Related papers: Convolution Quadrature for Wave Simulations
We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…
Numerical simulation of fluids plays an essential role in modeling many physical phenomena, which enables technological advancements, contributes to sustainable practices, and expands our understanding of various natural and engineered…
This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two-spatial dimensions. The…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features…
A phenomenological method is developed to consider elastic guided wave propagation in complex curved waveguides. The theory on guided wave propagation in hollow circular cylinders is used in order to verify the method. The results are…
The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge…
Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a…
This note presents in a technical though hopefully pedagogical way the three most common forms of neural network architectures: Feedforward, Convolutional and Recurrent. For each network, their fundamental building blocks are detailed. The…
The convolution formula is derived within the framework of the decay-chain method for decay channels with three and four particles in a final state. To get this formula exactly for unstable particle of any type one must modify the…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
This paper proposes a novel Convolutional Neural Network model for contour data analysis (ContourCNN) and shape classification. A contour is a circular sequence of points representing a closed shape. For handling the cyclical property of…
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…
Further results are reported for the one-component quaternionic wave equation recently introduced. A Lagrangian is found for the momentum-space version of the free equation; and another, nonlocal in time, is found for the complete equation.…