Lectures related to Kohonen Maps: Mini Projects 1

Quantum Monte Carlo: Basic Concepts

Covers the basic concepts of Quantum Monte Carlo and its application in spin chains, Markov chains, and Monte Carlo simulations.

Embedding Space: AdS and Euclidean Geometry

Covers the concept of embedding space for AdS and Euclidean geometry, discussing AdS isometries and Euclidean Ads.

Orthogonality and Gram-Schmidt Process

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Piston in a Screen: COMSOL Example

Demonstrates simulating a piston in a screen using COMSOL Multiphysics.

Piston on a Box: COMSOL Example 8

Covers the simulation of a piston on a box using COMSOL Multiphysics.

Simulation: Control of Dynamic Systems

Explores simulation of common structures and control of dynamic systems through friction and elasticity constants.

Euclidean Isometries: Properties and Applications

Explores the properties and applications of Euclidean isometries in R^2.

Euclidean Geometry: Operations and Constructions

Covers the fundamental operations and constructions in Euclidean geometry, focusing on algebraic interpretations and ruler-and-compass constructions.

Optimization and Simulation: Introduction to Simulation

Introduces state-of-the-art methods in optimization and simulation, covering topics like statistical analysis, variance reduction, and simulation projects.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Turbulence: Simulation and Models

Explores turbulence simulation, modeling forces, and flow features using CFD, emphasizing challenges and modeling assumptions.

Optimization on Manifolds

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Quantum Field Theory in Ads and CFT Correlators

Covers the concept of Quantum Field Theory in Ads and CFT correlators.

Capacitor and Self-Heating in a Wire

Covers the simulation of a capacitor and self-heating in a wire using Comsol.

Dipole Simulation: Acoustic Field Analysis

Covers the simulation of a dipole in COMSOL Multiphysics, analyzing the acoustic field.

Simulation & Optimization: Poisson Process & Random Numbers

Explores simulation pitfalls, random numbers, discrete & continuous distributions, and Monte-Carlo integration.

Turbulence Simulation and Models

Explores turbulence simulation, focusing on CFD, DNS, RANS, and LES.

Introduction to Euclidean Geometry

Introduces the fundamental concepts of Euclidean geometry, exploring postulates, parallel lines, and non-Euclidean geometries.

Introduction to Euclidean Elements

Introduces Euclidean Elements, discussing logical structure, types of propositions, definitions, common notions, and postulates.

Solid Mechanics: Modeling and Simulation

Introduces solid mechanics modeling and simulation using COMSOL Multiphysics.