A large aspect ratio leads to higher ion capacity in miniaturized ion trap mass spectrometers. The aspect ratio (AR) of an ion trap represents the ratio between an extended trapping dimension and the characteristic trapping dimension. In contrast to linear and rectilinear traps, changing the AR of a toroidal ion trap (TorIT) results in changes to the degree of curvature and shape of the trapping potential, and hence, on performance as a mass analyzer. SIMION simulations show that higher-order terms in the trapping potential vary strongly for small and moderate AR values (below ~10), with the effects asymptotically flattening for larger AR values. Because of the asymmetry in electrode geometry, the trapping center does not coincide with the geometric center of the trap, and this displacement also varies with AR. For instance, in the asymmetric TorIT, the saddle point in the trapping potential and the geometric trap center differ from +0.6 to -0.4 mm depending on AR. Ion secular frequencies also change with the AR. Whereas ions in the simplified TorIT have stable trajectories for any value of AR, ions in the asymmetric TorIT become unstable at large AR values. Variations in high-order terms, the trapping center, and secular frequencies with AR are a unique feature of toroidal traps, and require significant changes in trap design and operation as the aspect ratio is changed.

In calculating the time evolution of an atomic system on diffusive timescales, off-lattice kinetic Monte Carlo (OLKMC) can sometimes be used to overcome the limitations of Molecular Dynamics. OLKMC relies on the harmonic approximation to Transition State Theory, in which the rate of rare transitions from one energy minimum to a neighboring minimum scales exponentially with an energy barrier on the potential energy surface. This requires locating the index-1 saddle point, commonly referred to as a transition state, that separates two neighboring energy minima. In modeling the evolution of an atomic system, it is desirable to find all the relevant transitions surrounding the current minimum. Due to the large number of minima on the potential energy surface, exhaustively searching the landscape for these saddle points is a challenging task. In examining the particular case of isolated Lennard-Jones clusters of around 50 particles, we observe very slow convergence of the total number of saddle points found as a function of successful searches. We seek to understand this behavior by modeling the distribution of successful searches and sampling this distribution to create a stochastic process that mimics this behavior. Finally, we will discuss an improvement to a rejection scheme for OLKMC where we terminate searches that appear to be failing early in the search process.

Range improvements for livestock were analyzed for the Curlew National Grassland and Saddle Creek Allotment. Increases in aum's which were a result of range improvements were calculated and valued at $4.00 each. Internal rates of return for both study areas were computed with a 15-year project life span for estimated grazing capacity and permitted grazing. Rate of return was then set at 10 percent to calculate project life span for both permitted grazing and estimated grazing capacity for the two areas. Effects of range improvements for livestock on wildlife habitat were studied. Due to a lack of quantitative data, values could not be placed upon benefits and detriments which improvements for livestock had on wildlife. Positive and negative effects which range improvements for livestock had on wildlife are given for both study areas. An alternative grazing policy is suggested for both study areas. Internal rates of return for permitted grazing are calculated for a 15-year project life span. Internal rate of return was then set at 10 percent to calculate project life span necessary to provide that rate of return.

The subject of this diploma thesis is structural and constructional design of a new multifunctional building in Spišská Belá. It is a new detached building structure with one basement floor and three above-ground floors, designed on a plot number 1859 in cadastre unit Spišská Belá. The designed building is constructed of clay masonry system with contact thermal insulation and supported by strip foundations. Ceiling constructions of above-ground floors are made of prefabricated components. The basement ceiling is made of reinforced concrete. Object is roofed by saddle roof set on wooden roof truss. There are four three room flats, one accessible flat, bicycle shop and flats facilities, situated in the building. The focus during development was on wheelchair access.

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Optimization problems are ubiquitous in all quantitative scientific disciplines, from computer science and engineering to operations research and economics. Developing algorithms for solving various optimization problems has been the focus of mathematical research for years. In the last decade, optimization research has become even more popular due to its applications in the rapidly developing field of machine learning. In this thesis, we discuss a few fundamental and well-studied optimization problem classes: decentralized distributed optimization (Chapters 2 to 4), distributed optimization under similarity (Chapter 5), affinely constrained optimization (Chapter 6), minimax optimization (Chapter 7), and high-order optimization (Chapter 8). For each problem class, we develop the first provably optimal algorithm: the complexity of such an algorithm cannot be improved for the problem class given. The proposed algorithms show state-of-the-art performance in practical applications, which makes them highly attractive for potential generalizations and extensions in the future.

<p>Video coding schemes designed based on sequential or predictive coding models are vulnerable to the loss of encoded frames at the decoder end. Motivated by this observation, in this thesis we propose two new coding models: robust sequential coding and robust predictive coding. For the Gauss-Markov source with the mean squared error distortion measure, we characterize certain supporting hyperplanes of the rate region of these two coding problems. The proof is divided into three steps: 1) it is shown that each supporting hyperplane of the rate region of Gaussian robust sequential coding admits a max-min lower bound; 2) the corresponding min-max upper bound is shown to be achievable by a robust predictive coding scheme; 3) a saddle point analysis proves that the max-min lower bound coincides with the min-max upper bound. Furthermore, it is shown that the proposed robust predictive coding scheme can be implemented using a successive quantization system. Theoretical and experimental results indicate that this scheme has a desirable \self-recovery" property. Our investigation also reveals an information-theoretic minimax theorem and the associated extremal inequalities.</p> / Doctor of Philosophy (PhD)

