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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence in probability from moderate interacting SDE system to degenerate Keller-Segel systema
中度相互作用 SDE系统 凯勒-西格尔系统 概率收敛性
2023/4/13
In this talk I will present one of our recent work in rigorous derivation of the degenerate parabolic-elliptic Keller-Segel system. We establish the classical solution theory of the degenerate parabol...
A PRIORI ESTIMATES FOR MANY-BODY HAMILTONIAN EVOLUTION OF INTERACTING BOSON SYSTEM
Dispersive estimates interaction Morawetz type (correlation) estimates many-body Hamiltonian many-body Schrodinger equation quantum hydrodynamics BBGKY hierarchy
2015/10/16
We study the evolution of a many-particle system whose wave function obeys the N-body Schr¨ odinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle interactions in the...
Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons.I.
Second-Order Corrections Mean Field Evolution Weakly Interacting Bosons
2015/10/16
Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-fiel...
One-dimensional model of interacting-step fluctuations on vicinal surfaces:Analytical formulas and kinetic Monte Carlo simulations
One-dimensional model interacting-step fluctuations vicinal surfaces Analytical formulas kinetic Monte Carlo simulations
2015/10/16
We study analytically and numerically a one-dimensional model of interacting line defects steps fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for appr...
Second-order corrections to mean field evolution of weakly interacting Bosons.II
Second-order corrections Mean field evolution Weakly interacting bosons
2015/10/16
We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-o...
SECOND ORDER CORRECTIONS TO MEAN FIELD EVOLUTION FOR WEAKLY INTERACTING BOSONS, I
SECOND ORDER equation
2015/10/15
Inspired by the works of Rodnianski and Schlein [31]
and Wu [34, 35], we derive a new nonlinear Schr¨odinger equation
that describes a second-order correction to the usual tensor product (mean-ʂ...
SECOND-ORDER CORRECTIONS TO MEAN FIELD EVOLUTION OF WEAKLY INTERACTING BOSONS. II
SECOND-ORDER WEAKLY INTERACTING BOSONS
2015/10/15
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I [13], in which we derived a second-order correction
to a mean-field e...
PAIR EXCITATIONS AND THE MEAN FIELD APPROXIMATION OF INTERACTING BOSONS, I
PAIR EXCITATIONS MEAN FIELD APPROXIMATION
2015/10/15
In our previous work [20],[21] we introduced a correction to the mean eld approximation of interacting Bosons. This
correction describes the evolution of pairs of particles that leave
the condensat...
Hammersley's Interacting Particle Process and Longst Increasing Subsequences
Hammersley interaction the process of particles the Longst increasing subsequences
2015/7/14
Hammersley's Interacting Particle Process and Longst Increasing Subsequences。
Rao-Blackwellised Interacting Markov Chain Monte Carlo for Electromagnetic Scattering Inversion
Rao-Blackwellised Markov Chain Monte Carlo Electromagnetic Scattering Inversion
2012/11/22
The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from the global EM scattering measurement, ...
Causal categories: relativistically interacting processes
Causal categories General Relativity and Quantum Cosmology Category Theory
2011/10/10
Abstract: A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This stru...
A central limit theorem for adaptive and interacting Markov chains
MCMC interacting MCMC Limit theorems Statistics Theory
2011/9/5
Abstract: Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distrib...
On the concentration properties of Interacting particle processes
Concentration properties Feynman-Kac particle processes stochastic particle models
2011/9/1
Abstract: These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occup...
Simultaneous Sequential Detection of Multiple Interacting Faults
Simultaneous Sequential Multiple Interacting Faults
2011/1/18
Single fault sequential change point problems have become important in modeling for various
phenomena in large distributed systems, such as sensor networks. But such systems in many situations presen...
Conservative interacting particles system with anomalous rate of ergodicity
H¨ormander type generators conservative interacting particle system ergodicity
2011/1/17
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore,we show that convergence rate to equilibrium is expon...