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	Hamiltonian mechanics - Wikipedia, the free encyclopedia
		Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton.
		The Hamiltonian induces a special vector field on the symplectic manifold, known as the symplectic vector field.
		In particular, the Hamiltonian flow in this case is the same thing as the geodesic flow.
	en.wikipedia.org /wiki/Hamiltonian_mechanics (1321 words)

	Flow Equations for Hamiltonians
		The technique of Hamiltonian flow equations is applied to the canonical Hamiltonian of quantum electrodynamics in the front form and 3+1 dimensions.
		The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N.
		The asymptotic flow of the Hamiltonian is characterized by a non-local differential equation which only depends on one parameter - independent of the dissipative system nor of the truncation scheme.
	www.tphys.uni-heidelberg.de /~statphys/flowownabs.html (4033 words)

	Knowledge Flow :: Knowledge Management
		The notion of network flow is formalized in a branch of mathematics known as graph theory.
		Flow (psychology) is the feeling of complete and energized focus in an activity, with a high level of enjoyment and fulfillment as described by Mihaly Csikszentmihalyi.
		Flow (television) is a term used about how channels try to hold their audience by announcing the coming programs.
	reference.gourt.com /Knowledge-Management/Knowledge-Flow.html (646 words)

	Flow (mathematics) - Wikipedia, the free encyclopedia
		The idea of a vector flow, that is, the flow determined by a vector field, occurs in the areas of differential topology, Riemannian geometry and Lie groups.
		Specific examples of vector flows include the geodesic flow, the Hamiltonian flow, the Ricci flow, and the Anosov flow.
		Flows are usually required to be continuous or even differentiable, when the space $X$ has some additional structure (e.g.
	www.dictionpedia.com /en/Flow_(mathematics) (268 words)

	PlanetMath: Hamiltonian vector field
		is the Hamiltonian, then the flow of the Hamiltonian vector field
		Cross-references: flow, Hamiltonian, manifold, 1-form, symplectic vector field, vector field, smooth function, cotangent bundle, tangent bundle, isomorphism, symplectic manifold
		This is version 3 of Hamiltonian vector field, born on 2002-12-09, modified 2006-05-03.
	planetmath.org /encyclopedia/HamiltonianVectorField.html (102 words)

	flow \| English \| Dictionary & Translation by Babylon
		In fluid mechanics, the word flow is often used to mean a complete description of the motion of a fluid.
		Flow allows the user to produce various reports on the structure of Fortran 77 code, such as flow diagrams and common block tables.
		Flows can be calculated as differences in stocks adjusted to remove the effect of reclassifications, exchange rate variations, other revaluations and any other changes that do not arise from transactions.
	www.babylon.com /definition/flow/?uil=English (775 words)

	[No title]
		A different class of flows on the unit tangent bundle was introduced recently in physics literature, the Gaussian thermostat of an external field, \cite{H}.
		We define a generalized magnetic flow on the tangent bundle $TM$ (or the cotangent bundle $T^M$) by requiring that its velocity vector field $F$ satisfies $$ i_F(\omega - \gamma) = -dH, \tag{0.1} $$ where $\omega$ is the standard symplectic form, $H$ is a hamiltonian* and the 2-form $\gamma$ represents the generalized magnetic field.
		The vector field $F$ on $TM$ defined by \thetag{1.1} is a Hamiltonian vector field with the hamiltonian $H = \frac 12 v^2 +W$ and we have $i_F \omega = -dH$.
	www.ma.utexas.edu /mp_arc/papers/99-13 (1951 words)

	Vered Rom-Kedar: abstracts
		We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are ''acceptable''.
		Sufficient conditions are found so that a family of smooth Hamiltonian flows limits to a billiard flow as a parameter $\eps \goto 0$.
		Then, it is shown that in general, as opposed to the one-and-a-half degrees of freedom Hamiltonian system case, the near separatrix chaotic zone created by a physical ensemble of initial conditions is different than the one created by a single initial condition.
	www.wisdom.weizmann.ac.il /~vered/abstracts.html (2901 words)

