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The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to ...
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state. The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz.
More precisely, this example works to explain a kind of math called chaos theory, which looks at how small changes made to a system’s initial conditions—like the extra gust of wind from a ...
Magnetic billiards represent billiards where a charged particle is propagating under the presence of a perpendicular magnetic field. As a result, the particle trajectory changes from a straight line into an arc of a circle. The radius of this circle is inversely proportional to the magnetic field strength.
A double pendulum consists of two pendulums attached end to end.. In physics and mathematics, in the area of dynamical systems, a double pendulum, also known as a chaotic pendulum, is a pendulum with another pendulum attached to its end, forming a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions. [1]
The magnetic field =, where the magnetic vector potential, can be taken into account by using Peierls substitution, replacing the crystal momentum with the canonical momentum , where = (,) is the particle momentum operator and is the charge of the particle (= for the electron, is the elementary charge).
Experimental control of chaos by one or both of these methods has been achieved in a variety of systems, including turbulent fluids, oscillating chemical reactions, magneto-mechanical oscillators and cardiac tissues. [6] attempt the control of chaotic bubbling with the OGY method and using electrostatic potential as the primary control variable.
[23] [24] Visual patterns in nature find explanations in chaos theory, fractals, logarithmic spirals, topology and other mathematical patterns. For example, L-systems form convincing models of different patterns of tree growth. [19] The laws of physics apply the abstractions of mathematics to the real world, often as if it were perfect.