Parabolic partial differential equations | Partial differential equations | Functions of space and time
The diffusion equation is a parabolic partial differential equation. In physics, it describes the macroscopic behavior of many micro-particles in Brownian motion, resulting from the random movements and collisions of the particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such as materials science, information theory, and biophysics. The diffusion equation is a special case of convection–diffusion equation, when bulk velocity is zero. It is equivalent to the heat equation under some circumstances. (Wikipedia).
Diffusion equation (separation of variables) | Lecture 53 | Differential Equations for Engineers
Solution of the diffusion equation (heat equation) by the method of separation of variables. Here, the first step is to separate the variables. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/different
From playlist Differential Equations for Engineers
Diffusion equation (Fourier series) | Lecture 55 | Differential Equations for Engineers
Solution of the diffusion equation (heat equation). Here, we satisfy the initial conditions using a Fourier series. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.p
From playlist Differential Equations for Engineers
Diffusion equation | Lecture 52 | Differential Equations for Engineers
Derivation of the diffusion equation (same equation as the heat equation). Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subscribe to my channel: http://www.yo
From playlist Differential Equations for Engineers
Diffusion equation (eigenvalues) | Lecture 54 | Differential Equations for Engineers
Solution of the diffusion equation (heat equation). Here, we compute the eigenvalues of the separated differential equations. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-
From playlist Differential Equations for Engineers
A reaction-diffusion equation based on the Rock-Paper-Scissors automaton (longer version)
Like the short simulation https://youtu.be/Xeomrnw3JaI , this video shows a solution of a reaction-diffusion equation behaving in a similar way as the Belousov-Zhabotinsky chemical reactions, but is easier to simulate. At each point in space and time, there are three concentrations u, v, a
From playlist Reaction-diffusion equations
PDE | Heat equation: intuition
An introduction to partial differential equations. PDE playlist: http://www.youtube.com/view_play_list?p=F6061160B55B0203 Topics: -- intuition for one dimensional heat (or diffusion) equation, described as a model for the diffusion of heat in a thin metal rod
From playlist Mathematical Physics II - Youtube
Diffusion equation (example) | Lecture 56 | Differential Equations for Engineers
Solution of the diffusion equation (heat equation) for a dye initially concentrated in the middle of a pipe. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subs
From playlist Differential Equations for Engineers
Vorticity of colliding spirals in 3D in the Rock-Paper-Scissors reaction-diffusion equation
This is a 3D remake of the video https://youtu.be/QcxpZKWbLd4 showing the vorticity of a solution to the Rock-Paper-Scissors reaction-diffusion equation, in which the "viscosity" parameter, which is the constant multiplying the Laplace operator, increases over time. This has the effect of
From playlist Reaction-diffusion equations
Math: Partial Differential Eqn. - Ch.1: Introduction (40 of 42) The Diffusion Equation (Part 3 of 5)
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the general solution u(x,t)=f(beta)=? where beta=(x^2)/Kt to the general form of the diffusion equation. (Part 3 of 5) Next video in this series can be seen at: https://youtu.be/SkoNA5CyOcM
From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
Advanced asymptotics of PDEs and applications - 26 September 2018
http://www.crm.sns.it/event/424/ The aim of this workshop is to present and discuss recent advanced topics in analysis, numerical methods, and statistical physics methods for modeling and quantifying cellular functions and organization. We will focus here on recent the asymptotic of PDEs
From playlist Centro di Ricerca Matematica Ennio De Giorgi
Network Analysis. Lecture 11. Diffusion and random walks on graphs
Random walks on graph. Stationary distribution. Physical diffusion. Diffusion equation. Diffusion in networks. Discrete Laplace operator, Laplace matrix. Solution of the diffusion equation. Normalized Laplacian. Lecture slides: http://www.leonidzhukov.net/hse/2015/networks/lectures/lectu
From playlist Structural Analysis and Visualization of Networks.
