# Posts

Musings on science, math, engineering, and the environment.

• ## ODE fun with liquid flow into tanks with complicated geometries

By Cory Simon

We derive a dynamic model for the liquid level in a truncated square pyramidal tank when liquid flows in at a rate $q_i$ and is driven out of the tank by hydrostatic pressure.

• ## Surface tension catapults in mushrooms

By Cory Simon

Mushrooms have evolved a fascinating mechanism to discharge its spores.

• ## The orthogonal Procrustes problem

By Cory Simon

Two point sets $A$ and $B$ are “misaligned”; the points in $A$ correspond to rotated points in $B$ (with some noise). How do we recover the proper rotation matrix to align the points?

• ## Monte Carlo simulation of airline overbooking

By Mira Khare, Melanie Huynh, Arni Sturluson, Cory Simon

Airlines overbook flights to maximize profits. But by how much should they overbook? Simulations can address this question!

• ## Monte Carlo simulation of Buffon's Needle

By Arthur York

Modeling the probability of a needle intersecting a line when randomly dropped on a floor exhibiting infinite, equally spaced parallel lines. Uses analytical, geometrical, and simulation approaches to find the probability of a needle intersecting a line on the floor.

• ## Multiple dispatch and hierarchical data types in Julia

By Cory Simon

Julia is a programming language designed for numerical computing, and it supports multiple dispatch and type hierarchies.

• ## What is mathematics doing in a chemical engineering lecture?

By Cory Simon

I am teaching Process Dynamics & Simulation this quarter, which is a prelude to process control. The class involves a lot of mathematics. When preparing a part of my lecture on Euler’s formula, I came across this quote by Richard Feynman. Because it resonated with me, I read the last part to my students during class, but replaced all references...

• ## On toy models

By Cory Simon

On the utility of toy models; kidney donations and porous materials with rotating ligands.

• ## The freely jointed chain model

By Cory Simon

The freely jointed chain model captures much of the physics of a polymer. Here, we use statistical mechanics to derive a relationship between pulling force and end-to-end distance of a freely jointed chain. This is applicable to DNA unzipping experiments.