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Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

The solution of optimal control problems through the Hamilton-Jacobi-Bellman (HJB) equation offers guaranteed satisfaction of both the necessary and sufficient conditions for optimality. However, finding an exact solution to the HJB equation is a near impossible task for many optimal control problems. This thesis presents an approximation method for solving finite-horizon optimal control problems involving nonlinear dynamical systems. The method uses finite-order approximations of the partial derivatives of the cost-to-go function, and successive higher-order differentiations of the HJB equation. Natural byproducts of the proposed method provide sensitivities of the controls to changes in the initial states, which can be used to approximate the solution to neighboring optimal control problems. For highly nonlinear problems, the method is modified to calculate control sensitivities about a nominal trajectory. In this framework, the method is shown to provide accurate control sensitivities at much lower orders of approximation. Several numerical examples are presented to illustrate both applications of the approximation method.

In this paper we study a class of non-linear singular partial differential equation in complex domain Csub(t) x C n sub(x). Under certain assumptions, we prove the existence and uniqueness of holomorphic solution near origin of Csub(t) x C n sub(x).

The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by Gérard-Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.

The internal dynamics of powder systems under compression are as of yet not fully understood, and thus there is a necessity for approaches that can help in further clarifying and enhancing the level of understanding on this subject. To this end, the internal dynamics of powder systems under compression were probed by means of force distributions and a novel compaction equation. The determination of force distributions hinged on the use of carbon paper as a force sensor, where the imprints transferred from it onto white paper where converted through calibration into forces. Through analysis of these imprints, it was found that the absence of friction and bonding capacity between the particles composing the powder bed had no effect on how the applied load was transferred through the system. Additionally, it was found that pellet strength had a role to play in the homogeneity of force distributions, where, upon the occurrence of fracture, force distributions became less homogenous. A novel compaction equation was derived and tested on a series of systems composed of pellets with differing mechanical properties. The main value of the equation lay in its ability to predict compression behavior from single particle properties, and the agreement was especially good when a compact of zero porosity was formed. The utility of the equation was tested in two further studies, using a series of pharmaceutically relevant powder materials. It was established that the A parameter of the equation was a measure of the deformability of the powder material, much like the Heckel 1/K parameter, and can be used as a means to rank powders according to deformability, i.e. to establish plasticity scale. The equation also provided insights into the dominating compression mechanisms through an invariance that could be exploited to determine the point, at which the powder system became constrained, i.e. the end of rearrangement. Additionally, the robustness of the equation was demonstrated through fruitful analysis of a set of diverse materials. In summary, this thesis has provided insights and tools that can be translated into more efficient development and manufacturing of medicines in the form of tablets.

In October 2000 the Initiative for the Integration of Regional Infrastructure in South America (IIRSA) was launched. The purpose of the IIRSA is to improve integration of the South American countries and intraregional trade between them. One of the ultimate goals is to promote sustainable growth. The purpose of this paper is to find out if a better quantity and quality of transport infrastructure increases intraregional trade in South America. It is found that the quantity of transport infrastructure increases intraregional trade. On the other hand, there is no evidence for the quality of transport infrastructure increasing intraregional trade in South America. Furthermore, this paper investigates whether economic growth can be obtained through more trade. In other words, this paper examines if trade causes growth. The results do not confirm the trade-growth causality for all countries. The difference between the existence of a trade-growth causal relationship or not could be explained by the core commodities that the different South American countries export.

Since the end of World War II, foreign direct investment (FDI) has been leading the international financial capital flows and has tripled in 2000s over the decade earlier. With its positive effect on economic growth of host countries via spill-overs, it became a race among countries to attract multinational enterprises (MNEs) to invest in their countries. The introduction of European common currency theoretically helps reduce the transaction costs across borders with the reduction of exchange-rate uncertainties and associated costs of hedging, facilitation of international cost comparison. Moreover, mergers and acquisitions activities (M&As) account for 60-80% of FDI flows, and most MNEs engage in both export and setting up affiliates abroad, suggesting complementarity between trade and FDI. Thus reducing cross-border distance costs would encourage MNEs to increase its M&A activities abroad, resulting in more inward FDI flows in the eurozone, especially among member states. The gravity equation is used in this paper to estimate the euro effect from the dataset of inward FDI flows of 24 countries during 1993-2007 and the result confirms that common currency stimulates more intra-eurozone inward FDI flows by approximately 58%.

In this report we describe simulation of the surface current density on a PEC cylinder and the diffracted field for a line source above a finite PEC ground plane as a means to verify the Nero2D program. The results are compared with the exact solution and give acceptable errors. A terrain model for a communication link is studied in the report and we simulate the wave propagation for terrain with irregular shapes and different materials. The Nero2D program is based on the fast multipole method (FMM) to reduce computation time and memory. Gaussian sources are also studied to make the terrain model more realistic

A new multiresolution scheme based on interpolating scaling function(ISF) on adaptive gridding(AG) shows promising in the first principle calculation. We also use ISFs on solving Poisson equation(PE), and find good approximations on the expansions of the second derivatives of ISFs. It is simpler than the wavelet scheme and fully implements the fast wavelet transformation so that the method is very suitable to problems with frequently updating charge density such as the first-principle calculation in electronic structures in atoms, molecules, and solids. Although the scheme is similar to the AG scheme on real space, the ISFs can represent fields more effectively and it needs less grids than the scheme of real space does. This simple and effective method provides an alternative to both the real space and the wavelet methods in the first principle calculation. Also, The method can be easily parallelized due to the block structure of the grid layout.