In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of rotational and reverse mixed triple systems. Our principal proof technique applied is the difference method. Finally, this work contains a result on packing of complete mixed graphs on v vertices, Mv, with isomorphic copies of two of the mixed triples and a possible leave structure.

A Steiner triple system of order v, denoted STS(v), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic STS(v) when one of the cycles is of length one. In this case, the STS(v) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-rotational.

Purpose/Hypothesis: Mal de Debarquement Syndrome (MdDS) is a rare condition in which those afflicted perceive a chronic rocking or swaying sensation, often relieved when in motion and symptomatic when still. Etiology is uncertain; therefore, treatment options are limited. While there is reported success with medication, optokinetic stimulation or transcutaneous magnetic stimulation, there is no single treatment that works for all patients. This retrospective chart review investigated rehabilitation outcomes following sensorimotor, multi-axis, rotational (SMART) training to address MdDS symptoms. Number of Subjects: Forty-nine Materials and Methods: Forty-nine patients participated in 10-20 sessions of SMART training, with integrated use of a visual targeting system and physical therapy. Between sessions, patients were instructed to perform mindfulness breathing, relaxation and grounding techniques. Pre- and post-training Dizziness Handicap Inventory (DHI), 4-item Dynamic Gait Index (DGI), and computerized posturography including Sensory Organization Test (SOT) were assessed. Subjective change following rehabilitation was tracked at discharge, 5 weeks, 3 months, 6 months and 1 year post-training. Results: Mean age (SD) of patients was 52.9 (12.6) years with the majority (n=47) being female. Mean time from onset of symptoms (SD) was 50.8 (87.8) months suggesting chronic symptoms. At discharge, 42 of 49 patients reported improvements, with nearly half (n=24, 48.9%) of all patients reporting marked or moderate improvement in symptoms; whereas, 14 (28.6%) reported minimal improvement in symptoms. Based on paired t-tests, all outcome measures – DHI, MdDS severity Visual Analog Scale (VAS), Motion VAS, 4-item DGI, and SOT - improved significantly (p < 0.001) from initial evaluation to discharge. Several personal factors were associated with rehabilitation outcomes based on bivariate correlations. With some variation, patients sustaining improvements at 1 week post-discharge, generally continued to sustain at 5 weeks, 3 months, 6 months and 1 year. Conclusions: SMART training plus physical therapy resulted in improved performance outcomes and in significant reduction or resolution in MdDS symptoms. This study provides early evidence that this method of training has promising potential to aid in the management or recovery of MdDS. Clinical Relevance: MdDS is disorder with no specific cure. Treatment is limited. SMART training may serve as an effective outcome to reduce or resolve symptoms associated with MdDS.

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In the field of structural engineering it is of vital importance that the condition of an ageing structure is monitored to detect damages that could possibly lead to failure of the structure. Over the past few years various methods for monitoring the condition of structures have been proposed. With respect to civil and mechanical structures several methods make use of modal parameters such as, natural frequency, damping ratio and mode shapes. In the present work four methods for modal parameter estimation and two methods for have been evaluated for their application to multi degree of freedom structures. The methods evaluated for modal parameter estimation are: Wavelet transform, Hilbert-Huang transform, parametric system identification and peak picking. Through various numerical simulations the effectiveness of these methods is studied. It is found that the simple peak-picking method performs the best and is able to identify modal parameters most accurately in all the simulation cases that were considered in this study. The identified modal parameters are then used for locating the damage. Herein the flexibility and the rotational flexibility approaches are evaluated for damage detection. The approach based on the rotational flexibility is found to be more effective. / Master of Science

Operating temperature range is one of the primary design considerations for developing effective disc brake system performance. Very high braking temperatures can introduce effects detrimental to performance such as brake fade, premature wear, brake fluid vaporization, bearing failure, thermal cracks, and thermally-excited vibration [2]. This project is concerned with investigating deficiencies and proposing improvements in brake system Finite Element (FE) models in order to provide high quality descriptions of thermal behaviour during braking events. The work focuses on brake disc/pad models and the degree of rotational freedom allowed for the pad. Conventional models [10] allow no motion/or free motion of the pad. The present work investigates the effect on disc/pad interface temperature and pressure distributions of limited relaxations of this rotational restriction. Models are proposed, developed and validated that facilitate different rotational degrees of freedom (DoF) of the pad. An important influencing factor in friction brake performance is the development of an interface tribo-layer (ITL). It is reasonable to assume that allowing limited rotational motion of the pad will impact the development of the ITL (e.g. due to different friction force distributions) and hence influence temperature. Here the ITL is modelled in the numerical simulations as a function of its thickness distribution and thermal conductivity. Different levels of ITL thermal conductivity are defined in this work and results show that conductivity significantly a1qwffects interface temperature and heat partition ratio. The work is based around a set of test-rig experiments and FE model developments and simulations. For the experimental work, a small-scale test rig is used to investigate the friction induced bending moment effect on the pad/disc temperature. Significant non-uniform wear is observed across the friction surface of the pad, and reasons for the different wear rates are proposed and analyzed together with their effect on surface temperature. Following on from experiment a suite of models is developed in order to evidence the importance of limited pad motion and ITL behaviours. A 2D coupled temperature-displacement FE model is used to quantify the influence of different pad rotational degrees of freedom and so provide evidence for proposing realistic pad boundary settings for 3D models. Normal and high interface thermal conductance is used in 2D models and results show that the ITL thermal conductivity is an important factor influencing the maximum temperature of contact surfaces and therefore brake performance. The interface heat partition ratio is calculated by using the heat flux results and it is confirmed that this value is neither constant nor uniform across the interface surfaces. Key conclusions from the work are (i) that ITL thermal conductivity is an important factor influencing the interface temperature/heat flux distribution and their maximum values, (ii) that allowed motion of the pad significantly affects the interface pressure distribution and subsequently the temperature distribution, (iii) that the transient heat partition in friction braking is clearly quite different to the conventional friction-pair steady heat partition (the heat partition ratio is not uniformly distributed along the interface) and (iv) that the thickness of the ITL increases through braking events, reducing the heat transfer to the disc, and so providing a possible explanation for increasing pad temperature observed over the life time of a brake pad.

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