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Nov 02, 2017
Numerical Analysis

Direct sampling methods for inverse elastic scattering problems

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically…
Aug 04, 2011

Constructing EOB dynamics with numerical energy flux for intermedia…

A new scheme for computing dynamical evolutions and gravitational radiations for intermediate-mass-ratio inspirals (IMRIs) based on an effective one-…
Mar 27, 2015
Physics and Society
Social and Information Networks

Potts model based on a Markov process computation solves the communit…

Potts model is a powerful tool to uncover community structure in complex networks. Here, we propose a new framework to reveal the optimal number of c…
Jan 06, 2018
Analysis of PDEs

The work of Y. Deng was supported by NSF grant of China, No. 11601528, NSF grant of Hunan No.2017JJ3432, Mathematics and Interdisciplinary Sciences Project, Central South University. The work of H. Liu was supported by the startup fund and FRG grant…

Recovery of an embedded obstacle and the surrounding medium for Max…

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric f…
Dec 08, 2009
Analysis of PDEs

Direct and inverse obstacle scattering problems in a piecewise homo…

This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous mediu…
Jan 19, 2018
Numerical Analysis

A direct imaging method for inverse scattering by unbounded rough s…

This paper is concerned with the inverse scattering problem by an unbounded rough surface. A direct imaging method is proposed to reconstruct the rou…
Jul 11, 2011
Numerical Analysis
Probability

In this chapter, we investigate the concentration properties of the collection of Feynman-Kac particle measures introduced in section 1.4, in terms of the contraction parameters τk,l(n) and ¯¯¯τk,l(m) introduced in definition 3.3, and in corollary 3…

On the concentration properties of Interacting particle processes

These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle…
Aug 10, 2017
Dynamical Systems

In this part, we obtain the pointwise convergence with rationally independent rotation on the torus of the multiple ergodic averages.

On the convergence of the time average for skew-product structure and…

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-u…
Nov 21, 2016
Machine Learning
Computer Vision

Effective Deterministic Initialization for $k$-Means-Like Methods via…

The $k$-means clustering algorithm is popular but has the following main drawbacks: 1) the number of clusters, $k$, needs to be provided by the user …
Jun 05, 2019
Analysis of PDEs

Inverse electromagnetic source scattering problems with multi-frequen…

This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for solving inverse electromagnetic source scattering probl…
Aug 28, 2016

Binary Black Hole merger in f(R) theory

In the near future, gravitational wave detection is set to become an important observational tool for astrophysics. It will provide us with an excell…
Jun 19, 2019
Analysis of PDEs

Uniqueness in inverse electromagnetic scattering problem with phasele…

This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous …
Oct 05, 2017

Long-Term Postmerger Simulations of Binary Neutron Star Coalescence: …

It has been estimated that a significant proportion of binary neutron star merger events produce long-lived massive remnants supported by differentia…
Nov 16, 2013
Analysis of PDEs

Subsonic-sonic Limit of Approximate Solutions to Multidimensional Ste…

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible…
Jan 25, 2019
Numerical Analysis

A novel integral equation for scattering by locally rough surfaces an…

This paper is concerned with direct and inverse scattering by a locally perturbed infinite plane (called a locally rough surface in this paper) on wh…
Jun 24, 2018
Analysis of PDEs

Uniqueness in inverse scattering problems with phaseless far-field da…

This paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work ({\em…
Dec 07, 2017
Analysis of PDEs

Fast acoustic source imaging using multi-frequency sparse data

We consider the acoustic source imaging problems using multiple frequency data. Using the data of one observation direction/point, we prove that some…
Oct 19, 2016
Numerical Analysis

Recovering scattering obstacles by multi-frequency phaseless far-fiel…

It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacl…
Jan 18, 2018
Numerical Analysis

An FFT-based algorithm for efficient computation of Green's functions…

The integral equation method is widely used in numerical simulations of 2D/3D acoustic and electromagnetic scattering problems, which needs a large n…
Aug 06, 2018
Analysis of PDEs

Phaseless inverse source scattering problem: phase retrieval, uniquen…

Similar to the obstacle or medium scattering problems, an important property of the phaseless far field patterns for source scattering problems is th…
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