In applied mathematics, objective Eulerian coherent structures (OECSs) are the instantaneously most influential surfaces or curves that exert a major influence on nearby trajectories in a dynamical system over short time-scales, and are the short-time limit of Lagrangian coherent structures (LCSs). Such influence can be of different types, but OECSs invariably create a short-term coherent trajectory pattern for which they serve as a theoretical centerpiece. While LCSs are intrinsically tied to a specific finite time interval, OECSs can be computed at any time instant regardless of the multiple and generally unknown time scales of the system. In observations of tracer patterns in nature, one readily identifies short-term variability in material structures such as emerging and dissolving coherent features. However, it is often the underlying structure creating these features that is of interest. While individual tracer trajectories forming coherent patterns are generally sensitive with respect to changes in their initial conditions and the system parameters, OECSs are robust and reveal the instantaneous time-varying skeleton of complex dynamical systems. Despite OECSs are defined for general dynamical systems, their role in creating coherent patterns is perhaps most readily observable in fluid flows. Therefore, OECSs are suitable in a number of applications ranging from flow control to environmental assessment such as now-casting or short-term forecasting of pattern evolution, where quick operational decisions need to be made. Examples include floating debris, oil spills, surface drifters, and control of unsteady flow separation. (Wikipedia).
Eulerian Circuits and Eulerian Graphs | Graph Theory, Euler Graphs and Euler Circuits
What are Eulerian graphs and Eulerian circuits? Euler graphs and Euler circuits go hand in hand, and are very interesting. We’ll be defining Euler circuits first in today’s lesson, as well as showing an example of why these circuits might be interesting to begin with, then we go into Euler
From playlist Graph Theory
C39 A Cauchy Euler equation that is nonhomogeneous
A look at what to do with a Cauchy Euler equation that is non-homogeneous.
From playlist Differential Equations
Euler's formulas, Rodrigues' formula
In this video I proof various generalizations of Euler's formula, including Rodrigues' formula and explain their 3 dimensional readings. Here's the text used in this video: https://gist.github.com/Nikolaj-K/eaaa80861d902a0bbdd7827036c48af5
From playlist Algebra
General Solution to a Second Order Homogeneous Cauchy-Euler Equation (complex)
This video provides an example of how to solve a second order homogeneous Cauchy-Euler Equation with the auxiliary equation has complex solutions. Site: http://mathispower4u.com
From playlist Second Order Homogeneous Cauchy-Euler Differential Equations
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)
Objective Barriers to Passive Transport (Lecture 1) 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)
General Solution to a Second Order Homogeneous Cauchy-Euler Equation (distinct real)
This video provides an example of how to solve a second order homogeneous Cauchy-Euler Equation with the auxiliary equation has two distinct real roots. Site: http://mathispower4u.com
From playlist Second Order Homogeneous Cauchy-Euler Differential Equations
Derive the Auxiliary Equation for a Cauchy-Euler Equation
This video derives the auxiliarly or characteristic equation used to solve a second order Cauchy-Euler differential equation. Site: http://mathispoweru4.com
From playlist Second Order Homogeneous Cauchy-Euler Differential Equations
This is a video that explains Euler Groups and incudes a coding demonstration for constructing the Cayley Table. The link to the JS Fiddle is: https://jsfiddle.net/colebabiuch/jpem1d73/10/
From playlist Summer of Math Exposition Youtube Videos
Ex: Solve a Second Order Cauchy-Euler DE Initial Value Problem (Complex)
This video explains how to solve an initial value problem involving a second order Cauchy-Euler differential equation initial value problem. http://mathispower4u.com
From playlist Second Order Homogeneous Cauchy-Euler Differential Equations
Assimilation of Lagrangian data - Chris Jones
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
How to build a fluid clock - Theodore Dimitrios Drivas
Short Talks by Postdoctoral Members Topic: How to build a fluid clock Speaker: Theodore Dimitrios Drivas Affiliation: Member, School of Mathematics Date: February 01, 2022
From playlist Mathematics
The Chinese Postman Problem (Introduction to Graph Theory)
This video covers Eulerian, Semi-Eulerian, and regular graphs in the Chinese Postman Problem as well as applications of graph theory. This was made for 3Blue1Brown's Summer of Math Exploration video competition (link: https://www.3blue1brown.com/blog/some1). For more information about Eu
From playlist Summer of Math Exposition Youtube Videos
A detailed characterization of the hypersurface of pre-shocks for the Euler equa... - Steve Shkoller
Workshop on Recent developments in incompressible fluid dynamics Topic: A detailed characterization of the hypersurface of pre-shocks for the Euler equations Speaker: Steve Shkoller Affiliation: University of California, Davis Date: April 04, 2022 I will describe a new geometric approach
From playlist Mathematics
Turbulent superstructures in Rayleigh-B\’{e}nard convection by Joerg Schumacher
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
Solving Laplacian Systems of Directed Graphs - John Peebles
Computer Science/Discrete Mathematics Seminar II Topic: Solving Laplacian Systems of Directed Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: March 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Marc Levine - 1/3 Enumerative Geometry and Quadratic Forms
Notes: https://nextcloud.ihes.fr/index.php/s/BL5CJK4Ls8DT4S9 Enumerative Geometry and Quadratic Forms: Euler characteristics and Euler classes
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
DDPS | Data-driven methods for fluid simulations in computer graphics
Fluid phenomena are ubiquitous to our world experience: winds swooshing through trembling leaves, turbulent water streams running down a river, and cellular patterns generated from wrinkled flames are some few examples. These complex phenomena capture our attention and awe due to the beaut
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
General Solution to a Second Order Homogeneous Cauchy-Euler Equation (equal roots)
This video provides an example of how to solve a second order homogeneous Cauchy-Euler Equation with the auxiliary equation has two real equal roots. Site: http://mathispower4u.com
From playlist Second Order Homogeneous Cauchy-Euler Differential Equations
Introductionadvanced hydraulics course structure
Advanced Hydraulics by Dr. Suresh A Kartha,Department of Civil Engineering,IIT Guwahati.For more details on NPTEL visit http://nptel.iitm.ac.in
From playlist IIT Guwahati: Advanced Hydraulics | CosmoLearning.org Civil Engineering