Mathematical series | Ordinary differential equations | Asymptotic analysis
In mathematics, the method of dominant balance is used to determine the asymptotic behavior of solutions to an ordinary differential equation without fully solving the equation. The process is iterative, in that the result obtained by performing the method once can be used as input when the method is repeated, to obtain as many terms in the asymptotic expansion as desired. The process goes as follows: 1. * Assume that the asymptotic behavior has the form 2. * Make an informed guess as to which terms in the ODE might be negligible in the limit of interest. 3. * Drop these terms and solve the resulting simpler ODE. 4. * Check that the solution is consistent with step 2. If this is the case, then one has the controlling factor of the asymptotic behavior; otherwise, one needs try dropping different terms in step 2, instead. 5. * Repeat the process to higher orders, relying on the above result as the leading term in the solution. (Wikipedia).
Two metal forks, a cork, and a matchstick balance on the lip of a glass. The center of mass of the fork-cork-match system is well below the pivot point, so balance is able to return after small perturbations. Please be careful when playing with matches. For more details on this setup, see
From playlist Newtonian Mechanics
Identifying Dominant Balance Physics from Data - Jared Callaham
This video illustrates a new algorithm to identify local dominant physical balance relations from multiscale spatiotemporal data. Title: Learning dominant physical processes with data-driven balance models Paper: https://arxiv.org/abs/2001.10019 Authors: Jared L. Callaham, J. Nathan Kut
From playlist Research Abstracts from Brunton Lab
2D Equilibrium -- Balancing Games
How does everything even out? Learn what 2D Equilibrium is and how it effects the balance of life. License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Measurement
How to find DOMINATING STRATEGIES with Game Theory
Check out Brilliant ► https://brilliant.org/TreforBazett/ Join for free and the first 200 subscribers get 20% off an annual premium subscription. Thank you to Brilliant for sponsoring this playlist on Game Theory. Check out Episodes 1 & 2 of the Game Theory Playlist ► https://www.youtub
From playlist Game Theory
Game of Thrones: Balance of Power Over Time
Data visualization showing the balance of power in Game of Thrones over time . "Balance of Power" in this video essentially means how far a given character is from sitting on the iron throne at any point in time. Note that for all characters other than those actually sitting on the throne,
From playlist Data Visualizations
Voting Theory: Plurality Method and Condorcet Criterion
This video explains how to determine the winner of an election using the plurality methods and how to determine the Condorcet winner. Site: http://mathispower4u.com
From playlist Voting Theory
Fair Division: The Lone Divider Method
This video explains and provides an example of the lone divider method of fair division. Site: http://mathispower4u.com
From playlist Fair Division
Energy spectra of buoyancy driven 2D bubbly flows by Prasad Perlekar
Turbulence from Angstroms to light years DATE:20 January 2018 to 25 January 2018 VENUE:Ramanujan Lecture Hall, ICTS, Bangalore The study of turbulent fluid flow has always been of immense scientific appeal to engineers, physicists and mathematicians because it plays an important role acr
From playlist Turbulence from Angstroms to light years
Data-Driven Control: Eigensystem Realization Algorithm Procedure
In this lecture, we describe the eigensystem realization algorithm (ERA) in detail, including step-by-step algorithmic instructions. https://www.eigensteve.com/
From playlist Data-Driven Control with Machine Learning
Math for Liberal Studies: Sequential Pairwise Voting
In this video, we practice using sequential pairwise voting to find the winner of an election. We also discuss how sequential pairwise voting is related to the Condorcet method. If you haven't learned about the Condorcet method yet, you should watch this video first: http://www.youtube
From playlist Math for Liberal Studies
Solve 1-step equations (balance method)
Powered by https://www.numerise.com/ Solve 1-step equations (balance method)
From playlist Linear equations
Sparse Nonlinear Models for Fluid Dynamics with Machine Learning and Optimization
Reduced-order models of fluid flows are essential for real-time control, prediction, and optimization of engineering systems that involve a working fluid. The sparse identification of nonlinear dynamics (SINDy) algorithm is being used to develop nonlinear models for complex fluid flows th
From playlist Data-Driven Dynamical Systems with Machine Learning
Matrix Equations and Model Reduction, Lecture 2
Description
From playlist Gene Golub SIAM Summer School Videos
MRI-Driven Turbulence - Equilibrium Structure of Radiation-dominated... - Shigenobu Hirose
MRI-Driven Turbulence - Equilibrium Structure of Radiation-dominated Disk Segments Shigenobu Hirose The Earth Simulator Center, JAMSTEC June 18, 2008
From playlist Natural Sciences
Andre Nies: Randomness connecting to set theory and to reverse mathematics
Abstract : I will discuss two recent interactions of the field called randomness via algorithmic tests. With Yokoyama and Triplett, I study the reverse mathematical strength of two results of analysis. (1) The Jordan decomposition theorem says that every function of bounded variation is th
From playlist Logic and Foundations
Quantum Tunnelling in the Universe by Masahide Yamaguchi
PROGRAM: PHYSICS OF THE EARLY UNIVERSE - AN ONLINE PRECURSOR ORGANIZERS: Robert Brandenberger (McGill University, Montreal, Canada), Jerome Martin (Institut d'Astrophysique de Paris, France), Subodh Patil (Instituut-Lorentz for Theoretical Physics, Leiden, Netherlands) and L Sriramkumar (
From playlist Physics of The Early Universe - An Online Precursor
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
Eva Silverstein - BI for AI: Energy Conserving Dynamics for optimization and sampling
We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish some of its key properties analytically and numerically. The prototype is a discretization of Born-Infeld dynamics, with a squared relativisti
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Weighted Voting: Coalitions and Critical Players
This lesson defines and gives examples of coalitions and critical players in a weighted voting system. Site: http://mathispower4u.com
From playlist Weighted Voting