Current Project: Fluid Mechanics
During this past spring as an experiment and to satisfy my curiosity, I derived fluid mechanics from the underlying particle motion, while using the more standard derivation of fluid mechanics given in Fluid Mechanics by Kundo, Cohen and Dowling as a guide. My goal was to see if I could complete the derivation in a undirected or in this case semidirected scenario. In the end I was able to complete the derivation and once I finished it I began looking for similar derivations in books and articles. After some searching I found a derivation of fluid mechanics using a similar technique in the text book by Frank H. Shu The Physics of Astrophysics, Volume II: Gass Dynamics, the derivation is given in the second chapter. Now having completed this derivation of fluid mechanics and a previous derivation of the dynamics of strings I have some appreciation for difficulty of completing a derivation in an undirected manner. So with that in mind my goal for the summer is to complete similar derivations in fluid mechanics, to extend the derivation I have already completed and to do these derivations on my own so as to gain more experience in the process.
Completed Articles
Articles in Progress
 Fluid Mechanics from Particle Motion: Theoretical Applications
 Fluid Mechanics from Particle Motion: Computational Applications
Posts

Fluid Mechanics from Particle Motion
In January of 2016 I started taking my first class on fluid mechanics. In the first or second week of that class we started going over the derivation of the partial differential equations of fluid mechanics, but before covering the derivation we covered the concept of a fluid element. In... 
String Dynamics
Since finishing my first class on classical mechanics I have been interested in deriving the equations of motion for strings. Before I begin it should be noted that I do not have formal training in continuum mechanics, so the methods and definitions that I use may be nonstandard. 
PsiPy: Schrodinger's Equation (part 1)
This past fall I was taking my second quantum mechanics class. In that class we learnt how to deal with discreet quantum system using linear algebra and how to extend that notation to solve continuous systems. Midway though the semester I attempted to write a simple program to solve the... 
Memory and Markov
In a previous post I discussed how to generate a Markov Chain with a basic algorithm, but using that algorithm memory usage was a limiting factor. Now we will attempt to find a solution to the memory usage of the algorithm. If you are unfamiliar with how to generate a... 
An Improbable Prime
Over the last couple years security and privacy on the internet has become significant issue due to constant hacking and spying from groups and individuals both foreign and domestic. A common solution to such intrusions is cryptography, one common encryption algorithm is RSA encryption. RSA is a publickey encryption algorithm,... 
The Making of a Markov Chain
Before getting into how to make Markov Chains, lets quickly get a refresh on what a Markov Chain is. A Markov Chain is a set of states and state transition which are selected based on an assigned probability of occurring. The goal of a Markov chain is to model complex... 
What is Momentum?
When you took your first physics class you where introduced to the concept of momentum, and the discussion likely revolved around Newton’s second law of motion. This discussion would then culminate in the definition of momentum: . As you progressed in the sciences you learned more about momentum and why... 
An Introduction to Markov Chains
Markov chains are a statistical tool invented by Andrey Markov to model dependent statistical phenomenon. A Markov Chain is made from two components a discrete set of states and a set of stochastic state transitions. The idea is that if there are two states A and B and the state...
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