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Intermittency Transport
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). Experimentally, intermittency appears as long periods of almost periodic behavior interrupted by chaotic behavior. As control variables change, the chaotic behavior become more frequent until the system is fully chaotic. This progression is known as the intermittency route to chaos. 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 pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Space
In computer science, a state space is a discrete space representing the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space. Definition State spaces are useful in computer science as a simple model of machines. Formally, a state space can be defined as a tuple [''N'', ''A'', ''S'', ''G''] where: * ''N'' is a Set (mathematics), set of states * ''A'' is a set of arcs connecting the states * ''S'' is a nonempty subset of ''N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eindhoven University Of Technology
The Eindhoven University of Technology (), Abbreviation, abbr. TU/e, is a public university, public technical university in the Netherlands, situated in Eindhoven. In 2020–21, around 14,000 students were enrolled in its Bachelor of Science, BSc and Master of Science, MSc programs and around 1350 students were enrolled in its Doctor of Philosophy, PhD and EngD programs. In 2021, the TU/e employed around 3900 people. TU/e is the Dutch member of the EuroTech Universities Alliance, a partnership of European universities of science & technology. The other members are Technical University of Denmark (DTU), École Polytechnique Fédérale de Lausanne (EPFL), École Polytechnique (L’X), The Technion, and Technical University of Munich (TUM). History The Eindhoven University of Technology was founded as the ''Technische Hogeschool Eindhoven'' (THE) on 23 June 1956 by the Dutch government. It was the second institute of its kind in the Netherlands, after the Delft University of Tech ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluorescence Intermittency
Fluorescence intermittency, or blinking, is the phenomenon of random switching between ON (bright) and OFF (dark) states of the emitter under its continuous excitation. It is a common property of the nanoscale emitters (molecular fluorophores, colloidal quantum dots) related to the competition between the radiative and non-radiative relaxation pathways. The peculiar feature of such blinking in most cases is the power-law (in contrast to exponential) statistics of the ON and OFF time distributions, meaning that the measurements of the time-averaged intensity of a single emitter is not reproducible in different experiments and implying a complex dynamics of the involved process. In other words, in one experiment the emitter can blink frequently, while in another it may stay ON (or OFF) for almost entire length of the experiment (even for extremely long measurement times). For CdSe-ZnS core-shell nanocrystals, "charge trapping" is the dominant theory explaining observed power-law bl ... [...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 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. The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pipe Flow
In fluid mechanics, pipe flow is a type of fluid flow within a closed conduit, such as a pipe, duct or tube. It is also called as Internal flow. The other type of flow within a conduit is open channel flow. These two types of flow are similar in many ways, but differ in one important aspect. Pipe flow does not have a free surface which is found in open-channel flow. Pipe flow, being confined within closed conduit, does not exert direct atmospheric pressure, but does exert hydraulic pressure on the conduit. Not all flow within a closed conduit is considered pipe flow. Storm sewers are closed conduits but usually maintain a free surface and therefore are considered open-channel flow. The exception to this is when a storm sewer operates at full capacity, and then can become pipe flow. Energy in pipe flow is expressed as head and is defined by the Bernoulli equation. In order to conceptualize head along the course of flow within a pipe, diagrams often contain a hydraulic grade ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jet (fluid)
A jet is a stream of fluid that is projected into a surrounding medium, usually from some kind of a nozzle, aperture or orifice. Jets can travel long distances without dissipating. Jet fluid has higher speed compared to the surrounding fluid medium. In the case that the surrounding medium is assumed to be made up of the same fluid as the jet, and this fluid has viscosity, some of the surrounding fluid is carried along with the jet in a process called entrainment. Some animals, notably cephalopods, move by jet propulsion, as do rocket engines and jet engines. Applications Liquid jets are used in many different areas. In everyday life, you can find them for instance coming from the water tap, the showerhead, and from spray cans. In agriculture, they play a role in irrigation and in the application of crop protection products. In the field of medicine, you can find liquid jets for example in injection procedures or inhalers. Industry uses liquid jets for waterjet cutt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulent
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to 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. The onset of turbulence can be predicted by the dimensionless Reynolds number, the ratio of kinetic energy to viscous damping i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basin Of Attraction
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. In finite-dimensional systems, the evolving variable may be represented algebraically as an ''n''-dimensional vector. The attractor is a region in ''n''-dimensional space. In physical systems, the ''n'' dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate. If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crisis (dynamical Systems)
In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are varied. This global bifurcation occurs when a chaotic attractor comes into contact with an unstable periodic orbit or its stable manifold. As the orbit approaches the unstable orbit it will diverge away from the previous attractor, leading to a qualitatively different behaviour. Crises can produce intermittent behaviour. Grebogi, Ott, Romeiras, and Yorke distinguished between three types of crises: * The first type, a boundary or an exterior crisis, the attractor is suddenly destroyed as the parameters are varied. In the postbifurcation state the motion is transiently chaotic, moving chaotically along the former attractor before being attracted to a fixed point, periodic orbit, quasiperiodic orbit, another strange attractor, or diverging to infinity. * In the second type of crisis, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Orbit
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time. Iterated functions Given a mapping from a set into itself, :f: X \to X, a point in is called periodic point if there exists an >0 so that :\ f_n(x) = x where is the th iterate of . The smallest positive integer satisfying the above is called the ''prime period'' or ''least period'' of the point . If every point in is a periodic point with the same period , then is called ''periodic'' with period (this is not to be confused with the notion of a periodic function). If there exist distinct and such that :f_n(x) = f_m(x) then is called a preperiodic point. All periodic points are preperiodic. If is a diffeomorphism of a differentiable manifold, so that the derivative f_n^\prime is defined, then one says that a periodic point is ''hyperbolic'' if :, f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intermittency In Logistic Map, Cobweb Diagram
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). Experimentally, intermittency appears as long periods of almost periodic behavior interrupted by chaotic behavior. As control variables change, the chaotic behavior become more frequent until the system is fully chaotic. This progression is known as the intermittency route to chaos. 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 pe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
