Related papers: Homotopy analysis method applied to second-order f…
The homogeneous wave equation is solved by a time-domain boundary element method (BEM) using low-order shape functions for spatial, and the generalised convolution quadrature method (gCQ) by Lopez-Fernandez and Sauter for temporal…
In systems biology, it is becoming increasingly common to measure biochemical entities at different levels of the same biological system. Hence, data fusion problems are abundant in the life sciences. With the availability of a multitude of…
We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…
We study the light propagation in one-dimensional photonic crystal via nonlinear Four Wave Mixing (FWM) process. The linear and nonlinear refractive indexes are approximated with the first Fourier harmonic term. A system of the nonlinear…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
In the present paper, a new three-scale asymptotic homogenization method is proposed to study the electrical behavior of the cardiac tissue structure with multiple heterogeneities at two different levels. The first level is associated with…
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source…
We present a high sensitivity method allowing the measurement of the non linear dielectric susceptibility of an insulating material at finite frequency. It has been developped for the study of dynamic heterogeneities in supercooled liquids…
The generation of harmonics by atoms or ions in a two-color, coplanar field configuration with commensurate frequencies is investigated through both, an analytical calculation based on the Lewenstein model and the numerical ab initio…
A hidden symmetry of the nonlinear wave equation is exploited to analyse the propagation of paraxial and uniform atom-laser beams in time-independent, quadratic and cylindrical potentials varying smoothly along the propagation axis. The…
In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a…
We employ transformation optics to optimize the generic nonlinear wave interaction of second-harmonic generation from a pair of touching metallic wires. We demonstrate a 10 orders of magnitude increase in the second-harmonic scattering…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
We consider harmonics generation and wave-mixing by two-color multi photon resonant excitation of three-level atoms/molecules in strong laser fields. The coherent part of the spectra corresponding to multicolor harmonics generation is…
Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments…
Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…
The Holomorphic Embedding Load-Flow Method (HELM) was recently introduced as a novel technique to constructively solve the power-flow equations in power grids, based on advanced complex analysis. In this paper, the theoretical foundations…
In this article, we consider nonlinear complementarity problem. We introduce a new homotopy function for finding the solution of nonlinear complementarity problem through the trajectory . We show that the homotopy path approaching the…
We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which are used to model the…