We'll be running a regular journal club online. This is an informal event for our members discuss cutting edge research in applied mathematics and research.

See below for a list of suggested papers.

Submit a paper: If you have a paper you would like discussed or would like to discuss yourself submit it here!

Upcoming Occurrences

6pm 12th November 2020, Enda Carroll. 

Title:  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators, Steven H.Strogatz, Physica D, 2000

Original abstract: The Kuramoto model describes a large population of coupled limit-cycle oscillators whose natural frequencies are drawn from some prescribed distribution. If the coupling strength exceeds a certain threshold, the system exhibits a phase transition: some of the oscillators spontaneously synchronize, while others remain incoherent. The mathematical analysis of this bifurcation has proved both problematic and fascinating. We review 25 years of research on the Kuramoto model, highlighting the false turns as well as the successes, but mainly following the trail leading from Kuramoto’s work to Crawford’s recent contributions. It is a lovely winding road, with excursions through mathematical biology, statistical physics, kinetic theory, bifurcation theory, and plasma physics. 

Link to paper:  https://doi.org/10.1016/S0167-2789(00)00094-4

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Past Occurrences

8th October 2020, Edward Donlon, MSc. 

Title:  Lagaris, I. E., Likas, A., & Fotiadis, D. I. (1998). Artificial neural networks for solving ordinary and partial differential equations. IEEE transactions on neural networks, 9(5), 987-1000.

Original abstract: We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions and contains no adjustable parameters. The second part is constructed so as not to affect the boundary conditions. This part involves a feedforward neural network, containing adjustable parameters (the weights). Hence by construction the boundary conditions are satisfied and the network is trained to satisfy the differential equation. The applicability of this approach ranges from single ODE's, to systems of coupled ODE's and also to PDE's. In this article we illustrate the method by solving a variety of model problems and present comparisons with finite elements for several cases of partial differential equations.

Link to paper:  https://arxiv.org/abs/physics/9705023

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