 |
|
|
|
|
|
 |
 |
Neues aus der Welt der Wissenschaft |
|
|
|
|
|
|
Chaostheorie: Kleine Ursache, große Wirkung |
|
| | | Völlig unwichtig und harmlos wirkende Ereignisse können dennoch große Wirkung zeigen - so in etwa lautet eine Folgerung der Chaostheorie. Im Rahmen des Europäischen Forums Alpbach untersucht der Mathematiker Shankar Venkataramani das Auftreten solcher chaotischer Ereignisse in der Natur. In einem Gastbeitrag für science.ORF.at stellt der Wissenschaftler unter anderem Systeme vor, in denen sich dieses Verhalten beobachten lässt - und gibt einen Ausblick auf die Themenaspekte seines Alpbach-Seminars. |
|
|
|
|
|
|
Chaos |
|
| |
Von Shankar Venkataramani
What is Chaos? And more importantly, why should one care? These questions are at the heart of this seminar. The goal of the seminar is to explain what chaos is, and how the study of chaos may help reveal order and simplicity underlying many irregularities found in nature.
|
|
|
|
|
|
Continuity and Chaos |
|
| |
It is our intuition (a principle of "continuity"), that small actions should produce small results. It thus seems logical to believe that simple rules and actions should produce simple consequences. Conversely, one might also believe that, to have complex behavior in a system, one needs complex rules.
But we now know that even very simple rules can lead to very complex behavior. Also, this complexity is not something rare or exceptional. Rather, it is robust and it is all around us. This is called Chaos.
|
|
Seminar beim Europäischen Forum in Alpbach
Die Seminarwoche während des Europäischen Forums in Alpbach ("Continuity and Discontinuity", 14. August bis 30. August 2003) bildet alljährlich die Möglichkeit des intensiven Austausches und der Diskussion von Themen mit Wissenschaftlern aus unterschiedlichen Fachrichtungen. Shankar Venkataramani hält dabei ein Seminar ab mit dem Titel "Chaos and catastrophies: Modeling the unexpected". science.ORF.at stellt dieses und weitere Seminare in Form von Gastbeiträgen vor. |
|
|
 Mehr über das Europäische Forum Alpbach 2003 |
|
|
|
|
|
|
Where does one see Chaos? |
|
| |
Examples of systems that exhibit such complex, chaotic behavior, include weather patterns, the turbulent flow of liquids (like cream added to a cup of coffee), fluctuations in the stock market, water dripping from a faucet, irregular heartbeats, etc. It is therefore of great importance to understand, control and if possible, use such complex behavior.
Chaos is thus at the forefront of current research in many disciplines, including chemistry, physics, meteorology, biology, economics and mathematics.
|
|
|
|
|
|
What is the Butterfly effect? |
|
| |
Using a minimum of advanced mathematics and technical jargon, we will look the physics of chaos and its exotic-sounding companions, fractals and strange attractors. We will talk about the signatures of Chaos, in particular, the "butterfly effect", which means that a chaotic system is very sensitive to small changes, and tiny actions can create extraordinarily large results.
In addition to its obvious importance for practical issues, the butterfly effect has philosophical implications for our understanding of predictability, and the principle of scientific determinism.
|
|
|
|
|
|
From order to Chaos (to order?) |
|
| |
We will analyze the way in which a system that is regular (not chaotic) becomes chaotic. We will discover the basic mechanisms leading to chaos. And we discover the surprising notion of "Universality", that is the same kind of order actually underlies a wide variety of chaotic systems.
|
|
|
|
|
|
Coping with Chaos |
|
| |
We will talk about various real world systems that display chaos or its consequences. We will ask whether the Solar system is stable. About what causes the rings of Saturn? Can one control the weather? Is Chaos good for anything? Is there Chaos in the human body? Can one control Chaos?
|
|
|
|
|
|
Space, time and Complexity |
|
| |
The chaos that we have been discussing thus far is a feature of what are called "finite dimensional" systems. Many real world systems are actually "Infinite dimensional", and can thus have additional kinds of complexity.
We will conclude our discussion of Chaos, continuity and complexity by talking about a few infinite dimensional systems - Turbulence in fluid flows, Structure and pattern formation, Singularities for example in black hole formation, and finally collective behavior in networks.
|
|
| |
Über den Autor: Shankar C. Venkataramani
Shankar C. Venkataramani, 1971 in Indien geboren, B.Tech 1992 am Indian Institute of Technology in Madras, M.S. 1995 an der University of Maryland, Ph.D. 1996 an der University of Maryland (Dissertation: "Random walks in chaotic dynamics"), seit 1998 als Assistant Professor am Department of Mathematics der University of Chicago. Einige Schwerpunkte seiner Forschungstätigkeit: Collective behavior in Nonlinear systems with many degrees of freedom: Structure formation and Pattern formation, Singularities in solutions of Partial Differential Equations, Dynamical systems with Invariant Manifolds. |
|
|
Venkataramanis Homepage an der University of Chicago |
|
|
|
|
|
|
|
|
| |
Weitere Beiträge zum Forum Alpbach 2003 in science.ORF.at:
|
|
|
01.01.2010 |
