Do You Know a Friend Who Needs a Mathematician?


Recent events let me know I should make something explicit. I am interested in and looking for mathematical work. My particular skills are in numerical computing but anyone familiar with my writing knows my interest in education and communication. So I am not looking only for major projects. If you need someone to tutor you through the lesson on the directrix or the separatrix, I am game.

I am open also to computer programming work. My day job for the last decade and a half has got me terribly familiar with Asp.Net C#, SQL, Javascript, jQuery, and the OpenLayers GIS tools. Also I keep thinking to take a weekend and pick up Cobol, to put on the shelf beside my Fortran background.

Thank you for thinking of me.

Reversible and irreversible change


Entropy is hard to understand. It’s deceptively easy to describe, and the concept is popular, but to understand it is challenging. In this month’s entry CarnotCycle talks about thermodynamic entropy and where it comes from. I don’t promise you will understand it after this essay, but you will be closer to understanding it.

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Reversible change is a key concept in classical thermodynamics. It is important to understand what is meant by the term as it is closely allied to other important concepts such as equilibrium and entropy. But reversible change is not an easy idea to grasp – it helps to be able to visualize it.

Reversibility and mechanical systems

The simple mechanical system pictured above provides a useful starting point. The aim of the experiment is to see how much weight can be lifted by the fixed weight M1. Experience tells us that if a small weight M2 is attached – as shown on the left – then M1 will fall fast while M2 is pulled upwards at the same speed.

Experience also tells us that as the weight of M2 is increased, the lifting speed will decrease until a limit is reached when the weight difference between M2 and M1 becomes…

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Spontaneity and the performance of work


I’d wanted just to point folks to the latest essay in the CarnotCycle blog. This thermodynamics piece is a bit about how work gets done, and how it relates to two kinds of variables describing systems. The two kinds are known as intensive and extensive variables, and considering them helps guide us to a different way to regard physical problems.

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Imagine a perfect gas contained by a rigid-walled cylinder equipped with a frictionless piston held in position by a removable external agency such as a magnet. There are finite differences in the pressure (P1>P2) and volume (V2>V1) of the gas in the two compartments, while the temperature can be regarded as constant.

If the constraint on the piston is removed, will the piston move? And if so, in which direction?

Common sense, otherwise known as dimensional analysis, tells us that differences in volume (dimensions L3) cannot give rise to a force. But differences in pressure (dimensions ML-1T-2) certainly can. There will be a net force of P1–P2 per unit area of piston, driving it to the right.

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The driving force

In thermodynamics, there exists a set of variables which act as “generalised forces” driving a system from one state to…

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