Diffusion, Super-Diffusion and Non-Local Linear Response in Anomalous Transport by Anupam Kundu
DISCUSSION MEETING: STATISTICAL PHYSICS OF COMPLEX SYSTEMS ORGANIZERS: Sumedha (NISER, India), Abhishek Dhar (ICTS-TIFR, India), Satya Majumdar (University of Paris-Saclay, France), R Rajesh (IMSc, India), Sanjib Sabhapandit (RRI, India) and Tridib Sadhu (TIFR, India) DATE: 19 December 20
From playlist Statistical Physics of Complex Systems - 2022
François Golse: Linear Boltzmann equation and fractional diffusion
Abstract: (Work in collaboration with C. Bardos and I. Moyano). Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient σ. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)
From playlist Partial Differential Equations
Diffusion in Biological Systems by Heiko Rieger
PROGRAM STATISTICAL BIOLOGICAL PHYSICS: FROM SINGLE MOLECULE TO CELL ORGANIZERS: Debashish Chowdhury (IIT-Kanpur, India), Ambarish Kunwar (IIT-Bombay, India) and Prabal K Maiti (IISc, India) DATE: 11 October 2022 to 22 October 2022 VENUE: Ramanujan Lecture Hall 'Fluctuation-and-noise' a
From playlist STATISTICAL BIOLOGICAL PHYSICS: FROM SINGLE MOLECULE TO CELL (2022)
Dynamics Close to Integrability: A Hydrodynamics Prospective by Jacopo De Nardis
DISCUSSION MEETING : HYDRODYNAMICS AND FLUCTUATIONS - MICROSCOPIC APPROACHES IN CONDENSED MATTER SYSTEMS (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, India), Keiji Saito (Keio University, Japan) and Tomohiro Sasamoto (Tokyo Institute of Technology, Japan) DATE : 06 September 2021 to
From playlist Hydrodynamics and fluctuations - microscopic approaches in condensed matter systems (ONLINE) 2021
Dispersion in confined and fluctuating systems by David Dean
DISCUSSION MEETING : STATISTICAL PHYSICS OF COMPLEX SYSTEMS ORGANIZERS : Sumedha (NISER, India), Abhishek Dhar (ICTS-TIFR, India), Satya Majumdar (University of Paris-Saclay, France), R Rajesh (IMSc, India), Sanjib Sabhapandit (RRI, India) and Tridib Sadhu (TIFR, India) DATE : 19 December
From playlist Statistical Physics of Complex Systems - 2022
Objective Barriers To Passive Transport (Lecture 2) by George Haller
DISCUSSION MEETING WAVES, INSTABILITIES AND MIXING IN ROTATING AND STRATIFIED FLOWS (ONLINE) ORGANIZERS: Thierry Dauxois (CNRS & ENS de Lyon, France), Sylvain Joubaud (ENS de Lyon, France), Manikandan Mathur (IIT Madras, India), Philippe Odier (ENS de Lyon, France) and Anubhab Roy (IIT M
From playlist Waves, Instabilities and Mixing in Rotating and Stratified Flows (ONLINE)
Bronwyn Hajek: Shock Me Amadeus
Associate Professor Bronwyn Hajek, applied mathematician at the University of South Australia, is an expert in developing and solving mathematical models using nonlinear PDEs. During her upcoming SMRI visit, Hajek and her USyd collaborator Dr Robby Marangell will apply Lie symmetry method
From playlist SMRI Interviews
Math: Partial Differential Eqn. - Ch.1: Introduction (39 of 42) The Diffusion Equation (Part 2 of 5)
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the general solution u(x,t)=f(beta)=? where beta=(x^2)/Kt to the general form of the diffusion equation. (Part 2 of 5) Next video in this series can be seen at: https://youtu.be/nxXTV9kaYPs
From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
Stochastic Resetting - CEB T2 2017 - Evans - 1/3
Martin Evans (Edinburgh) - 09/05/2017 Stochastic Resetting We consider resetting a stochastic process by returning to the initial condition with a fixed rate. Resetting is a simple way of generating a nonequilibrium stationary state in the sense that the process is held away from any eq
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester