Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved ma...
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ISBN:
(数字)9783540281252
Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.
The book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new program...
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ISBN:
(数字)9783030441012
ISBN:
(纸本)9783030441005;9783030441036
The book will appeal to mathematicians and electrical engineers. Further, it introduces algorithm and program developers to recent advances in the other fields, while industry experts will be introduced to new programming tools and mathematical methods.
Simulation ist neben Theorie und Experiment die dritte Säule wissenschaftlicher Forschung und technischer Entwicklung. Computer-Berechnungen sind zu einer wesentlichen Antriebskraft im Bereich der Technik und der...
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ISBN:
(数字)9783211271834
ISBN:
(纸本)9783211211373
Simulation ist neben Theorie und Experiment die dritte Säule wissenschaftlicher Forschung und technischer Entwicklung. Computer-Berechnungen sind zu einer wesentlichen Antriebskraft im Bereich der Technik und der Naturwissenschaften geworden. Speziell für diese Anwendungsbereiche wurde MATLAB entwickelt. MATLAB ist ein auf mathematisch/numerischen Methoden beruhendes Problemlösungswerkzeug, das sowohl bequeme Benutzeroberflächen bietet, als auch die individuelle Programmierung gestattet. MATLAB hat sich durch seine Erweiterungsmöglichkeit in Form von "Toolboxen" zu einem universell einsetzbaren Werkzeug auf den verschiedensten Gebieten (Signalverarbeitung, Regelungstechnik, Fuzzy Logic etc.) entwickelt.
Dieses Buch ist auf die neueste MATLAB-Version 7 abgestimmt und behandelt unter anderem detailliert die Lösung numerischer Problemstellungen mit Hilfe von MATLAB.
Typing plays an important role in software development. Types can be consid ered as weak specifications of programs and checking that a program is of a certain type provides a verification that a program satisfi...
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ISBN:
(数字)9781461204336
ISBN:
(纸本)9781461267577
Typing plays an important role in software development. Types can be consid ered as weak specifications of programs and checking that a program is of a certain type provides a verification that a program satisfies such a weak speci fication. By translating a problem specification into a proposition in constructive logic, one can go one step further: the effectiveness and unifonnity of a con structive proof allows us to extract a program from a proof of this proposition. Thus by the "proposition-as-types" paradigm one obtains types whose elements are considered as proofs. Each of these proofs contains a program correct w.r.t. the given problem specification. This opens the way for a coherent approach to the derivation of provably correct programs. These features have led to a "typeful" programming style where the classi cal typing concepts such as records or (static) arrays are enhanced by polymor phic and dependent types in such a way that the types themselves get a complex mathematical structure. Systems such as Coquand and Huet's Calculus of Con structions are calculi for computing within extended type systems and provide a basis for a deduction oriented mathematical foundation of programming. On the other hand, the computational power and the expressive (impred icativity !) of these systems makes it difficult to define appropriate semantics.
Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second s...
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ISBN:
(数字)9783319002637
ISBN:
(纸本)9783319002620;9783319343341
Gabrio Piola works had an enormous impact on the development of applied mathematics and continuum mechanics. An excellent scientific committee who took it upon themselves to translate his complete works. In a second step, they commented Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and proofs that he has set milestones in applied mathematics.;This book presents Piola's original Italian text together with ist translations and their comments. It shows impressively that Gabrio Piola’s work must still be regarded as a modern theory.
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