Information In The Non-Stationary Case

Information estimates such as the ``direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that, as the number of trials increases indefinitely, the direct (or ``plug-in'') estimate of marginal entropy converges (with probability 1) to the entropy of the time-averaged conditional distribution of the response, and the direct estimate of the conditional entropy converges to the time-averaged entropy of the conditional distribution of the response. Under joint stationarity and ergodicity of the response and stimulus, the difference of these quantities converges to the mutual information. When the stimulus is deterministic or non-stationary the direct estimate of information no longer estimates mutual information, which is no longer meaningful, but it remains a measure of variability of the response distribution across time

Direct Evidence of an Eruptive, Filament-Hosting Magnetic Flux Rope Leading to a Fast Solar Coronal Mass Ejection

Magnetic flux ropes (MFRs) are believed to be at the heart of solar coronal mass ejections (CMEs). A well-known example is the prominence cavity in the low corona that sometimes makes up a three-part white-light (WL) CME upon its eruption. Such a system, which is usually observed in quiet-Sun regions, has long been suggested to be the manifestation of an MFR with relatively cool filament material collecting near its bottom. However, observational evidence of eruptive, filament-hosting MFR systems has been elusive for those originating in active regions. By utilizing multi-passband extreme-ultra-violet (EUV) observations from SDO/AIA, we present direct evidence of an eruptive MFR in the low corona that exhibits a hot envelope and a cooler core; the latter is likely the upper part of a filament that undergoes a partial eruption, which is later observed in the upper corona as the coiled kernel of a fast, WL CME. This MFR-like structure exists more than one hour prior to its eruption, and displays successive stages of dynamical evolution, in which both ideal and non-ideal physical processes may be involved. The timing of the MFR kinematics is found to be well correlated with the energy release of the associated long-duration C1.9 flare. We suggest that the long-duration flare is the result of prolonged energy release associated with the vertical current sheet induced by the erupting MFR.Comment: 14 pages, 9 figures, to be published in The Astrophysical Journal; accompanying animations can be found at https://www.cfa.harvard.edu/~bchen/publications/Chen+2014_MFR

A 3D radiative transfer framework: X. Arbitrary Velocity Fields in the Co-moving Frame

3-D astrophysical atmospheres will have random velocity fields. We seek to combine the methods we have developed for solving the 1-D problem with arbitrary flows to those that we have developed for solving the fully 3-D relativistic radiative transfer problem in the case of monotonic flows. The methods developed in the case of 3-D atmospheres with monotonic flows, solving the fully relativistic problem along curves defined by an affine parameter, are very flexible and can be extended to the case of arbitrary velocity fields in 3-D. Simultaneously, the techniques we developed for treating the 1-D problem with arbitrary velocity fields are easily adapted to the 3-D problem. The algorithm we present allows the solution of 3-D radiative transfer problems that include arbitrary wavelength couplings. We use a quasi-analytic formal solution of the radiative transfer equation that significantly improves the overall computation speed. We show that the approximate lambda operator developed in previous work gives good convergence, even neglecting wavelength coupling. Ng acceleration also gives good results. We present tests that are of similar resolution to what has been presented using Monte-Carlo techniques, thus our methods will be applicable to problems outside of our test setup. Additional domain decomposition parallelization strategies will be explored in future work.Comment: 9 pages, 9 figures, A&A, in press, new version matches copy edited version, definition restore

Remarks on the Theory of Cosmological Perturbation

It is shown that the power spectrum defined in the Synchronous Gauge can not be directly used to calculate the predictions of cosmological models on the large-scale structure of universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian Gauge.Comment: 13 pages, 1 figure, minor changes, to be published in Chinese Physics Letter

Hawking radiation in a dd-dimensional static spherically-symmetric black Hole surrounded by quintessence

We present a solution of Einstein equations with quintessential matter surrounding a $d$-dimensional black hole, whose asymptotic structures are determined by the state of the quintessential matter. We examine the thermodynamics of this black hole and find that the mass of the black hole depends on the equation of state of the quintessence, while the first law is universal. Investigating the Hawking radiation in this black hole background, we observe that the Hawking radiation dominates on the brane in the low-energy regime. For different asymptotic structures caused by the equation of state of the quintessential matter surrounding the black hole, we learn that the influences by the state parameter of the quintessence on Hawking radiation are different.Comment: 16 pages, Accepted for publication in Phys. Rev.

First Principles Study of Work Functions of Double Wall Carbon Nanotubes

Using first-principles density functional calculations, we investigated work functions (WFs) of thin double-walled nanotubes (DWNTs) with outer tube diameters ranging from 1nm to 1.5nm. The results indicate that work function change within this diameter range can be up to 0.5 eV, even for DWNTs with same outer diameter. This is in contrast with single-walled nanotubes (SWNTs) which show negligible WF change for diameters larger than 1nm. We explain the WF change and related charge redistribution in DWNTs using charge equilibration model (CEM). The predicted work function variation of DWNTs indicates a potential difficulty in their nanoelectronic device applications.Comment: 11 pages, 3 figures, to appear as rapid communication on Physical Review

Characteristics of profiles of gamma-ray burst pulses associated with the Doppler effect of fireballs

In this paper, we derive in a much detail the formula of count rates, in terms of the integral of time, of gamma-ray bursts in the framework of fireballs, where the Doppler effect of the expanding fireball surface is the key factor to be concerned. Effects arising from the limit of the time delay due to the limited regions of the emitting areas in the fireball surface and other factors are investigated. Our analysis shows that the formula of the count rate of fireballs can be expressed as a function of $\tau$ which is the observation time scale relative to the dynamical time scale of the fireball. The profile of light curves of fireballs depends only on the relative time scale, entirely independent of the real time scale and the real size of the objects. It displays in detail how a cutoff tail, or a turn over, feature (called a cutoff tail problem) in the decay phase of a light curve can be formed. This feature is a consequence of a hot spot in the fireball surface, moving towards the observer, and was observed in a few cases previously. By performing fits to the count rate light curves of six sample sources, we show how to obtain some physical parameters from the observed profile of the count rate of GRBs. In addition, the analysis reveals that the Doppler effect of fireballs could lead to a power law relationship between the $FWHM$ of pulses and energy, which were observed previously by many authors.Comment: 38 pages, 10 figures; accepted for publication in ApJ (10 December 2004, v617