Related papers: Nonlinear eigenvalue problems for coupled Helmholt…
In Part I of this paper, we introduced a two dimensional eigenvalue problem (2DEVP) of a matrix pair and investigated its fundamental theory such as existence, variational characterization and number of 2D-eigenvalues. In Part II, we…
The (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint and nonlinear spectral problems that arise in the theory of wave scattering. They connect to the direct and inverse scattering problems in many…
Solving for the lowest energy eigenstate of the many-body Schrodinger equation is a cornerstone problem that hinders understanding of a variety of quantum phenomena. The difficulty arises from the exponential nature of the Hilbert space…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
Nonlinear eigenvalue problems for pairs of homogeneous convex functions are particular nonlinear constrained optimization problems that arise in a variety of settings, including graph mining, machine learning, and network science. By…
In this paper we present benchmark problems for non-selfadjoint elliptic eigenvalue problems with large defect and ascent. We describe the derivation of the benchmark problem with a discontinuous coefficient and mixed boundary conditions.…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
NP problems are closely related to practical optimization challenges but often suffer from exponential increases in computation time as problem sizes grow. Quantum annealing offers a promising approach to solve NP problems faster than…
We consider a planar waveguide with combined Dirichlet and Neumann conditions imposed in a "twisted" way. We study the discrete spectrum and describe it dependence on the configuration of the boundary conditions. In particular, we show that…
In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable…
A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed guaranteed computation methods for both eigenvalues and…
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to…
Mathematical settings in which heterogeneous structures affect electron transport through a tube-shaped quantum waveguide are studied, highlighting the interaction between heterogeneities and geometric parameters like curvature and torsion.…
In this paper we study the variational method and integral equation methods for a conical diffraction problem for imperfectly conducting gratings modeled by the impedance boundary value problem of the Helmholtz equation in periodic…
We claim that changes of scales and fine-structure could increase from multisoliton behavior of internal waves dynamics and, further, in the so-called "wave mixing". We consider initial-boundary problems for Euler equations with a…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
The Lane-Emden equation, a nonlinear second-order ordinary differential equation, plays a fundamental role in theoretical physics and astrophysics, particularly in modeling the structure of stellar interiors. Also referred to as the…
The paper aims to reveal the relationship between the geometrical features and linear and nonlinear optical properties of InAs quantum dots (QDs). This problem is justified by the extreme variety offered by the recent advances in growth…