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We address extremum problems for spectral quantities associated with operators of the form $\Delta^2-\tau\Delta$ with Dirichlet boundary conditions, for non-negative values of $\tau$. The focus is on two shape optimisation problems:…
The concept of optimal communication channels shapes our understanding of wave-based communication. Its analysis, however, always pertains to specific communication-domain geometries, without a general theory of scaling laws or fundamental…
A quantum emitter efficiently coupled to a nanophotonic waveguide constitutes a promising system for the realization of single-photon transistors, quantum-logic gates based on giant single-photon nonlinearities, and high bit-rate…
We revisit the old problem of which is the best single particle basis to express a Hubbard-like lattice model. A rigorous variational solution of this problem leads to equations in which the answer depends in a self-consistent manner on the…
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called potentials; equivalently, potentials can be defined as a…
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this,…
We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which…
In many applications, a state-space model depends on a parameter which needs to be inferred from a data set. Quite often, it is necessary to perform the parameter inference online. In the maximum likelihood approach, this can be done using…
Fundamental antenna limits of the gain-bandwidth product are derived from polarizability calculations. This electrostatic technique has significant value in many antenna evaluations. Polarizability is not available in closed form for most…
Following recent interest in the qualitative analysis of some optimal control and shape optimisation problems, we provide in this article a detailed study of the optimisation of Robin boundary conditions in PDE constrained calculus of…
We study measures and point configurations optimizing energies based on multivariate potentials. The emphasis is put on potentials defined by geometric characteristics of sets of points, which serve as multi-input generalizations of the…
Capacity scaling laws are analyzed in an underwater acoustic network with $n$ regularly located nodes on a square. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of $n$. In the network, we…
We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-$\delta'$ contact interaction at the well edge. This contact potential is defined by appropriate…
In this paper, we study the optimization of the first Laplacian eigenvalue on axisymmetric doubly connected domains under positive Robin boundary conditions. Under additional geometric constraints, we prove that spherical shells maximize…
The scaling limit of the higher level Bethe Ansatz (HLBA) equations for a macroscopically half-filled Hubbard chain is considered. These equations practically decouple into three disjoint sets which are again of the BA type, and correspond…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
We consider the following eigenvalue optimization in the composite membrane problem with fractional Laplacian: given a bounded domain $\Omega\subset \mathbb{R}^n$, $\alpha>0$ and $0<A<|\Omega|$, find a subset $D\subset \Omega$ of area $A$…
We derive an effective Hamiltonian for the ionic Hubbard model at half filling, extended to include nearest-neighbor repulsion. Using a spin-particle transformation, the effective model is mapped onto simple spin-1 models in two particular…
Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light…