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Example research essay topic: Chaos Theory Quantum Physics - 1,175 words

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... lly named the discipline Chaos Theory. Another word that is vital to understanding the Complexity theory is complex. What makes us determine which system is more complex then another? There are many discussions of this question. In Exploring Complexity, Nobel Laureate Ilya Prigogine explains that the complexity of the system is defined by the complexity of the model necessary to effectively predict the behavior of the system.

The more the model must look like the actual system to predict system results, the more complex the system is considered to be. The most complex system example is the weather, which, as demonstrated by Edward Lorenz, can only be effectively modeled with an exact duplicate of itself. One example of a simple system to model is to calculate the time it takes for a train to go from city A to city B if it travels at a given speed. To predict the time we need only to know the speed that the train is traveling (in mph) and the distance (in miles). The simple formula would be mph / m , which is a simple system. But the pile of stones, which appears to be a simple system, is actually very complex.

If we want to predict which stone will end up at which place in the pile then you would have to know very detailed information about the stones, including their weights, shapes, and starting location of each stone to make an accurate prediction. If there is a minor difference between the shape of one stone in the model and the shape of the original stone, the modeled results will be very different. The system is very complex, thus making prediction very difficult... The generator of unpredictability in complex systems is what Lorenz calls "sensitivity to initial conditions" or "the butterfly effect. " The concept means that with a complex, nonlinear system, a tiny difference in starting position can lead to greatly varied results. For example, in a difficult pool shot a tiny error in aim causes a slight change in the balls path. However, with each ball it collides with, the ball strays farther and farther from the intended path.

Lorenz once said that "if a butterfly is flapping its wings in Argentina and we cannot take that action into account in our weather prediction, then we will fail to predict a thunderstorm over our home town two weeks from now because of this dynamic. " (Lorenz, 1987) The general rule for complex systems is that one cannot create a model that will accurately predict outcomes but one can create models that simulate the processes that the system will go through to create the models. This realization is impacting many activities in business and other industries. For instance, it raises considerable questions relating to the real value of creating organizational visions and mission statements as currently practices. Like physics, the Chaos theory provides a foundation for the study of all other scientific disciplines.

It is a variety of methods for incorporating nonlinear dynamics into the study of science. Attempts to change the discipline and make it a separate form of science have been strongly resisted. The work represents a reunification of the sciences for many in the scientific community. One of Lorenz's best accomplishments supporting the Chaos Theory was the Lorenz Attractor. The Lorenz Attractor is based on three differential equations, three constants, and three initial conditions. The attractor represents the behavior of gas at any given time, and its condition at any given time depends upon its condition at a previous time.

If the initial conditions are changed by even a tiny amount, checking the attractor at a later time will show numbers totally different. This is because small differences will reproduce themselves recursively until numbers are entirely unlike the original system with the original initial conditions. But, the plot of the attractor, or the overall behavior of the system will be the same. A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had any secret for us, we could still know the situation approximately.

If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon has been predicted, that it is governed by the laws. But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible... " (Poincare, 1973) The Complexity theory has developed from mathematics, biology, and chemistry, but mostly from physics and particularly thermodynamics, the study of turbulence leading to the understanding of self-organizing systems and system states (equilibrium, near equilibrium, the edge of chaos, and chaos). "The concept of entropy is actually the physicists application of the concept of evolution to physical systems. The greater the entropy of a system, the more highly evolved is the system. " (Prigogine, 1974) The Complexity theory is also having a major impact on quantum physics and attempts to reconcile the chaos of quantum physics with the predictability of Newton's universe. With complexity theory, the distinctions between the different disciplines of sciences are disappearing.

For example, fractal research is now used for biological studies. But there is a question as to whether the current research and academic funding will support this move to interdisciplinary research. Complexity is already affecting many aspects of our lives and has a great impacts on all sciences. It is answering previously unsolvable problems in cosmology and quantum mechanics. The understanding of heart arrhythmias and brain functioning has been revolutionized by complexity research. There have been a number of other things developed from complexity research, such a the Sim Life, Sim Ant, etc.

which are a series of computer programs. Fractal mathematics are critical to improved information compression and encryption schemes needed for computer networking and telecommunications. Genetic algorithms are being applied to economic research and stock predictions. Engineering applications range from factory scheduling to product design, with pioneering work being done at places like DuPont and Deere & Co. Another element of the nonlinear dynamics, Fractals, have appeared everywhere, most recently in graphic applications like the successful Fractal Design Painter series of products.

Fractal image compression techniques are still being researched, but promise such amazing results as 600: 1 graphic compression ratios. The movie special effects industry would have much less realistic clouds, rocks, and shadows without fractal graphic technology. Though it is one of the youngest sciences, the Chaos Theory holds great promise in the fields of meteorology, physics, mathematics, and just about anything else you can think of.


Free research essays on topics related to: quantum physics, initial conditions, complexity, complex systems, chaos theory

Research essay sample on Chaos Theory Quantum Physics

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