Analytical study of the Least Squares Quasi-Newton method for interaction problems

Often in nature different systems interact, like fluids and structures, heat and electricity, populations of species, etc. It is our aim in this thesis to find, describe and analyze solution methods to solve the equations resulting from the mathematical models describing those interacting systems. Even if powerful solvers often already exist for problems in a single physical domain (e.g. structural or fluid problems), the development of similar tools for multi-physics problems is still ongoing. When the interaction (or coupling) between the two systems is strong, many methods still fail or are computationally very expensive. Approaches for solving these multi-physics problems can be broadly put in two categories: monolithic or partitioned. While we are not claiming that the partitioned approach is panacea for all coupled problems, we will only focus our attention in this thesis on studying methods to solve (strongly) coupled problems with a partitioned approach in which each of the physical problems is solved with a specialized code that we consider to be a black box solver and of which the Jacobian is unknown. We also assume that calling these black boxes is the most expensive part of any algorithm, so that performance is judged by the number of times these are called. In 2005 Vierendeels presented a new coupling procedure for this partitioned approach in a fluid-structure interaction context, based on sensitivity analysis of the important displacement and pressure modes which are detected during the iteration process. This approach only uses input-output couples of the solvers (one for the fluid problem and one for the structural problem). In this thesis we will focus on establishing the properties of this method and show that it can be interpreted as a block quasi-Newton method with approximate Jacobians based on a least squares formulation. We also establish and investigate other algorithms that exploit the original idea but use a single approximate Jacobian. The main focus in this thesis lies on establishing the algebraic properties of the methods under investigation and not so much on the best implementation form

Trust Based Participant Driven Privacy Control in Participatory Sensing

Widespread use of sensors and multisensory personal devices generate a lot of personal information. Sharing this information with others could help in various ways. However, this information may be misused when shared with all. Sharing of information between trusted parties overcomes this problem. This paper describes a model to share information based on interactions and opinions to build trust among peers. It also considers institutional and other controls, which influence the behaviour of the peers. The trust and control build confidence. The computed confidence bespeaks whether to reveal information or not thereby increasing trusted cooperation among peers.Comment: 14 page

On relations between one-dimensional quantum and two-dimensional classical spin systems

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion paper (J. Hutchinson, J. P. Keating, and F. Mezzadri, arXiv:1503.05732). In particular, we use three approaches: the Trotter-Suzuki mapping; the method of coherent states; and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in our previous article for the classical systems identified.Comment: 36 page