Related papers: A PML method for signal-propagation problems in ax…
Due to discretization effects and truncation to finite domains, many electromagnetic simulations present non-physical modifications of Maxwell's equations in space that may generate spurious signals affecting the overall accuracy of the…
This paper is concerned with three-dimensional acoustic wave scattering in two-layer media, where the two homogeneous layers are separated by a locally perturbed plane featuring an axially symmetric perturbation. A fast novel boundary…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
Structure-preserving methods can be derived for the Vlasov-Maxwell system from a discretisation of the Poisson bracket with compatible finite-elements for the fields and a particle representation of the distribution function. These…
Three-dimensional Polarized Light Imaging (3D-PLI) is a promising technique to reconstruct the nerve fiber architecture of human post-mortem brains from birefringence measurements of histological brain sections with micrometer resolution.…
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…
Here a viable and never before investigated mechanism of propagation of spikes along neurons is proposed. In the following, velocity of propagation of small-amplitude pressure waves through the cytoplasmic interior of myelinated and…
Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the…
As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding…
When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of…
Dispersion lies at the heart of real-time signal processing systems across the entire electromagnetic spectrum from radio to optics. However, the performance and applicability of such systems have been severely plagued by distortions due to…
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…
We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. The methodology addresses two well-known challenges in nonlinear optics:…
The main task in this paper is to prove that the perfectly matched layers (PML) method converges exponentially with respect to the PML parameter, for scattering problems with periodic surfaces. In [5], a linear convergence is proved for the…
This paper considers the problem of optimally deploying omnidirectional sensors, with potentially limited sensing radius, in a network-like environment. This model provides a compact and effective description of complex environments as well…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
The Helmholtz scattering problem with high wave number is truncated by the perfectly matched layer (PML) technique and then discretized by the linear continuous interior penalty finite element method (CIP-FEM). It is proved that the…
Propagation of extremely short electromagnetic pulses in a homogeneous doubly-resonant medium is considered in the framework of the total Maxwell-Duffing-Lorentz model, where the Duffing oscillators (anharmonic oscillators with cubic…
Based on the perfectly matched layer (PML) technique, this paper develops a high-accuracy boundary integral equation (BIE) solver for acoustic scattering problems in locally defected layered media in both two and three dimensions. The…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…