The chemical oxygen-iodine laser (COIL) has several important military and industrial applications. The concern of this work is do develop a partial differential equation model describing optical behavior in the COIL. Optical behavior of the COIL has traditionally been investigated via a ray tracing method. Photons are represented as discrete particles, and their behavior is described by the geometry of the system. We develop an optical model wherein photons have a wave description. In order to construct the mathematical model, we utilize the theory of paraxial wave optics and Gaussian beams. Doing so allows us to incorporate physical effects such as diffusion/diffraction and refraction into the model. After describing the optical model, we present numerical methods for obtaining approximate solutions to the model in the cases of one and two transverse directions. Results are presented illustrating the efficacy of the numerical methods. / Ph. D.

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Master 's thesis deals with design of a drivetrain of six cylinder inline engine with cylinder deactivation for heavy agricultural vehicles. In this thesis were devised various possibilities of crankshaft balancing, the best design solution of counterweight was based on optimization in software Catia. Further, the crankshaft was analysed for force and momentum loading and torsional vibration, based on which, the torsional vibration damper was designed. There were considered several options for cylinder deactivation, which were analysed for finest run of engine and the best thermal distribution. Based on these criteria, the best option was to deactivate 2nd and 5th cylinder. The crankshaft was analysed for the fatigue failure by finite element method. The fatigue failure is the most dangerous case for the crankshaft, the resulting safety factor for this limit state is 3,05.

The first part of this thesis deals with the examination of the eccentricity of the crank mechanism for individual variables kinematics and dynamics of crank mechanism, analyticaly computed in Matlab. Then it compares the different possibilities of balancing moments of inertia forces and propose a specific design chosen for the value of eccentricity. In the second part is designed a model of crankshaft mechanism based on the investigated parameters. These parameters were carried out by structural analysis in Ansys.

Due to the interesting financial moment we are living, my motivations to write this Master thesis has mostly been the behavior of interest rates and models that can be used predict them. Thus, in this dissertation I have presented theHull-White model and the way to calibrate it against market data so it can be used to price interest rate derivatives. The reader can find both theoretical and practical presentations and examples along with the code to program them byhim/herself.

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In this thesis we present the Stefan problem with two boundary conditions, one constant and one time-dependent. This problem is a classic example of a free boundary problem in partial differential equations, with a free boundary moving in time. Some properties are being proved for the one-dimensional case and the important Stefan condition is also derived. The importance of the maximum principle, and the existence of a unique solution are being discussed. To numerically solve this problem, an analysis when the time t goes to zero is being done. The approximative solutions are shown graphically with proper error estimates.

This research involves the study of a one- and two-cylinder convertible reciprocating Freon compressor for air conditioning or refrigeration purposes. The main concern is the reduction of the vibration (noise) caused during the operation of the compressor. Vibration is a main concern when the compressor is shifted from the one-cylinder operation to the two-cylinder operation mode and the reverse of this shift. The objectives for this research are (1) to investigate the shaking force due to the reciprocating mass at high frequencies, which are up to 4600 Hz (80w) in this research; (2) to determine the dominant force for compressor vibration among the three possible sources of shaking force due to reciprocating mass, impact forces due to clearance at the connecting rod - piston joint, and the z-axis force from the motor torque due to the rotor's conductor rods being skewed at an angle; (3) to minimize the difference in change of kinetic energies when switching between the one- and two-cylinder operating modes of the compressor. The properties of the vibration in one- and two-cylinder operation have been studied and results have been analyzed in terms of kinetic energies generated in different setting of operation of the compressor. Dynamic simulation for the impact force is computed using SIMULINK. The Z-axis force due to the motor is computed. Results indicated that shaking force due to the reciprocating mass is the dominant force for only the first two harmonics (w, 2w). An optimization routine based on Hooke and Jeeves pattern search method is developed and an optimized setting of angle, force, and torque for balancing of the crankshaft to achieve objective (3) is determined. / Master of Science

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Made available in DSpace on 2015-03-04T18:51:08Z (GMT). No. of bitstreams: 1 Apresentacao.pdf: 101300 bytes, checksum: 62de93a7615eeb9b5d3dd49f5ba22f68 (MD5) Previous issue date: 2006-03-28 / Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior / This work deals with the stability analysis of the fully discrete transport problem obtained using a stable finite element method in space and the generalized trapeizoidal family of methods in time. Depeding on the range of parameters the Galerkin and the Streamline Upwind Petrov-Galerkin Methods are introduced. We evaluate the accuracy and stability properties of the methods. The sawtooth pattern in time is observed,caused by spurious higher modes when Crank-Nicolson method is used. We derive a stability analysis of the fully discrete method and investigate the techniques proposed in literature to damp oscillations. We propose a new stability condition to overcome the spurious modes. The proposed methodology is apllied to a one-dimensional contaminant transport problems in a saturated porous media that considers a radioactive contaminant decay at a constant rate. / Nesta dissertação apresenta-se a análise de métodos totalmente discretos, estabilizados espacialmente, para a resolução de problemas de transporte unidimensionais convectivos-difusivos-reativos, lineares e transientes que modelam o transporte de contaminantes radioativos com decaimento a uma taxa constante em um meio poroso saturado. O método de elementos finitos clássico de Galerkin é usado no espaço quando o problema de transporte é pura e/ou predominantemente difusivo, ao passo que quando a convecção domina, o método SUPG (Streamline Upwind Petrov-Galerkin) é utilizado. O método de elementos finitos é combinado a um esquema discreto de integração no tempo, os algoritmos trapezoidais generalizados. Observa-se que a solução aproximada pode apresentar oscilações espúrias quando o método de Crank-Nicolson é utilizado. São consideradas diversas metodologias propostas na literatura para amortecer tais oscilações. Como consequência da análise de estabilidade desenvolvida, uma nova condição de estabilidade é proposta.