Entropy Everywhere Entropy in my life This post was suppose to be the second part in a multi-part series about the heat equation as an example in high performance computing (HPC), unfortunately, Hurricane Ida had other plans and her strength is greater than my ability to power and remotely access Tulane’s computing cluster, Cypress. As… Continue reading Maximum Entropy
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Parallel Computing with the 1-D Heat Equation: Part 1
Derivation of the 1-D Heat Equation and Basic Numerical Methods When I took a course in Large Scale Computation at Tulane University, I learned a lot and forgot a lot. Understanding how to take a physical phenomena or problem and develop software that is scalable and highly parallelizable, along with optimizing the software for the … Continue reading Parallel Computing with the 1-D Heat Equation: Part 1
Introduction to Capillary Bridges with Minimal Surface Problem
Capillary bridges Capillary bridges are the minimized surface between two rigid bodies. My interest is in studying small drops of water between a two chemically distinct plates, where the one plate might be hydrophilic and the other might be hydrophobic. The resulting shape and physical phenomena are important in understanding the forces between this droplet… Continue reading Introduction to Capillary Bridges with Minimal Surface Problem
Bernoulli-Laplace Model of Diffusion
Bernoulli-Laplace The Bernoulli-Laplace model of diffusion describes the flow of two incompressible liquids between two containers. It may be described as two urns that contain balls each. Initially, the balls in the left urn are all red and the balls in the right urn are all blue. At each step, pick a ball at random… Continue reading Bernoulli-Laplace Model of Diffusion
The Ehrenfest Urn Model
Paul Ehrenfest Paul Ehrenfest is one of premier statistical mechanics of all time. Following in the footsteps of his advisor, and the father of statistical mechanics, Ludwig Boltzmann, Ehrenfest was renowned for his focus and clarity on fundamental problems. The Ehrenfest Model The Ehrenfest model, sometimes called the urn model or the dog-flea model, is… Continue reading The Ehrenfest Urn Model
Metropolis-Hastings
Metropolis-Hastings Algorithm History of Metropolis-Hastings One of, if not the most, popular Markov chain Monte Carlo (MCMC) methods is the famous Metropolis-Hastings algorithm. Metropolis-Hastings has its roots grounded in statistical mechanics, and was originally used to calculate the equation of state for simple Lennard-Jones particles in two dimensions. The nature of statistical mechanics produces problems… Continue reading Metropolis-Hastings