[PDF] Global Regularity And Uniqueness Of Solutions In A Surface Growth Model Using Rigorous A Posteriori Methods eBook

Author : Christian Nolde
Publisher : Logos Verlag Berlin GmbH
Page : 98 pages
File Size : 37,83 MB
Release : 2017
Category : Mathematics
ISBN : 3832544534

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The use of rigorous numerical methods to approach problems which can not be solved using standard methods (yet) has increased signifiantly in recent years. In this book, riogorous a-posteriori methods are used to study the time evolution of a surface growth model, given by a fourth order semi-linear parabolic partial differential equation, where standard methods fail to verify global uniqueness and smoothness of solutions. Based on an arbitrary numerical approximation, a-posteriori error-analysis is applied in order to prevent a blow up analytically. This is a method that in a similar way also applies to the three dimensional Navier-Stokes equations. The main idea consists of energy-estimates for the error between solution and approximation that yields a scalar differential equation controlling the norm of the error with coefficients depending solely on the numerical data. This allows the solution of the differential equation to be bounded using only numerical data. A key technical tool is a rigorous eigenvalue bound for the nonlinear operator linearized around the numerical approximation. The presented method succeeds to show global uniqueness for relatively large initial conditions, which is demonstrated in many numerical examples.

Author : Simo Särkkä
Publisher : Cambridge University Press
Page : 327 pages
File Size : 39,31 MB
Release : 2019-05-02
Category : Business & Economics
ISBN : 1316510085

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With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Author : Peter K. Friz
Publisher : Springer Nature
Page : 346 pages
File Size : 17,71 MB
Release : 2020-05-27
Category : Mathematics
ISBN : 3030415562

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With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH

Author : Ghenadii Korotcenkov
Publisher : Momentum Press
Page : 432 pages
File Size : 38,17 MB
Release : 2012-07-15
Category : Technology & Engineering
ISBN : 1606503146

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Chemical sensors are integral to the automation of myriad industrial processes and everyday monitoring of such activities as public safety, engine performance, medical therapeutics, and many more. This 4 volume reference work covering simulation and modeling will serve as the perfect complement to Momentum Press's 6 volume reference works 'Chemical Sensors: Fundamentals of Sensing Materials' and 'Chemical Sensors: Comprehensive Sensor Technologies', which present detailed information related to materials, technologies, construction and application of various devices for chemical sensing. This 4 volume comprehensive reference work analyzes approaches used for computer simulation and modeling in various fields of chemical sensing and discusses various phenomena important for chemical sensing such as bulk and surface diffusion, adsorption, surface reactions, sintering, conductivity, mass transport, interphase interactions, etc. In this work it will be shown that theoretical modeling and simulation of the processes, being a basic for chemical sensors operation, could provide considerable progress in choosing both optimal materials and optimal configurations of sensing elements for using in chemical sensors. Each simulation and modeling volume in the present series reviews modeling principles and approaches peculiar to specific groups of materials and devices applied for chemical sensing. Volume 2: Conductometric-Type Sensors covers phenomenological modeling and computational design of conductometric chemical sensors based on nanostructured materials such as metal oxides, carbon nanotubes and graphene. This volume contains an overview of the approaches used to quantitatively evaluate characteristics of sensitive structures in which electric charge transport depends on the interaction between the surfaces of the structures and chemical compounds in the surrounding.

Author : A. C. Antoulas
Publisher : SIAM
Page : 244 pages
File Size : 36,82 MB
Release : 2020-01-13
Category : Mathematics
ISBN : 1611976081

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Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Author :
Publisher :
Page : 64 pages
File Size : 46,52 MB
Release : 1958-01
Category :
ISBN :

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The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.

Author : Cédric Villani
Publisher : Springer Science & Business Media
Page : 970 pages
File Size : 30,97 MB
Release : 2008-10-26
Category : Mathematics
ISBN : 3540710507

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At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.