If the Laplacian of a function is zero everywhere, it is called Harmonic. Harmonic functions arise all the time in physics, capturing a certain notion of "stability", whenever one point in space is influenced by its neighbors.
From playlist Fourier
Applications of analysis to fractional differential equations
I show how to apply theorems from analysis to fractional differential equations. The ideas feature the Arzela-Ascoli theorem and Weierstrass' approximation theorem, leading to a new approach for solvability of certain fractional differential equations. When do fractional differential equ
From playlist Mathematical analysis and applications
Physics - Advanced E&M: Ch 1 Math Concepts (13 of 55) What is the Laplacian of a Scalar (Field)?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain, develop the equation, and give examples of the Laplacian of a scalar (field). Next video in this series can be seen at: https://youtu.be/2VXFzhcGT3U
From playlist PHYSICS 67 ADVANCED ELECTRICITY & MAGNETISM
In this video, we are going to visualize the concept of FRACTIONAL DERIVATIVE in a new geometric way.
From playlist Summer of Math Exposition Youtube Videos
Differential Equations | The Laplace Transform of a Derivative
We establish a formula involving the Laplace transform of the derivative of a function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Laplace Transform
Overview of fractions - free math help - online tutor
👉 Learn how to understand the concept of fractions using parts of a whole. Fractions are parts of a whole and this concept can be illustrated using bars and circles. This concept can also be extended to understand equivalent fractions. When a whole bar is divided into, say, two equal parts
From playlist Learn About Fractions
A worked example of computing the laplacian of a two-variable function.
From playlist Fourier
Li Wang: An asymptotic preserving method for Levy Fokker Planck equation with fractional...
CIRM VIRTUAL EVENT Recorded during the meeting "Kinetic Equations: from Modeling, Computation to Analysis" the March 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide m
From playlist Virtual Conference
Juan Luis Vázquez: The theory of nonlinear diffusion with fractional operators
Abstract: In this talk I will report on some of the progress made by the author and collaborators on the topic of nonlinear diffusion equations involving long distance interactions in the form of fractional Laplacian operators. The nonlinearities are of the following types: porous medium,
From playlist Partial Differential Equations
Boundary driven lattice gas with long jumps by Cedric Bernardin
PROGRAM CLASSICAL AND QUANTUM TRANSPORT PROCESSES : CURRENT STATE AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Alberto Imparato (University of Aarhus, Denmark), Anupam Kundu (ICTS-TIFR, India), Carlos Mejia-Monasterio (Technical University of Madrid, Spain) and Lamberto Rondoni (Polytechn
From playlist Classical and Quantum Transport Processes : Current State and Future Directions (ONLINE)2022
DDPS | Applications of Fractional Operators from Optimal Control to Machine Learning
In this talk from June 3, 2021, Professor Harbir Antil of George Mason University discusses fractional operators and their applications to optimal control and Deep Neural Networks (DNNs). Fractional calculus and its application to anomalous diffusion has recently received a tremendous amo
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Camillo De Lellis: Ill-posedness for Leray solutions of the ipodissipative Navier-Stokes equations
Abstract: In a joint work with Maria Colombo and Luigi De Rosa we consider the Cauchy problem for the ipodissipative Navier-Stokes equations, where the classical Laplacian −Δ is substited by a fractional Laplacian (−Δ)α. Although a classical Hopf approach via a Galerkin approximation shows
From playlist Partial Differential Equations
Physics Ch 67.1 Advanced E&M: Review Vectors (45 of 55) What is the Laplacian?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will find the Laplacian of f(x,y,z)=x^4+x^2y+5z^3+8. Next video in this series can be seen at: https://youtu.be/9r0TOm-gKrc
From playlist PHYSICS 67.1 ADVANCED E&M VECTORS & FIELDS
Fractional Calderon problem Lecture 1 by Tuhin Ghosh
DISCUSSION MEETING WORKSHOP ON INVERSE PROBLEMS AND RELATED TOPICS (ONLINE) ORGANIZERS: Rakesh (University of Delaware, USA) and Venkateswaran P Krishnan (TIFR-CAM, India) DATE: 25 October 2021 to 29 October 2021 VENUE: Online This week-long program will consist of several lectures by
From playlist Workshop on Inverse Problems and Related Topics (Online)
Eulalia Nualart: Asymptotics for some non-linear stochastic heat equations
Abstract: Consider the following stochastic heat equation, ∂ut(x)/∂t = −ν(−Δ)α/2ut(x)+σ(ut(x))F˙(t,x),t[is greater than]0,x∈ℝd. Here −ν(−Δ)α/2 is the fractional Laplacian with ν[is greater than]0 and α∈(0,2], σ:ℝ→ℝ is a globally Lipschitz function, and F˙(t,x) is a Gaussian noise which is
From playlist Probability and Statistics
MFEM Workshop 2022 | Stochastic Fractional PDEs: Random Field Generation & Topology Optimization
The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s second community workshop was held on October 25, 2022, with participants around the world. Learn more about MFEM at https://mfem.o
From playlist MFEM Community Workshop 2022
Francesca Da Lio: Analysis of nonlocal conformal invariant variational problems, Lecture III
There has been a lot of interest in recent years for the analysis of free-boundary minimal surfaces. In the first part of the course we will recall some facts of conformal invariant problems in 2D and some aspects of the integrability by compensation theory. In the second part we will show
From playlist Hausdorff School: Trending Tools
A visual understanding for how the Laplace operator is an extension of the second derivative to multivariable functions.
From playlist Fourier
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
When do fractional differential equations have maximal solutions?
When do fractional differential equations have maximal solutions? This video discusses this question in the following way. Firstly, a comparison theorem is formulated that involves fractional differential inequalities. Secondly, a sequence of approximative problems involving polynomials
From playlist Research in Mathematics