Parabolic partial differential equations | Partial differential equations | Functions of space and time

Diffusion equation

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).

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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.

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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

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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

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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)

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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

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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

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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)

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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

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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

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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

Related pages

Differential operator | Product rule | Trace (linear algebra) | Convection–diffusion equation | Finite difference | Brownian motion | Density | Del | Information theory | Continuity equation | Linear differential equation | Green's function | Random walk | Fokker–Planck equation | Heat equation | Tensor | Convolution | Numerical solution of the convection–diffusion equation | Isotropy | Transpose | Structure tensor | Parabolic partial differential equation