arXiv subjects

Rui Liu

Publications and source records attributed to Rui Liu.

At least 487 records · Page 27Linked to original sources

arXiv2014

Chromospheric Rapid Blueshifted Excursions Observed with IBIS and Their Association with Photospheric Magnetic Field Evolution

Chromospheric rapid blueshifted excursions (RBEs) are suggested to be the disk counterparts of type II spicules at the limb and believed to contribute to the coronal heating process. Previous identification of RBEs was mainly based on feature detection using Dopplergrams. In this paper, we study RBEs on 2011 October 21 in a very quiet region at the disk center, which were observed with the high-cadence imaging spectroscopy of the Ca II 8542 A line from the Interferometric Bidimensional Spectrometer (IBIS). By using an automatic spectral analysis algorithm, a total of 98 RBEs are identified during a 11 minute period. Most of these RBEs have either a round or elongated shape, with an average area of 1.2 arcsec^2. The detailed temporal evolution of spectra from IBIS makes possible a quantitative determination of the velocity (~16 km/s) and acceleration (~400 m/s^2) of Ca II 8542 RBEs, and reveal an additional deceleration (~-160 m/s^2) phase that usually follows the initial acceleration. In addition, we also investigate the association of RBEs with the concomitant photospheric magnetic field evolution, using coordinated high-resolution and high-sensitivity magnetograms made by Hinode. Clear examples are found where RBEs appear to be associated with the preceding magnetic flux emergence and/or the subsequent flux cancellation. However, a further analysis with the aid of the Southwest Automatic Magnetic Identification Suite does not yield a significant statistical association between these RBEs and magnetic field evolution. We discuss the implications of our results in the context of understanding the driving mechanism of RBEs.

astro-ph.SR↗

arXiv2014

Dilations of frames, operator valued measures and bounded linear maps

We will give an outline of the main results in our recent AMS Memoir, and include some new results, exposition and open problems. In that memoir we developed a general dilation theory for operator valued measures acting on Banach spaces where operator-valued measures (or maps) are not necessarily completely bounded. The main results state that any operator-valued measure, not necessarily completely bounded, always has a dilation to a projection-valued measure acting on a Banach space, and every bounded linear map, again not necessarily completely bounded, on a Banach algebra has a bounded homomorphism dilation acting on a Banach space. Here the dilation space often needs to be a Banach space even if the underlying space is a Hilbert space, and the projections are idempotents that are not necessarily self-adjoint. These results lead to some new connections between frame theory and operator algebras, and some of them can be considered as part of the investigation about "noncommutative" frame theory.

math.FA↗

arXiv2014

Dilations for Systems of Imprimitivity acting on Banach Spaces

Motivated by a general dilation theory for operator-valued measures, framings and bounded linear maps on operator algebras, we consider the dilation theory of the above objects with special structures. We show that every operator-valued system of imprimitivity has a dilation to a probability spectral system of imprimitivity acting on a Banach space. This completely generalizes a well-kown result which states that every frame representation of a countable group on a Hilbert space is unitarily equivalent to a subrepresentation of the left regular representation of the group. The dilated space in general can not be taken as a Hilbert space. However, it can be taken as a Hilbert space for positive operator valued systems of imprimitivity. We also prove that isometric group representation induced framings on a Banach space can be dilated to unconditional bases with the same structure for a larger Banach space This extends several known results on the dilations of frames induced by unitary group representations on Hilbert spaces.

math.FA↗

arXiv2014

Early Evolution of an Energetic Coronal Mass Ejection and Its Relation to EUV Waves

We study a coronal mass ejection (CME) associated with an X-class flare, whose initiation is clearly observed in low corona with high-cadence, high-resolution EUV images, providing us a rare opportunity to witness the early evolution of an energetic CME in detail. The eruption starts with a slow expansion of cool overlying loops (~1 MK) following a jet-like event in the periphery of the active region. Underneath the expanding loop system a reverse S-shaped dimming is seen immediately above the brightening active region in hot EUV passbands. The dimming is associated with a rising diffuse arch (~6 MK), which we interpret as a preexistent, high-lying flux rope. This is followed by the arising of a double hot channel (~10 MK) from the core of the active region. The higher structures rise earlier and faster than lower ones, with the leading front undergoing extremely rapid acceleration up to 35 km s$^2$. This suggests that the torus instability is the major eruption mechanism and that it is the high-lying flux rope rather than the hot channels that drives the eruption. The compression of coronal plasmas skirting and overlying the expanding loop system, whose aspect ratio $h/r$ increases with time as a result of the rapid upward acceleration, plays a significant role in driving an outward-propagating global EUV wave and a sunward-propagating local EUV wave, respectively.

astro-ph.SR↗

arXiv2014

Slow Rise and Partial Eruption of a Double-Decker Filament. II. Modeling by a Double Flux Rope Equilibrium

