Free Energy And Self Interacting Particles
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Free Energy And Self Interacting Particles
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Author : Takashi Suzuki
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-08
Free Energy And Self Interacting Particles written by Takashi Suzuki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-08 with Mathematics categories.
* Examines a nonlinear system of parabolic PDEs arising in mathematical biology and statistical mechanics * Describes the whole picture, i.e., the mathematical and physical principles * Suitable for researchers and grad students in mathematics and applied mathematics who are interested in nonlinear PDEs in stochastic processes, cellular automatons, variational methods, and their applications to physics, chemistry, biology, and engineering
Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model
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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2015-11-19
Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-19 with Mathematics categories.
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Chemotaxis Reaction Network Mathematics For Self Organization
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Author : Takashi Suzuki
language : en
Publisher: World Scientific
Release Date : 2018-07-27
Chemotaxis Reaction Network Mathematics For Self Organization written by Takashi Suzuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-27 with Science categories.
This monograph is devoted to recent mathematical theories on the bottom up self-organization observed in closed and isolated thermo-dynamical systems. Its main features include:
Vortex Dynamics
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Author : İlkay Bakırtaş
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-09-28
Vortex Dynamics written by İlkay Bakırtaş and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-28 with Science categories.
This book discusses vortex dynamics theory from physics, mathematics, and engineering perspectives. It includes nine chapters that cover a variety of research results related to vortex dynamics including nonlinear optics, fluid dynamics, and plasma physics.
Singularities Of Solutions To Chemotaxis Systems
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Author : Piotr Biler
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-12-02
Singularities Of Solutions To Chemotaxis Systems written by Piotr Biler and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-02 with Mathematics categories.
The Keller-Segel model for chemotaxis is a prototype of nonlocal systems describing concentration phenomena in physics and biology. While the two-dimensional theory is by now quite complete, the questions of global-in-time solvability and blowup characterization are largely open in higher dimensions. In this book, global-in-time solutions are constructed under (nearly) optimal assumptions on initial data and rigorous blowup criteria are derived.
Mean Field Theories And Dual Variation
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Author : Takashi Suzuki
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-01
Mean Field Theories And Dual Variation written by Takashi Suzuki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-01 with Mathematics categories.
A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.
Mathematical Methods For Cancer Evolution
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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2017-06-13
Mathematical Methods For Cancer Evolution written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-13 with Mathematics categories.
The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.
Soft Matter Self Assembly
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Author : C.N. Likos
language : en
Publisher: IOS Press
Release Date : 2016-07-14
Soft Matter Self Assembly written by C.N. Likos and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-14 with Science categories.
Self-assembly is one of the key concepts in contemporary soft condensed matter. It is an umbrella term which encompasses the various modes of spontaneous organization of micrometer-and submicrometer-sized particles into ordered structures of various degrees of complexity, yet it often relies on remarkably simple interactions and mechanisms. Self-assembly is one of the key principles used by nature to construct living matter, where it frequently takes place in a hierarchical fashion. This book contains the lectures from the Enrico Fermi summer school: Soft Matter Self-assembly, held in Varenna, Italy, in June and July 2015. The primary aim of the school was to cover the most exciting modern aspects of self-assembly in soft condensed matter physics, and to enable Ph.D. students and postdocs to engage with some of the most exciting and current topics in the physics of colloids through a series of mini-courses and seminars hosted by leading figures in the field. Subjects covered include: colloids with directional bonding; pathways of self-organization; self-assembly hydrodynamics; polymer structure and dynamics; liquid-crystal colloid dispersions; and self-organizing nanosystems. The proceedings also include two reprints from Reviews of Modern Physics, and will be of interest to both students and experts in the field.
Free Energy Calculations
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Author : Christophe Chipot
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-15
Free Energy Calculations written by Christophe Chipot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-15 with Science categories.
This volume offers a coherent account of the concepts that underlie different approaches devised for the determination of free energies. It provides insight into the theoretical and computational foundations of the subject and presents relevant applications from molecular-level modeling and simulations of chemical and biological systems. The book is aimed at a broad readership of graduate students and researchers.
Computational Biochemistry And Biophysics
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Author : Oren M. Becker
language : en
Publisher: CRC Press
Release Date : 2001-02-09
Computational Biochemistry And Biophysics written by Oren M. Becker and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-09 with Science categories.
Covering theoretical methods and computational techniques in biomolecular research, this book focuses on approaches for the treatment of macromolecules, including proteins, nucleic acids, and bilayer membranes. It uses concepts in free energy calculations, conformational analysis, reaction rates, and transition pathways to calculate and interpret biomolecular properties gleaned from computer-generated membrane simulations. It also demonstrates comparative protein structure modeling, outlines computer-aided drug design, discusses Bayesian statistics in molecular and structural biology, and examines the RISM-SCF/MCSCF approach to chemical processes in solution.