	Relative Hofer-Zehnder capacity and periodic orbits in twisted cotangent bundles, Viktor L. Ginzburg, Başak Z. ...
		We show that almost all low levels of a function on a geometrically bounded symplectically aspherical manifold carry contractible periodic orbits of the Hamiltonian flow, provided that the function attains its minimum along a closed symplectic submanifold.
		The latter is carried out by proving that the flow of a Hamiltonian with sufficiently large variation has a nontrivial contractible one-periodic orbit when the Hamiltonian is constant and equal to its maximum near a symplectic submanifold and supported in a neighborhood of the submanifold.
		[GG2] —, A $C^2$-smooth counterexample to the Hamiltonian Seifert conjecture in $\mathbbR^4$, Ann.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.dmj/1084479317 (1035 words)

	Flow - Wikipedia, the free encyclopedia
		Flow, another name for "flux" in physics, which is the rate at which something travels through a given cross section
		Environmental flow, in ecology, the discharge or level of water necessary in a river or water source to sustain a healtly ecosystem
		Flow (mathematics), the one-dimensional (continuous, differentiable) action of a group, usually arising in the solution of differential equations
	en.wikipedia.org /wiki/Flow (387 words)

	Abstracts
		We show that the critical value of the lift of L to a covering of M equals the infimum of the values of k such that the energy level k bounds an exact Lagrangian graph in the cotangent bundle of the covering.
		We conclude the paper showing other applications such as the existence of minimizing periodic orbits in every homotopy class with energy greater than c_u(L) and homologically trivial periodic orbits such that the action of L+k is negative if c_u(L) dvi file Available.
		A particular attention is paid to the case when the flow is derived from an optical Hamiltonian and when the invariant measure is the Liouville measure on compact energy levels.
	www.cimat.mx /~renato/abstracts.html (944 words)

	Brian Dolan: Research Interests (Site not responding. Last check: 2007-11-03)
		It is possible to define the concept of distances on the space of parameters, giving rise to a metric on the space (the metric is essentially the matrix of expectation values of the two-point functions of the theory).
		It is also possible to describe the vector flow of the renormalisation group as a Hamiltonian flow on a symplectic space.
		This is analogous to the Hamiltonian flow of classical mechanics, albeit irreversible flow in this case.
	www.thphys.may.ie /staff/bdolan/research-technical.html (310 words)

	[No title]
		When $L$ and $L'$ are hamiltonian isotopic, these pages coincide (up to a horizontal translation) with the terms of the Serre-spectral sequence of the path-loop fibration $\Omega L\to PL\to L$.
		In an application to Hamiltonian dynamics we relate the existence of bounded and periodic orbits on non-compact level hypersurfaces of Palais-Smale Hamiltonians with just one singularity which is neat to the lack of self-duality (in the sense of Spanier-Whitehead) of the sublink of the singularity.
		The connection maps associated in Conley index theory to an attractor-repellor decomposition with respect to the direct flow and its inverse are Spanier-Whitehead duals in the stably parallelizable context and are duals modulo a certain Thom construction in general.
	www.dms.umontreal.ca /~cornea/abstracts.html (1334 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Let the torus T^2n be equipped with the standard symplectic structure and a Hamiltonian H that is periodic in the time variable.
		A subharmonic solution is a periodic orbit of the Hamiltonian flow with minimal period an integral multiple m of the period of H, with m>1.
		We prove: If the Hamiltonian flow has only finitely many orbits with the same period as H, then there are subharmonic solutions with arbitrarily high minimal period.
	math.hunter.cuny.edu /~mbenders/nancy.txt (102 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		For Hamiltonian flows this in effect is equivalent to identifying an area preserving map in the Poincare surface of section.
		This property is utilized here to convert the Hamiltonian flow problem of the dynamic evolution of self- focusing of an electromagnetic beam (width/phase front curvature dynamics) with beam propagation distance into an equivalent mapping problem for a wide range of initial conditions.
		This property is utilized here to convert the Hamiltonian flow problem of the dynamic evolution of the nonlinear Schrodinger Equation which is thereby converted to a map in a restricted sense.
	www.spie.org /web/abstracts/2000/2039.html (4210 words)

