Partial differential equations | Dynamical systems

Phase space method

In applied mathematics, the phase space method is a technique for constructing and analyzing solutions of dynamical systems, that is, solving time-dependent differential equations. The method consists of first rewriting the equations as a system of differential equations that are first-order in time, by introducing additional variables. The original and the new variables form a vector in the phase space. The solution then becomes a curve in the phase space, parametrized by time. The curve is usually called a trajectory or an orbit. The (vector) differential equation is reformulated as a geometrical description of the curve, that is, as a differential equation in terms of the phase space variables only, without the original time parametrization. Finally, a solution in the phase space is transformed back into the original setting. The phase space method is used widely in physics. It can be applied, for example, to find traveling wave solutions of reaction–diffusion systems. (Wikipedia).

Video thumbnail

A Stationary Phase Method for a Class of Nonlinear Equations - Yen Do

Yen Do Georgia Institute of Technology October 26, 2010 In this talk I will describe a real-variable method to extract long-time asymptotics for solutions of many nonlinear equations (including the Schrodinger and mKdV equations). The method has many resemblances to the classical stationa

From playlist Mathematics

Video thumbnail

Special Relativity: 2 - Spacetime Diagrams

An introduction to spacetime diagrams which are a valuable tool used to understand special relativity. The second in a series on special and general relativity. Let us know what you think of these videos by filling out our short survey at http://tinyurl.com/astronomy-pulsar. Thank you!

From playlist Special Relativity

Video thumbnail

Javascript games programming using Phaser in Dreamweaver lesson 7 - Firing bullets

In this lesson will manage to shoot the bullets in the same direction / angle as the space ship (player) object. We also control the rate at which they are shot so you can't shoot too many bullets at once.

From playlist Javascript game making with Phaser

Video thumbnail

Fourier Transform Technique for Solving PDEs (Part 2)

In this video, we study how to solve a PDE (the 1-dimensional Heat Equation) using the Fourier Transform technique.

From playlist Mathematical Physics II Uploads

Video thumbnail

Phase Plane Plots

We discuss the use of Phase Plane Plots for understanding the qualitative behavior of systems of differential equations.

From playlist Mathematical Physics I Uploads

Video thumbnail

Convolution in the time domain

Now that you understand the Fourier transform, it's time to start learning about time-frequency analyses. Convolution is one of the best ways to extract time-frequency dynamics from a time series. Convolution can be conceptualized and implemented in the time domain or in the frequency doma

From playlist OLD ANTS #3) Time-frequency analysis via Morlet wavelet convolution

Video thumbnail

Phase Velocity versus Group Velocity: Wave Dispersion

Wave Propagation: Explanation of Group Velocity, Phase Velocity, and Dispersion. My Patreaon page is at https://www.patreon.com/EugeneK

From playlist Physics

Video thumbnail

Spacetime Diagrams: An Easy Way to Visualize Special Relativity (Physics by Parth G)

If you've seen a distance-time graph before, you'll pick up spacetime diagrams very quickly... and understand their true power in visualizing special relativity! A spacetime diagram is any diagram that shows the behavior of an object through space and time. However, the term most commonly

From playlist Relativity by Parth G

Video thumbnail

Phase separation in the Allen-Cahn equation, with a start in slow motion

Like the video https://youtu.be/t1swj0QJUTw this simulation shows a solution of the Allen-Cahn equation for phase separation, on a rectangular domain with periodic boundary conditions, starting from a random initial configuration. Time has been slowed down at the beginning, to give a bette

From playlist Reaction-diffusion equations

Video thumbnail

Complex Langevin Simulations of the Matrix Model for Superstrings by Jun Nishimura

PROGRAM Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (ONLINE) ORGANIZERS: David Berenstein (UCSB), Simon Catterall (Syracuse University), Masanori Hanada (University of Surrey), Anosh Joseph (IISER, Mohali), Jun Nishimura (KEK Japan), David Sc

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography (Online)

Video thumbnail

Ingrid Membrillo Solis (2/24/21): Liquid crystals dynamics: what persistent homology reveals

Title: The dynamics of the phase transition in liquid crystals: what persistent homology reveals Abstract: Liquid crystals are a state of matter that present physical properties interpolating between those of conventional liquids and those of crystals. The phase dynamics of liquid crystal

From playlist AATRN 2021

Video thumbnail

Ian Robinson - Progress towards Machine Learning Phasing for Bragg Coherent Diffractive Imaging

Recorded 13 October 2022. Ian Robinson of Brookhaven National Laboratory presents "Progress towards Machine Learning Phasing for Bragg Coherent Diffractive Imaging" at IPAM's Diffractive Imaging with Phase Retrieval Workshop. Abstract: The crystallographic “phase problem” relates to the fa

From playlist 2022 Diffractive Imaging with Phase Retrieval - - Computational Microscopy

Video thumbnail

Bound-preserving numerical solutions of variable density two-phase flows

Date and Time: Thursday, November 11, 12:00pm Eastern time zone Speaker: Beatrice Riviere, Rice University Abstract: Modeling pore-scale flows modeling is important for many applications relevant to energy and environment. Phase-field models are popular models because they implicitly tra

From playlist SIAM Geosciences Webinar Series

Video thumbnail

Mohammad Farazmand: "Accelerated Gradient Optimization: A Multiscale Analysis"

Machine Learning for Physics and the Physics of Learning 2019 Workshop III: Validation and Guarantees in Learning Physical Models: from Patterns to Governing Equations to Laws of Nature "Accelerated Gradient Optimization: A Multiscale Analysis" Mohammad Farazmand - North Carolina State Un

From playlist Machine Learning for Physics and the Physics of Learning 2019

Video thumbnail

Patterns, Universality and Computational Algorithms - Nigel Goldenfeld

Nigel Goldenfeld University of Illinois at Urbana-Champaign December 1, 2010 Can we use computational algorithms to make accurate predictions of physical phenomena? In this talk, intended for non-experts, I will give examples where complicated space-time phenomena can be exquisitely captu

From playlist Mathematics

Video thumbnail

Lec 19 | MIT 3.320 Atomistic Computer Modeling of Materials

Free Energies and Physical Coarse-Graining View the complete course at: http://ocw.mit.edu/3-320S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 3.320 Atomistic Computer Modeling of Materials

Video thumbnail

Geometric Methods for Orbit Integration - Scott Tremaine

Geometric Methods for Orbit Integration Scott Tremaine Institute for Advanced Study July 14, 2009

From playlist PiTP 2009

Video thumbnail

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.

Video thumbnail

Nandini Ananth - Quantum dynamics from classical trajectories - IPAM at UCLA

Recorded 14 April 2022. Nandini Ananth of Cornell University, Chemistry, presents "Quantum dynamics from classical trajectories" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: Semiclassical approximations based on the path integral formulation of quantum mechanics emplo

From playlist 2022 Model Reduction in Quantum Mechanics Workshop

Video thumbnail

Phase space representation of billiards interpolating between a circle and a hexagon

In this simulation, I wanted to see what happens when you continuously deform the boundary of a billiard from a circle to a regular hexagon. The billiard in a circle has very regular dynamics (the technical work is "integrable"), because a given trajectory always hits the boundary with the

From playlist Particles in billiards

Related pages

Orbit (dynamics) | Reaction–diffusion system | Curve | Dynamical system | Phase space | Fisher's equation | Applied mathematics