JMFT

The heat equation $$ \begin{align} u_t &= u_{xx}, \quad x \in \mathbb{R}, \quad t > 0, \\ u(x, 0) &= u_0(x) \end{align} $$ admits a self-similar solution of the form $$ K(x, t) = \frac{1}{(4 \pi t)^{1/2}} \exp\left(\frac{-x^2}{4t}\right) $$ when the initi…

Following the saga about dates, times and timezones and times and clocks in computer systems...

Here are a few different ways to do the same thing. x = [1, 2, 3, 4] # Option 1 x[0] # Option 2 x.

Function decorators are one of the most powerful features in the Python language, as they provide a succinct way to modify the behaviours of functions – often providing a quick one-liner to endow functions with useful behaviours or properties.

I am working on a project in which I have a sequence of photos (JPEG files, all the same size) that I want to put into a slideshow, along with a background soundtrack.

I am supervising an intro to fluid dynamics course.

The Part II Mathematical Biology course is an excellent introduction to mathematical modelling of dynamical systems, and opens the way to many applications in diverse areas.

This is a high-level, informal summary of the proof of the Arnold-Liouville theorem as stated and proved in V.

Fluid dynamics is a huge and broad topic spanning physics, maths, engineering, geosciences, and many more.

from functools import reduce from itertools import count FACTORS = {3: 'fizz', 5: 'buzz'} fizzbuzz = lambda n: reduce( str.

Jupyter notebooks are an excellent way to provide interactivity.

Just some of my old notes that I dug up on the method of characteristics from when I taught this in 2021: download I'll write these up properly later.

Over the Christmas holiday I've had a chance to play around with a few ideas that I've had with signal processing.

I have access to a scanner that can scan multiple pages, but does not have a duplexer.

This page lists things possibly of interest to my Part IB Quantum Mechanics students.

The following discussion is meant to give some more formalism to students of the Variational Principles course and perhaps tie it to material that they might have come across in analysis or linear algebra courses.

This page, which will be updated occasionally, summarises important results and useful formulae for the Part IB Quantum Mechanics course.

This is the second article about how working with temporal information in computer systems.

Here are some notes for my Fluid Dynamics II students about vectors, pseudovectors and how they transform under reflections. $$ \newcommand{n}{\mathbf{n}} \newcommand{r}{\mathbf{r}} \newcommand{v}{\mathbf{v}} \newcommand{L}{\mathbf{L}} \newcommand{R}{\mat…

Many cultural and religious traditions place a lot of importance in names, and hold that names have power.

One reason why Python is such a popular and powerful language is that it is straightforward to learn and make good progress.

I was a volunteer and organiser for codebar for several years and was heavily involved in outreach activities during my time at Cambridge.

This is a collection of notes about time and related concepts.

I have been reading – at a very shallow level – about category theory (wiki), and thinking about its applicability to software and system design for data engineering.

Emergency services, GPs, hospitals, transportation systems and the like are funded, at least in part, by public money.

Having reliable, detailed but searchable logs is an essential part of any application, especially of long-running services that need to be debugged and monitored for uptime and stability.

The basic way to create and initialize an object in Python is using the default constructor, defined as the __init__() method: class MyClass: def __init__(self, x: float) -> None: self.x: float = x print(f"created an object with x = {x…

A little investment into building a GUI for live visualizations and control provides huge improvements in iteration speed.

Originally written May 2022.

I recently asked the following questions: Assuming all other requirements are the same: Is a vegan a vegetarian?

This website is now self-hosted on a Raspberry Pi server at home.

A quiz: What does the following JavaScript code print and why?

Most people are introduced to the term 'uncertainty principle' in the context of quantum mechanics.

In the previous post I discussed how, when measuring the frequency (tempo) of a signal that itself changes in time, there is necessarily a tradeoff between the precision in the measured frequency and precision in the time at which the measurement is taken:

What is a variational principle?

This page is intended to give a little context behind the "Bohr model" that is introduced in the first part of the Part IB Quantum Mechanics course.