Made available in DSpace on 2014-06-11T19:23:03Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-02Bitstream added on 2014-06-13T20:49:51Z : No. of bitstreams: 1 fernandes_kp_me_botib.pdf: 889153 bytes, checksum: 01148ee553bfc1cc8cd4f8a2a919693b (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Considera-se a construção de métodos compacto e não compacto de quarta ordem para resolver numericamente as equações de Navier-Stokes na formulação função corrente em uma malha uniforme. Aplica-se esses métodos de alta ordem em um canal-tipo estenose e o conjunto das equações não lineares resultantes da discretização é resolvido pelo método de Newton. Erros RMS e máximo, bem como linhas de corrente são apresentados / This work considers the development of compact and wide fourth-order schemes for solving the Navier-Stokes equations in the streamfunction formulation on a uniform grid. These high order schemes are applied in a stenosis channel-type and the set of nonlinear equations resulting from the discretization is solved by Newton’s method. The RMS and maximum errors, and also the streamlines are shown

abstract: The objective of the research is to develop guidelines for identifying when settlement or seismic loading presents a threat to the integrity of geosynthetic elements for both side slope and cover systems in landfills, and advance further investigation for parameters which influence the strains in the barrier systems. A numerical model of landfill with different side slope inclinations are developed by the two-dimensional explicit finite difference program FLAC 7.0, beam elements with a hyperbolic stress-strain relationship, zero moment of inertia, and interface elements on both sides were used to model the geosynthetic barrier systems. The resulting numerical model demonstrates the load-displacement behavior of geosynthetic interfaces, including whole liner systems and dynamic shear response. It is also through the different results in strains from the influences of slope angle and interface friction of geosynthetic liners to develop implications for engineering practice and recommendations for static and seismic design of waste containment systems. / Dissertation/Thesis / M.S. Civil Engineering 2013

Orientador: Kátia Lucchesi Cavalca Dedini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-17T14:50:07Z (GMT). No. of bitstreams: 1 Alves_DiogoStuani_M.pdf: 4752857 bytes, checksum: 6027628d11d6b6a8db09521349fd47b8 (MD5) Previous issue date: 2011 / Resumo: Os mancais lubrificados hidrodinamicamente estão presentes em muitas aplicações modernas, especialmente em maquinas rotativas que necessitam de operações mais precisas. Nestes casos, a lubrificação é essencial para a máquina, pois, diminui o atrito entre as peças internas e previne o contato metal-metal, além de agir como elemento de vinculo dinâmico para as pistas do mancal. Devido ao cisalhamento do lubrificante durante a operação, tem-se o aquecimento do fluido e com isso uma modificação nas condições de lubrificação, já que a viscosidade, parâmetro que caracteriza as particularidades do escoamento, diminui com o aumento da temperatura. A diminuição da viscosidade causa diminuição do atrito viscoso, o que acarreta em diminuição da capacidade de carga, gerando efeitos negativos nos coeficientes equivalentes e sendo possível, em alguns casos, a observação de contato direto entre as partes metálicas. Sendo assim, o estudo do atrito e das condições de lubrificação durante a operação de máquinas é de extrema importância em problemas como manutenção, durabilidade e confiabilidade de máquinas. Utilizando o método das diferenças finitas, é possível resolver simultaneamente as equações de Reynolds e da energia, que são responsáveis pelas distribuições de pressão e temperatura, respectivamente. Com isso, é possível analisar as diferenças de pressão, disposição do eixo no interior do mancal e coeficientes equivalentes de rigidez e amortecimento, de um modelo em que se usa viscosidade variante com a temperatura (termohidrodinâmico) e de um modelo que não apresenta esse fenômeno (isotérmico). Finalmente, utilizando um software de dinâmica de rotores, foi obtida a resposta dinâmica de um sistema mancal-rotor para turbocompressores / Abstract: The hydrodynamic lubricated bearings are present in modern applications, especially in rotational machines that need precisely operations. In those cases, the lubrication is essential for the machine, because it reduces the wear between the internal parts and prevents the metallic contact, and also, acts like an element of dynamic link for the bearing. Due to the lubricant shear, the fluid heats up and modifications on the lubrication conditions occurs, since the viscosity, parameter that characterize the flow, decreases with the increase of the temperature. The decrease of visco ity causes a decrease in the viscous friction, which entails in a decrease of the load sustaining capacity, negative effects in the equivalent coefficients and possible observation of metallic contact. So, the study of friction and lubrication conditions during the machine operation is extremely important on maintenance, durability and reliability of machines. Using the finite difference method it is possible to solve, simultaneously, the Reynolds and the energy equations that are responsible for the pressure and temperature distribution, respectively. Therewith, it is possible to analyze the differences in pressure, shaft position in the bearing and equivalent stiffness and damping coefficients, for a model that uses changes in viscosity with the temperature (thermohydrodynamic) and for a model that does not take it in account (isothermal). Finally, using a rotordynamic software (ROTORTEST), the dynamic response of a turbocharger bearing-rotor system was obtained and analyzed / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientador: Luiz Felipe Mendes de Moura / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T19:08:20Z (GMT). No. of bitstreams: 1 Campos_MarcoDonisetede_D.pdf: 12731674 bytes, checksum: de4ae78b0a17ad29927779fc24893a33 (MD5) Previous issue date: 2014 / Resumo: O presente trabalho tem como objetivo aplicar o método de diferenças finitas de alta ordem na solução de problemas bi e tridimensionais convectivo-difusivos transientes. As simulações numéricas foram realizadas para investigar, nos problemas lineares, o termo de dissipação viscosa na equação de transferência de calor bidimensional com ênfase, no caso tridimensional, na aplicação envolvendo troca de calor num canal retangular. Para problemas não lineares, o método de Newton para a linearização do termo convectivo foi usado para resolver a equação de Burgers bi e tridimensionais. O esquema desenvolvido mostrou-se simples, computacionalmente rápido, podendo ser aplicado para problemas bi e tridimensionais. Nas aplicações propostas, quando possível, as soluções analíticas disponíveis na revisão da literatura foram utilizadas para comparações com as soluções numéricas e validação do código, sendo a análise dos resultados feita a partir das normas L2 e L? / Abstract: The present study aims to apply the high-order Finite Difference Method to transient diffusive-convective problems in two and three dimensions. Numerical simulations have been undertaken to investigate, in the linear problems, the viscous dissipation term in the two-dimensional heat transfer equation with emphasis, in the three-dimensional case, on the application involving heat exchange in a rectangular channel. For nonlinear problems, the Newton's method for the linearization of the convective term was used for solving the two and three dimensional Burgers equation. This scheme is simple, computationally fast and can be applied for two or three-dimensional problems. For the proposed applications, whenever possible, the analytical solutions found in the literature review were used to compare with the numerical solutions. The analysis of results was done from the L2 and L? norms / Doutorado / Termica e Fluidos / Doutor em Engenharia Mecânica

