Friday, July 3, 2009
my master,, \(^0^)/
hye everyone,,diz is my 1st post,,ooppsss actually 2nd..hihihih next week i will start my 1st class for my master,,n i have decided to take applied mathematic,,i dont noe whether it is easy or not,,but from the name i think its quite tough,,huuhhu,, and now i guess i have started doing on my thesis because my lecturer email me diz evening and gave me an example of journal to guide me for my thesis,,so i will confirm with my lecturer about it diz monday,,(tp tkut la nk jmpe die),,hihihihi For my thesis, im doing about chaos,,and i dont really noe about it and im still studying it,,so i cant explain to all of u,,hihiih,, so later after i master about chaos i will tell u all k,, hurm i tried to upload my graft about chaos but it doesnt work,, sbb format die laen,,huhuh so xley la nk tjuk kt korng,, pas 2 every week i have progress report,,kne present depan my lecturer and his phd student,,(terkontang kanting aku awal2),,kne report la pe yg kte dpt dlm week 2,,huhuuh,, and every day bace journal,,ngantokss nak2 lagi pagi2 dtg office pas 2 bace,, almost every morning aku tertdo dlm blik 2,,hikhikhik,,ok la 2 je nak cite,,nanti si janet bising tnye ble aku nk post dlm blog nih,,gems pon same,,hahhaha
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Chaos theory is an area of inquiry in mathematics, physics, and philosophy which studies the behavior of certain dynamical systems that are highly sensitive to initial conditions. This sensitivity is popularly referred to as the butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.[1] This happens even though these systems are deterministic, meaning that their future dynamics are fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos.
Chaotic behavior can be observed in many natural systems, such as the weather.[2] Explanation of such behavior may be sought through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots.
In common usage, "chaos" means "in a state of disorder",[3] but the adjective "chaotic" is defined more precisely in chaos theory. Although there is no universally accepted mathematical definition of chaos, a commonly-used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[4]
it must be sensitive to initial conditions,
it must be topologically mixing, and
its periodic orbits must be dense.
Sensitivity to initial conditions means that each point in such a system is arbitrarily closely approximated by other points with significantly different future trajectories. Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behaviour. However, it has been shown that the last two properties in fact imply sensitivity to initial conditions[5][6] (an alternative, weaker, definition of chaos uses only the first two properties in the above list[7]).
Sensitivity to initial conditions is popularly known as the "butterfly effect," so called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C. entitled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas? The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the system might have been vastly different.
*** there is a movie,Chaos acted by Jason Statham and Ryan Philippe
the easiest way to get more journal, article, etc, go to UKM WEB, PTSL, subscribe the springer-verlag and other journals for free. But, only in UKM, no other places....If u still blur, someone who has gone through this particular process of becoming an academician will offer his favor.chill........
From Encyclopedia of Britannica...
in mechanics and mathematics, apparently random or unpredictable behaviour in systems governed by deterministic laws. A more accurate term, “deterministic chaos,” suggests a paradox because it connects two notions that are familiar and commonly regarded as incompatible. The first is that of randomness or unpredictability, as in the trajectory of a molecule in a gas or in the voting choice of a particular individual from out of a population. In conventional analyses, randomness was considered more apparent than real, arising from ignorance of the many causes at work. In other words, it was commonly believed that the world is unpredictable because it is complicated. The second notion is that of deterministic motion, as that of a pendulum or a planet, which has been accepted since the time of Isaac Newton as exemplifying the success of science in rendering predictable that which is initially complex.
In recent decades, however, a diversity of systems have been studied that behave unpredictably despite their seeming simplicity and the fact that the forces involved are governed by well-understood physical laws. The common element in these systems is a very high degree of sensitivity to initial conditions and to the way in which they are set in motion. For example, the meteorologist Edward Lorenz discovered that a simple model of heat convection possesses intrinsic unpredictability, a circumstance he called the “butterfly effect,” suggesting that the mere flapping of a butterfly's wing can change the weather. A more homely example is the pinball machine: the ball's movements are precisely governed by laws of gravitational rolling and elastic collisions—both fully understood—yet the final outcome is unpredictable.
In classical mechanics the behaviour of a dynamical system can be described geometrically as motion on an “attractor.” The mathematics of classical mechanics effectively recognized three types of attractor: single points (characterizing steady states), closed loops (periodic cycles), and tori (combinations of several cycles). In the 1960s a new class of “strange attractors” was discovered by the American mathematician Stephen Smale. On strange attractors the dynamics is chaotic. Later it was recognized that strange attractors have detailed structure on all scales of magnification; a direct result of this recognition was the development of the concept of the fractal (q.v.; a class of complex geometric shapes that commonly exhibit the property of self-similarity), which led in turn to remarkable developments in computer graphics.
Applications of the mathematics of chaos are highly diverse, including the study of turbulent flow of fluids, irregularities in heartbeat, population dynamics, chemical reactions, plasma physics, and the motion of groups and clusters of stars.
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