Dendrites are tree-like topological spaces, and in this thesis, the physical characteristics of various random fractal versions of this type of set are investigated. This work will contribute to the development of analysis on fractals, an area which has grown considerably over the last twenty years. First, a collection of random self-similar dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have often relied on the scaling factors being bounded uniformly away from zero. However, using a percolative argument, and taking advantage of the tree-like structure of the sets considered here, it is shown that this condition is not necessary; a simple condition on the tail of the distribution of the scaling factors at zero is all that is assumed. The scaling factors of these recursively defined structures form what is known as a multiplicative cascade, and results about the height of this random object are also obtained. With important physical and probabilistic applications, the heat equation has justifiably received a substantial amount of attention in a variety of settings. For certain types of fractals, it has become clear that a key factor in estimating the heat kernel is the volume growth with respect to the resistance metric on the space. In particular, uniform polynomial volume growth, which occurs for many deterministic self-similar fractals, immediately implies uniform (on-diagonal) heat kernel behaviour. However, in the random fractal setting, this is frequently not the case, and volume fluctuations are often observed. Motivated by this, an analysis of how volume fluctuations lead to corresponding heat kernel fluctuations for measure-metric spaces equipped with a resistance form is conducted here. These results apply to the aforementioned random self-similar dendrites, amongst other examples. The continuum random tree (CRT) of Aldous is an important random example of a measure-metric space, and fits naturally into the framework of the previous paragraph. In this thesis, quenched (almost-sure) volume growth asymptotics for the CRT are deduced, which show that the behaviour in almost-every realisation is not uniform. Applying the results introduced above, these yield heat kernel bounds for the CRT, demonstrating that heat kernel fluctuations occur almost-surely. Finally, a new representation of the CRT as a random self-similar dendrite is presented.

A simple two scale compactification scheme for the E(8) x E(8) heterotic string is studied. The internal space used is a direct product of two compact spaces, each with its own length scale. Compactification on the smaller 4-dimensional (4d) manifold is carried out to obtain 6d theories with simple supersymmetry (SUSY). Assuming the background torsion vanishes, we show that this manifold must be K3. Compactification on K3 is studied in detail. Also analyzed are the two possible torsion-free compactifications on the orbifold K3$ sp prime$ (the limit of the manifold K3). The compactification from 6d to 4d on the larger scale 2d manifold results in Grand Unified Theories (GUT's) with broken SUSY. We show that it is not possible to generate a realistic theory using our scheme. Strings exclude what is conceivable from the perspective of point field theories: getting a realistic GUT from a 6d theory with simple SUSY.

No description available.

Demographically open public spaces provide valuable grounds for engaging diverse ideologies. While the rise of society and passive consumption of mass culture excludes “action” and “speech” from the public realm and threatens human plurality, a public space in which to hold public debates and discussions will reengage public roles in the public realm. And it will consequently act as a new site for citizenship and new “space of appearance.” Such space becomes even more essential in a society that dreads conflict. Focusing on Iranian society, the proposal integrates this overlooked opportunity by offering temporary debate interventions to be used around the Iranian cities on a regular basis, envisioning a culture of dialogue incrementally developing. This is a way of approaching a sociological issue with the help of Architecture, making a role for public space in promoting a culture, a culture that encourages human plurality and appreciates engaging the wide range of diverse ideologies, convictions and viewpoints. Rather than proposing a closed narrative and one single architectural solution for the space of public debate, the thesis imagines an architectural toolkit for application to the specific cultural and urban context.

Play is inarguably an important part of human development. Through play, children as young as three years of age learn social skills and values that will form the foundation of their development in to adult life. Children can be excluded from play for many reasons. Any visible or cognitive differences in a child can cause them to be marginalized in playgroups or daycares and later in their development, at school and camps. This makes it difficult for them to experience the types of play that are so important to their healthy development. This thesis examines the existing standards for accessible design, finding the contradictions in the information available, and exposing the gaps of information that make it impossible for designers to create truly inclusive play spaces for children. Collaboration with Camp Trillium, one of the foremost pediatric oncology camp programs in Ontario, will be a useful tool for gaining insight into the healing powers of inclusive play experiences for children. The product of this thesis will be the design of a system for creating inclusive play spaces that will allow children who have been marginalized by disabilities and illness to play freely with others. These fully-inclusive play spaces will aim to foster a new understanding of inclusivity in children; teaching those without distinguishing differences the value of relationships with people of differing challenges, and instilling in marginalized children a sense of self that helps them develop the confidence and social ability to penetrate the boundaries that have been inflicted on them.

In this thesis Finsler geometry is extensively reviewed. The geometrization of fields by a Finslerian approach is considered. Also unification of electrodynamics and gravitation with suitable Finslerian metrics is examined.

Graduation date: 2000

Typescript. / Thesis (Ph. D.)--University of Hawaii, 1971. / Bibliography: leaves 73-74. / vi, 74 l

This research examines the problem of urban open space design in the city with an increasing ultraviolet radiation (UVR) and covers aspects of behaviour scenarios, built sunshade design and choice of sunshade plants for landscaping / Thesis (PhDArchitectureandDesign)--University of South Australia, 2001

From opera theatre to home theatre (the making of) theatrical spaces and devices in the landscape -- No abstract provided.