Related papers: Optimal Currents on Arbitrarily Shaped Surfaces
Quasi-normal-eigenvalue optimization is studied under constraints $b_1(x) \le B(x) \le b_2 (x)$ on structure functions $B$ of 2-side open optical or mechanical resonators. We prove existence of various optimizers and provide an example when…
We present a general problem formulation for optimal parameter estimation based on quantized observations, with application to antenna array communication and processing (channel estimation, time-of-arrival (TOA) and direction-of-arrival…
We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
One of the most popular approaches for solving total variation-regularized optimization problems in the space of measures are Particle Gradient Flows (PGFs). These restrict the problem to linear combinations of Dirac deltas and then perform…
Existing optimization methods are used to calculate the upper-bounds on radiation efficiency with and without the constraint on self-resonance. These bounds are used for the design and assessment of small electric-dipole-type antennas. We…
We study theoretically the spontaneous edge current in a small chiral superconductor with surface roughness. We obtained self-consistent solutions of the pair potential and the vector potential by solving the quasiclassical Eilenberger…
Chains of resonators in the form of spring-mass systems have long been known to exhibiting interesting properties such as band gaps. Such features can be leveraged to manipulate the propagation of waves such as the filtering of specific…
The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper…
This paper introduces a computational approach to identify performance constraints in the time-domain, offering a way to design systems in pulse operation. This work presents a comprehensive application of convex optimization to determine…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
Using a time-dependent approach the analysis and optimization of a planar FEL-amplifier with an axial magnetic field and an irregular waveguide is performed. By applying methods of nonlinear dynamics three-dimensional equations of motion…
We show that the use of the electromagnetic inverse source framework offers great flexibility in the design of metasurfaces. In particular, this approach is advantageous for antenna design applications where the goal is often to satisfy a…
Adaptive mesh refinement efficiently facilitates the computation of gravitational waveforms in numerical relativity. However, determining precisely when, where, and to what extent to refine when solving the Einstein equations poses…
A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied shape and data analysis. It is based on the Courant-Fischer…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
In optical metrology, grating-like structures are used as tools to evaluate the performance of lithographic techniques. In particular, several shape parameters characterize those structures. One of them, termed side-wall angle, suffers from…
Huygens' metasurfaces have demonstrated the ability to tailor electromagnetic wavefronts with passive low-profile structures. The fundamental constraint enabling passive and ideally lossless solutions is the conservation of the normal real…
This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…