In this thesis, we develop preconditioned iterative methods for the solution of matrix systems arising from PDE-constrained optimization problems. In order to do this, we exploit saddle point theory, as this is the form of the matrix systems we wish to solve. We utilize well-known results on saddle point systems to motivate preconditioners based on effective approximations of the (1,1)-block and Schur complement of the matrices involved. These preconditioners are used in conjunction with suitable iterative solvers, which include MINRES, non-standard Conjugate Gradients, GMRES and BiCG. The solvers we use are selected based on the particular problem and preconditioning strategy employed. We consider the numerical solution of a range of PDE-constrained optimization problems, namely the distributed control, Neumann boundary control and subdomain control of Poisson's equation, convection-diffusion control, Stokes and Navier-Stokes control, the optimal control of the heat equation, and the optimal control of reaction-diffusion problems arising in chemical processes. Each of these problems has a special structure which we make use of when developing our preconditioners, and specific techniques and approximations are required for each problem. In each case, we motivate and derive our preconditioners, obtain eigenvalue bounds for the preconditioners where relevant, and demonstrate the effectiveness of our strategies through numerical experiments. The goal throughout this work is for our iterative solvers to be feasible and reliable, but also robust with respect to the parameters involved in the problems we consider.

Cette thèse s'intéresse à la conception de méthodes de discrétisation non-conforme pour un modèle de poromécanique. Le but de ce travail est de simplifier les couplages liant la géomécanique d'un milieu poreux à l'écoulement polyphasique compositionnel ayant cours en son sein tels qu'ils sont réalisés actuellement dans l'industrie pétrolière, en discrétisant sur un même maillage, typiquement non-conforme car à l'image de la lithologie, la mécanique et l'écoulement. La nouveauté consiste donc à traiter la mécanique par une méthode d'approximation non-conforme sur maillages généraux. Dans cette thèse, nous nous concentrons sur un modèle d'élasticité linéaire. Les difficultés inhérentes à son approximation non-conforme sont son manque de coercivité (se traduisant par la nécessité de satisfaire une inégalité de Korn sur un espace discret discontinu), ainsi que le phénomène de verrouillage numérique lorsque le matériau tend à devenir incompressible. Dans une première partie, nous construisons un espace d'approximation sur maillages généraux, s'apparentant à une extension de l'espace de Crouzeix-Raviart. Nous explicitons ses propriétés d'approximation et de conformité, et montrons que ce dernier est adapté à une discrétisation primale coercive et robuste au locking du modèle d'élasticité sur maillages généraux. La méthode proposée est moins coûteuse que son équivalent éléments finis (en termes de propriétés) P2. Nous nous intéressons dans une deuxième partie à l'approximation non-conforme d'un modèle couplé de poroélasticité. Nous étudions la convergence d'une famille de schémas numériques dont la discrétisation en espace utilise le formalisme des schémas Gradient, auquel appartient la méthode développée pour la mécanique. Nous prouvons la convergence de telles approximations vers la solution de régularité minimale du problème continu, indépendamment des paramètres physiques du système / This manuscript focuses on the conception of nonconforming discretization methods for a poromechanical model. The aim of this work is to ease the coupling between the geomechanics and the multiphase compositional Darcy flow in porous media by discretizing mechanics and flow on the same mesh, typically nonconforming as it represents the lithology. Hence, the novelty hinges on a nonconforming treatment of mechanics on general meshes. In this work, we focus on a linear elasticity model. The nonconforming approximation of such a model is not straightforward owing to its lack of coercivity (meaning that a discrete Korn's inequality must hold on a discontinuous discrete space) and to the numerical locking phenomenon occurring as the material becomes incompressible. In a first part, we design an approximation space on general meshes, which can be viewed as an extension of the so-called Crouzeix-Raviart space. We study its approximation and conformity properties, and prove that this latter is well-adapted to the design of a primal, coercive, and locking-free discretization of the elasticity model on general meshes. The proposed method is less costly than its finite element equivalent (in terms of properties) P2. In a second part, we tackle the nonconforming approximation of a coupled poroelasticity model. We study the convergence of a family of numerical schemes whose space discretization relies on the Gradient schemes framework, to which belongs the method developed for mechanics. We prove the convergence of such approximations toward the minimal regularity solution of the continuous problem, and independently of the choice of physical parameters

Interpretation of changes of humeral asymmetry during the Holocene period was based on the analysis of upper limb muscle activity during cereal grinding using the saddle quern and rotary quern. The aim of the diploma thesis was to test if the dominant upper limb muscle activity during cereal grinding using the saddle quern and rotary quern might be estimated by measuring the activity of musculus deltoideus (pars clavicularis), musculus infraspinatus, musculus pectoralis major and musculus triceps brachii (caput longum). Using surface electromyography, we have analyzed activity of musculus biceps brachii, musculus deltoideus (pars clavicularis), musculus deltoideus (pars acromialis), musculus deltoideus (pars spinalis), musculus pectoralis major, musculus infraspinatus, musculus triceps brachii (caput laterale) and musculus triceps brachii (caput longum) during cereal grinding using the saddle quern and rotary quern in 25 subjects. Consistent with our prediction, musculus biceps brachii was the least active muscle during saddle quern grinding and clockwise rotary grinding, therefore it is possible to exclude musculus biceps brachii from the sample of analyzed muscles. Pars clavicularis, pars acromialis and pars spinalis of musculus deltoideus were more active during rotary quern grinding than...