Safety constraints are ubiquitous in many robotic applications. For instance, aerial robots such as quadrotors or hexcoptors need to realize fast collision-free flight, and bipedal robots have to choose their discrete footholds properly to gain the desired friction and pressure contact forces. In this thesis, we address the safety critical control problem for fully-actuated and under-actuated mechanical systems. Since many mechanical systems evolve on nonlinear manifolds, we extend the concept of Control Barrier Function to a new concept called geometric Control Barrier Function which is specifically designed to handle safety constraints on manifolds. This type of Control Barrier Function stems from geometric control techniques and has a coordinate free and compact representation. In a similar fashion, we also extend the concept of Control Lyapunov Function to the concept of geometric Control Lyapunov Function to realize tracking on the manifolds. Based on these new geometric versions of CLF and CBF, we propose a general control design method for fully-actuated systems with both state and input constraints. In this CBF-CLF-QP control design, the control input is computed based on a state-dependent Quadratic Programming (QP) where the safety constraints are strictly enforced using geometric CBF but the tracking constraint is imposed through a type of relaxation. Through this type of relaxation, the controller could still keep the system state safe even in the cases when the reference is unsafe during some time period. For a single quadrotor, we propose the concept of augmented Control Barrier Function specifically to let it avoid external obstacles. Using this augmented CBF, we could still utilize the idea of CBF-CLF-QP controller in a sequential QP control design framework to let this quadrotor remain safe during the flight. In meantime, we also apply the geometric control techniques to the aerial transportation problem where a payload is carried by multiple quadrotors through cable suspension. This type of transportation method allows multiple quadrotors to share the payload weight, but introduces internal safety constraints at the same time. By employing both linear and nonlinear techniques, we are able to carry the payload pose to follow a pre-defined reference trajectory.

Geometric modeling of biomolecules plays an important role in the study of biochemical processes. Many simulation methods depend heavily on the geometric models of biomolecules. Among various studies, shape analysis is one of the most important topics, which reveals the functionalities of biomolecules.

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No description available.

By applying geometric analysis to some experimental maze situations the present study attempted to determine if a continuity in the responding of experimental Ss existed. This continuity in responding might suggest the presence of alternative explanations for the behavior of these Ss in some maze problems. The study made use of a modified version of the Tolman, Ritchie, and Kalish (1946a) experiment using six runways during training rather than one. The results of the study show that three of the six groups obtained the identical angle of choice, angle between the runway trained on and the runway chosen during the experimental trial, indicating the possibility of an underlying behavioral factor determining this continuity in responding.

Orientador: Yukio Kobayashi / Banca: Paulo César Rioli Duarte de Souza / Banca: Gilberto de Magalhães Bento Gonçalves / Resumo: No presente trabalho buscou-se determinar o comportamento das características geométricas do cordão da solda e o desempenho da soldagem, através do processo de soldagem com arame tubular autoprotegido e corrente pulsada. As características geométricas estudadas foram largura do cordão, penetração da solda e altura do reforço. Para definir o desempenho da soldagem analisou-se o rendimento de deposição e a taxa de deposição. Como metal de base utilizou-se o aço ABNT 1010 de espessura 6,35mm. O arame utilizado foi o AWS E71T-11 com diâmetro 1,1mm. A soldas foram realizadas por simples deposição, utilizando-se uma fonte de solda microprocessada, mantendo-se a velocidade de soldagem e a distancia tocha/peça constante. Durante o processo de soldagem os parâmetros de pulso analisados foram a corrente de pico (Ap), corrente de base (Ab), freqüência de pulso (F) e tempo de pico (Tp). Para coleta dos dados foi utilizada uma placa de aquisição de dados com interface a um microcomputador. De posse dos dados, foi aplicada a técnica de ANOVA, com o objetivo de identificar, quantificar e localizar a significância das dispersões. Verificou-se que a tensão média tem grande influência nas características geométricas do cordão de solda e de desempenho da soldagem. Para cada incremento de F provocou uma redução da largura do cordão de solda e aumento da penetração, altura do reforço, taxa de deposição e rendimento de deposição. O incremento Tp acarretou a formação de cordões mais largos, como também a redução na altura do reforço, penetração, taxa de deposição e rendimento de deposição. A variação de Ap não teve influência sobre largura do cordão, a altura do reforço, taxa de deposição e rendimento de deposição. / Abstract: In the present work one searched to determine the behavior of the geometric characteristics of the bead weld and the performance of the welding, through the process self-shielded flux cored arc welding and pulsed current. The studied geometric characteristics had been width of bead, penetration of the weld, height of the reinforcement. To define the performance of the welding one analyzed the deposition efficiency and the deposition rate. As metal base was used steel ABNT 1010 with thickness 6, 35 mm. The used wire was the AWS E71T-11 with diameter 1,1 mm. The welds had been carried through by simple deposition, using themselves a microprocessed weld power source, remaining constant it welding speed and the stick-out. During the welding process the analyzed parameters of pulse had been the peak current (Ap), base current (Ab), pulse frequency (F) and peak duration (Tp). For collection of the data a plate of acquisition of data with interface to a microcomputer was used. Of ownership of the data, the ANOVA technique was applied, with the objective to identify, to quantify and to locate the significance of the dispersions. It was verified that the mean voltage has great influence in the geometric characteristics of the bead weld and the performance of the welding. For each increment of F it provoked a reduction of the width of the bead weld and increase of the penetration, height of the reinforcement, deposition rate and deposition efficiency. The Tp increment caused the wider bead weld formation, as also the reduction in the height of the reinforcement, penetration, deposition rate and deposition efficiency. The variation of Ap did not have influence on width of the bead weld, the height of the reinforcement, deposition rate and deposition efficiency. / Mestre

