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Chirikov Criterion
The Chirikov criterion or Chirikov resonance-overlap criterion was established by the Russian physicist Boris Chirikov. Back in 1959, he published a seminal article, 1 . Here is the perturbation parameter, while is the resonance-overlap parameter, given by the ratio of the unperturbed resonance width in frequency (often computed in the pendulum approximation and proportional to the square-root of perturbation), and the frequency difference between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border. See also Chirikov criterion at ScholarpediaChirikov standard mapand standard map The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side 2\pi onto itself. It is constructed by a Poincaré's surface of section of the kicked rota ... * Boris Chirikov anBoris Chirikov at Scholar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boris Chirikov
Boris Valerianovich Chirikov (russian: Борис Валерианович Чириков; 6 June 1928 – 12 February 2008) was a Soviet and Russian physicist. He was the founder of the physical theory of Hamiltonian chaos and made pioneering contributions to the theory of quantum chaos. In 1959, he invented the Chirikov criterion which gives an analytical estimate for the overlap of resonances and provides the conditions for transition from integrability to global chaos in Hamiltonian dynamical systems. Life and physics Boris Chirikov was born in the city Oryol, Russia, USSR. Graduated from the Moscow Institute of Physics and Technology in 1952, he worked with Budker at the Kurchatov Institute and moved with him to Siberia in September 1959 to work at the Institute founded by Budker in Akademgorodok, Novosibirsk (now Budker Institute of Nuclear Physics). He became a corresponding member of the Russian Academy of Sciences in 1983, and a full member in 1992. He worked at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kurchatov Institute
The Kurchatov Institute (russian: Национальный исследовательский центр «Курчатовский Институт», 'National Research Centre "Kurchatov Institute) is Russia's leading research and development institution in the field of nuclear energy. It is named after Igor Kurchatov and is located at 1 Kurchatov Square, Moscow. In the Soviet Union it was known as I. V. Kurchatov Institute of Atomic Energy (russian: Институт Атомной Энергии им. И.В. Курчатова), abbreviated KIAE (russian: КИАЭ). Between 1991 and 2010, it was known as the Russian Scientific Centre "Kurchatov Institute" () before its name was changed to National Research Centre. History Until 1955 known under a secret name "Laboratory No. 2 of the USSR Academy of Sciences", the Kurchatov Institute was founded in 1943 with the initial purpose of developing nuclear weapons. The majority of Soviet nuclear reactors were designed in the insti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Resonance
In physics, nonlinear resonance is the occurrence of resonance in a nonlinear system. In nonlinear resonance the system behaviour – resonance frequencies and modes – depends on the amplitude of the oscillations, while for linear systems this is independent of amplitude. The mixing of modes in non-linear systems is termed resonant interaction. Description Generically two types of resonances have to be distinguished – linear and nonlinear. From the physical point of view, they are defined by whether or not external force coincides with the eigen-frequency of the system (linear and nonlinear resonance correspondingly). Vibrational modes can interact in a resonant interaction when both the energy and momentum of the interacting modes is conserved. The conservation of energy implies that the sum of the frequencies of the modes must sum to zero: : \omega_n=\omega_+ \omega_+ \cdots + \omega_, with possibly different \omega_i=\omega(\mathbf_i), being eigen-frequencies of the lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Map
The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side 2\pi onto itself. It is constructed by a Poincaré's surface of section of the kicked rotator, and is defined by: :p_ = p_n + K \sin(\theta_n) :\theta_ = \theta_n + p_ where p_n and \theta_n are taken modulo 2\pi. The properties of chaos of the standard map were established by Boris Chirikov in 1969. Physical model This map describes the Poincaré's surface of section of the motion of a simple mechanical system known as the kicked rotator. The kicked rotator consists of a stick that is free of the gravitational force, which can rotate frictionlessly in a plane around an axis located in one of its tips, and which is periodically kicked on the other tip. The standard map is a surface of section applied by a stroboscopic projection on the variables of the kicked rotator. The variables \theta_n and p_n respectively determine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
