the pursuit of science for understanding our natural world
03 - 01 - 2020
[ genetic engineering ]

Jennifer Doudna, in an excerpt from "A Crack in Creation", highlights how the development of the revolutionary CRISPR-Cas9 genome editing technology justifies funding fundamental research.

29 - 11 - 2019
[ combinatorics ]

The "stars and bars" formulation is an intuitive way to solve a particular combinatorics problem. Here, for memorability, we formulate a combinatorics problem as cookies and coffees.

the German tank problem
15 - 11 - 2019
[ statistics , probability , combinatorics , estimation ]

The simplified German tank problem is as follows. During World War 2, the Germans labeled their tanks with sequential serial numbers. The Allied forces used the serial numbers on a captured subset of the German tanks (data!) to estimate the total number of tanks the Germans had.

Porous Coordination Cage Mo24(tBu-bdc)24
07 - 07 - 2019
[ materials ]

An interactive visualization of metal-organic cuboctahedron Mo24(tBu-bdc)24, which holds promise for vehicular natural gas storage and delivery.

ODE fun with liquid flow into tanks with complicated geometries
22 - 03 - 2019
[ chemical engineering , process dynamics ]

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
28 - 11 - 2018
[ biology , thermodynamics ]

Mushrooms have evolved a fascinating mechanism to discharge its spores.

The orthogonal Procrustes problem
27 - 10 - 2018

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
24 - 07 - 2018
[ optimization ]

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
11 - 04 - 2018
[ simulation , computer programming ]

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
28 - 03 - 2018
[ Julia ]

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?
25 - 01 - 2018
[ education , math ]

Richard Feynman on Euler's formula.

On toy models
29 - 12 - 2017
[ modeling ]

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

The freely jointed chain model
06 - 10 - 2017
[ statistical mechanics ]

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.