Gunter Faust

Die Erforschung des Chaos

17. Febr. 2011 Schon vor 16 Jahren erschien die erste Auflage von „Die Erforschung des Chaos“. Nachdem John Argyris 2004 im hohen Alter von 91 Jahren Die Erforschung des Chaos. Studienbuch für Naturwissenschaftler und Ingenieure. 1995. Vieweg+Teubner 790 S., 254 SW-Abb., 86 Farbabb., 24 Tabellen, 170 Seit Ihrem Aufkommen wurde die Chaosforschung als eine von wenigen mathematisch-physikalischen Gebieten von der Öffentlichkeit mit großem Interesse Die Erforschung des Chaos: Dynamische Systeme John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich ISBN: 9783662545454 Kostenloser Versand

Finite element analysis of four different implants inserted in different positions to stabilize an idealized trochanteric femoral fracture

Biomechanical analysis of the ideal placement of new intramedullary implants for stabilization of trochanteric fractures is not currently available. The aim of the presented study is to determine to what extent four intermedullary nails (Gliding-Nail, Gamma-Nail, PFN-A and Targon-PF), inserted in different positions, differ mechanically. A proximal femur was reconstructed on the basis of clinical CT data as a surface model. Load application equivalent to the one-leg stance phase during gait was assumed, taking into account a limited number of active muscle forces. The four implants were inserted cranially and caudally into the bone structure and a model of a trochanteric fracture was created. Criteria with point ratings were introduced to quantify a favourable fracture healing situation. Finite element simulation showed clear differences between the different implants with regard to the distributions of stress and strain at the two fracture surfaces in the model and the von Mises stress in the implant itself. It was apparent for three implants under investigation that the caudal position generated better fracture healing conditions than the cranial position. Only the Targon PF demonstrated better fracture healing conditions in the cranial position. Evaluation based on the point rating system revealed that the caudal position was the ideal position for the PFN-A, Gamma-Nail and Gliding-Nail. The Targon-PF demonstrated some advantages over the other implants in the caudal position.

Limit load analysis of thick-walled concrete structures - a finite element approach to fracture

Abstract The paper illustrates the interaction of constitutive modelling and finite element solution techniques for limit load prediction of concrete structures. On the constitutive side, an engineering model of concrete fracture is developed in which the Mohr-Coulomb criterion is augmented by tension cut-off to describe incipient failure. Upon intersection with the stress path the failure surface collapses for brittle behaviour according to one of three softening rules — no-tension, no-cohesion, and no-friction. The stress transfer accompanying the energy dissipation during local failure is modeled by several fracture rules which are examined with regard to ultimate load prediction. On the numerical side the effect of finite element idealization is studied first as far as ultimate load convergence is concerned. Subsequently, incremental tangential and initial load techniques are compared together with the effect of step size. Limit load analyses of a thick-walled concrete ring and a lined concrete reactor closure conclude the paper along with engineering examples.

An Exploration of Dynamical Systems and Chaos

Descriptive synopsis of the text.- Mathematical introduction to dynamical systems.- Dynamical systems without dissipation.- Dynamical systems with dissipation.- Local bifurcation theory.- Convective flow: Benard problem.- Routes to chaos.- Turbulence.- Computer experiments.

Routes to chaos and turbulence. A computational introduction

We propose to survey in this paper different routes to chaos arising in nonlinear dynamic systems emphasizing where appropriate the connection with the intriguing phenomenon of turbulence in a viscous fluid. The onset of turbulence displays, in particular, clear chaotic characteristics. On the other hand, fully developed turbulence cannot be analysed presently by chaos theory as it stands and demands an expansion of the basic theory to incorporate spatial dependencies. Here we shall refer only to the onset of turbulence. Our approach is essentially a computational exploration and illustration.

Xάoς An adventure in chaos

Abstract The conception of this paper has its origin in the plenar lecture on chaos delivered by the senior author at the WCCM II in Stuttgart, 1990. Our aim is to reproduce the spirit but not the detailed structure of the lecture. A verbatim reproduction of an oral presentation, however successful — or otherwise —it may have been, does not automatically entail a convincing printed document. A discourse does not ensure an informative scientific text — the contrary is probably true. Conscious of these difficulties, we decided to compose a paper that — whilst not too far removed from the original presentation — should also include scholarly contributions that one expects to find and peruse in the printed word. It has to be admitted that the set task caused us considerable teasers and occasional dilemmas. Should these prove to have been unjustified, thanks should be extended by readers and authors alike to Prudence Lawday-Gienger and Karl Straub who supported the authors with uncanny skill and critical linguistic and scientific mastery from the inception of the paper to the completion of the ultimate text.

Wege zum Chaos

Im folgenden wollen wir eine Reihe von mathematischen Modellen vorstellen, die zu zeitlich chaotischem Verhalten fuhren. Wir werden dabei verschiedene Moglichkeiten kennenlernen, wie regulare Dynamik in chaotische ubergehen kann. Das Uberraschende dabei ist, das es gar nicht so sehr auf die Form des Bewegungsgesetzes im einzelnen ankommt, sondern das die einzelnen Wege ins Chaos universellen Charakter haben.

Local Bifurcation Theory

Variations in the control parameters of dynamical systems generate completely new long-term patterns of motion. The Duffing equation (2.2.8) previously mentioned (see also Colour Plates XXVII, XXV, pp. 761, 751 and section 10.5) illustrates how small changes in the frequency or amplitude of the driving force as well as in the damping can cause qualitative changes in the physical behaviour. The investigation of bifurcations in the field of natural and engineering sciences is of great importance because each bifurcation is accompanied by a split into new states of equilibrium and drastic qualitative changes in the motion. Bifurcations can have destructive effects, if, for example, they trigger the dangerous aeroelastic fluttering of wings in aircraft. However, they may also be desirable, as in the case of Rayleigh-B’enard convection (see Chapter 7), where they contribute to the improvement of the heat and mass transport.

Descriptive Synopsis of the Text

This book is conceived as an elementary introduction to the modern theory of nonlinear dynamical systems with particular emphasis on the exploration of chaotic phenomena. One might ask why yet another book should be published when the literature on chaos and non-linear oscillations already fills shelf after shelf following the stormy developments in this branch of science since the 1970s. The reasons which prompted us have been detailed in the preface.

Mathematical Introduction to Dynamical Systems

In this chapter, we present in the simplest possible manner a survey of some of the fundamental mathematical concepts and tools which are required for the qualitative analysis of the long-term behaviour of dynamical systems. A knowledge of the theory of linear differential equations is a pre-requisite for the comprehension of non-linear dynamics. The reader can find more detailed discussions in Chapters 5 and 6 of this book.