The twistor description of integrable systems

The theory of twistors and the theory of integrable models have, for many years, developed independently of each other. However, in recent years it has been shown that there is considerable overlap between these two apparently disparate areas of mathematical physics. The aim of this thesis is twofold; firstly to show how many known integrable models may be given a natural geometrical/twistorial interpretation, and secondly to show how this leads to new integrable models, and in particular new higher dimensional models. After reviewing those elements of twistor theory that are needed in the thesis, a generalisation of the Yang-Mills self-duality equations is constructed. This is the framework into which many known examples of integrable models may be naturally fitted, and it also provides a simple way to construct higher dimensional generalisations of such models. Having constructed new examples of (2 + l)-dimensional integrable models, one of these is studied in more detail. Embedded within this system are the sine-Gordon and Non-Linear Schrodinger equations. Some solutions of this (2 + l)-dimensional integrable model are found using the 'Riemann Problem with Zeros' method, and these include the sohton solutions of the SG and NLS equations. The relation between this approach and one based the Atiyah-Ward ansatze is dicussed briefly. Scattering of localised structures in integrable models is very different from scattering in non-integrable models, and to illustrate this the scattering of vortices in a modified Abelian-Higgs model is considered. The scattering is studied, for small speeds, using the 'slow motion approximation' which involves the calculation of a moduli space metric. This metric is found for a general TV-lump vortex configuration. Various examples of scattering processes are discussed, and compared with scattering in an integrable model. Finally this geometrical approach is compared with other approaches to the study of integrable systems, such as the Hirota method. The thesis closes with some suggestions for how the KP equation may be fitted into this geometrical/twistorial scheme

Coarse grain modeling of spall failure in molecular crystals: role of intra-molecular degrees of freedom

We use a recently developed thermodynamically accurate mesodynamical method (Strachan and Holian 2005 Phys. Rev. Lett. 94 014301) where groups of atoms are represented by mesoparticles to characterize the shock compression and dynamical failure (spall) of a model molecular crystal. We characterize how the temperature rise caused by the shockwave depends on the specific heat of the degrees of freedom (DoFs) internal to the mesoparticles (Cint) and the strength of the coupling between the internal DoFs and the mesoparticles. We find that the temperature of the shocked material decreases with increasing Cint and decreasing coupling and quantify these effects. Our simulations also show that the threshold for plastic deformation (the Hugoniot elastic limit) depends on the properties of the internal DoFs while the threshold for failure is very insensitive to them. These results have implications on the results of all-atom MD simulations, whose classical nature leads to a significant overestimation of the specific heat of molecular materials

Harmonic vector fields on Riemannian manifolds

This dissertation investigates harmonic vector fields which are special mappings on Riemannian manifolds with many interesting properties. It aims for a sharp definition of these fields through a focus on several aspects of geometry. Key concepts include the Weitzenböck formula, the divergence theorem, the Euler-Lagrange equation and the Sasaki metric. This particular metric contains horizontal and vertical components which are used to define vertical energy and this, in turn, leads to a definition of harmonic vector fields which are later generalised by the Cheeger-Gromoll metric and the general definition of a harmonic vector field. The dissertation also concentrates on some specific examples of harmonic vector fields such as harmonic unit vector fields, the Hopf vector field, conformal gradient fields on the unit sphere and on the hyperbolic space. The key outcome of this research, presented in the concluding subsections of the dissertation, is the discovery of two new examples that give fresh insight into this important aspect of differential geometry

Incidental learning of trust from eye-gaze: Effects of race and facial trustworthiness

Humans rapidly make inferences about individuals’ trustworthiness on the basis of their facial features and perceived group membership. We examine whether incidental learning about trust from shifts in gaze direction is influenced by these facial features. To do so, we examined two types of face category: the race of the face and the initial trustworthiness of the face based on physical appearance. We find that cueing of attention by eye-gaze is unaffected by race or initial levels of trust, whereas incidental learning of trust from gaze behaviour is selectively influenced. That is, learning of trust is reduced for other race faces, as predicted by reduced abilities to identify members of other races (Experiment 1). In contrast, converging findings from an independently gathered set of data showed that the initial trustworthiness of faces did not influence learning of trust (Experiment 2). These results show that learning about the behaviour of other race faces is poorer than for own-race faces, but that this cannot be explained by differences in the perceived trustworthiness of different groups

IEA BESTEST Multi-Zone Non-Airflow In-Depth Diagnostic Cases: Preprint

This paper documents a set of in-depth diagnostic test cases for multi-zone heat transfer models that do not include the heat and mass transfer effects of airflow between zones. The multi-zone non-airflow test cases represent an extension to IEA BESTEST (Judkoff and Neymark 1995a)

IEA BESTEST Multi-Zone Non-Airflow In-Depth Diagnostic Cases: Preprint

This paper documents a set of in-depth diagnostic test cases for multi-zone heat transfer models that do not include the heat and mass transfer effects of airflow between zones. The multi-zone non-airflow test cases represent an extension to IEA BESTEST (Judkoff and Neymark 1995a)

International Energy Agency Building Energy Simulation Test and Diagnostic Method (IEA BESTEST) Multi-Zone Non-Airflow In-Depth Diagnostic Cases: MZ320 -- MZ360

This report documents a set of diagnostic test cases for multi-zone heat transfer models. The methodology combines empirical validation, analytical verification, and comparative analysis techniques