This thesis describes possible applications of Prony's method in timing analysis of digital circuits. Such applications include predicting the future shape of the waveform in DTA(Dynamic Timing Analysis) and delay look-up table in STA(Static Timing Analysis). Given some equally spaced output values, the traditional Prony's method can be used to extract poles and residues of a linear system, i.e. to characterize a waveform using an exponential function. In this thesis, not only values but also equally spaced derivatives are tested. Still using same idea of the traditional Prony's method, poles and residues can also be extracted with those values and derivatives. The resultant poles and residues will be used to predict the output waveform in DTA analysis. The benefits brought by the using of derivatives include less simulation steps and less CPU time consuming than the regular constant step simulation. As a matter of fact, the Prony's method can precisely approximate a complicated waveform. Such property can be applied for STA analysis. The Prony's approximation can be used to precisely record an output waveform, which is used as an entry of the look-up table of STA. Since the accuracy of STA analysis relies on the accuracy of the input and output waveform in the look-up table, the accuracy of the Prony's approach is promising.

This thesis describes possible applications of Prony's method in timing analysis of digital circuits. Such applications include predicting the future shape of the waveform in DTA(Dynamic Timing Analysis) and delay look-up table in STA(Static Timing Analysis). Given some equally spaced output values, the traditional Prony's method can be used to extract poles and residues of a linear system, i.e. to characterize a waveform using an exponential function. In this thesis, not only values but also equally spaced derivatives are tested. Still using same idea of the traditional Prony's method, poles and residues can also be extracted with those values and derivatives. The resultant poles and residues will be used to predict the output waveform in DTA analysis. The benefits brought by the using of derivatives include less simulation steps and less CPU time consuming than the regular constant step simulation. As a matter of fact, the Prony's method can precisely approximate a complicated waveform. Such property can be applied for STA analysis. The Prony's approximation can be used to precisely record an output waveform, which is used as an entry of the look-up table of STA. Since the accuracy of STA analysis relies on the accuracy of the input and output waveform in the look-up table, the accuracy of the Prony's approach is promising.

The development and advancement of microelectronics technology have been dramatically. The time and cost, for research and optimization of process and equipment, can be saved by using flow simulation. The governing equations of flow field, inside chemical vapor deposition (CVD) reactor, are constructed, dispersed, and solved by grid mesh and numerical method. At present, rapid thermal process (RTP) is becoming more important and popular for thin-film depositing technology. In this thesis, vertical type single wafer RTCVD reactor in poly-silicon thin-film depositing process is analyzed by numerical method. Several operating process parameters, such as: (a) the gap between shower head and wafer surface, (b) gas inlet velocity in shower head, and (c) operating pressure inside chamber of reactor, are considered for discussion and analysis of steady or unsteady phenomenon in three steps of thin-film depositing process, including (¢¹) heating for wafer, (¢º) deposition in steady state, (¢») cooling after deposition etc.. As shown in the results, each operating parameters performs different relations and phenomenon in these steady and unsteady steps: Operating pressure can affect the activity of chemical reaction strongly in unsteady or steady region. Larger gap between wafer and shower head causes less influence by flow effects or buoyancy. And also, radiation heat transfer, which is adopted by RTCVD process, can decrease the influence of some parameters on flow field.

No description available.

In the present study, a computational method was developed, validated and applied for the determination of parameters of a constitutive model for a ceramic material. An optimization algorithm, based on a direct search method, was applied to the determination of the load-displacement response of the specimen, and for the identification of the parameters of the constitutive model.A one-dimensional nonlinear initial-boundary value problem of wave propagation in a composite bar made of dissimilar materials was formulated and solved numerically. Convergence of the numerical scheme was studied, and range of convergence was established. Numerical scheme was validated for a number of benchmark problems with known analytical solutions, and for the problems solved using finite element method. Investigation of the accuracy of the displacement and strain responses was conducted; known limitations of the Kolsky's method for split Hopkinson pressure bar were revealed. For numerical examples considered in the present study, comparison of performance of the optimized finite-difference solver and of the finite element code LS-DYNA showed that the finite-difference code is about 10 times faster.Developed method and solutions were applied for the identification of the parameters of the Johnson-Holmquist constitutive model for five sets of experimental data for aluminum oxide AD995. Results of analysis revealed significant sensitivity of stress response to variation of fractured strength model parameters and damage model parameters.For the determined values of parameters, detailed parametric study of stress field, damage accumulation, and velocity field, was conducted with the help of the finite element method.It was found that the accuracy of the simulation using the JH-2 constitutive model changes with the rate of damage accumulation in the ceramic material.The damage patterns and history of damage development, obtained numerically, agreed qualitatively with the fracture history and its patterns, observed in the recovered Macor ceramics available in the literature.A method for image analysis of the photographic images of the lateral sides of the recovered specimen was proposed. It was used to quantify density of the damage in the specimen and to establish a better integral approach to predict amount of damage inside the specimen.

