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A stochastic pump is a classical stochastic system that responds with nonzero, on average, currents to periodic changes of parameters. The stochastic pump effect can be interpreted in terms of a geometric phase in evolution of the moment generating function of stochastic currents. [11]
The motion is periodic, repeating itself in a sinusoidal fashion with constant amplitude A. In addition to its amplitude, the motion of a simple harmonic oscillator is characterized by its period T = 2 π / ω {\displaystyle T=2\pi /\omega } , the time for a single oscillation or its frequency f = 1 / T {\displaystyle f=1/T} , the number of ...
Periodic motion is motion in which the position(s) of the system are expressible as periodic functions, all with the same period. For a function on the real numbers or on the integers , that means that the entire graph can be formed from copies of one particular portion, repeated at regular intervals.
Consequently, it is a special type of spatiotemporal oscillation that is a periodic function of both space and time. Periodic travelling waves play a fundamental role in many mathematical equations, including self-oscillatory systems, [1] [2] excitable systems [3] and reaction–diffusion–advection systems. [4]
The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space.
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such ...
has oscillation 0 at every finite , and 2 at −∞ and +∞. or 1, −1, 1, −1, 1, −1... has oscillation 2. In the last example the sequence is periodic, and any sequence that is periodic without being constant will have non-zero oscillation. However, non-zero oscillation does not usually indicate periodicity.
Specific periodic one-dimensional equations include the Kronig–Penney model and Mathieu's equation. Mathematically Bloch's theorem is interpreted in terms of unitary characters of a lattice group, and is applied to spectral geometry. [20] [21] [22]