Related papers: Nonlinear bang-bang eigenproblems and optimization…
This paper is concerned with an optimisation problem of Robin Laplacian eigenvalue with respect to an indefinite weight, which is formulated as a shape optimisation problem thanks to the known bang-bang distribution of the optimal weight…
We develop an approximate quasi-static theory describing the low-frequency plasmonic resonances of slender nanometallic rings and configurations thereof. First, we use asymptotic arguments to reduce the plasmonic eigenvalue problem…
In this paper we investigate a minimization problem related to the principal eigenvalue of the $s$-wave Schr\"{o}dinger operator. The operator depends nonlinearly on the eigenparameter. We prove the existence of a solution for the…
We derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the…
The optical resonance problem is similar to but different from time-steady Schr\"{o}dinger equation. One big challenge is that the eigenfunctions in resonance problem is exponentially growing. We give physical explanation to this boundary…
We study the spectral problems associated with the finite-difference operators $H_N = 2 \cosh(p) + V_N(x)$, where $V_N(x)$ is an arbitrary polynomial potential of degree $N$. These systems can be regarded as a solvable deformation of the…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
The nonlocal order parameter equation for nonlinear optical resonator is approximated in the limit of high Fresnel number by the Swift- Hohenberg equation. The exact soliton and periodic solutions of the Swift- Hohenberg equation for…
In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and…
The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, although Bakushinskii has shown that there are always…
Using gravitational waves to probe the geometry of the ringing remnant black hole formed in a binary black hole coalescence is a well-established way to test Einstein's theory of general relativity. However, doing so requires knowledge of…
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…
Optimization of resonances associated with 1-D wave equations in inhomogeneous media is studied under the constraint $\| B \|_1 <= m$ on the nonnegative function $B \in L^1 (0,\ell)$ that represents the medium's structure. From the Physics…
In this article we study some optimal design problems related to nonstandard growth eigenvalues ruled by the $g-$Laplacian operator. More precisely, given $\Omega\subset \R^n$ and $\alpha,c>0$ we consider the optimization problem $\inf \{…
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…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an…
We consider the multiphase shape optimization problem $$\min\Big\{\sum_{i=1}^h\lambda_1(\Omega_i)+\alpha|\Omega_i|:\ \Omega_i\ \hbox{open},\ \Omega_i\subset D,\ \Omega_i\cap\Omega_j=\emptyset\Big\},$$ where $\alpha>0$ is a given constant…
The maximum amplitude of mechanical oscillators coupled to optical cavities are studied both analytically and numerically. The optical backaction on the resonator enables self-sustained oscillations whose limit cycle is set by the dynamic…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…