Coalescing Particle Systems And Applications To Nonlinear Fokker Planck Equations
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Coalescing Particle Systems And Applications To Nonlinear Fokker Planck Equations
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Author : Gleb Zhelezov
language : en
Publisher:
Release Date : 2017
Coalescing Particle Systems And Applications To Nonlinear Fokker Planck Equations written by Gleb Zhelezov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation, such as the Patlak-Keller-Segel (PKS) model, or its multispecies variant. We then show that the presented numerical method is well-suited for the simulation of the formation of finite-time singularities in the PKS, as well as PKS pre- and post-blow-up dynamics. Additionally, we present numerical evidence that blow-up with an increasing total second moment in the two species Keller-Segel system occurs with a linearly increasing second moment in one component, and a linearly decreasing second moment in the other component.
Nonlinear Equations In Many Particle Systems
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Author : Mathematisches Forschungsinstitut Oberwolfach
language : en
Publisher:
Release Date : 1993
Nonlinear Equations In Many Particle Systems written by Mathematisches Forschungsinstitut Oberwolfach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Nonlinear Markov Processes And Kinetic Equations
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Author : Vassili N. Kolokoltsov
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-15
Nonlinear Markov Processes And Kinetic Equations written by Vassili N. Kolokoltsov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-15 with Mathematics categories.
A nonlinear Markov evolution is a dynamical system generated by a measure-valued ordinary differential equation with the specific feature of preserving positivity. This feature distinguishes it from general vector-valued differential equations and yields a natural link with probability, both in interpreting results and in the tools of analysis. This brilliant book, the first devoted to the area, develops this interplay between probability and analysis. After systematically presenting both analytic and probabilistic techniques, the author uses probability to obtain deeper insight into nonlinear dynamics, and analysis to tackle difficult problems in the description of random and chaotic behavior. The book addresses the most fundamental questions in the theory of nonlinear Markov processes: existence, uniqueness, constructions, approximation schemes, regularity, law of large numbers and probabilistic interpretations. Its careful exposition makes the book accessible to researchers and graduate students in stochastic and functional analysis with applications to mathematical physics and systems biology.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.
Application Of Scaling Properties Of The Vlasov And The Fokker Planck Equations To Improved Macroparticle Models
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Author :
language : en
Publisher:
Release Date : 2001
Application Of Scaling Properties Of The Vlasov And The Fokker Planck Equations To Improved Macroparticle Models written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Numerical simulations of cooling processes over minutes or hours of real time are usually carried out using direct solution of the Fokker-Planck equation. However, by using scaling rules derived from that equation, it is possible to use macroparticle representations of the beam distribution. Besides having applications for cooling alone, the macroparticle approach allows combining the cooling process with other dynamical processes which are represented by area-preserving maps. A time-scaling rule derived from the Vlasov equation can be used to adjust the time step of a map-based dynamics calculation to one more suitable for combining with a macroparticle Fokker-Planck calculation. The time scaling for the Vlasov equation is also useful for substantially more rapid calculations when a macroparticle model of a conservative multiparticle system requires a large number of macroparticles to faithfully produce the collective potential or when the model must simulate a long time period.
International Aerospace Abstracts
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Author :
language : en
Publisher:
Release Date : 1993
International Aerospace Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Aeronautics categories.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1992
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mechanics, Applied categories.
Annual Report
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Author : National Center for Atmospheric Research (U.S.)
language : en
Publisher:
Release Date : 1970
Annual Report written by National Center for Atmospheric Research (U.S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Atmosphere categories.
Princeton Companion To Applied Mathematics
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Author : Nicholas J. Higham
language : en
Publisher: Princeton University Press
Release Date : 2015-09-09
Princeton Companion To Applied Mathematics written by Nicholas J. Higham and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Computer Physics Research Trends
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Author : Silvan J. Bianco
language : en
Publisher: Nova Publishers
Release Date : 2007
Computer Physics Research Trends written by Silvan J. Bianco and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computers categories.
This book includes within its scope: computational models in physics and physical chemistry; computer programs in physics and physical chemistry; computational models and programs associated with the design, control, and analysis of experiments; numerical methods and algorithms; algebraic computation; impact of advanced computer architecture and special purpose computers on computing in the physical sciences; software topics, including programming environments, languages, data bases, expert systems, and graphics packages related to physical sciences; and, analysis of computer systems performance.