On the Controllability of Nonlinear Control Systems

In this paper, some discussions for the controllability in nonlinear systems are presented. At first various concepts about controllability are denned. In section 3, one dimensional systems are treated and sufficient conditions for controllability are obtained. In section 4, we discuss the controllability of nonlinear systems with controls appearing linearly and show that it is possible to reduce the controllability of the given system to that of some lower dimensional system. One result in section 3 is extended to n-dimensional system in the following section. In section 6, the concept of the controllability in the local sense is introduced according to L. Markus. At last, relations between various concepts of controllability are shown

Time Resolved Correlation measurements of temporally heterogeneous dynamics

Time Resolved Correlation (TRC) is a recently introduced light scattering technique that allows to detect and quantify dynamic heterogeneities. The technique is based on the analysis of the temporal evolution of the speckle pattern generated by the light scattered by a sample, which is quantified by $c\_I(t,\tau)$, the degree of correlation between speckle images recorded at time $t$ and $t+\tau$. Heterogeneous dynamics results in significant fluctuations of $c\_I(t,\tau)$ with time $t$. We describe how to optimize TRC measurements and how to detect and avoid possible artifacts. The statistical properties of the fluctuations of $c\_I$ are analyzed by studying their variance, probability distribution function, and time autocorrelation function. We show that these quantities are affected by a noise contribution due to the finite number $N$ of detected speckles. We propose and demonstrate a method to correct for the noise contribution, based on a $N\to \infty$ extrapolation scheme. Examples from both homogeneous and heterogeneous dynamics are provided. Connections with recent numerical and analytical works on heterogeneous glassy dynamics are briefly discussed.Comment: 19 pages, 15 figures. Submitted to PR

Cosmic ray short burst observed with the Global Muon Detector Network (GMDN) on June 22, 2015

We analyze the short cosmic ray intensity increase ("cosmic ray burst": CRB) on June 22, 2015 utilizing a global network of muon detectors and derive the global anisotropy of cosmic ray intensity and the density (i.e. the omnidirectional intensity) with 10-minute time resolution. We find that the CRB was caused by a local density maximum and an enhanced anisotropy of cosmic rays both of which appeared in association with Earth's crossing of the heliospheric current sheet (HCS). This enhanced anisotropy was normal to the HCS and consistent with a diamagnetic drift arising from the spatial gradient of cosmic ray density, which indicates that cosmic rays were drifting along the HCS from the north of Earth. We also find a significant anisotropy along the HCS, lasting a few hours after the HCS crossing, indicating that cosmic rays penetrated into the inner heliosphere along the HCS. Based on the latest geomagnetic field model, we quantitatively evaluate the reduction of the geomagnetic cut-off rigidity and the variation of the asymptotic viewing direction of cosmic rays due to a major geomagnetic storm which occurred during the CRB and conclude that the CRB is not caused by the geomagnetic storm, but by a rapid change in the cosmic ray anisotropy and density outside the magnetosphere.Comment: accepted for the publication in the Astrophysical Journa

IBEX: The First Five Years (2009-2013)

The Interstellar Boundary Explorer (IBEX) returned its first five years of scientific observations from 2009 to 2013. In this study, we examine, validate, initially analyze, and provide to the broad scientific community this complete set of energetic neutral atom (ENA) observations for the first time. IBEX measures the fluxes of ENAs reaching 1 AU from sources in the outer heliosphere and most likely the very nearby interstellar space beyond the heliopause. The data, maps, and documentation provided in this study represent the fourth major release of the IBEX data, incorporate important improvements, and should be used for future studies and as the citable reference for the current version of the IBEX data. In this study, we also examine five years of time evolution in the outer heliosphere and the resulting ENA emissions. These observations show a complicated variation with a general decrease in the ENA fluxes from 2009 to 2012 over most regions of the sky, consistent with a 2-4 year recycle time for the previously decreasing solar wild flux. In contrast, the heliotail fluxes continue to decrease, again consistent with a significantly more distant source in the downwind direction. Finally, the Ribbon shows the most complicated time variations, with a leveling off in the southern hemisphere and continued decline in the northern one; these may be consistent with the Ribbon source being significantly farther away in the north than in the south. Together, the observations and results shown in this study expose the intricacies of our heliopshere\u27s interaction with the local interstellar medium

AVERAGE SPATIAL DISTRIBUTION OF COSMIC RAYS BEHIND THE INTERPLANETARY SHOCK-GLOBAL MUON DETECTOR NETWORK OBSERVATIONS

We analyze the galactic cosmic ray (GCR) density and its spatial gradient in Forbush Decreases (FDs) observed with the Global Muon Detector Network (GMDN) and neutron monitors (NMs). By superposing the GCR density and density gradient observed in FDs following 45 interplanetary shocks (IP-shocks), each associated with an identified eruption on the Sun, we infer the average spatial distribution of GCRs behind IP-shocks. We find two distinct modulations of GCR density in FDs, one in the magnetic sheath and the other in the coronal mass ejection (CME) behind the sheath. The density modulation in the sheath is dominant in the western flank of the shock, while the modulation in the CME ejecta stands out in the eastern flank. This east-west asymmetry is more prominent in GMDN data responding to similar to 60 GV GCRs than in NM data responding to similar to 10 GV GCRs, because of the softer rigidity spectrum of the modulation in the CME ejecta than in the sheath. The geocentric solar ecliptic-y component of the density gradient, G(y), shows a negative (positive) enhancement in FDs caused by the eastern (western) eruptions, while G(z) shows a negative (positive) enhancement in FDs caused by the northern (southern) eruptions. This implies that the GCR density minimum is located behind the central flank of IP-shocks and propagating radially outward from the location of the solar eruption. We also confirmed that the average Gz changes its sign above and below the heliospheric current sheet, in accord with the prediction of the drift model for the large-scale GCR transport in the heliosphere.ArticleASTROPHYSICAL JOURNAL. 825(2):100 (2016)journal articl