O conhecimento da distribuição da umidade no solo para diferentes tipos de solos e diferentes vazões pode ser aplicado na otimização do dimensionamento de um sistema de irrigação, no manejo da água na zona radicular, bem como, auxiliar na aplicação eficiente de fertilizantes na rizosfera. Portanto, objetivou-se com a presente pesquisa desenvolver um modelo numérico bidimensional capaz de simular a distribuição da umidade no perfil de solo para diferentes sistemas de irrigação. Sendo que para tal, o modelo utiliza o método das diferenças finitas, mediante uma discretização da solução da equação de Richards e o método iterativo de Picard, o qual foi utilizado para garantir a conservação da massa. O modelo numérico ainda torna possível considerar a extração de água pelas plantas e a evaporação da água na superfície do solo. E para avaliar o seu desempenho foi feita uma análise de sensibilidade. O modelo matemático foi desenvolvido no Departamento de Engenharia de Biossistemas, pertencente à Escola Superior de Agricultura \"Luiz de Queiroz\" - ESALQ/USP. A linguagem de programação utilizada foi Fortran 90. A estrutura computacional foi feita de forma a permitir ao usuário a entrada de informações tais como: a) dados do perfil do solo, no que se refere às suas propriedades físico-hídricas, b) informações sobre o tipo de irrigação, tempo de simulação, tempo de aplicação de água via irrigação. O programa permite ao usuário a opção entre simular a extração de água pela as plantas ou não. Para a validação do modelo foram utilizados os dados obtidos por Rivera (2004), em um experimento conduzindo no antigo Departamento de Engenharia Rural da Escola Superior de Agricultura \"Luiz de Queiroz\". O desempenho do modelo foi avaliado com base nos parâmetros estatísticos: índice de concordância de Willmott; coeficiente de eficiência, raiz quadrada do erro médio, erro médio e o erro máximo absoluto. A análise de sensibilidade do modelo foi avaliada em função dos parâmetros: densidade de fluxo de água, condutividade hidráulica do solo saturado, alfa e n (parâmetros de ajuste da curva de retenção). Pelos resultados obtidos, o modelo apresentou um desempenho satisfatório na simulação dos perfis de umidade em relação aos dados medidos em condições de experimento em solo não saturado. Em relação à análise de sensibilidade, o modelo apresentou maior sensibilidade aos parâmetros de fluxo de entrada e ao parâmetro n da equação de retenção, indicando que tais parâmetros de entrada, necessitam ser determinados com maior precisão. Houve baixa sensibilidade ao parâmetro \"alfa\" da curva de retenção. / The soil moisture distribution for different soil types under different flow regimes can be used to optimize the design of an irrigation system, water manage water in the root zone, or increase the precision of the application of fertilizers in the rhizosphere. Therefore, the objective of this research was to develop a two-dimensional numerical model capable of simulating the soil moisture distribution in soil profile for different irrigation systems. The model is a finite difference solution of the Richards equation solution, in which the Picard iteration method is used to ensure the conservation of mass. The numerical model also takes water extraction by plants and water evaporation on the soil surface into account. The mathematical model was developed in the Department of Biosystems Engineering, College of Agriculture \"Luiz de Queiroz\", ESALQ / USP. It was coded in Fortran 90, and structured to allow interactive input of a) physical and hydraulic properties soil profile, and b) type of irrigation, irrigation application time, and simulation. The simulation of water extraction by the plants is optional. And to evaluate its performance a sensitivity analysis was done. Data obtained in an experiment carried out in the older Rural Engineering Department, College of Agriculture \"Luiz de Queiroz\" by Rivera (2004), were used to validate the model. Model performance was evaluated using the Willmott index of agreement; efficiency coefficient, root mean square error, average error and the maximum absolute error. Sensitivity analyses were performed on the density of water flow, saturated hydraulic conductivity, and on alpha and n (setting parameters of the soil water retention curve). From the results obtained, the model satisfactory simulated the measured soil moisture distributions in the experimental soil moisture profiles. The model was most sensitive to variations in the parameters of the input stream and to n, a parameter in the soil water retention equation (van Genuchten model, 1980). This results is indicative that these input parameters need to be determined with greater accuracy. The model output was not very sensitive to alpha, a shape parameter in the soil water retention curve.