The classical SIR and SIS epidemiological models are extended by considering the number of adequate contacts per infective in unit time as a function of the total population in such a way that this number grows less rapidly as the total population increases. A diffusion term is added to the SIS model and this leads to a reaction–diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the SIR and SIS models, with the disease–free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, for both models, the endemic equilibrium is locally asymptotically stable and traveling wave solutions are found for the SIS diffusion model. Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous SIR and SIS models are presented. In particular, for the SIS model, a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided. On the other hand the SIS model is extended to a Volterra integral equation, for which the existence of multiple endemic equilibria is proved. This fact is confirmed by numerical simulations. / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted

The sound generated by high speed trains can be exacerbated by the presence of trackside structures. Tunnels are the principal structures that have a strong influence on the noise produced by trains. A train entering a tunnel causes air to flow in and out of the tunnel portal, forming a monopole source of low frequency sound ["infrasound"] whose wavelength is large compared to the tunnel diameter. For the compact case, when the tunnel diameter is small, incompressible flow theory can be used to compute the Green's function that determines the monopole sound. However, when the infrasound is "shielded" from the far field by a large "flange" at the tunnel portal, the problem of calculating the sound produced in the far field is more complex. In this case, the monopole contribution can be calculated in a first approximation in terms of a modified Compact Green's function, whose properties are determined by the value at the center of a. disk (modelling the flange) of a diffracted potential produced by a thin circular disk. In this thesis this potential is calculated numerically. The scattering of sound by a thin circular disk is investigated using the Finite Difference Method applied to the three dimensional Helmholtz equation subject to appropriate boundary conditions on the disk. The solution is also used to examine the unsteady force acting on the disk.

