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	Adiabatic invariant - Wikipedia, the free encyclopedia
		An adiabatic invariant in general is a property of motion which is conserved to exponential accuracy in the small parameter representing the typical rate of change of the gross properties of the body.
		The adiabatic condition is violated in transit-time magnetic pumping, where the length of a magnetic mirror is oscillated at the bounce frequency, resulting in net heating.
		The total magnetic flux Φ enclosed by a drift surface is the third adiabatic invariant, associated with the periodic motion of mirror-trapped particles drifting around the axis of the system.
	en.wikipedia.org /wiki/Adiabatic_invariant (446 words)

	Adiabatic invariant - the free encyclopedia (Site not responding. Last check: 2007-10-09)
		An adiabatic invariant in general is a property of motion which is conserved to exponential accuracy in the smallparameter representing the typical rate of change of the gross properties of the body.
		The adiabatic condition is violated in transit-time magnetic pumping, where the length of a magneticmirror is oscillated at the bounce frequency, resulting in net heating.
		The total magnetic flux Φ enclosed by a drift surface is the third adiabatic invariant, associated with the periodicmotion of mirror-trapped particles drifting around the axis of the system.
	www.world-knowledge-encyclopedia.com /default.asp?t=Adiabatic_invariant (396 words)

	[ whollyshift.info \| Adiabatic invariant Resources ] (Site not responding. Last check: 2007-10-09)
		An adiabatic invariant in usual is a inheritance of gesticulation which is conserved to exponential accuracy in the undersized restriction representing the general standard of copper of the gross properties of the body.
		For periodic motion, the adiabatic invariants are the spunky integrals taken prepared a aeon of the motion.
		The adiabatic mode is violated in transit-time drawing pumping, where the length of a drawing mirror is oscillated at the bounce frequency, arrangementing in net heating.
	www.whollyshift.info /Adiabatic_invariant (539 words)

	The second adiabatic invariant
		We have seen that there is an adiabatic invariant associated with the periodic gyration of a charged particle around magnetic field-lines.
		Thus, it is reasonable to suppose that there is a second adiabatic invariant associated with the periodic bouncing motion of a particle trapped between two mirror points on a magnetic field-line.
		In other words, the second invariant is proportional to the loop integral of the parallel (to the magnetic field) velocity taken over a bounce orbit.
	farside.ph.utexas.edu /teaching/plasma/lectures/node24.html (550 words)

	(Q-5) The Atomic Nucleus and Bohr's model of the Atom
		Adiabatic invariants occur in all sorts of periodic motions, including Kepler motion, which was taken as the model of the motion of an electron around the nucleus.
		Adiabatic invariants again attracted attention in the 1950s, in the study of the motion of ions and electrons in rarefied plasmas.
		The preservation of those invariants turned out to be essential to the trapping of particles in the magnetic fields of Earth and other planets, and also to many plasma phenomena in space and in the lab.
	www.phy6.org /stargaze/Q5.htm (1714 words)

	The Motion of Magnetically Trapped Particles -- History (Site not responding. Last check: 2007-10-09)
		Adiabatic invariance again surfaced decades later, in the study of ions and electrons moving in space.
		He apparently did not realize that this was an adiabatic invariant of the sort defined by Ehrenfest: this was pointed out at about the same time by the Russian physicists Lev Landau (Nobel, 1962) and Solomon Lifshitz, as a worked-out example for the student in their textbook on the theory of fields.
		A "second" adiabatic invariant, also important in the theory of radiation trapped in the Earth's field, was derived by Grad, Longmire and Rosenbluth while studying the confinement of laboratory plasma, and a related "third" invariant was introduced shortly afterwards by Northrop and Teller.
	www.geophys.washington.edu /Space/ESS205/Education/whtrap2.html (611 words)

	Adiabatic - Qwika
		Adiabatic Adiabatic - of the Greek adiabatos (impenetrable), it is...
		Adiabatic invariant An adiabatic invariant in general is a property of...
		Adiabatic index The adiabatic index of a gas, is the ratio...
	www.qwika.com /find/Adiabatic (443 words)

