This thesis proposes a new proof of the acoustic transparency theorem for material with a bounded variation. The theorem states that if the material properties (density, bulk modulus) is of bounded variation, the net power transmitted through the point z = 0 over a time interval [−T,T] is greater than some constant times the energy at the time zero over a spatial interval [0,Z], provided that T equals the time of travel of a wave from 0 to Z. This means the reflected energy of an input into the earth will be received. Otherwise, the reflections may not arrive at the surface. A proof gives a lower bound for material properties (density, bulk modulus) with bounded variation using sideways energy estimate. A different lower bound that works only for piecewise constant coefficients is also given. It gives a lower bound by analyzing reflections and transmissions of the waves at the jumps of the material properties. This thesis also gives an example to illustrate that the bounded variation assumption may not be necessary for the medium to be transparent. This thesis also discusses relations between the transparency property and the data of an inverse problem.

In this thesis, we have analyzed the accuracy and stability aspects of weak boundary and interface conditions (WBCs) for high order finite difference methods on Summations-By-Parts (SBP) form. The numerical technique has been applied to wave propagation and flow problems. The advantage of WBCs over strong boundary conditions is that stability of the numerical scheme can be proven. The boundary procedures in the advection-diffusion equation for a boundary layer problem is analyzed. By performing Navier-Stokes calculations, it is shown that most of the conclusions from the model problem carries over to the fully nonlinear case. The work was complemented to include the new idea of using WBCs on multiple grid points in a region, where the data is known, instead of at a single point. It was shown that we can achieve high accuracy, an increased rate of convergence to steady-state and non-reflecting boundary conditions by using this approach. Using the SBP technique and WBCs, we have worked out how to construct conservative and energy stable hybrid schemes for shocks using two different approaches. In the first method, we combine a high order finite difference scheme with a second order MUSCL scheme. In the second method, a procedure to locally change the order of accuracy of the finite difference schemes is developed. The main purpose is to obtain a higher order accurate scheme in smooth regions and a low order non-oscillatory scheme in the vicinity of shocks. Furthermore, we have analyzed the energy stability of the MUSCL scheme, by reformulating the scheme in the framework of SBP and artificial dissipation operators. It was found that many of the standard slope limiters in the MUSCL scheme do not lead to a negative semi-definite dissipation matrix, as required to get pointwise stability. Finally, high order simulations of shock diffracting over a convex wall with two facets were performed. The numerical study is done for a range of Reynolds numbers. By monitoring the velocities at the solid wall, it was shown that the computations were resolved in the boundary layer. Schlieren images from the computational results were obtained which displayed new interesting flow features.

Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-30T13:11:31Z No. of bitstreams: 1 DissPWBJ.pdf: 4236598 bytes, checksum: c67ea4f748a05ba51123274cfad1b4ab (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T18:59:20Z (GMT) No. of bitstreams: 1 DissPWBJ.pdf: 4236598 bytes, checksum: c67ea4f748a05ba51123274cfad1b4ab (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T18:59:32Z (GMT) No. of bitstreams: 1 DissPWBJ.pdf: 4236598 bytes, checksum: c67ea4f748a05ba51123274cfad1b4ab (MD5) / Made available in DSpace on 2016-10-10T18:59:46Z (GMT). No. of bitstreams: 1 DissPWBJ.pdf: 4236598 bytes, checksum: c67ea4f748a05ba51123274cfad1b4ab (MD5) Previous issue date: 2016-03-07 / Não recebi financiamento / The virtualization of computing resources is becoming increasingly frequent for several purposes. An example is desktop virtualization, in which the user’s workstation is virtualized, executed in a data center, and delivered to users as a service. Users can access their virtual desktops over the network, from anywhere, anytime, using simplified clients as smartphones or tablets. Besides mobility, desktop virtualization brings significant reduction in management costs and administration of desktops. In the present work we propose a model that estimates the energy consumption of a desktop virtualization service. The proposed model aims to assist decision-making on the provision of resources and improving energy efficiency. The model takes into account energy consumption during all the lifecycle of a virtualized desktop since the instantiation. From the experiments, applying the model, it was concluded that for applications with low transmission rate of frames and commands, such as a web browser, it is better to instantiate an VD instead of running as a local desktop. It happens because the energy cost of running is amortized through the sharing of resources between the various connected users into the server, in addition to the low cost of transmission. The best energy efficiency has been obtained as a result of instantiating an VD on a datacenter (DC) with acessible through a local area network (LAN), in which the energy consumption per bit transmission is suffucuently low to compensate energy cost of VD migration between different DCs. / A virtualização de recursos computacionais está se tornando cada vez mais frequente para diversas finalidades. Um exemplo é a virtualização de desktops, em que a estação de trabalho do usuário é virtualizada e executada em um centro de dados, e são entregues aos seus usuários sob a forma de um serviço. Os usuários podem acessar seus desktops virtuais via Internet, de qualquer lugar e a qualquer hora, utilizando clientes simplificados como smartphones ou tablets. Além da mobilidade, a virtualização de desktops traz enorme redução nos custos de gerência e administração. Esta dissertação propõe um modelo que a permite estimar o custo energético de um serviço de virtualização de desktops. Esse modelo tem por finalidade auxiliar a tomada de decisões sobre o provisionamento de recursos, melhorando a eficiência energética. Para essa estimativa, são considerados os custos energéticos que compõem a entrega do desktop virtual, desde a instanciação até sua execução no centro de dados. A partir dos experimentos realizados, aplicando o modelo proposto, foi possível concluir que para aplicações com taxa de transmissão de quadros e comandos baixa ou regular, como um navegador web por exemplo, consome-se menos energia para executar um VD do que executar um desktop local. Isso acontece porque o custo energético de execução é amortizado por meio do compartilhamento de recursos entre os diversos usuários conectados ao mesmo servidor, além do baixo custo de transmissão. A melhor eficiência energética obtida foi resultado de instanciar um VD em um datacenter (DC) com acesso a rede local (LAN), em que o consumo energético de transmissão por bit é menor e tão pequeno que compensou no decorrer do tempo, inclusive, o custo energético da migração do VD entre diferentes DCs.