# Category Archives: Applied Mathematics

## Wave Trapping Around Islands

Islands are subject to tides, seismic waves as well as wind generated waves. If any of these are trapped, that is the energy of the wave goes continuously around the

## Natural Ventilation

The study of how to ventilate a room without recourse to air conditioning has practical application to theatres and libraries where all but the quietest noise has to be avoided.

## Wind Driven Circulation

In the ocean the main gyres responsible for how the sea circulates are generated by the climatic winds. In this project you will derive the equations that govern this process

## The Numerical Solution of the p-Laplace Equation in a Geometry with Sharp Corners

Certain types of fluids do not respond in a linear way to external forces – they are called non-Newtonian fluids. A simple model of a non-Newtonian fluid which is widely

## Perturbation Methods

Perturbation methods are used to investigate solutions to mathematical problems in which exact solutions can’t be found but in which there is a parameter whose size (usually very small) allows

## Non-linear Waves

This project concerns deriving equations that govern the propagation of waves on water, then solving them. These equations have two well-known solutions, the solitary wave (or soliton) and cnoidal waves.

## Waves

Wave motion is found everywhere: sound waves, water waves, electromagnetic waves, traffic waves and Mexican waves are just some examples. The mathematical description of wave motion can be fairly straightforward,

## Chebychev Polynomials

In this project the aim is to study the mathematical properties of Chebychev polynomials and their role in numerical approximation. The concept of ‘good’ and ‘best’ numerical approximations and the

## Particle methods for fluid dynamics

Particle-based numerical methods have been used extensively by Hollywood in modelling dramatic events such as floods or sinking ships. This project would investigate smoothed particle hydrodynamics (SPH) models or, possibly,

## Numerical methods for PDE’s

Partial differential equations describe how the three/four dimensional world works. Solving such equations is the key to understanding the behaviour of many physical, chemical, biological or financial systems. A large

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