	Milankovitch cycles - Wikipedia, the free encyclopedia
		As the eccentricity of the orbit evolves, the semi-major axis of the orbital ellipse remains unchanged.
		From the perspective of the perturbation theory used in celestial mechanics to compute the evolution of the orbit, the semi-major axis is an adiabatic invariant.
		The invariable plane, the plane that represents the angular momentum of the solar system, is approximately the orbital plane of Jupiter.
	en.wikipedia.org /wiki/Milankovitch_cycles (2408 words)

	Hexapedia - Primordial fluctuations (via CobWeb/3.1 planet03.csc.ncsu.edu) (Site not responding. Last check: 2007-10-09)
		Adiabatic fluctuations are density variations in all forms of matter and energy which have equal fractional over/under densities.
		So for example, an adiabatic photon overdensity of a factor of two would also correspond to a electron overdensity of two.
		While it is usually assumed that the initial flucuations are adiabatic, the possibility of isocurvature fluctuations can be considered given current cosmological data.
	www.hexafind.com.cob-web.org:8888 /encyclopedia/Primordial_fluctuations (427 words)

	Adiabatic Heating (Site not responding. Last check: 2007-10-09)
		The term "adiabatic" describes things that are impermeable to heat transfer; for example, an adiabaticboundary is a boundary that is impermeable to heat transfer.
		Anotherexample is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings.
		The dry adiabatic lapse rateapplies to air which is below its dew point, ie which is not saturated by water vapor, whereas the wet adiabatic lapse rate applies to air which has reached itsdew point.
	www.eurostudent.net /info/46058-adiabatic-heating.html (698 words)

	Background: McIlwain's (B,L) coordinate system
		is an adiabatic invariant of motion for all particles mirroring at A and A'.
		Due to the conservation of the second invariant of motion J, I also is an adiabatic invariant for all particles mirroring at A and A'.
		The adiabatic invariant I is then obtained by substituting A and A' by M and M' in the first equation.
	www.spenvis.oma.be /spenvis/help/background/magfield/bl.html (917 words)

	Action-angle coordinates - Wikipedia, the free encyclopedia
		Action-angle coordinates are also useful in perturbation theory of Hamiltonian mechanics, especially in determining adiabatic invariants.
		One of the earliest results from chaos theory, for the non-linear perturbations of dynamical systems with a small number of degrees of freedom is the KAM theorem, which states that the invariant tori are stable under small perturbations.
		The use of action-angle variables was central to the solution of the Toda lattice, and to the definition of Lax pairs, or more generally, the idea of the isospectral evolution of a system.
	en.wikipedia.org /wiki/Action-angle_coordinates (665 words)

	B2
		Rather than detailing the zoo of proposed structure formation models, only the adiabatic inflationary model will be considered here (this choice of model is motivated by the fact that it fits the observed temperature anisotropies better than the others).
		Adiabatic models further stipulate that while the overall density of the universe varied, the fraction of the material in any particular form (neutrinos, photons, baryons, cold dark matter, etc.) was initially a constant throughout space.
		Therefore, in the adiabatic inflationary scenario, a well defined pattern of initial perturbations was created in the first fraction of a second after the big bang.
	quiet.uchicago.edu /capmap/b2.htm (218 words)

	Invariant
		In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations.
		In physics, invariants are quantities (usually some functions of the dynamical variables) conserved (unchanged) during the time evolution of the physical system.
		An adiabatic invariant in general is a property of motion which is conserved to exponential accuracy in the...
	musicrecognition.morarecognition.com /invariant (776 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Dmitry Vainshtein Space Research Institute Moscow ---end--- Adiabatic chaos in a two-dimensional mapping ---end--- Lecture Hall, Room 1, Ziskind Building Sunday 11 00 12 00 1998 3 1 A close to identity symplectic mapping describing the dynamics of a charged particle in the field of an infinitely wide packet of electrostatic waves is studied.
		This phenomena is explained by a random change of an adiabatic invariant of the problem occuring when a phase trajectory crosses a resonance curve.
		The width of the chaos region and the density of the set of invariant curves near the boundary of the chaos region are estimated.
	www.wisdom.weizmann.ac.il /~/Seminars/WWW/sem.1998:03:01:11:00:1:23221.dat (142 words)

