Related papers: FE-Holomorphic Operator Function Method for Nonlin…
We present in this paper a numerical study of the vibrational eigenvectors of a two-dimensional amorphous material, previously deeply studied from the point of view of mechanical properties and vibrational eigen-frequencies [7-10].…
The Evans function is a well known tool for locating spectra of differential operators in one spatial dimension. In this paper we construct a multidimensional analogue as the modified Fredholm determinant of a ratio of Dirichlet-to-Robin…
A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at…
We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding…
Electrically-excited electroelastic extensional vibrations of an arbitrarily cut three-dimensional piezocrystal resonator are analyzed variationally. A set of trigonometric trial functions applicable to a waveguide behavior of the resonator…
The effect of the initial uniaxial stress and a surrounding elastic matrix on the transverse vibration response of a single-layered graphene sheet (SLGS) is investigated through a theoretical formulation that is based on the nonlocal…
We consider a class of eigenvalue problems for poly-harmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain…
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters,…
Numerical simulation of nonlinear elastic wave propagation in solids with cracks is indispensable for decoding the complicated mechanisms associated with the nonlinear ultrasonic techniques in Non-Destructive Testing (NDT). Here, we…
This paper studies the eigenvalue problem $K \psi = \lambda \psi$ associated with a Fredholm integral operator $K$ defined by a smooth kernel. The focus is on analyzing the convergence behaviour of numerical approximations to eigenvalues…
This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…
We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the…
For soft robots to work effectively in human-centered environments, they need to be able to estimate their state and external interactions based on (proprioceptive) sensors. Estimating disturbances allows a soft robot to perform desirable…
By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator. As a consequence, we prove existence of a bifurcation point for a non-linear inclusion…
High-frequency micrometrical vibrations have been shown to greatly influence the adhesive performance of soft interfaces, however a detailed comparison between theoretical predictions and experimental results is still missing. Here, the…
We consider a charged particle which is driven by a time-dependent flux threading a circular ring system. Various approaches including classical treatment, Fourier expansion method, time-evolution method, and Lewis-Riesenfeld method are…
The article is devoted to the following question. Consider a periodic self-adjoint difference (differential) operator on a graph (quantum graph) G with a co-compact free action of the integer lattice Z^n. It is known that a local…
The study of resonances of the Schr\"{o}dinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds…
We examine the stability of a soft dielectric plate deformed by the coupled effects of a mechanical pre-stress applied on its lateral faces and an electric field applied through its thickness under charge control. The electric field is…
The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…