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Sommerfeld Effect
In mechanics, Sommerfeld effect is a phenomenon arising from feedback in the energy exchange between vibrating systems: for example, when for the rocking table, under given conditions, energy transmitted to the motor resulted not in higher revolutions but in stronger vibrations of the table. It is named after Arnold Sommerfeld. In 1902, A. Sommerfeld analyzed the vibrations caused by a motor driving an unbalanced weight and wrote that "''This experiment corresponds roughly to the case in which a factory owner has a machine set on a poor foundation running at 30 horsepower. He achieves an effective level of just 1/3, however, because only 10 horsepower are doing useful work, while 20 horsepower are transferred to the foundational masonry''". First mathematical descriptions of Sommerfeld effect were suggested by I. Blekhman and V. Konenko. Hidden attractors in Sommerfeld effect In the theory of hidden oscillations, Sommerfeld effect is explained by the multistability and presence in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics. He served as doctoral supervisor for many Nobel Prize winners in physics and chemistry (only J. J. Thomson's record of mentorship is comparable to his). He introduced the second quantum number (azimuthal quantum number) and the third quantum number (magnetic quantum number). He also introduced the fine-structure constant and pioneered X-ray wave theory. Early life and education Sommerfeld was born in 1868 to a family with deep ancestral roots in Prussia. His mother Cäcilie Matthias (1839–1902) was the daughter of a Potsdam builder. His father Franz Sommerfeld (1820–1906) was a physician from a leading family in Königsberg, where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Court Postal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, 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 number, 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 (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, a dynamical system has a State ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Attractor
In the bifurcation theory, a bounded oscillation that is born without loss of stability of stationary set is called a hidden oscillation. In nonlinear control theory, the birth of a hidden oscillation in a time-invariant control system with bounded states means crossing a boundary, in the domain of the parameters, where local stability of the stationary states implies global stability (see, e.g. Kalman's conjecture). If a hidden oscillation (or a set of such hidden oscillations filling a compact subset of the phase space of the dynamical system) attracts all nearby oscillations, then it is called a hidden attractor. For a dynamical system with a unique equilibrium point that is globally attractive, the birth of a hidden attractor corresponds to a qualitative change in behaviour from monostability to bi-stability. In the general case, a dynamical system may turn out to be multistable and have coexisting local attractors in the phase space. While trivial attractors, i.e. stable equ ... [...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] |
Physical Phenomena
Physical may refer to: *Physical examination, a regular overall check-up with a doctor *Physical (Olivia Newton-John album), ''Physical'' (Olivia Newton-John album), 1981 **Physical (Olivia Newton-John song), "Physical" (Olivia Newton-John song) *Physical (Gabe Gurnsey album), ''Physical'' (Gabe Gurnsey album) *Physical (Alcazar song), "Physical" (Alcazar song) (2004) *Physical (Enrique Iglesias song), "Physical" (Enrique Iglesias song) (2014) *Physical (Dua Lipa song), "Physical" (Dua Lipa song) (2020) *"Physical (You're So)", a 1980 song by Adam & the Ants, the B side to "Dog Eat Dog (Adam and the Ants song)#"Physical (You're So)", Dog Eat Dog" *Physical (TV series), ''Physical'' (TV series), an American television series See also {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