The fractional Laplacian is a promising mathematical tool due to its ability to capture the anomalous diffusion and model the complex physical phenomenon with long-range interaction, such as fractional quantum mechanics, image processing, jump process, etc. One of the important applications of fractional Laplacian is a turbulence intermittency model of fractional Navier-Stokes equation which is derived from Boltzmann's theory. However, the efficient computation of this model on bounded domains is challenging as highly accurate and efficient numerical methods are not yet available. The bottleneck for efficient computation lies in the low accuracy and high computational cost of discretizing the fractional Laplacian operator. Although many state-of-the-art numerical methods have been proposed and some progress has been made for the existing numerical methods to achieve quasi-optimal complexity, some issues are still fully unresolved: i) Due to nonlocal nature of the fractional Laplacian, the implementation of the algorithm is still complicated and the computational cost for preparation of algorithms is still high, e.g., as pointed out by Acosta et al \cite{AcostaBB17} 'Over 99\% of the CPU time is devoted to assembly routine' for finite element method; ii) Due to the intrinsic singularity of the fractional Laplacian, the convergence orders in the literature are still unsatisfactory for many applications including turbulence intermittency simulations. To reduce the complexity and computational cost, we consider two numerical methods, finite difference and spectral method with quasi-linear complexity, which are summarized as follows. We develop spectral Galerkin methods to accurately solve the fractional advection-diffusion-reaction equations and apply the method to fractional Navier-Stokes equations. In spectral methods on a ball, the evaluation of fractional Laplacian operator can be straightforward thanks to the pseudo-eigen relation. For general smooth computational domains, we propose the use of spectral methods enriched by singular functions which characterize the inherent boundary singularity of the fractional Laplacian. We develop a simple and easy-to-implement fractional centered difference approximation to the fractional Laplacian on a uniform mesh using generating functions. The weights or coefficients of the fractional centered formula can be readily computed using the fast Fourier transform. Together with singularity subtraction, we propose high-order finite difference methods without any graded mesh. With the use of the presented results, it may be possible to solve fractional Navier-Stokes equations, fractional quantum Schrodinger equations, and stochastic fractional equations with high accuracy. All numerical simulations will be accompanied by stability and convergence analysis.

As traditional communication technology we use in our day-to-day life reaches its limitations, the international community searches for new methods to communicate information. One such novel approach is the so-called molecular communication system. During the last few decades, molecular communication systems become more and more popular. The main difference between traditional communication and molecular communication systems is that in the latter, information transfer occurs through chemical means, most often between microorganisms. This process already happens all around us naturally, for example, in the human body. Even though the molecular communication topic is attractive to researchers, and a lot of theoretical results are available - one cannot claim the same about the practical use of molecular communication. As for experimental results, a few studies have been done on the macroscale, but investigations at the micro- and nanoscale ranges are still lacking because they are a challenging task. In this work, a self-contained introduction of the underlying theory of molecular communication is provided, which includes knowledge from different areas such as biology, chemistry, communication theory, and applied mathematics. Two numerical methods are implemented for three well-studied partial differential equations of the MC field where advection, diffusion, and the reaction are taken into account. Numerical results for test cases in one and three dimensions are presented and discussed in detail. Conclusions and essential analytical and numerical future directions are then drawn.

The short rate is central in the context of interest-rate markets as well as broader finance. As such, accurate modelling of this rate is of particular importance in the pricing of interest-rate options, especially during times of high volatility where increased demand is seen for simpler and lower risk investments. Recent interest has moved away from models of a pure continuous nature towards models that can account for discontinuities in the short rate. These are more representative of real world movements where the short rate is seen to jump due to current and scheduled market information. This dissertation examines this phenomenon in the context of a Vasicek short rate model and accounts for random-sized jumps at deterministic times following ideas similar to those introduced by Kim and Wright (2014). Finite difference methods are used successfully to find PDE solutions via backwards diffusion of the option value equation to its initial state. This procedure is implemented computationally and compared to Monte Carlo benchmark methods in order to assess its accuracy. In both non-jump and jump settings the method constructed was able to accurately price the call option specified and proved to be a viable means for pricing interest-rate options when stochastically-sized discontinuities are present at known times between inception and expiry. Furthermore the method showed that the stochastic discontinues in the short rate most notably affect the option price in the region around and just out of the money.

Yes / When modeling objects that are small compared with the wavelength, e.g., biological cells at radio frequencies, the standard finite-difference time-domain (FDTD) method requires extremely small time-step sizes, which may lead to excessive computation times. The problem can be overcome by implementing a quasi-static approximate version of FDTD based on transferring the working frequency to a higher frequency and scaling back to the frequency of interest after the field has been computed. An approach to modeling and analysis of biological cells, incorporating a generic lumped-element membrane model, is presented here. Since the external medium of the biological cell is lossy material, a modified Berenger absorbing boundary condition is used to truncate the computation grid. Linear assemblages of cells are investigated and then Floquet periodic boundary conditions are imposed to imitate the effect of periodic replication of the assemblages. Thus, the analysis of a large structure of cells is made more computationally efficient than the modeling of the entire structure. The total fields of the simulated structures are shown to give reasonable and stable results at 900,1800, and 2450 MHz. This method will facilitate deeper investigation of the phenomena in the interaction between electromagnetic fields and biological systems.