Monte Carlo methods | Statistical data types | Sampling techniques | Randomized algorithms | Stochastic simulation
Mean-field particle methods are a broad class of interacting type Monte Carlo algorithms for simulating from a sequence of probability distributions satisfying a nonlinear evolution equation. These flows of probability measures can always be interpreted as the distributions of the random states of a Markov process whose transition probabilities depends on the distributions of the current random states. A natural way to simulate these sophisticated nonlinear Markov processes is to sample a large number of copies of the process, replacing in the evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo and Markov chain Monte Carlo methods these mean-field particle techniques rely on sequential interacting samples. The terminology mean-field reflects the fact that each of the samples (a.k.a. particles, individuals, walkers, agents, creatures, or phenotypes) interacts with the empirical measures of the process. When the size of the system tends to infinity, these random empirical measures converge to the deterministic distribution of the random states of the nonlinear Markov chain, so that the statistical interaction between particles vanishes. In other words, starting with a chaotic configuration based on independent copies of initial state of the nonlinear Markov chain model, the chaos propagates at any time horizon as the size the system tends to infinity; that is, finite blocks of particles reduces to independent copies of the nonlinear Markov process. This result is called the propagation of chaos property. The terminology "propagation of chaos" originated with the work of Mark Kac in 1976 on a colliding mean-field kinetic gas model. (Wikipedia).
Mean-Field Theory | Ising model | Solid State Physics
In this video we introduce three steps that are common to all mean-field theories. We then apply those steps to the Ising model and thereby solve it in the limit of infinite dimensions. #CondensedMatter Our recommendation: https://amzn.to/2MOHACT (Affiliate-Link) This book covers a lot o
From playlist Condensed Matter, Solid State Physics
Particle Physics 1: Introduction
Part 1 of a series: covering introduction to Quantum Field Theory, creation and annihilation operators, fields and particles.
From playlist Particle Physics
Li Chen: Mean field limit of many particle system with non Lipschitz force
The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory. Abstract: We apply a probabilistic method to derive the mean field limit for an interacting particle model in two dimensions. The model under investigation contains the velocity alignment effec
From playlist Workshop: Probabilistic and variational methods in kinetic theory
What are Quantum Fields? | Introduction to Quantum Field Theory
In this video, we will discuss what makes a quantum field "quantum" and give a soft introduction to quantum field theory. Contents: 00:00 Introduction 03:00 Quantization 05:36 Appendix Follow us on Instagram: https://www.instagram.com/prettymuchvideo/ If you want to help us get rid of
From playlist Quantum Mechanics, Quantum Field Theory
Quantum field theory, Lecture 2
This winter semester (2016-2017) I am giving a course on quantum field theory. This course is intended for theorists with familiarity with advanced quantum mechanics and statistical physics. The main objective is introduce the building blocks of quantum electrodynamics. Here in Lecture 2
From playlist Quantum Field Theory
Quantum Field Theory 5c - Classical Electrodynamics III
We end with a derivation of the classical interaction Hamiltonian for a charged particle moving in an electromagnetic field. There is a lot of "turn the crank" math in this installment, but the final result will be key to our continued development of quantum field theory.
From playlist Quantum Field Theory
Quantum Field Theory 2a - Field Quantization I
In the previous video we saw how the quantum harmonic oscillator provides a model system in which we can describe the creation and destruction of energy quanta. In 1925 Born, Heisenberg and Jordan presented a way to apply these ideas to a continuous field. (Note: My voice is lower and slow
From playlist Quantum Field Theory
Quantum Field Theory 6a - Interacting Fields I
We can now calculate the quantum interaction Hamiltonian for the electron and photon fields. The result is a quantum field theory that can describe the emission and absorption of photons by an atom. Error: At 2:26 omega-sub-k (in the H-hat-sub-r expression) should be outside the parenthe
From playlist Quantum Field Theory
A mathematics bonus. In this lecture I remind you of a way to calculate the cross product of two vector using the determinant of a matrix along the first row of unit vectors.
From playlist Physics ONE
Shi Jin: Efficient Numerical Methods for Particle Systems - lecture 2
We will first outline the asymptotic-transition from quantum to classical, to kinetic and then the hydrodynamic equations, and then show how such asymptotics can guide the design and analysis of the so-called asymptotic-preserving schemes that offer efficient multiscale computations betwee
From playlist Virtual Conference
Kinetic Simulations of Astrophysical Plasmas, Part 1 - Anatoly Spitkovsky
Kinetic Simulations of Astrophysical Plasmas, Part 1 Anatoly Spitkovsky Princeton University July 15, 2009
From playlist PiTP 2009
Kinetic Simulations of Astrophysical Plasmas, Part 2 - Anatoly Spitkovsky
Kinetic Simulations of Astrophysical Plasmas, Part 2 Anatoly Spitkovsky Princeton University July 20, 2009
From playlist PiTP 2009
Natalia Tronko: Exact conservation laws for gyrokinetic Vlasov-Poisson equations
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Antoine Rousseau: Wind energy: from downscaled forecasts to mills production
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Mathematical Physics
Collisionless Dynamics and Smoothed Particle Hydrodynamics, Part 2 - Volker Springel
Collisionless Dynamics and Smoothed Particle Hydrodynamics, Part 2 Volker Springel Max Planck Institute for Astrophysics July 15, 2009
From playlist PiTP 2009
Mod-02 Lec-10 Template Methods - II
Nano structured materials-synthesis, properties, self assembly and applications by Prof. A.K. Ganguli,Department of Nanotechnology,IIT Delhi.For more details on NPTEL visit http://nptel.ac.in
Cosmological Simulations (Lecture 1) by R. Angulo
Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i
From playlist Cosmology - The Next Decade
Nano structured materials-synthesis, properties, self assembly and applications by Prof. A.K. Ganguli,Department of Nanotechnology,IIT Delhi.For more details on NPTEL visit http://nptel.ac.in
Monika Ritsch-Marte - Phase Retrieval and Optical Trapping - IPAM at UCLA
Recorded 13 October 2022. Monika Ritsch-Marte of the Medical University of Innsbruck presents "Phase Retrieval and Optical Trapping" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: Phase retrieval, i.e. the reconstruction of the complex field from intensity images by
From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy
Lecture 9 | New Revolutions in Particle Physics: Basic Concepts
(December 1, 2009) Leonard Susskind discusses the equations of motion of fields containing particles and quantum field theory, and shows how basic processes are coded by a Lagrangian. Stanford University: http://www.stanford.edu/ Stanford Continuing Studies Program: http://csp.stan
From playlist Lecture Collection | Particle Physics: Basic Concepts