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 $\alpha |\mu|^{-1}$, where $\alpha$ is the strength of fluctuations and $|\mu|$ 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

Flare‐generated shock evolution and geomagnetic storms during the “Halloween 2003 epoch”: 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 ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant, $0<\alpha< 1$. Unlike the case $\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\alpha$ 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 $(t^*-t)^{1/(2-\alpha)}$, where $t^*$ 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