	Bipolarons (Site not responding. Last check: 2007-10-09)
		This form posses no translation invariancy and corresponds to the phenomenological approach, where the polarization potential well is assumed to be fixed in space.
		In /4/ and /11/ a consistent adiabatic translation-invariant bipolaron theory is developed, based on the Bogolubov-Tyablikov adiabatic theory.
		According to this approach the bipolaron movements are divided in the adiabatic limit.
	skms.impb.psn.ru /ls06_e.php (333 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The theory involves a particular 'constant of motion', the Lewis-Riesenfeldt invariant, and a construction of suitable (integrable) Hamiltonian.
		The Lewis invariant is a constant of motion for parametrically excited linear 1D-oscillators.
		The invariant was found useful for examining the motion in strongly focused accelerators.
	www.wavegroup.irfu.se /~tbl/semabstracts/990331 (177 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The position of these, many years ago theoretically predicted, peaks can be used to distinguish between adiabatic and isocurvature fluctuations as well as to decide whether the geometry of the universe is flat or curved.
		Nearly scale invariant adiabatic models with flat geometry of the universe fit incredibly well to the CMB data.
		However, recently the pre-big bang with suitably decaying axions has shown to be able to produce adiabatic fluctuations with nearly scale invariant spectrum and thus the axions may be rescued.
	www.fys.uio.no /epf/spatind2002/Valiviita.htm (549 words)

	[No title]
		Kato's results were further extended in \cite{asy} who showed that an adiabatic theorem can be formulated and proven without any assumption on the nature of the spectral type also for the initial data, thereby dropping the condition that the initial data lie in a subspace corresponding to an eigenvalue with fixed multiplicity.
		Rather, we stick to the traditional usage of Born, Fock and Kato, where by the adiabatic theorem we refer to the remarkable fact, quite unlike perturbation theory, that there is a precise control on the evolution for Hamiltonians that undergo a {\em finite} variation.
		In the case that there is a gap in the spectrum the adiabatic theorem holds because the eigenstate is protected by a gap from tunneling out of the spectral subspace.
	www.ma.utexas.edu /mp_arc/papers/98-370 (2997 words)

	Student Abstracts: PPPL - Physics
		The adiabatic magnetic moment invariant for the motion of a charged particle in a spatially uniform, time-dependent magnetic field B(t) is studied numerically.
		The principle of adiabatic invariance tells us that the action variable of a system will be nearly constant over a time interval of order 1/e where e is the order of the rate of change the perturbed system's frequency.
		In plasma physics, adiabatic invariance is the reason why magnetic mirror machines are capable of confining charged particles in a plasma.
	www.scied.science.doe.gov /scied/Abstracts2005/PPPLphys.htm (2917 words)

	Astron. Astrophys. 337, 487-494 (1998) (Site not responding. Last check: 2007-10-09)
		We therefore present a new form of the wave equation, the invariant of which is extremely simple and does not contain derivatives of the thermodynamic variables.
		The invariant of the wave equation is nearly constant around the temperature minimum.
		The case of the wave equation with a linear invariant is studied analytically.
	aa.springer.de /bibs/8337002/2300487/small.htm (341 words)

	Publications Equipe 1A (Site not responding. Last check: 2007-10-09)
		One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior.
		The aim is to determine the threshold of break-up of invariant tori and its mechanism.
		The analysis of this transformation indicates that the break-up of invariant tori is a universal mechanism.
	www.u-bourgogne.fr /LPUB/TSM/Pub1b/liste2002.htm (823 words)

	Supression of coherent interchange modes in a magnetic dipole with (Site not responding. Last check: 2007-10-09)
		Since low-frequency interchange instabilities preserve the electron's first and second adiabatic invariant, the wave-particle interaction is described with a two-dimensional phase-space that is directly observable.
		For applied fields of sufficient intensity and pulse-length, we observe (1) the suppression of coherent interchange fluctuations, (2) a reduction of radial transport of energetic electrons, and (3) a steepening of the density gradient of confined plasma.
		Possible explanations include breaking the second adiabatic invariant so as to fill "phase-space holes" and enhancing the plasma density so as to increase the stabilizing polarization current.
	flux.aps.org /meetings/YR01/DPP01/abs/S200019.html (184 words)

