Singularities of Transition Processes in Dynamical Systems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Singularities of Transition Processes in Dynamical Systems PDF full book. Access full book title Singularities of Transition Processes in Dynamical Systems by Alexander N. Gorban. Download full books in PDF and EPUB format.
Author: Alexander N. Gorban Publisher: ISBN: Category : Languages : en Pages : 52
Book Description
The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters of the system and accuracy of relaxation. This system of times contains: the time before the first entering of the motion into -neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the -neighbourhood of the limit set. The singularities of relaxation times as functions of (, ) under fixed are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.
Author: Alexander N. Gorban Publisher: ISBN: Category : Languages : en Pages : 52
Book Description
The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters of the system and accuracy of relaxation. This system of times contains: the time before the first entering of the motion into -neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the -neighbourhood of the limit set. The singularities of relaxation times as functions of (, ) under fixed are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.
Author: S.N. Pnevmatikos Publisher: Elsevier ISBN: 008087214X Category : Mathematics Languages : en Pages : 467
Book Description
This volume is an account of the lectures delivered at the international Conference ``Singularities and Dynamical Systems-83''. The main purpose of the Conference was to create conditions of scientific contact between mathematicians and physicists who have singularities and dynamical systems as common interests.
Author: Alexander N. Gorban Publisher: Springer Science & Business Media ISBN: 3540358889 Category : Science Languages : en Pages : 554
Book Description
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. All contributions are by experts whose specialities span a wide range of fields within science and engineering.
Author: Emil Simiu Publisher: Princeton University Press ISBN: 9780691050942 Category : Mathematics Languages : en Pages : 244
Book Description
This text develops a unified treatment of deterministic and stochastic systems that extends the Melnikov method to physically realisable stochastic planar systems.
Author: Tian Ma Publisher: Springer Science & Business Media ISBN: 1461489636 Category : Mathematics Languages : en Pages : 575
Book Description
This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields.
Author: V.I. Arnol'd Publisher: Springer Science & Business Media ISBN: 3662067986 Category : Mathematics Languages : en Pages : 241
Book Description
This book is devoted to applications of singularity theory in mathematics and physics, covering a broad spectrum of topics and problems. "The book contains a huge amount of information from all the branches of Singularity Theory, presented in a very attractive way, with lots of inspiring pictures." --ZENTRALBLATT MATH
Author: Yuriy M. Bunkov Publisher: Springer Science & Business Media ISBN: 9401141061 Category : Science Languages : en Pages : 388
Book Description
Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.
Author: Stanley Alama Publisher: American Mathematical Soc. ISBN: 9780821873311 Category : Mathematics Languages : en Pages : 284
Book Description
This book contains papers presented at the "Workshop on Singularities in PDE and the Calculus of Variations" at the CRM in July 2006. The main theme of the meeting was the formation of geometrical singularities in PDE problems with a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and their resolution often requires a combination of methods coming from areas such as functional and harmonic analysis, differential geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions and domain walls; vortices in Ginzburg-Landau type models for superconductivity and superfluidity; the Ohna-Kawasaki model for di-block copolymers; models of image enhancement; and Monge-Ampere functions. The articles give a sampling of problems and methods in this diverse area of mathematics, which touches a large part of modern mathematics and its applications.
Author: Wolfgang Götze Publisher: Oxford University Press on Demand ISBN: 0199235341 Category : Science Languages : en Pages : 654
Book Description
Amorphous condensed matter can exhibit complex motions on time scales which extend up to those relevant for the functioning of biomaterials. The book presents the derivation of a microscopic theory for amorphous matter, which exhibits the evolution of such complex motions as a new paradigm of strongly interacting particle systems.e
Author: Alexander N. Gorban
Author: Alexander N. Gorban
Author: Aleksandr Nikolaevich Gorbanʹ
Author: S.N. Pnevmatikos
Author: Alexander N. Gorban
Author: Emil Simiu
Author: Tian Ma
Author: V.I. Arnol'd
Author: Yuriy M. Bunkov
Author: Stanley Alama
Author: Wolfgang Götze