28,726 research outputs found
Higher order first integrals of motion in a gauge covariant Hamiltonian framework
The higher order symmetries are investigated in a covariant Hamiltonian
formulation. The covariant phase-space approach is extended to include the
presence of external gauge fields and scalar potentials. The special role of
the Killing-Yano tensors is pointed out. Some non-trivial examples involving
Runge-Lenz type conserved quantities are explicitly worked out.Comment: 13 pages, references added, accepted for publication in MPL
Seven Steps Towards the Classical World
Classical physics is about real objects, like apples falling from trees,
whose motion is governed by Newtonian laws. In standard Quantum Mechanics only
the wave function or the results of measurements exist, and to answer the
question of how the classical world can be part of the quantum world is a
rather formidable task. However, this is not the case for Bohmian mechanics,
which, like classical mechanics, is a theory about real objects. In Bohmian
terms, the problem of the classical limit becomes very simple: when do the
Bohmian trajectories look Newtonian?Comment: 16 pages, LaTeX, uses latexsy
Variance Reduction For A Discrete Velocity Gas
We extend a variance reduction technique developed by Baker and Hadjiconstantinou [1] to a discrete velocity gas. In our previous work, the collision integral was evaluated by importance sampling of collision partners [2]. Significant computational effort may be wasted by evaluating the collision integral in regions where the flow is in equilibrium. In the current approach, substantial computational savings are obtained by only solving for the deviations from equilibrium. In the near continuum regime, the deviations from equilibrium are small and low noise evaluation of the collision integral can be achieved with very coarse statistical sampling. Spatially homogenous relaxation of the Bobylev-Krook-Wu distribution [3,4], was used as a test case to verify that the method predicts the correct evolution of a highly non-equilibrium distribution to equilibrium. When variance reduction is not used, the noise causes the entropy to undershoot, but the method with variance reduction matches the analytic curve for the same number of collisions. We then extend the work to travelling shock waves and compare the accuracy and computational savings of the variance reduction method to DSMC over Mach numbers ranging from 1.2 to 10.Aerospace Engineering and Engineering Mechanic
Far Field Deposition Of Scoured Regolith Resulting From Lunar Landings
As a lunar lander approaches a dusty surface, the plume from the descent engine impinges on the ground, entraining loose regolith into a high velocity dust spray. Without the inhibition of a background atmosphere, the entrained regolith can travel many kilometers from the landing site. In this work, we simulate the flow field from the throat of the descent engine nozzle to where the dust grains impact the surface many kilometers away. The near field is either continuum or marginally rarefied and is simulated via a loosely coupled hybrid DSMC - Navier Stokes (DPLR) solver. Regions of two-phase and polydisperse granular flows are solved via DSMC. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20m to 3m. The dust and gas motions are fully coupled using an interaction model that conserves mass, momentum, and energy statistically and inelastic collisions between dust particles are also accounted for. Simulations of a 4 engine configuration are also examined, and the erosion rates as well as near field particle fluxes are discussed.Astronom
The turbulent generation of outward traveling Alfvenic fluctuations in the solar wind
From an analysis of the incompressible MHD equations, it is concluded that the frequent observation of outward propagating Alfvenic fluctuations in the solar wind can arise from early stages of in situ turbulent evolution, and need not reflect coronal processes
On the theory of large amplitude Alfven waves
Large amplitude Alfvenic disturbances of arbitrary spatial shape and polarization are described by MHD equations, without resort to the usual assumption of planarity. However, because of their nonplanar nature, the direction of propagation of these disturbances cannot, in general, be determined by looking for minima in a variance matrix constructed from observed field fluctuations. When such minima exist, one is observing that subset of interplanetary Alfven waves that is essentially planar
Bohmian Mechanics and Quantum Information
Many recent results suggest that quantum theory is about information, and
that quantum theory is best understood as arising from principles concerning
information and information processing. At the same time, by far the simplest
version of quantum mechanics, Bohmian mechanics, is concerned, not with
information but with the behavior of an objective microscopic reality given by
particles and their positions. What I would like to do here is to examine
whether, and to what extent, the importance of information, observation, and
the like in quantum theory can be understood from a Bohmian perspective. I
would like to explore the hypothesis that the idea that information plays a
special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure
Sewing sound quantum flesh onto classical bones
Semiclassical transformation theory implies an integral representation for
stationary-state wave functions in terms of angle-action variables
(). It is a particular solution of Schr\"{o}dinger's time-independent
equation when terms of order and higher are omitted, but the
pre-exponential factor in the integrand of this integral
representation does not possess the correct dependence on . The origin of
the problem is identified: the standard unitarity condition invoked in
semiclassical transformation theory does not fix adequately in a
factor which is a function of the action written in terms of and
. A prescription for an improved choice of this factor, based on
succesfully reproducing the leading behaviour of wave functions in the vicinity
of potential minima, is outlined. Exact evaluation of the modified integral
representation via the Residue Theorem is possible. It yields wave functions
which are not, in general, orthogonal. However, closed-form results obtained
after Gram-Schmidt orthogonalization bear a striking resemblance to the exact
analytical expressions for the stationary-state wave functions of the various
potential models considered (namely, a P\"{o}schl-Teller oscillator and the
Morse oscillator).Comment: RevTeX4, 6 page
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DSMC Modeling Of Gasdynamics, Radiation And Fine Particulates In Ionian Volcanic Jets
Aerospace Engineerin
Possible potentials responsible for stable circular relativistic orbits
Bertrand's theorem in classical mechanics of the central force fields
attracts us because of its predictive power. It categorically proves that there
can only be two types of forces which can produce stable, circular orbits. In
the present article an attempt has been made to generalize Bertrand's theorem
to the central force problem of relativistic systems. The stability criterion
for potentials which can produce stable, circular orbits in the relativistic
central force problem has been deduced and a general solution of it is
presented in the article. It is seen that the inverse square law passes the
relativistic test but the kind of force required for simple harmonic motion
does not. Special relativistic effects do not allow stable, circular orbits in
presence of a force which is proportional to the negative of the displacement
of the particle from the potential center.Comment: 11 pages, Latex fil
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