	[No title]
		A few milestones in the history of the adiabatic theorem were the following: Kato \cite{k} proved the theorem for Hamiltonians with a non-degenerate eigenvalue separated from the rest of the spectrum, without any assumption on the nature of the rest of the spectrum.
		Subsequent works on the exponential accuracy of the adiabatic approximation have been performed by Nenciu \cite{n4} who proved the existence of ``superadiabatic evolution operators,'' {\it i.e.}, exponentially accurate approximations of the evolution generated by (\ref{schro}).
		Exponential accuracy of the adiabatic theorem was also tackled using powerful pseudo-differential operator techniques by Sj\"ostrand \cite{sj} and by Martinez \cite{m} who studied the exponential decay rate of the transition probability as a function of the parameters of the problem using this method.
	www.ma.utexas.edu /mp_arc/papers/01-288 (2847 words)

	Acoustic (Site not responding. Last check: 2007-10-09)
		In the adiabatic case [(a) solid lines, numerical results and (b) heuristic picture], the potential enhances the first compression through infall and decays leaving the oscillator strongly displaced from the zero point.
		Notice that for the first cycle of the adiabatic and isocurvature oscillations, the gravitational force mimics a driving force of approximately twice the natural period.
		Heights of the peaks in a scale invariant adiabatic model.
	background.uchicago.edu /~whu/concepts/figb.html (251 words)

	Glossary
		Adiabatic invariant--An invariant of a motion is a quantity which does not change as time advances.
		For instance, the energy of a system is often an invariant (for a swinging pendulum, or a planet and the Sun), and knowing that it stays constant is a great help in calculating the motion.
		Adiabatic invariants are quantities associated with approximately periodic motions.
	www-istp.gsfc.nasa.gov /Education/gloss.html (5877 words)

	The third adiabatic invariant
		It is clear, by now, that there is an adiabatic invariant associated with every periodic motion of a charged particle in an electromagnetic field.
		Thus, there must be a third adiabatic invariant associated with the precession of particles around the Earth.
		Likewise, a slow decrease in the strength of the solar wind would cause an outward radial motion of the Van Allen belts.
	farside.ph.utexas.edu /teaching/plasma/lectures/node25.html (383 words)

	Gyroresonant interactions of radiation belt particles with a monochromatic electromagnetic wave
		In both cases, termed “adiabatic” and “nonadiabatic,” the first adiabatic invariant of the particle is broken during a resonant interaction, leading to change in energy and pitch angle.
		The adiabatic case is characterized by a limited range of resonant phase and a well-defined value of the change of the invariant.
		In the nonadiabatic case the phase at resonance ranges over 0 to 2π, and only the magnitude of the change of the invariant is determined; a phase factor gives the invariant change an effectively random sign.
	www.agu.org /pubs/crossref/2000/2000JA000008.shtml (335 words)

	Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow
		Having this set of approximate action--angle variables, we are able to calculate the invariant surfaces and the resonant surfaces associated with a nonintegrable perturbation of a two-action flow.
		2 we show the locations in the meridian plane of both the adiabatic invariant and the resonances for a particular value of the parameters.
		To illustrate this, we choose the flow parameters such that the relative geometry of the adiabatic invariants and the resonances matches that of Fig.
	www.imedea.uib.es /Nonlinear/research_topics/chaotic_ad/spheres_prl.html (2051 words)

	Adiabatic invariants (Site not responding. Last check: 2007-10-09)
		A particle's gyromotion is one example of a periodic motion amenable to the construction of an approximate constant of the motion (or invariant).
		is known as the first adiabatic invariant of a plasma particle.
		The second or longitudinal adiabatic invariant is associated with the periodic bouncing of particles in magnetic flux tubes and magnetic bottles:
	www.physics.usyd.edu.au /~cairns/teaching/lecture2/node10.html (200 words)

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