Environmental flows (e.g. river and atmospheric flows) governed by the shallow water equations (SWE) are usually dominated by the advective mechanism over multiple time-scales. The combination of time dependency and nonlinear advection creates difficulties in the numerical solution of the SWE. A fully-implicit scheme is desirable because a relatively large time step may be used in a simulation. However, nonlinearity in a fully implicit method results in a system of nonlinear equations to be solved at each time step. To address this difficulty, a new method for implicit solution of unsteady nonlinear advection equations is developed in this research. This Time-Centered Split (TCS) method uses a nested application of the midpoint rule to computationally decouple advection terms in a temporally second-order accurate time-marching discretization. The method requires solution of only two sets of linear equations without an outer iteration, and is theoretically applicable to quadratically-nonlinear coupled equations for any number of variables. To explore its characteristics, the TCS algorithm is first applied to onedimensional problems and compared to the conventional nonlinear solution methods. The temporal accuracy and practical stability of the method is confirmed using these 1D examples. It is shown that TCS can computationally linearize unsteady nonlinear advection problems without either 1) outer iteration or 2) calculation of the Jacobian. A family of the TCS method is created in one general form by introducing weighting factors to different terms. We prove both analytically and by examples that the value of the weighting factors does not affect the order of accuracy of the scheme. In addition, the TCS method can not only computationally linearize but also decouple an equation system of coupled variables using special combinations of weighting factors. Hence, the TCS method provides flexibilities and efficiency in applications. / text

ITC/USA 2012 Conference Proceedings / The Forty-Eighth Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2012 / Town and Country Resort & Convention Center, San Diego, California / In this paper, a novel zigzag scanning concept of quantized coefficients for H.264/AVC is introduced. In order to scan the quantized coefficients efficiently, the statistical occurrence values of the quantized coefficients after the final mode decision are utilized. We develop a zigzag scanning pattern by reordering the statistical occurrence values in descending order. In addition, we consider the temporal and spatial correlation among the frames to classify the zigzag scanning pattern. In particular, we focus on the macroblock level zigzag scanning so that the proposed method will have the different zigzag scanning pattern based on the macroblock. Experimental results show that the proposed scheme reduces the total bits up to 4.05% and 3.67% while introducing either negligible loss of video quality for intra- and inter mode, respectively.

This dissertation focuses on the development and implementation of a new method to solve the time-dependent form of the linear Boltzmann transport equation for reactor transients. This new method allows for a stable solution to the fully explicit form of the transport equation with delayed neutrons by employing an error-controlled, adaptive Runge-Kutta-Fehlberg (RKF) method to differentiate the time domain. Allowing for the time step size to vary adaptively and as needed to resolve the time-dependent behavior of the angular flux and neutron precursor concentrations. The RKF expansion of the time domain occurs at each point and is coupled with a Source Iteration to resolve the spatial behavior of the angular flux at the specified point in time. The decoupling of the space and time domains requires the application of a quasi-static iteration between solving the time domain using adaptive RKF with error control and resolving the space domain with a Source Iteration sweep. The research culminated with the development of the 1-D Adaptive Runge-Kutta Time-Dependent Transport code (ARKTRAN-TD), which successfully implemented the new method and applied it to a suite of reactor transient benchmarks.

Discrete Event Simulation on GPUs employing parallel heap data structure is the focus of this thesis. Two traditional algorithms, one being conservative and other being optimistic, for parallel discrete event simulation have been implemented on GPUs using CUDA. The first algorithm is the safe-window algorithm (conservative). It has produced expected performance when compared to sequential simulation. The second algorithm, known as SyncSim, is an optimistic simulation algorithm previously designed to be space efficient and reduce rollbacks. This algorithm is re-implemented on GPU platform with necessary changes on the logic simulator and the parallel heap implementation. The performance of the parallel heap when working with a logic simulator has also been validated against the results indicated in previous research paper on parallel heap without the logic simulator.

Value of information is one of the key features of decision analysis. This work deals with providing a consistent and functional methodology to determine VOI on proposed well tests in the presence of uncertainties. This method strives to show that VOI analysis with the help of discretized versions of continuous probability distributions with conventional decision trees can be very accurate if the optimal method of discrete approximation is chosen rather than opting for methods such as Monte Carlo simulation to determine the VOI. This need not necessarily mean loss of accuracy at the cost of simplifying probability calculations. Both the prior and posterior probability distributions are assumed to be continuous and are discretized to find the VOI. This results in two steps of discretizations in the decision tree. Another interesting feature is that there lies a level of decision making between the two discrete approximations in the decision tree. This sets it apart from conventional discretized models since the accuracy in this case does not follow the rules and conventions that normal discrete models follow because of the decision between the two discrete approximations. The initial part of the work deals with varying the number of points chosen in the discrete model to test their accuracy against different correlation coefficients between the information and the actual values. The latter part deals more with comparing different methods of existing discretization methods and establishing conditions under which each is optimal. The problem is comprehensively dealt with in the cases of both a risk neutral and a risk averse decision maker. / text

