Taylor Expansions and Catastrophes
Author : T. Poston
Publisher : Pitman Publishing
Page : 182 pages
File Size : 35,43 MB
Release : 1976
Category : Mathematics
ISBN :
Author : T. Poston
Publisher : Pitman Publishing
Page : 182 pages
File Size : 35,43 MB
Release : 1976
Category : Mathematics
ISBN :
Author : Peter Timothy Saunders
Publisher : Cambridge University Press
Page : 162 pages
File Size : 44,24 MB
Release : 1980-06-30
Category : Mathematics
ISBN : 9780521297820
An introduction to catastrophe theory, a mathematical theory which deals with those changes which occur abruptly rather than smoothly. Includes many applications to illustrate the different ways in which catastrophe can be used in life, physical and social sciences.
Author : Tim Poston
Publisher : Courier Corporation
Page : 514 pages
File Size : 10,92 MB
Release : 2014-05-05
Category : Mathematics
ISBN : 0486143783
First integrated treatment of main ideas behind René Thom's theory of catastrophes stresses detailed applications in the physical sciences. Mathematics of theory explained with a minimum of technicalities. Over 200 illustrations clarify text designed for researchers and postgraduate students in engineering, mathematics, physics and biology. 1978 edition. Bibliography.
Author : A. Okninski
Publisher : Elsevier
Page : 303 pages
File Size : 49,3 MB
Release : 1992-06-12
Category : Science
ISBN : 0080868274
This book aims to provide a straightforward introduction to chemical applications of the catastrophe theory. It is primarily intended for chemists interested in placing chemical reactions in the broader context of non-linear science, but it has a practical relevance for scientists in general. Catastrophe theory deals with those non-linear phenomena in which a continuous change in the control parameters results in a discontinuous alteration of a characteristic quantity of the system. The author discusses the origins of catastrophe theory, giving examples of occurrences in the areas of physics, chemistry and biology. Elementary theory and non-chemical applications are also described. The chemical kinetics and methods of analysis of chemical kinetic equations arising from elementary and generalized catastrophe theories are reviewed. Finally, the theory is applied to analyse and classify phenomena associated with the stability loss that may occur in chemical reactions. The book contains over 100 figures and an extensive subject index.
Author : Michel Demazure
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 41,3 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3642571344
Based on a lecture course, this text gives a rigorous introduction to nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach allowing a clear focus on the essential mathematical structures. It brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.
Author : Robert Gilmore
Publisher : Courier Corporation
Page : 696 pages
File Size : 47,79 MB
Release : 1993-01-01
Category : Technology & Engineering
ISBN : 9780486675398
This advanced-level treatment describes the mathematics of catastrophe theory and its applications to problems in mathematics, physics, chemistry and engineering. 28 tables. 397 black-and-white illustrations. 1981 edition.
Author : Domencio Castrigiano
Publisher : CRC Press
Page : 281 pages
File Size : 31,42 MB
Release : 2019-06-03
Category : Mathematics
ISBN : 0429970358
Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to
Author : Yilong Bai
Publisher : Springer Nature
Page : 497 pages
File Size : 49,88 MB
Release : 2019-09-03
Category : Technology & Engineering
ISBN : 9813291923
This book introduces a trans-scale framework necessary for the physical understanding of breakdown behaviors and presents some new paradigm to clarify the mechanisms underlying the trans-scale processes. The book, which is based on the interaction of mechanics and statistical physics, will help to deepen the understanding of how microdamage induces disaster and benefit the forecasting of the occurrence of catastrophic rupture. It offers notes and problems in each part as interesting background and illustrative exercises. Readers of the book would be graduate students, researchers, engineers working on civil, mechanical and geo-engineering, etc. However, people with various background but interested in disaster reduction and forecasting, like applied physics, geophysics, seismology, etc., may also be interested in the book.
Author : Bart M. Haar Romeny
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 20,52 MB
Release : 2008-10-24
Category : Computers
ISBN : 140208840X
Many approaches have been proposed to solve the problem of finding the optic flow field of an image sequence. Three major classes of optic flow computation techniques can discriminated (see for a good overview Beauchemin and Barron IBeauchemin19951): gradient based (or differential) methods; phase based (or frequency domain) methods; correlation based (or area) methods; feature point (or sparse data) tracking methods; In this chapter we compute the optic flow as a dense optic flow field with a multi scale differential method. The method, originally proposed by Florack and Nielsen [Florack1998a] is known as the Multiscale Optic Flow Constrain Equation (MOFCE). This is a scale space version of the well known computer vision implementation of the optic flow constraint equation, as originally proposed by Horn and Schunck [Horn1981]. This scale space variation, as usual, consists of the introduction of the aperture of the observation in the process. The application to stereo has been described by Maas et al. [Maas 1995a, Maas 1996a]. Of course, difficulties arise when structure emerges or disappears, such as with occlusion, cloud formation etc. Then knowledge is needed about the processes and objects involved. In this chapter we focus on the scale space approach to the local measurement of optic flow, as we may expect the visual front end to do. 17. 2 Motion detection with pairs of receptive fields As a biologically motivated start, we begin with discussing some neurophysiological findings in the visual system with respect to motion detection.
Author : J. Barkley Rosser
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 37,45 MB
Release : 2013-03-14
Category : Business & Economics
ISBN : 9401716137
From Catastrophe to Chaos: A General Theory of Economic Discontinuities presents and unusual perspective on economics and economic analysis. Current economic theory largely depends upon assuming that the world is fundamentally continuous. However, an increasing amount of economic research has been done using approaches that allow for discontinuities such as catastrophe theory, chaos theory, synergetics, and fractal geometry. The spread of such approaches across a variety of disciplines of thought has constituted a virtual intellectual revolution in recent years. This book reviews the applications of these approaches in various subdisciplines of economics and draws upon past economic thinkers to develop an integrated view of economics as a whole from the perspective of inherent discontinuity.