287 research outputs found
Linear systems with adiabatic fluctuations
We consider a dynamical system subjected to weak but adiabatically slow
fluctuations of external origin. Based on the ``adiabatic following''
approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the
strength of fluctuations and 1/|\mu| refers to the time scale of evolution of
the unperturbed system to obtain a linear differential equation for the average
solution. The theory is applied to the problems of a damped harmonic oscillator
and diffusion in a turbulent fluid. The result is the realization of
`renormalized' diffusion constant or damping constant for the respective
problems. The applicability of the method has been critically analyzed.Comment: Plain Latex, no figure, 21 page
Theory of Adiabatic fluctuations : third-order noise
We consider the response of a dynamical system driven by external adiabatic
fluctuations. Based on the `adiabatic following approximation' we have made a
systematic separation of time-scales to carry out an expansion in , where is the strength of fluctuations and is the
damping rate. We show that probability distribution functions obey the
differential equations of motion which contain third order terms (beyond the
usual Fokker-Planck terms) leading to non-Gaussian noise. The problem of
adiabatic fluctuations in velocity space which is the counterpart of Brownian
motion for fast fluctuations, has been solved exactly. The characteristic
function and the associated probability distribution function are shown to be
of stable form. The linear dissipation leads to a steady state which is stable
and the variances and higher moments are shown to be finite.Comment: Plain Latex, no figures, 28 pages; to appear in J. Phys.
Minimal Work Principle and its Limits for Classical Systems
The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte
Thermodynamics of adiabatic feedback control
We study adaptive control of classical ergodic Hamiltonian systems, where the
controlling parameter varies slowly in time and is influenced by system's state
(feedback). An effective adiabatic description is obtained for slow variables
of the system. A general limit on the feedback induced negative entropy
production is uncovered. It relates the quickest negentropy production to
fluctuations of the control Hamiltonian. The method deals efficiently with the
entropy-information trade off.Comment: 6 pages, 1 figur
An extra push from entrance-channel effects
Symmetric heavy-ion collisions are known to display an `extra-push' effect.
That is, the energy at which the s-wave transmission is 0.5 lies significantly
higher than the nominal Coulomb barrier. Despite this, however, the capture
cross section is still greatly enhanced below the uncoupled barrier. It is
shown that this phenomenon can be simply explained in terms of entrance-channel
effects which account for long-range Coulomb excitations.Comment: 9 pages, 4 ps figures, uses elsart.cl
Flareâgenerated shock evolution and geomagnetic storms during the âHalloween 2003 epochâ: 29 October to 2 November
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95151/1/jgra17876.pd
Finite time singularities in a class of hydrodynamic models
Models of inviscid incompressible fluid are considered, with the kinetic
energy (i.e., the Lagrangian functional) taking the form in 3D Fourier representation, where
is a constant, . Unlike the case (the usual Eulerian
hydrodynamics), a finite value of results in a finite energy for a
singular, frozen-in vortex filament. This property allows us to study the
dynamics of such filaments without the necessity of a regularization procedure
for short length scales. The linear analysis of small symmetrical deviations
from a stationary solution is performed for a pair of anti-parallel vortex
filaments and an analog of the Crow instability is found at small wave-numbers.
A local approximate Hamiltonian is obtained for the nonlinear long-scale
dynamics of this system. Self-similar solutions of the corresponding equations
are found analytically. They describe the formation of a finite time
singularity, with all length scales decreasing like ,
where is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal
pape
Propagation of an Earth-directed coronal mass ejection in three dimensions
Solar coronal mass ejections (CMEs) are the most significant drivers of
adverse space weather at Earth, but the physics governing their propagation
through the heliosphere is not well understood. While stereoscopic imaging of
CMEs with the Solar Terrestrial Relations Observatory (STEREO) has provided
some insight into their three-dimensional (3D) propagation, the mechanisms
governing their evolution remain unclear due to difficulties in reconstructing
their true 3D structure. Here we use a new elliptical tie-pointing technique to
reconstruct a full CME front in 3D, enabling us to quantify its deflected
trajectory from high latitudes along the ecliptic, and measure its increasing
angular width and propagation from 2-46 solar radii (approximately 0.2 AU).
Beyond 7 solar radii, we show that its motion is determined by an aerodynamic
drag in the solar wind and, using our reconstruction as input for a 3D
magnetohydrodynamic simulation, we determine an accurate arrival time at the
Lagrangian L1 point near Earth.Comment: 5 figures, 2 supplementary movie
Major Geomagnetic Storms (Dst less than or equal to -100 nT) Generated by Corotating Interaction Regions
Seventy-nine major geomagnetic storms (minimum Dst less than or equal to -100 nT) observed in 1996 to 2004 were the focus of a Living with a Star Coordinated Data-Analysis Workshop (CDAW) in March, 2005. In 9 cases, the storm driver appears to have been purely a corotating interaction region (CIR) without any contribution from coronal mass ejection-related material (interplanetary coronal mass ejections, ICMEs). These storms were generated by structures within CIRs located both before and/or after the stream interface that included persistently southward magnetic fields for intervals of several hours. We compare their geomagnetic effects with those of 159 CIRs observed during 1996 - 2005. The major storms form the extreme tail of a continuous distribution of CIR geoeffectiveness which peaks at Dst approx. -40 nT but is subject to a prominent seasonal variation of - 40 nT which is ordered by the spring and fall equinoxes and the solar wind magnetic field direction towards or away from the Sun. The O'Brien and McPherron [2000] equations, which estimate Dst by integrating the incident solar wind electric field and incorporating a ring current loss term, largely account for the variation in storm size. They tend to underestimate the size of the larger CIR-associated storms by Dst approx. 20 nT. This suggests that injection into the ring current may be more efficient than expected in such storms. Four of the nine major storms in 1996 - 2004 occurred during a period of less than three solar rotations in September - November, 2002, also the time of maximum mean IMF and solar magnetic field intensity during the current solar cycle. The maximum CIR-storm strength found in our sample of events, plus additional 23 probable CIR-associated Dst less than or equal to -100 nT storms in 1972 - 1995, is (Dst = -161 nT). This is consistent with the maximum storm strength (Dst approx. -180 nT) expected from the O'Brien and McPherron equations for the typical range of solar wind electric fields associated with CIRs. This suggests that CIRs alone are unlikely to generate geomagnetic storms that exceed these levels
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