Let Y be a subvariety of an algebraic torus, Tevelv (24) defined and studied tropical compactifications as certain nice compactifications of Y. We give a criterion for certain compactification to be a schön compactification, and as a corollary, we show that any variety contains an open very affine schön variety. Using toric schemes defined over a discrete valuation ring, we generalize the theory of tropical compactification to the nonconstant coefficient case, i.e. for varieties defined over a discrete valuation ring. / text

The current development of consumer electronics, driven by the effort to manufacture smaller products with increased performance, has amplified the chance for inducing higher thermal stresses to these systems. In an effort to devise more effective cooling methods for these systems, many scholars have studied the convective cooling of discrete heating elements. This report discusses a methodology for fabricating and testing a suitable flat plate design with discrete heating elements for both natural and forced convection cooling experiments. There were two plate design attempts: (i) an aluminum plate and (ii) a R3315 hydrostatic-resistance plastic foam plate. For the purpose of conducting experiments for the discrete heating elements, the foam plate design was found to be an appropriate design. After designing a proper foam plate, several experiments were conducted for the natural convection case. The combination of parameters such as the geometric location and power output ratio between heaters that resulted in the maximum thermal conductance were studied. / text

Energy methods are used extensively in the formulation of discrete system models. They simplify the systematic integration of diverse kinematic schemes, and are well suited for characterizing complex energy domain coupling effects. Continuum mechanics models are by contrast normally based on partial differential equation descriptions of the physical system. The research presented here develops a new Hamiltonian method for the simulation of distributed parameter electromagnetic and thermo-electromagnetic systems. It expands the application of current system dynamics modeling techniques, to encompass complex distributed parameter electromagnetic systems. / text

Στην εργασία αυτή παρουσιάζονται ορισμένοι αλγόριθμοι που συνδέονται με ορθογώνια πολυώνυμα και διακριτά ολοκληρώσιμα συστήματα. Οι κανόνες των αλγορίθμων αυτών είναι ρητού τύπου και συνδέουν τιμές που αφορούν την εξέλιξη των αλγορίθμων στην περίπτωση ιδιομορφιών. Αυτοί οι ιδιάζοντες κανόνες συνιστούν ένα από τα κοινά γνωρίσματα με ορισμένα ολοκληρώσιμα συστήματα στο πλέγμα ΖxZ συγκεκριμένα αυτό του "περιορισμού των ιδιομορφιών". Παρουσιάζονται οι κανόνες των αλγορίθμων ε, ρ και qd όπως και κανόνες που προκύπτουν από τους δύο πρώτους των οποίων η μορφή είναι αναλλοίωτη από μετασχηματισμούς Moebius. Η τελευταία αυτή ιδιότητα βοηθά στην εύρεση ιδιαζόντων κανόνων για τον περιορισμό των ιδιομορφιών. Ο αλγόριθμος qd συνδέεται τόσο με τα ορθογώνια πολυώνυμα στην πραγματική ευθεία όσο και με το διακριτού χρόνου πλέγμα Toda. Παρουσιάζεται η εύρεση του τριδιαγώνιου πίνακα Jacobi από τις σχέσεις που συνδέουν γειτονικές ακολουθίες ορθογωνίων πολυωνύμων. Ο πίνακας Jacobi εκφράζει την γραμμική αναδρομική σχέση τριών διαδοχικών ορθογωνίων πολυωνύμων. Ανάλογη κατασκευή για ορθογώνια πολυώνυμα στον μοναδιαίο κύκλο είναι περισσότερο πολύπλοκη και δεν καταλήγει πάντοτε σε πολυδιαγώνιο πίνακα. Παρουσιάζονται σχετικά πρόσφατα αποτελέσματα για τα ορθογώνια πολυώνυμα στον μοναδιαίο κύκλο και ο πενταδιαγώνιος πίνακας CMV. / In this paper are introduced some algorithms which are connected with orthogonal polynomials and descrete integrable systems. The rules of these algorithms are fraction type and combine the terms which are on the vertex of a rombus. We mainly introduce the rules which relate the evolution of the algorithms in the case of singular rules. These rules introduce one of the common characteristics with some integrable systems in the ZxZ lattice, in particular the "singularity confinement". We introduce the rules of the ε-, ρ- and qd-algorithms as well as the rules which follow from the first two whose type is unchangeable from Moebius transformations. This last property helps in finding proper rules for the singularity confinement. The qd-algorithm is connected not only with the orthogonal polynomials in the real line, but also with the discrete time Toda lattice. We also introduce the finding of the tri-diagonal Jacobi matrix from relations which combine adjacent sequences of orthogonal polynomials. The Jacobi matrix represent the three-term linear reccurence relation of orthogonal polynomials. Correspondent construction for orthogonal polynomials on the unit circle is much more complicated and doesn't conclude always in a poly-diagonal matrix. We introduce some recent results for orthogonal polynomials on the unit circle and the five-diagonal CMV matrix.

Η θεωρία γραφημάτων είναι ένας κλάδος των μαθηματικών που έχει ευρεία πρακτική εφαρμογή. Πολυάριθμα προβλήματα που προκύπτουν σε διαφορετικές επιστήμες, όπως ψυχολογία, χημεία, βιομηχανική μηχανική, διοίκηση, μάρκετινγκ και εκπαίδευση, μπορούν να παρασταθούν ως προβλήματα από τη θεωρία γραφημάτων. / -