Edinburgh SIAM Student Chapter Conference 2011

The conference took place at ICMS, South College Street, Edinburgh on February 1st 2011. It consisted of two sessions, one on optimisation and the other on PDEs, with a plenary speaker for each. Photos of the conference can be found here.

The prize for best poster was awarded to Martin Takac, University of Edinburgh, while the prize for best talk went to Michael Watson, Heriot-Watt University.

Plenary Speakers

Professor Roger Fletcher FRS FRSE, University of Dundee

The fall and rise of the Steepest Descent method. Abstract 

Dr. Kevin Painter, Heriot Watt University

Does Mathematics Have a Place in the Lab? Abstract

PDE Session

Stochastic Thermostating for Molecular Dynamics - Charles Matthews, Edinburgh University

In Molecular Dynamics, thermostats are often used to control the overall system temperature and sample the canonical distribution. However, many of these methods can sometimes perform terribly on harmonic systems (such as Hoover's classic example of the 1d harmonic oscillator) or significantly disrupt the dynamics (such as Langevin). We will give a short introduction to the pitfals of using these thermostats as well as demonstrate some recent successes using a coloured noise thermostat, based on the recent work of Ceriotti, Bussi and Parrinello.

Thermodynamic modelling of the acid gases system phase behaviour - Haifan Liu, Heriot-Watt University

Acid gases (ex: CO2) are one of the major concerns during the upstream oil and gas productions as well as the downstream gas processing operations.

A better understanding of the phase behaviour becomes crucial for the predictions of the properties of the acid gas mixtures since the demand of energy pushes the production operations under the more and more extreme working conditions(ex: P>100bars while T->0 Celsius) during some offshore deep water operations.

Based on the statistical thermodynamics as well as the numerical algorithms, thermodynamic modelling allows us to achieve much more precise prediction results for the applications in the industry.

Development of the Superficial Retinal Vascular Plexus: Mathematical Modelling and Numerical Simulation - Michael Watson, Heriot-Watt University

Due to its high consumption of oxygen, the retinal vasculature is extremely vulnerable to a number a vascular insults.  In some serious cases, such as retinopathy of prematurity (ROP) or diabetic retinopathy, the related insults can lead to blindness.  The superficial retinal vascular plexus evolves from a dense mesh of vessels, grown away from the optic nerve, to a much more sparse, well-defined final structure.  In order to obtain an insight into the underlying processes, we have developed a hybrid model describing the evolution of the vascular plexus.  The model incorporates a number of important features including discrete in-growth of astrocytes and endothelial cells, blood flow in the nascent vasculature, and transmural oxygen transport to the surrounding tissue.

Optimisation Session

Dynamic Network Flow Models and Optimization Techniques - Ute Ziegler, RWTH Aachen

Nowadays, the use of PDE-based dynamic network flow models have become a useful tool to study the macroscopic behaviour of traffic flow, evacuation and production networks. In several cases, it is possible to reformulate the models to a mixed integer programming problem. This enables us to answer different optimization aspects using branch-and-cut procedures.

Complexity analysis of randomized coordinate descent methods - Martin Takac, Edinburgh University

In today's digital world there is a clear need to solve optimization problems of unprecedented sizes. Problems like this arise naturally in large networks and data mining applications.

Classical second-order optimization methods require at every iteration the calculation of the Hessian, first-order methods of the gradient. However, for problems of large-enough dimension, even the calculation of the function value may be prohibitive.

In this talk we give iteration complexity analysis of a randomized coordinate descent method for minimizing convex functions, generalizing and improving on recent results of Nesterov. We will also briefly describe two applications: Truss Topology Design and the Google problem.

Solving SCOPF Problems by a Structure Exploiting Interior Point Method - Naiyuan Chiang, Edinburgh University

The aim of this talk is to introduce what the Security Constrained Optimal Power Flow (SCOPF) model is. In addition, we describe how the linearised (n-1) SCOPF model can be formulated with a bordered block diagonal structure. Then, we demonstrate the advantages of solving this reformulated model by the Object-Oriented Parallel Solver (OOPS). We give results on several instances of the SCOPF.