[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

The numerical modelling of multi-physics phenomena: The shape casting process

In this paper a computer simulation tool capable of modelling multi-physics processes in complex geometry has been developed and applied to the casting process. The quest for high-quality complex casting components demanded by the aerospace and automobile industries, requires more precise numerical modelling techniques and one that need to be generic and modular in its approach to modelling multi-processes problems. For such a computer model to be successful in shape casting, the complete casting process needs to be addressed, the major events being:-• Filling of hot liquid metal into a cavity mould • Solidification and latent heat evolution of liquid metal • Convection currents generated in liquid metal by thermal gradients • Deformation of cast and stress development in solidified metal • Macroscopic porosity formation The above phenomena combines the analysis of fluid flow, heat transfer, change of phase and thermal stress development. None of these events can be treated in isolation as they inexorably interact with each other in a complex way. Also conditions such as design of running system, location of feeders and chills, moulding materials and types of boundary conditions can all affect on the final cast quality and must be appropriately represented in the model.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Using an interactive software environment for the parallelization of real-world scientific applications

The parallelization of real-world compute intensive Fortran application codes is generally not a trivial task. If the time to complete the parallelization is to be significantly reduced then an environment is needed that will assist the programmer in the various tasks of code parallelization. In this paper the authors present a code parallelization environment where a number of tools that address the main tasks such as code parallelization, debugging and optimization are available. The ParaWise and CAPO parallelization tools are discussed which enable the near automatic parallelization of real-world scientific application codes for shared and distributed memory-based parallel systems. As user involvement in the parallelization process can introduce errors, a relative debugging tool (P2d2) is also available and can be used to perform nearly automatic relative debugging of a program that has been parallelized using the tools. A high quality interprocedural dependence analysis as well as user-tool interaction are also highlighted and are vital to the generation of efficient parallel code and in the optimization of the backtracking and speculation process used in relative debugging. Results of benchmark and real-world application codes parallelized are presented and show the benefits of using the environment

Design of parallel algorithms for fractal video compression

The intrinsic independent features of the optimal codebook cubes searching process in fractal video compression systems are examined and exploited. The design of a suitable parallel algorithm reflecting the concept is presented. The Message Passing Interface (MPI) is chosen to be the communication tool for the implementation of the parallel algorithm on distributed memory parallel computers. Experimental results show that the parallel algorithm is able to reduce the compression time and achieve a high speed-up without changing the compression ratio and the quality of the decompressed image. A scalability test was also performed, and the results show that this parallel algorithm is scalable.

Parallel genetic algorithms for the solution of inverse heat conduction problems

A parallel genetic algorithm (PGA) is proposed for the solution of two-dimensional inverse heat conduction problems involving unknown thermophysical material properties. Experimental results show that the proposed PGA is a feasible and effective optimization tool for inverse heat conduction problems

Reviews: making mathematics with needlework

Review of Making Mathematics with Needlework, edited by Sarah-Marie Belcastro and Carolyn Yackel, published by AK Peters Ltd, 2007 (ISBN 978-1-56881-331-8).

Computational magnetohydrodynamics - Application

There are many processes, particularly in the nuclear and metals processing industries, where electromagnetic fields are used to influence the flow behaviour of a fluid. Procedures exploiting finite volume (FV) methods in both structured and unstructured meshes have recently been developed which enable this influence to be modelled in the context of conventional FV CFD codes. A range of problems have been tackled by the authors, including electromagnetic pumps and brakes, weirs and dams in steelmaking tundishes and interface effects in aluminium smelting cells. Two cases are presented here, which exemplify the application of the new procedures. The first case investigates the influence of electromagnetic fields on solidification front progression in a tin casting and the second case shows how the liquid metals free surface may be controlled through an externally imposed magnetic field in the semi-levitation casting process.

Multilevel refinement for the vehicle routing problem

Multilevel approaches to computational problems are pervasive across many areas of applied mathematics and scientific computing. The multilevel paradigm uses recursive coarsening to create a hierarchy of approximations to the original problem, then an initial solution is found for the coarsest problem and iteratively refined and improved at each level, coarsest to finest. The solution process is aided by the global perspective (or `global view') imparted to the optimisation by the coarsening. This paper looks at their application to the Vehicle Routing Problem.

Grey video compression methods using fractals

The authors' experience in the treatment of grey video compression using fractals is summarized and compared with other research in the same field. Experience with parallel and distributed computing is also discussed.