Lectures related to Stochastic Analysis: Incompressible Viscous Fluids & SPDEs on Graphs

Inviscid Flows: Understanding Fluid Dynamics

Explores inviscid flows, Reynolds number importance, linear deformations, and volume change in fluid dynamics.

Fluid Mechanics: Foundations and Applications

Covers the foundations of fluid mechanics, focusing on flow problem descriptions and solutions.

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Newton's 2nd Law: Fluid Dynamics

Discusses Newton's 2nd Law in fluid dynamics and incompressible Newtonian fluids.

Untitled

Fluid Dynamics: Equations and State

Explores fluid dynamics concepts like energy argument, momentum balance, and equation of state for perfect fluids.

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Fluid Dynamics: Differential Conservation Laws and Equations

Covers the differential approach to fluid dynamics, focusing on conservation laws and the Cauchy stress tensor.

Incompressible Fluid Mechanics: Differential Analysis

Covers mass and momentum conservation, Navier-Stokes equations, and analytical methods in incompressible fluid mechanics.

Shortest Path Algorithms: BFS and Dijkstra

Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

Information Theory: Basics

Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Introduction to Fluid Mechanics

Covers the basics of fluid mechanics, including fluid properties, pressure, viscosity, and fluid behavior at rest and in motion.

Cavity Method: Mean Field Theory

Explores the Cavity Method in Mean Field Theory, analyzing spins in an external field within a graph.

Incompressible Fluid Mechanics

Covers the foundations of incompressible fluid mechanics, conservation laws, and general flow equations, with a focus on practical issues and class logistics.

Fluid Dynamics: Ideal Fluids

Explores physical models for microsystems, ideal fluids, Navier-Stokes equations, incompressible fluids, Reynolds number, and molecular dynamics.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Networked Control Systems: Laplacian Flow and Heat Equation

Explores Laplacian flow, heat equation analogies, and microgrid networked controllers.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.