This thesis studies the physics of multilayer heterostructures grown from topological insulators (TIs), primarily bismuth selenide and antimony telluride, and other topologically trivial materials. This is done by extending a standard low-energy 3D TI Hamiltonian and varying its associated material parameters across the simulation domain. New results arising from the position-dependent TI interface model are found. For the first time, this method is incorporated into a density-functional theory (DFT) solver in order to study the self-consistent charge density in multilayer TI heterostructures due to the interface states. The thesis is structured as follows. The introduction (Ch. 1) presents a pedagogical review of the theory of 3D TIs and low-energy Hamiltonians used to study them, as well as typical methods in solid state physics that are made use of throughout the thesis. Chapter 2 presents the position-dependent Hamiltonian, showing new evidence for topological features of bulk states including varying degrees of band mixing and inversion; also, interface state tunnelling is shown to be affected by atomic layer orbital overlap, and incomplete localisation of surface states is demonstrated for antimony telluride. Chapter 3 presents a new DFT model of TI heterostructure interfaces and shows how conduction through TI interface states can be controlled with an electric field. Chapter 4 covers the extension of the model in Ch. 1 to 2D cross-sections of TI wires and heterostructures, showing for the first time evidence of localisation of conduction almost entirely within the inner interfaces of a 2D heterostructure wire. Chapter 5 presents our work with magnetic fields, demonstrating evolution of interface and bulk states with changing magnetic field and Landau level, as well as presenting new evidence for more complex spin structures in bismuth selenide arising from Landé factor signs. Our conclusions are presented in Chapter 6.

Exact solution to the vibration of rectangular plates is available only for plates with two opposite edges subject to simply supported conditions. Otherwise, they are analysed by using approximate methods. There are several approximate methods to conduct a vibration analysis, such as the Rayleigh-Ritz method, the Finite Element Method, the Finite Difference Method, and the Superposition Method. The Rayleigh-Ritz method and the finite element method give upper bound results for the natural frequencies of plates. However, there is a disadvantage in using this method in that the error due to discretisation cannot be calculated easily. Therefore, it would be good to find a suitable method that gives lower bound results for the natural frequencies to complement the results from the Rayleigh-Ritz method. The superposition method is also a convenient and efficient method but it gives lower bound solution only in some cases. Whether it gives upper bound or lower bound results for the natural frequencies depends on the boundary conditions. It is also known that the finite difference method always gives lower bound results. This thesis presents bounded eigenvalues, which are dimensionless form of natural frequencies, calculated using the superposition method and the finite difference method. All computations were done using the MATLAB software package. The convergence tests show that the superposition method gives a lower bound for the eigenvalues of fully clamped plates, and an upper bound for the completely free plates. It is also shown that the finite difference method gives a lower bound for the eigenvalues of completely free plates. Finally, the upper bounds and lower bounds for the eigenvalues of fully clamped and completely free plates are given.

<p>Photonic Crystal (PC) devices are the most exciting advancement in the field of photonics. The use of computational techniques has made considerable improvements in photonic crystals design. We present here an ultrahigh quality factor (Q) photonic crystal slab nanocavity formed by the local width modulation of a line defect. We show that only shifting two holes away from a line defect is enough to attain an ultrahigh Q value. We simulated this double heterostructure nano cavity by using Finite Difference Time Domain (FDTD) technique. We observed that photonic crystal cavities are very sensitive to the frequency, size and position of the source. So we must choose the right values for these parameters.</p>

This paper involves the calculation for composition of different layer used in laser structure and the simulation of cavity, formed by creating air columns in the InGaAsP medium, for square lattice. The aim of this project is to fabricate approximately zero threshold current lasers. This project involves FDTD simulation for optimizing dimension of the device, fabrication of laser structure and finally characterization of the device structure. / Singapore-MIT Alliance (SMA)

