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Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor.Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards ...
Folded-towel map attractor. A hyperchaotic system is a dynamical system with a bounded attractor set, on which there are at least two positive Lyapunov exponents. [1]Since on an attractor, the sum of Lyapunov exponents is non-positive, there must be at least one negative Lyapunov exponent.
Chaos theory has been used for many years in cryptography. In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. These algorithms include image encryption algorithms, hash functions, secure pseudo-random number generators, stream ciphers, watermarking, and steganography. [119]
This state, Olam haTohu was read by Luria in Genesis 1:2 "And the earth was tohu wa-bohu (Chaos and Void), with darkness over the surface of the deep.", like discreet, sequential concentric circles. They become a domain of pluralism rather than of unity. The world of chaos has very high level of light but weak vessels.
Quantum chaos is the field of physics attempting to bridge the theories of quantum mechanics and classical mechanics. The figure shows the main ideas running in each direction. Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory.
Chien-Shiung Wu, after whom the Wu experiment is named, designed the experiment and led the team that carried out the test of the conservation of parity in 1956.. The Wu experiment was a particle and nuclear physics experiment conducted in 1956 by the Chinese American physicist Chien-Shiung Wu in collaboration with the Low Temperature Group of the US National Bureau of Standards. [1]
A semipopular account of the universal scaling theory for the period doubling route to chaos is presented. "Feigenbaum, Mitchell J." Publications. Astrophysics Data System. Feigenbaum, Mitchell J. (1 July 1978). "Quantitative universality for a class of nonlinear transformations". Journal of Statistical Physics. 19 (1): 25– 52.
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.