the modulated surface is described…
Spatial light modulators are widely used to perform modulations of different properties of the electromagnetic field. In this work, a simple optimization method for general double-pass setups was developed. It takes into account the…
High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the computational mesh with non-smooth features to represent them…
We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…
Elastic metasurfaces offer precise control over elastic waves for applications such as vibration isolation, sensing, and imaging. However, achieving high-efficiency and scattering-free performance with complex functionalities remains a…
Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an…
Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…
The progress of realizing colloidal structures mimicking natural forms of organization in condensed matter is inherently limited by the availability of suitable colloidal building blocks. To enable new forms of crystalline and…
Many magnetic structures in the solar atmosphere evolve rather slowly so that they can be assumed as (quasi-)static or (quasi-)stationary and represented via magneto-hydrostatic (MHS) or stationary magneto-hydrodynamic (MHD) equilibria,…
To identify under what conditions guiding-centre or full-orbit tracing should be used, an estimation of the spatial variation of the magnetic field is proposed, not only taking into account gradient and curvature terms but also parallel…
Quasi-poloidal (QP) magnetic fields have desirable properties for confining plasma: no radial drift of guiding centres (with positive implications for neoclassical transport), zero Pfirsch-Schl\"uter current, a lower level of damping for…
In this work, we introduce new direct search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy black box oracle for the lower-level problem, and deal both with smooth and potentially…
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential…
Directed self-assembly (DSA) of block-copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP mixtures to form nanoscale…
In this work, we demonstrate a method for constructing the Solov'ev equilibrium with any given 2D shape surrounded by a vacuum region using external poloidal field coils. The computational domain consists of two parts: the plasma region,…
The equivalence between the natural minimization of energy in a dynamical system and the minimization of an objective function characterizing a combinatorial optimization problem offers a promising approach to designing dynamical…
Infinitesimal electric and magnetic dipoles are widely used as an equivalent radiating source model. In this paper, an improved method for dipole extraction from magnitude-only electromagnetic-field data based on genetic algorithm and…