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity, and are interpolated using cubic splines. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier-Stokes equations are discretized on a staggered Cartesian grid by a second order accurate projection method for pressure and velocity. / Singapore-MIT Alliance (SMA)

This study uses the PIC (Particle-in-cell) method to simulate unsteady three-dimensional dynamics of particles in argon plasma under low pressure, high density, and weak ionization between two planar electrodes subject to a sudden biased voltage. Plasma has been widely used in materials processing, film manufacturing, nuclear fusion, lamps, etc. Properties of plasmas are also becoming important area for research. This work includes elastic collisions between electrons and neutrals, ions and neutrals, and inelastic collisions resulting in ionization from impacting neutrals by electrons, and charge exchange between ions and neutrals, and Coulomb collisions between electrons and ions. The model ignores secondary electron emission, recombination between ions and electrons, and assumes uniform distribution of the neutrals having velocity of Maxwellian distribution. The computed results show the effects of elastic and inelastic collisions on the characteristics of plasma and sheath (space charge region) in front of the workpiece surface. Unsteady mass, momentum and energy transport from the bulk plasma through sheath to the workpiece is confirmatively and exploratorily studied after successful comparison between PIC prediction and experimental data has been made.

This paper provides an overview of the finite difference method and its application to approximating financial partial differential equations (PDEs) in incomplete markets. In particular, we study German’s [6] stochastic volatility PDE derived from indifference pricing. In [6], it is shown that the first order- correction to derivatives valued by indifference pricing can be computed as a function involving the stochastic volatility PDE itself. In this paper, we present three explicit finite difference models to approximate the stochastic volatility PDE and compare the resulting valuations to those generated by an Euler- Maruyama Monte Carlo pricing algorithm. We also discuss the significance of boundary condition choice for explicit finite difference models.

The primary objective of the presented research is to develop a class of integrated compact silicon diffractive sensors (CSDS) based on in-plane diffraction gratings. This class of sensors uses a silicon-on-insulator (SOI) substrate to limit costs, exploit established fabrication processes, enable integration of supporting electronics, and use the well-understood telecommunications wavelength of 1.55µm. Sensing is achieved by combining constant-diffraction-efficiency and highly-angularly-selective in-plane resonance-domain diffraction gratings. Detection is based on the diffraction efficiency of the highly angularly selective grating. In this research, the design processes for the constant-diffraction-efficiency and the highly angularly selective gratings are detailed. Grating designs are optimized with rigorous coupled-wave analysis (RCWA) and simulated with finite-difference time-domain (FDTD) analysis. Fabrication results are presented for the CSDS gratings. An inductively coupled plasma (ICP) Bosch etch process enables grating fabrication to within one percent of designed values with nearly vertical sidewalls. Experimental results are presented for individual CSDS gratings, the prototype sensor, and a prototype linear sensor array. The results agree well with simulation. The linear sensor array prototype demonstrates the intrinsic splitting mechanism and forms the basis of a 2-D sensor array. Finally, a toluene sensor was functionally demonstrated. The proof-of-concept device includes a polymer immobilization layer and microfluidic delivery of toluene. Toluene concentrations as low as 100ppm are measured, corresponding to a refractive index change of 3x10⁻⁴ RIU.

The aim of this thesis in the nanoelectronics domain is to present a contribution to the analysis of the quantum electronic transport phenomena in nanostructures. For this purpose, we specifically develop the phase field matching theory (PFMT). Within this algebraic approach the electronic properties of the system are described by the tight-binding formalism, whereas the analysis of the transport properties based on the phase matching of the electronic states of the leads to the states of the molecular nanojunctions. By comparing some of our results with those of the first principles methods, we have shown the correctness and fonctionality of our approach. Moreover, our method can be considered as a practical and general alternative to the Green's function-based techniques, and is applied in this work to model the electronic transport across mono and diatomic nanojunctions, consisting of mono and multivalent Na, Cu, Co, C, Si, Ga and As elements.