Entrainment (physics) - AbsoluteAstronomy.com

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Entrainment
Entrainment may refer to:* Air entrainment, the intentional creation of tiny air bubbles in concrete* Brainwave entrainment, the practice of entraining one's brainwaves to a desired frequency...

for other types.

Entrainment has been used to refer to the process of mode locking of coupled driven oscillators, which is the process whereby two interacting oscillating

Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

systems, which have different periods when they function independently, assume a common period. The two oscillators may fall into synchrony

Synchronization

Synchronization is timekeeping which requires the coordination of events to operate a system in unison. The familiar conductor of an orchestra serves to keep the orchestra in time....

, but other phase relationships are also possible.

The system with the greater frequency slows down, and the other accelerates. Christian Huygens, a notable physicist

Physicist

A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

, introduced the concept after he noticed, in 1666, that two pendulum clock

Pendulum clock

A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is a resonant device; it swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates...

s had moved into the same swinging rhythm, and subsequent experiments duplicated this process. Notably, the two pendulum clocks stabilized not in synchrony, but in an "odd sympathy

Odd sympathy

The phrase odd sympathy appears in the record of a letter by Dutch mathematician and physicist Christiaan Huygens to Sir Robert Moray as presented to the Royal Society of London, relating to the tendency of two pendulum clocks to synchronize with opposite phases when suspended side by side...

" or antiphase. They satisfy the definition of entrainment because they have the same period, even though they have opposite phase. The accepted explanation for this is that small amounts of energy are transferred between the two systems when they are out of phase in such a way as to produce negative feedback

Negative feedback

Negative feedback occurs when the output of a system acts to oppose changes to the input of the system, with the result that the changes are attenuated. If the overall feedback of the system is negative, then the system will tend to be stable.- Overview :...

. As they assume a more stable phase relationship, the amount of energy gradually reduces to zero. In the realm of physics, Huygens observations are related to resonance

Resonance

In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

and the resonant coupling of harmonic oscillators, which also gives rise to sympathetic vibrations

Sympathetic resonance

Sympathetic resonance is a harmonic phenomenon wherein a formerly passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. The classic example is demonstrated with two similar tuning-forks of which one is mounted on a wooden box. If the other one is...

.

A 2002 study of Huygen's observations show that an antiphase stable oscillation was somewhat fortuitous, and that there are other possible stable solutions, including a "death state" where a clock stops running, depending on the strength of the coupling between the clocks.

Mode locking between driven oscillators can be easily demonstrated using mechanical metronomes on a common, easily movable surface. Such mode locking is important for many biological systems including the proper operation of pacemakers.

The use of the word entrainment in the modern Physics literature most often refers to the movement of one fluid by another. The use of the word to refer to mode locking of non-linear coupled oscillators appears mostly after about 1980, and remains relatively rare in comparison.

A similar coupling phenomenon was characterized in hearing aid

Hearing aid

A hearing aid is an electroacoustic device which typically fits in or behind the wearer's ear, and is designed to amplify and modulate sound for the wearer. Earlier devices, known as "ear trumpets" or "ear horns", were passive funnel-like amplification cones designed to gather sound energy and...

s when the adaptive feedback cancellation

Adaptive feedback cancellation

Adaptive feedback cancellation is a common method of cancelling audio feedback in a varietyof electro-acoustic systems such as digital hearing aids. The time varying acoustic feedback leakage paths can only be eliminated with adaptive feedback cancellation...

is used. This chaotic

Chaos theory

Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

artifact (entrainment) is observed when correlated input signals are presented to an adaptive feedback canceller.

Additional References

Filter Entrainment Avoidance with a Frequency Domain Transform Algorithm http://www.wipo.int/pctdb/en/wo.jsp?IA=WO2008051571&WO=2008051571&DISPLAY=DESC

Entrainment Avoidance with Pole Stabilization http://www.wipo.int/pctdb/en/wo.jsp?IA=WO2008051569&WO=2008051569&DISPLAY=DESC

Entrainment Avoidance with a Transform Domain Algorithm http://www.freshpatents.com/Entrainment-avoidance-with-a-transform-domain-algorithm-dt20080424ptan20080095388.php

Entrainment Avoidance with an Auto Regressive Filter http://www.wipo.int/pctdb/en/wo.jsp?IA=WO2008051570&WO=2008051570&DISPLAY=STATUS

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.

See also

Additional References