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Related papers: Computation of shape Taylor expansions

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We employ a scalar model to exemplify the use of contour deformations when solving Lorentz-invariant integral equations for scattering amplitudes. In particular, we calculate the onshell 2 -> 2 scattering amplitude for the scalar system.…

High Energy Physics - Phenomenology · Physics 2019-11-06 Gernot Eichmann , Pedro Duarte , M. T. Peña , Alfred Stadler

Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…

Machine Learning · Computer Science 2025-07-15 Guoyou Wang , Yihua Tan , Shiqi Liu

In this paper, we propose a method to calculate the exact Taylor series of the scattering matrix in general multiterminal tight-binding systems to arbitrary order N, which allows us to find the Taylor expansion of Landauer conductance in…

Mesoscale and Nanoscale Physics · Physics 2020-06-15 Carlos Ramirez , Mauricio J. Rodriguez , Bryan D. Gomez

A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…

Atomic Physics · Physics 2007-05-23 Nark Nyul Choi , Min-Ho Lee , Sung Ho Suck Salk

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…

Numerical Analysis · Mathematics 2018-03-14 Xia Ji , Xiaodong Liu , Yingxia Xi

We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…

Numerical Analysis · Mathematics 2013-10-22 Mourad Sini , Nguyen Trung Thành

A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…

Sound · Computer Science 2015-06-15 Joakim Andén , Stéphane Mallat

A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As the linear sampling method, the method sets up ill-posed integral equations and uses the (approximate) solutions to…

Analysis of PDEs · Mathematics 2018-08-01 Juan Liu , Jiguang Sun

Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…

Numerical Analysis · Mathematics 2025-07-17 Felipe Vico , Leslie Greengard , Michael O'Neil , Manas Rachh

Often, the unknown diffusivity in diffusive processes is structured by piecewise constant patches. This paper is devoted to efficient methods for the determination of such structured diffusion parameters by exploiting shape calculus. A…

Optimization and Control · Mathematics 2021-04-12 Volker Schulz , Martin Siebenborn , Kathrin Welker

A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on…

Classical Physics · Physics 2023-02-27 Dorian Bouchet , Emmanuel Bossy

In this paper, we consider acoustic or electromagnetic scattering in two dimensions from an infinite three-layer medium with thousands of wavelength-size dielectric particles embedded in the middle layer. Such geometries are typical of…

Numerical Analysis · Mathematics 2015-06-22 Jun Lai , Motoki Kobayashi , Leslie Greengard

We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the…

Materials Science · Physics 2009-11-10 Michele Lazzeri , Francesco Mauri

The long standing problem on finding the height correlation function is studied by the inverse scattering problem. We propose a new method in the frame work of Kirchhoff theory which we call "path derivation of scattered wave (PDSW)" in…

Optics · Physics 2015-06-12 M. Zamani , S. M. Fazeli , M. Salami , S. Vasheghani Farahani , G. R. Jafari

We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…

Analysis of PDEs · Mathematics 2020-10-05 Yves Capdeboscq , Roland Griesmaier , Marvin Knöller

We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…

Numerical Analysis · Mathematics 2025-03-14 Davide Pradovera , Monica Nonino , Ilaria Perugia

We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…

Numerical Analysis · Mathematics 2016-04-08 Charles L. Epstein , Michael O'Neil

This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…

Numerical Analysis · Mathematics 2026-02-03 Junping Wang

We consider the rationally extended exactly solvable Eckart potentials which exhibit extended shape invariance property. These potentials are isospectral to the conventional Eckart potential. The scattering amplitude for these rationally…

High Energy Physics - Theory · Physics 2015-09-30 Rajesh Kumar Yadav , Avinash Khare , Bhabani Prasad Mandal

We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable…

Numerical Analysis · Mathematics 2017-09-18 Bo Wang , Li-Lian Wang , Ziqing Xie