	Math Seminars. (Site not responding. Last check: 2007-11-03)
		Periodic orbits of Hamiltonian flows near symplectic extrema
		The goal of this work, joint with Ely Kerman, is to obtain generalizations of the Weinstein--Moser theorem for Hamiltonians having Bott-nondegenerate extrema along symplectic submanifolds.
		In particular, we aim at establishing the existence of periodic orbits of the Hamiltonian flow on the levels near such an extremum.
	www.math.psu.edu /dynsys/abstracts/ginzburg.html (121 words)

	On the classical statistical mechanics of non-Hamiltonian systems (Site not responding. Last check: 2007-11-03)
		It is shown that compressible phase space flows generate coordinate transformations with a nonunit Jacobian, leading to a metric on the phase space manifold which is nontrivial.
		One of the signatures of non-Hamiltonian flow is that it can have a nonzero phase space compressibility, a property that distinguishes it from the Hamiltonian case, which is always incompressible.
		Since Hamiltonian flow preserve the measure of phase space, it is usually assumed that this space can be treated mathematically as a Euclidean manifold.
	homepages.nyu.edu /~mt33/glville/geo_lville2.html (2086 words)

	Abstracts (Site not responding. Last check: 2007-11-03)
		For several types of stable flows and representations of the fundamental group of the underlying manifold, Reidemeister torsion for the representation can be computed from the periodic orbits of the flow.
		Reidemeister torsion and integrable Hamiltonian systems Let N be a 4-dimensional symplectic manifold and let H be a real function on N such that there is a Bott function f independent of H with {H,f}=0.
		Assuming that the Aubry set of the system consists in a finite number of hyperbolic periodic orbits of the Euler-Lagrange flow, we study the vanishing-viscosity limit, from the viscous equation to the inviscid problem.
	www.matem.unam.mx /~hector/abstracts.html (470 words)

	Liouville's theorem (Hamiltonian) - Wikipedia, the free encyclopedia
		In Hamiltonian mechanics, the phase space is a smooth manifold that comes naturally equipped with a smooth measure (locally, this measure is the 6n-dimensional Lebesgue measure).
		The theorem says this smooth measure is invariant under the Hamiltonian flow.
		In the frame of invariant Hamiltonian formalism, the theorem about existence of symplectic structure on invariant phase space turns out to be a deep generalization of the theorem about Poincaré invariant.
	en.wikipedia.org /wiki/Liouville's_theorem_(Hamiltonian) (978 words)

	Global Diffusion in a Realistic Three-Dimensional Time-Dependent Nonturbulent Fluid Flow (Site not responding. Last check: 2007-11-03)
		On the other hand, the case of two actions, which is also generic for a class of flows, displays in Liouvillian maps a new phenomenon of resonance-induced diffusion leading to global transport throughout phase space [].
		To illustrate this, we choose the flow parameters such that the relative geometry of the adiabatic invariants and the resonances matches that of Fig.
		We expect to see in the stroboscopic maps of such flows the resonance-induced diffusion characteristic of two-action maps, consisting of motion on invariant surfaces interspersed with periods of motion on resonant surfaces.
	www.imedea.uib.es /nonlinear/research_topics/chaotic_ad/spheres_prl.html (2051 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		The latter is of great interest, as it is used to construct the optimal feedback mapping, a preferred notion of solution to a control problem.
		After describing the mentioned basic objects, I will discuss the properties of the Hamiltonian system, focusing on the structure guaranteed by the convexity of the underlying problem.
		The crucial property - preservation of monotone operators by the Hamiltonian flow - will be shown to have far reaching consequences for the value function and the optimal feedback.
	oldweb.cecm.sfu.ca /CECMColloquium/oct18.html (149 words)

	ENSTA - Course AOT12
		The aim of this course is to introduce the theory of Hamiltonian systems linked to analytical mechanics and specifically to show the great richness of their geometric and dynamic structure.
		Once we have defined the concept of an integrable system, something that is of particular importance in physics, we shall investigate their perturbations.
		Symplectic reworking of a Hamiltonian flow, Hamilton-Jacobi equation
	www.ensta.fr /Base_cours/cours.php?lng=0&sigle=AOT12 (185 words)

