|
Quasiperiodicity
Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement. It is different from the mathematical concept of an almost periodic function, which has increasing regularity over multiple periods. The mathematical definition of quasiperiodic function is a completely different concept; the two should not be confused. Climatology Climate oscillations that appear to follow a regular pattern but which do not have a fixed period are called ''quasiperiodic''. Within a dynamical system such as the ocean-atmosphere oscillations may occur regularly, when they are forced by a regular external forcing: for example, the familiar winter-summer cycle is forced by variations in sunlight from the (very close to perfectly) periodic motion of the earth aro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-periodic Oscillations
In X-ray astronomy, quasi-periodic oscillation (QPO) is the manner in which the X-ray light from an astronomical object flickers about certain frequencies. In these situations, the X-rays are emitted near the inner edge of an accretion disk in which gas swirls onto a compact object such as a white dwarf, neutron star, or black hole. The QPO phenomenon promises to help astronomers understand the innermost regions of accretion disks and the masses, radii, and spin periods of white dwarfs, neutron stars, and black holes. QPOs could help test Albert Einstein's theory of general relativity which makes predictions that differ most from those of Newtonian gravity when the gravitational force is strongest or when rotation is fastest (when a phenomenon called the Lense–Thirring effect comes into play). However, the various explanations of QPOs remain controversial and the conclusions reached from their study remain provisional. A QPO is identified by performing a power spectrum of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasiperiodic Motion
In mathematics and theoretical physics, quasiperiodic motion is in rough terms the type of motion executed by a dynamical system containing a finite number (two or more) of incommensurable frequencies. That is, if we imagine that the phase space is modelled by a torus ''T'' (that is, the variables are periodic like angles), the trajectory of the system is modelled by a curve on ''T'' that wraps around the torus without ever exactly coming back on itself. A quasiperiodic function on the real line is the type of function (continuous, say) obtained from a function on ''T'', by means of a curve :''R'' → ''T'' which is linear (when lifted from ''T'' to its covering Euclidean space), by composition. It is therefore oscillating, with a finite number of underlying frequencies. (NB the sense in which theta functions and the Weierstrass zeta function in complex analysis are said to have quasi-periods with respect to a period lattice is something distinct from this.) The theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
System
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity. Etymology The term ''system'' comes from the Latin word ''systēma'', in turn from Greek ''systēma'': "whole concept made of several parts or members, system", literary "composition"."σύστημα" Henry George Liddell, Robert Scott, '' [...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] |
Systems Theory
Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" by expressing synergy or emergent behavior. Changing one component of a system may affect other components or the whole system. It may be possible to predict these changes in patterns of behavior. For systems that learn and adapt, the growth and the degree of adaptation depend upon how well the system is engaged with its environment and other contexts influencing its organization. Some systems support other systems, maintaining the other system to prevent failure. The goals of systems theory are to model a system's dynamics, constraints, conditions, and relations; and to elucidate principles (such as purpose, measur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seasonality
In time series data, seasonality is the presence of variations that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consists of periodic, repetitive, and generally regular and predictable patterns in the levels of a time series. Seasonal fluctuations in a time series can be contrasted with cyclical patterns. The latter occur when the data exhibits rises and falls that are not of a fixed period. Such non-seasonal fluctuations are usually due to economic conditions and are often related to the "business cycle"; their period usually extends beyond a single year, and the fluctuations are usually of at least two years. Organisations facing seasonal variations, such as ice-cream vendors, are often interested in knowing their performance relative to the normal seasonal variation. Seasonal variations in the labour market can be attributed to the entrance of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasiperiodic Tiling
A quasiperiodic tiling is a tiling of the plane that exhibits local periodicity under some transformations: every finite subset of its tiles reappears infinitely often throughout the tiling, but there is no nontrivial way of superimposing the whole tiling onto itself so that all tiles overlap perfectly. See * Aperiodic tiling and Penrose tiling for a mathematical viewpoint. * Quasicrystal for a physics viewpoint. Tessellation {{sia, mathematics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasiperiodic Function
In mathematics, a quasiperiodic function is a function that has a certain similarity to a periodic function. A function f is quasiperiodic with quasiperiod \omega if f(z + \omega) = g(z,f(z)), where g is a "''simpler''" function than f. What it means to be "''simpler''" is vague. A simple case (sometimes called arithmetic quasiperiodic) is if the function obeys the equation: : f(z + \omega) = f(z) + C Another case (sometimes called geometric quasiperiodic) is if the function obeys the equation: : f(z + \omega) = C f(z) An example of this is the Jacobi theta function, where :\vartheta(z+\tau;\tau) = e^{-2\pi iz - \pi i\tau}\vartheta(z;\tau), shows that for fixed \tau it has quasiperiod \tau; it also is periodic with period one. Another example is provided by the Weierstrass sigma function, which is quasiperiodic in two independent quasiperiods, the periods of the corresponding Weierstrass ''℘'' function. Functions with an additive functional equation : f(z + \omega ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Function
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function that is not periodic is called aperiodic. Definition A function is said to be periodic if, for some nonzero constant , it is the case that :f(x+P) = f(x) for all values of in the domain. A nonzero constant for which this is the case is called a period of the function. If there exists a least positive constant with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period. A function with period will repeat on intervals of length , and these intervals are sometimes also referred to as periods of the function. Geometrically, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
El Niño–Southern Oscillation
El Niño–Southern Oscillation (ENSO) is an irregular periodic variation in winds and sea surface temperatures over the tropical eastern Pacific Ocean, affecting the climate of much of the tropics and subtropics. The warming phase of the sea temperature is known as ''El Niño'' and the cooling phase as '' La Niña''. The ''Southern Oscillation'' is the accompanying atmospheric component, coupled with the sea temperature change: ''El Niño'' is accompanied by high air surface pressure in the tropical western Pacific and ''La Niña'' with low air surface pressure there. The two periods last several months each and typically occur every few years with varying intensity per period. The two phases relate to the Walker circulation, which was discovered by Gilbert Walker during the early twentieth century. The Walker circulation is caused by the pressure gradient force that results from a high-pressure area over the eastern Pacific Ocean, and a low-pressure system over Indonesia. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase-locked
In mathematics, particularly in dynamical systems, Arnold tongues (named after Vladimir Arnold) Section 12 in page 78 has a figure showing Arnold tongues. are a pictorial phenomenon that occur when visualizing how the rotation number of a dynamical system, or other related invariant property thereof, changes according to two or more of its parameters. The regions of constant rotation number have been observed, for some dynamical systems, to form geometric shapes that resemble tongues, in which case they are called Arnold tongues. Arnold tongues are observed in a large variety of natural phenomena that involve oscillating quantities, such as concentration of enzymes and substrates in biological processes and cardiac electric waves. Sometimes the frequency of oscillation depends on, or is constrained (i.e., ''phase-locked'' or ''mode-locked'', in some contexts) based on some quantity, and it is often of interest to study this relation. For instance, the outset of a tumor triggers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
