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Fundamental bounds on antenna gain are found via convex optimization of the current density in a prescribed region. Various constraints are considered, including self-resonance and only partial control of the current distribution. Derived…
Theoretical treatments of strong-field physics have long relied on the numerical solution of the time-dependent Schr\"odinger equation. The most effective such treatments utilize a discrete spatial representation---a grid. Since most…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
We consider the unit ball $\Omega\subset \mathbb{R}^N$ ($N\ge2$) filled with two materials with different conductivities. We perform shape derivatives up to the second order to find out precise information about locally optimal…
We are concerned with the quantitative study of the electric field perturbation due to the presence of an inhomogeneous conductive rod embedded in a homogenous conductivity. We sharply quantify the dependence of the perturbed electric field…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…
When two perfectly conducting inclusions are located closely to each other, the electric field concentrates in a narrow region in between two inclusions, and becomes arbitrarily large as the distance between two inclusions tends to zero.…
This paper develops a framework connecting discrete adjoint gradient-error analysis with an optimization method that uses directional error tolerances, and applies it to airfoil shape optimization governed by a conservative full-potential…
Numerical simulations of convection in a layer filled with ideal gas are presented. The control parameters are chosen such that there is a significant variation of density of the gas in going from the bottom to the top of the layer. The…
A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the twelve values at the three Gauss points on each of the four edges. Due to the existence of one…
We calculate the effective electromagnetic Lagrangian up to the lowest-order corrections in the derivatives for two fermionic systems of interest in condensed matter physics in the linearized approximation of the tight-binding Hamiltonian…
A rigorous analytical representation for the multiple scattering coefficients of the fields radiated by an infinite grating of dielectric circular cylinders excited by an obliquely incident plane electromagnetic wave is derived in terms of…
The optimal insulation of a heat conducting body by a thin film of variable thickness can be formulated as a nondifferentiable, nonlocal eigenvalue problem. The discretization and iterative solution for the reliable computation of…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
We consider the two-dimensional version of Calder\`on's problem. When the D-N map is assumed to be known up to an error level $\varepsilon_0$, we investigate how the resolution in the determination of the unknown conductivity deteriorates…
In high-contrast composites, if an inclusion is in close proximity to the matrix boundary, then the stress, which is represented by the gradient of a solution to the Lam\'{e} systems of linear elasticity, may exhibits the singularities with…
We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…
One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or approximation of vector-valued functions on Delaunay meshes in…