	20a
		of the tangent bundle is an invariant manifold for the Lagrangian flow.
		The large gap problem of Arnold diffusion was overpassed recently for such systems by variational methods of Mather (Xia), by geometrical methods using secondary KAM-tori (de la Llave, Delshams, Seara), and by the method of separatrix map (Treschev).
		For the Hamiltonian above homogenization is equivalent to a large deviation result for Brownian motion among random obstacles (Snitzman).
	www.aimath.org /WWN/dynpde/articles/html/20a (1307 words)

	Biophysics & Statistical Physics Group: non-Hamiltonian molecular dynamics
		Although (Hamiltonian) molecular dynamics has proven to be a very useful tool, it has one basic restriction: It can in principle generate only equilibrium properties of the microcanonical ensemble.
		Although the mechanical consequences of this procedure might be straightforward, the implications on the statistical mechanics of the system are less evident.
		Below are snapshots from a simple non-Hamiltonian simulation, a polymer stretching and collapsing under shear flow in constant temperature.
	www.apmaths.uwo.ca /~mkarttu/nHmd.shtml (335 words)

	Lenya Ryzhik
		Passive tracer in a slowly decorrelating random flow with a large mean, (with T. Komorowski), (pdf), Preprint, 2006.
		Bounds on the speed of propagation of the KPP fronts in a cellular flow (with A. Novikov), (pdf), to appear in Archive for Rational Mechanics and Analysis, 2006.
		The KPP system in a periodic flow with a heat loss (with P. Gordon and N. Vladimirova), (ps,pdf), Nonlinearity, 18, 2005, 571-589.
	www.math.uchicago.edu /~ryzhik (1172 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		In the renormalization group (RG) method, developed by Wilson, states above a certain cutoff are removed from the theory, and the Hamiltonian is modified to produce the same results for all physical measurements that involve the remaining modes.
		The parameters that specify the different interaction strengths in the Hamiltonian change ("flow") as the cutoff energy is reduced.
		In this approach we start by separating the Hamiltonian into a ``free-particle'' part H0 and a part that involves residual electronic interactions V. For instance, H0 might be any type of mean field Hamiltonian, and we used the Hartree-Fock Hamiltonian.
	www.chem.purdue.edu /kais/Developing.html (290 words)

	MD-PS 2002 Talks Titles and Abstacts
		A completely integrable flow is a flow whose phase space contains an open dense set fibred by invariant tori, and the flow on these tori is a translation-type flow.
		A common method to demonstrate the real-analytic non-integrability of a hamiltonian flow has been to demonstrate the existence of a subsystem that is incompatible with real-analytic integrability.
		We also construct a smoothly integrable hamiltonian flow on a Poisson manifold that preserves a smooth positive measure with respect to which the time one map has positive entropy.
	www.math.umd.edu /~mmb/md02/abstracts.html (2767 words)

	CMS/CSHPM Summer 2005 Meeting
		We prove global well-posedness in the subcritical and critical cases, while ill-posedness is shown in the supercritical case.
		In 1922 Jeffery derived an ODE for the motion of the principal axis of a rotationally symmetric, elongated ellipsoid in a Stokes flow.
		Jeffery's equation finds applications in flow problems arising in the manufacture of artifacts with immersed objects (glass, metal or plastic "sticks") to modify the elastoplastic behaviour of the product.
	www.cms.math.ca /SMC/Reunions/ete05/abs/pde.e (1003 words)

	Real and Complex Geometry Seminar (Site not responding. Last check: 2007-11-03)
		The Weinstein-Moser theorem establishes the existence of periodic orbits of a Hamiltonian flow on all level sets near a nondegenerate extremal point of the Hamiltonian.
		In particular, variational techniques are used to prove the existence of periodic orbits on a sequence of level sets approaching such a submanifold.
		As an application we prove that there are periodic orbits of this motion on a sequence of energy levels converging to zero.
	www.tau.ac.il /~biranp/Seminars/RC/2000-1/09.05.2001.Kerman.html (127 words)

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