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Pomeau–Manneville Scenario
In the theory of dynamical systems (or turbulent flow), the Pomeau–Manneville scenario is the transition to chaos (turbulence) due to intermittency. Named after Yves Pomeau Yves Pomeau, born in 1942, is a French mathematician and physicist, emeritus research director at the CNRS and corresponding member of the French Academy of sciences. He was one of the founders of thLaboratoire de Physique Statistique, École No ... and Paul Manneville. References Dynamical systems Chaos theory Turbulence {{chaos-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This increases the energy needed to pump fluid through a pipe. The onset of turbulence can be predicted by the dimensionless Rey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yves Pomeau
Yves Pomeau, born in 1942, is a French mathematician and physicist, emeritus research director at the CNRS and corresponding member of the French Academy of sciences. He was one of the founders of thLaboratoire de Physique Statistique, École Normale Supérieure, Paris He is the son of René Pomeau. Career Yves Pomeau did his state thesis in plasma physics, almost without any adviser, at the University of Orsay-France in 1970. After his thesis, he spent a year as a postdoc with Ilya Prigogine in Brussels. He was a researcher at the CNRS from 1965 to 2006, ending his career as DR0 in the Physics Department of the Ecole Normale Supérieure (ENS) (Statistical Physics Laboratory) in 2006. He was a lecturer in physics at the École Polytechnique for two years (1982–1984), then a scientific expert with the Direction générale de l'armement until January 2007. He was Professor, with tenure, part-time at the Department of Mathematics, University of Arizona, from 1990 to 2008. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intermittency
In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics ( Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency). Pomeau and Manneville described three routes to intermittency where a nearly periodic system shows irregularly spaced bursts of chaos. These (type I, II and III) correspond to the approach to a saddle-node bifurcation, a subcritical Hopf bifurcation, or an inverse period-doubling bifurcation. In the apparently periodic phases the behaviour is only nearly periodic, slowly drifting away from an unstable periodic orbit. Eventually the system gets far enough away from the periodic orbit to be affected by chaotic dynamics in the rest of the state space, until it gets close to the orbit again and returns to the nearly periodic behaviour. Since the time spent near the periodic orbit depends sensitively on how closely the system entered its vicinity (in turn dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Manneville
Paul may refer to: * Paul (given name), a given name (includes a list of people with that name) * Paul (surname), a list of people People Christianity *Paul the Apostle (AD c.5–c.64/65), also known as Saul of Tarsus or Saint Paul, early Christian missionary and writer * Pope Paul (other), multiple Popes of the Roman Catholic Church * Saint Paul (other), multiple other people and locations named "Saint Paul" Roman and Byzantine empire * Lucius Aemilius Paullus Macedonicus (c. 229 BC – 160 BC), Roman general * Julius Paulus Prudentissimus (), Roman jurist * Paulus Catena (died 362), Roman notary * Paulus Alexandrinus (4th century), Hellenistic astrologer * Paul of Aegina or Paulus Aegineta (625–690), Greek surgeon Royals *Paul I of Russia (1754–1801), Tsar of Russia * Paul of Greece (1901–1964), King of Greece Other people *Paul the Deacon or Paulus Diaconus (c. 720 – c. 799), Italian Benedictine monk *Paul (father of Maurice), the father of Maur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical Systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometrical manif ... [...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] |