Thesis advisor: Michael J. Naughton / Geometrically generalized analytical expressions for device transport are derived from first principles for a photovoltaic junction. Subsequently, conventional planar and unconventional coaxial and hemispherical photovoltaic architectures are applied to detail the device physics of the junction based on their respective geometry. For the conventional planar cell, the one-dimensional transport equations governing carrier dynamics are recovered. For the unconventional coaxial and hemispherical junction designs, new multi-dimensional transport equations are revealed. Physical effects such as carrier generation and recombination are compared for each cell architecture, providing insight as to how non-planar junctions may potentially enable greater energy conversion efficiencies. Numerical simulations are performed for arrays of vertically aligned, nanostructured coaxial and hemispherical amorphous silicon solar cells and results are compared to those from simulations performed for the standard planar junction. Results indicate that fundamental physical changes in the spatial dependence of the energy band profile across the intrinsic region of an amorphous silicon p-i-n junction manifest as an increase in recombination current for non-planar photovoltaic architectures. Despite an increase in recombination current, however, the coaxial architecture still appears to be able to surpass the efficiency predicted for the planar geometry, due to the geometry of the junction leading to a decoupling of optics and electronics. / Thesis (PhD) — Boston College, 2012. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.

The first part of this thesis establishes a series of geometric ineqalities related to fractional integration in some geometric settings, including bilinear and multilinear forms. In the second part of this thesis, we study some kinds of rearrangement inequalities. In particular, some applications of rearrangement inequalities will be given, for instance, the determination of the extremals of some geometric problems. By competing symmetries and rearrangement inequalities, we prove the sharp versions of geometric inequalities introduced in the first part in Euclidean spaces. Meanwhile, there are the corresponding conformally equivalent formulations in unit sphere and in hyperbolic space. The last part is about collaborative work on the regularity of the Hardy-Littlewood maximal functions. We give a simple proof to improve Tanaka's result of the paper entitled "A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function". Our proof is based on the behaviour of the local maximum of the non-centered Hardy-Littlewood maximal function.

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between layers, while close packing leads to geometrically induced curvature singularities. When creation of voids is penalized by external pressure, the system trades off these competing effects, leading to various accommodating formations. Three two dimensional energy based nonlinear models are presented to describe the formation of voids at areas of intense geological folding. For each model the layers are assumed to be flexible elastic beams under hard unilateral contact constraint; which are solved as quasi-static obstacle problems with a free boundary. In each case an application of Kuhn-Tucker theory leads to representation as a nonlinear fourth order differential equation. Firstly a single layered model for voiding is presented. An elastic layer is forced into a V-shaped singularity by a uniform overburden pressure, where the fourth order free boundary problem is shown to have a unique, convex, symmetric solution. Drawing parallels with the Kuhn-Tucker theory, virtual work and ideas of duality, the physical significance of this differential equation is emphasised. Finally, appropriate scaling of either the potential energy or the differential equation shows the solutions scale to a single parametric group, for which the size of the void scales inversely with the ratio of overburden pressure to bending stiffness of the layer. Common to structural geology, one or several especially thick layers can dominate the deformation process. As a result, the remaining weak layers must accommodate into the geometry imposed by these competent layers. The second model, extends the first by introducing a plastic hinge to replicate the geometry imposed by the competent layer, and also axial springs to resist the slip over the limbs. The equilibrium equations for the system are investigated using the mathematical techniques developed for the first model. Under rigid loading the system may snap from an initially flat state to a convex voiding solution, as seen in the first model. However, if resistance to slip is high, the slightest imperfection causes the system to jump to a convoluted up-buckled solution, following a de-stiffened path to a point of self contact. These solutions have similarities with the delamination of carbon fibre composites. Finally, we extend the two single layered models to a simple multilayered model, which describes the periodic formation of voids in a chevron fold. The model shows that in the limit of high overburden pressures solutions form voids every layer, producing straight limbs punctured by sharp corners. This analysis shows good agreement when compared with recent experiments. This work provides the basis for future work on the buckling of thin multilayer assemblies in which voids may develop, and emphasizes the importance of the intricate nonlinear constraints of layers fitting together in multilayered folds.

OBJECTIVE: The objective of this study is to determine the earliest time point in growth when a difference in mandibular shape of dolichocephalic and brachycephalic subjects is distinguishable. MATERIALS & METHODS: 11 dolichocephalic and 14 brachycephalic subjects were selected using lateral cephalograms from the Forsyth/Moorrees Twin Study using a method described by Rocky Mountain Orthodontics. 23 landmarks outlining the mandible were identified on the lateral cephalograms of each subject from their earliest age (5-8 years) to their latest (16-18 years) using TPSdig software. The 2 dimensional coordinates for each landmark were then exported to TPSUtil. From TPSUtil, the TPS data was then converted to a .csv file in Microsoft Excel and imported into MorphoJ for analysis. Primary morphometric analysis consisted of generalized Procrustes analysis, principal component analysis, and discriminant function analysis. RESULTS: The first 5 principal components for both facial types accounted for the majority of the variance. Discriminant function analyses were not significant for any phenotype or age group pairing, suggesting that the overall shape difference was too small to be detected between groups and over time starting at age 7. A plot of the Procrustes coordinates for the brachycephalic group versus the dolichocephalic group revealed that there were differences in shape between the two phenotypes, but this difference was statistically insignificant. CONCLUSIONS: The mandible increases in size with age, with minimal change in shape. Mandibular shape is established by the age of 7. The difference in mandibular shapes of the two phenotypes was not statistically significant.