47 research outputs found

    Numerical Simulation

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    Nowadays mathematical modeling and numerical simulations play an important role in life and natural science. Numerous researchers are working in developing different methods and techniques to help understand the behavior of very complex systems, from the brain activity with real importance in medicine to the turbulent flows with important applications in physics and engineering. This book presents an overview of some models, methods, and numerical computations that are useful for the applied research scientists and mathematicians, fluid tech engineers, and postgraduate students

    Updating the Lambda modes of a nuclear power reactor

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    [EN] Starting from a steady state configuration of a nuclear power reactor some situations arise in which the reactor configuration is perturbed. The Lambda modes are eigenfunctions associated with a given configuration of the reactor, which have successfully been used to describe unstable events in BWRs. To compute several eigenvalues and its corresponding eigenfunctions for a nuclear reactor is quite expensive from the computational point of view. Krylov subspace methods are efficient methods to compute the dominant Lambda modes associated with a given configuration of the reactor, but if the Lambda modes have to be computed for different perturbed configurations of the reactor more efficient methods can be used. In this paper, different methods for the updating Lambda modes problem will be proposed and compared by computing the dominant Lambda modes of different configurations associated with a Boron injection transient in a typical BWR reactor. (C) 2010 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish Ministerio de Educacion y Ciencia under projects ENE2008-02669 and MTM2007-64477-AR07, the Generalitat Valenciana under project ACOMP/2009/058, and the Universidad Politecnica de Valencia under project PAID-05-09-4285.González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ. (2011). Updating the Lambda modes of a nuclear power reactor. Mathematical and Computer Modelling. 54(7):1796-1801. https://doi.org/10.1016/j.mcm.2010.12.013S1796180154

    Positivity preserving solutions of partial integro-differential equations

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2009."May 15th, 2009."Includes bibliographical references (leaves 246-249).Differential equations are one of the primary tools for modeling phenomena in chemical engineering. While solution methods for many of these types of problems are well-established, there is growing class of problems that lack standard solution methods: partial integro-differential equations. The primary challenges in solving these problems are due to several factors, such as large range of variables, non-local phenomena, multi-dimensionality, and physical constraints. All of these issues ultimately determine the accuracy and solution time for a given problem. Typical solution techniques are designed to handle every system using the same methods. And often the physical constraints of the problem are not addressed until after the solution is completed if at all. In the worst case this can lead to some problems being over-simplified and results that provide little physical insight. The general concept of exploiting solution domain knowledge can address these issues. Positivity and mass-conservation of certain quantities are two conditions that are difficult to achieve in standard numerical solution methods. However, careful design of the discretizations can achieve these properties with a negligible performance penalty. Another important consideration is the stability domain. The eigenvalues of the discretized problem put restrictions on the size of the time step. For "stiff' systems implicit methods are generally used but the necessary matrix inversions are costly, especially for equations with integral components. By better characterizing the system it is possible to use more efficient explicit methods.(cont.) This work improves upon and combines several methods to develop more efficient methods. There are a vast number of systems that be solved using the methods developed in this work. The examples considered include population balances, neural models, radiative heat transfer models, among others. For the capstone portion, financial option pricing models using "jump-diffusion" motion are considered. Overall, gains in accuracy and efficiency were demonstrated across many conditions.by Alexander M. Lewis.Ph.D

    Applications

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    Model Order Reduction

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    An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
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