This thesis describes possible applications of Prony's method in timing analysis of digital circuits. Such applications include predicting the future shape of the waveform in DTA(Dynamic Timing Analysis) and delay look-up table in STA(Static Timing Analysis). Given some equally spaced output values, the traditional Prony's method can be used to extract poles and residues of a linear system, i.e. to characterize a waveform using an exponential function. In this thesis, not only values but also equally spaced derivatives are tested. Still using same idea of the traditional Prony's method, poles and residues can also be extracted with those values and derivatives. The resultant poles and residues will be used to predict the output waveform in DTA analysis. The benefits brought by the using of derivatives include less simulation steps and less CPU time consuming than the regular constant step simulation. As a matter of fact, the Prony's method can precisely approximate a complicated waveform. Such property can be applied for STA analysis. The Prony's approximation can be used to precisely record an output waveform, which is used as an entry of the look-up table of STA. Since the accuracy of STA analysis relies on the accuracy of the input and output waveform in the look-up table, the accuracy of the Prony's approach is promising.

In this thesis we study boundary value problems for the Laplace equation on do mains with smooth boundary. Central to our analysis is a relation, known as the global relation, that couples the boundary data for a given BVP. Previously, the global re lation has primarily been applied to elliptic PDEs defined on polygonal domains. In this thesis we extend the use of the global relation to domains with smooth boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and invertible integral operator. Following this, we show that the F_p-transform naturally arises in the global relation for the Laplace equation on domains with smooth boundary. Using properties of the F_p-transform, we show that the global relation defines a continuously invertible map between the Dirichlet and Neumann data for a given BVP for the Laplace equation. Following this, we construct a numerical method that uses the global relation to find the Neumann data, given the Dirichlet data, for a given BVP for the Laplace equation on a domain with smooth boundary.

Doctor of Philosophy / Department of Mathematics / Alexander G. Ramm / In this thesis, the author presents several numerical methods for solving scalar and electromagnetic wave scattering problems. These methods are taken from the papers of Professor Alexander Ramm and the author, see [1] and [2]. In Chapter 1, scalar wave scattering by many small particles of arbitrary shapes with impedance boundary condition is studied. The problem is solved asymptotically and numerically under the assumptions a << d << λ, where k = 2π/λ is the wave number, λ is the wave length, a is the characteristic size of the particles, and d is the smallest distance between neighboring particles. A fast algorithm for solving this wave scattering problem by billions of particles is presented. The algorithm comprises the derivation of the (ORI) linear system and makes use of Conjugate Orthogonal Conjugate Gradient method and Fast Fourier Transform. Numerical solutions of the scalar wave scattering problem with 1, 4, 7, and 10 billions of small impedance particles are achieved for the first time. In these numerical examples, the problem of creating a material with negative refraction coefficient is also described and a recipe for creating materials with a desired refraction coefficient is tested. In Chapter 2, electromagnetic (EM) wave scattering problem by one and many small perfectly conducting bodies is studied. A numerical method for solving this problem is presented. For the case of one body, the problem is solved for a body of arbitrary shape, using the corresponding boundary integral equation. For the case of many bodies, the problem is solved asymptotically under the physical assumptions a << d << λ, where a is the characteristic size of the bodies, d is the minimal distance between neighboring bodies, λ = 2π/k is the wave length and k is the wave number. Numerical results for the cases of one and many small bodies are presented. Error analysis for the numerical method are also provided.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-08-17T17:45:38Z No. of bitstreams: 2 Dissertação - Ademir Alves de Brito Júnior - 2016.pdf: 4581696 bytes, checksum: fb086c82c7a1661645e7f2006d2ae319 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-08-18T12:03:26Z (GMT) No. of bitstreams: 2 Dissertação - Ademir Alves de Brito Júnior - 2016.pdf: 4581696 bytes, checksum: fb086c82c7a1661645e7f2006d2ae319 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-08-18T12:03:26Z (GMT). No. of bitstreams: 2 Dissertação - Ademir Alves de Brito Júnior - 2016.pdf: 4581696 bytes, checksum: fb086c82c7a1661645e7f2006d2ae319 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-05-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, a numerical version of Unscented Transform was developed. In the developed approach, any probability distributions can be mapped by means of linear or non-linear functions, thus allowing fast acquisition of the probability distributions of the outputs/ simulation model responses, or more specifically, the evaluation of the uncertainty model. For practical purposes of distribution mapping, the computational cost is considerably lower than that demanded by the Monte Carlo method, which is based on a massive random sampling, thus presenting high computational cost. The application in Biomechanics problems shows the efficiency of the proposed method. / Neste trabalho, foi desenvolvida uma versão numérica da Transformada da Incerteza (expressão utilizada para denominar a Unscented Transform). Na abordagem elaborada, quaisquer distribuições de probabilidade podem ser mapeadas por meio de funções lineares ou não-lineares, permitindo assim a obtenção ágil das distribuições de probabilidade das saídas/respostas do modelo de simulação ou, mais especificamente, do modelo de avaliação de incertezas. Para propósitos práticos de mapeamento de distribuições, o custo computacional se mostra consideravelmente menor que aquele demandado pelo método de Monte Carlo, o qual é baseado em amostragem aleatória massiva, apresentando assim alto custo computacional. A aplicação em problemas de Biomecânica como a avaliação mecânica do osso humano e avaliação de incertezas da marcha humana por meio da dinâmica inversa, mostra a eficiência do método proposto em vista de outros métodos conhecidos como o de Monte Carlo.

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