Force-free equilibria containing two vertically arranged magnetic flux ropes of like chirality and current direction are considered as a model for split filaments/prominences and filament-sigmoid systems. Such equilibria are constructed analytically through an extension of the methods developed in Titov & Démoulin (1999) and numerically through an evolutionary sequence including shear flows, flux emergence, and flux cancellation in the photospheric boundary. It is demonstrated that the analytical equilibria are stable if an external toroidal (shear) field component exceeding a threshold value is included. If this component decreases sufficiently, then both flux ropes turn unstable for conditions typical of solar active regions, with the lower rope typically being unstable first. Either both flux ropes erupt upward, or only the upper rope erupts while the lower rope reconnects with the ambient flux low in the corona and is destroyed. However, for shear field strengths staying somewhat above the threshold value, the configuration also admits evolutions which lead to partial eruptions with only the upper flux rope becoming unstable and the lower one remaining in place. This can be triggered by a transfer of flux and current from the lower to the upper rope, as suggested by the observations of a split filament in Paper~I (Liu et al. 2012). It can also result from tether-cutting reconnection with the ambient flux at the X-type structure between the flux ropes, which similarly influences their stability properties in opposite ways. This is demonstrated for the numerically constructed equilibrium.

astro-ph.SR↗

arXiv2014

A Prominence Eruption Driven by Flux Feeding from Chromospheric Fibrils

We present multi-wavelength observations of a prominence eruption originating from a quadrupolar field configuration, in which the prominence was embedded in a side-arcade. Within the two-day period prior to its eruption on 2012 October 22, the prominence was perturbed three times by chromospheric fibrils underneath, which rose upward, became brightened, and merged into the prominence, resulting in horizontal flows along the prominence axis, suggesting that the fluxes carried by the fibrils were incorporated into the magnetic field of the prominence. These perturbations caused the prominence to oscillate and to rise faster than before. The absence of intense heating within the first two hours after the onset of the prominence eruption, which followed an exponential increase in height, indicates that ideal instability played a crucial role. The eruption involved interactions with the other side-arcade, leading up to a twin coronal mass ejection, which was accompanied by transient surface brightenings in the central arcade, followed by transient dimmings and brightenings in the two side-arcades. We suggest that flux feeding from chromospheric fibrils might be an important mechanism to trigger coronal eruptions.

astro-ph.SR↗

arXiv2014

An Unorthodox X-Class Long-Duration Confined Flare

We report the observation of an X-class long-duration flare which is clearly confined. It appears as a compact-loop flare in the traditional EUV passbands (171 and 195 Å), but in the passbands sensitive to flare plasmas (94 and 131 Å), it exhibits a cusp-shaped structure above an arcade of loops like other long-duration events. Inspecting images in a running difference approach, we find that the seemingly diffuse, quasi-static cusp-shaped structure consists of multiple nested loops that repeatedly rise upward and disappear approaching the cusp edge. Over the gradual phase, we detect numerous episodes of loop rising, each lasting minutes. A differential emission measure analysis reveals that the temperature is highest at the top of the arcade and becomes cooler at higher altitudes within the cusp-shaped structure, contrary to typical long-duration flares. With a nonlinear force-free model, our analysis shows that the event mainly involves two adjacent sheared arcades separated by a T-type hyperbolic flux tube (HFT). One of the arcades harbors a magnetic flux rope, which is identified with a filament that survives the flare owing to the strong confining field. We conclude that a new emergence of magnetic flux in the other arcade triggers the flare, while the preexisting HFT and flux rope dictate the structure and dynamics of the flare loops and ribbons during the long-lasting decay phase, and that a quasi-separatrix layer high above the HFT could account for the cusp-shaped structure.

astro-ph.SR↗

arXiv2014

Temperature evolution of magnetic flux rope in a failed solar eruption

In this presentation, we report for the first time the detailed temperature evolution process of the magnetic flux rope in a failed solar eruption. Occurred on January 05, 2013, the flux rope was impulsively accelerated to a speed of ~ 400 km/s in the first minute, then decelerated and came to a complete stop in two minutes. The failed eruption resulted in a large-size high-lying (~ 100 Mm above the surface) high-temperature "fire ball" sitting in the corona for more than two hours. The time evolution of the thermal structure of the flux rope was revealed through the differential emission measure analysis technique, which produced temperature maps using observations of the Atmospheric Imaging Assembly on board Solar Dynamic Observatory. The average temperature of the flux rope steadily increased from ~ 5 MK to ~ 10 MK during the first nine minutes of the evolution, which was much longer than the rise time (about three minutes) of the associated soft X-ray flare. We suggest that the flux rope be heated by the energy release of the continuing magnetic reconnection, different from the heating of the low-lying flare loops, which is mainly produced by the chromospheric plasma evaporation. The loop arcade overlying the flux rope was pushed up by ~ 10 Mm during the attempted eruption. The pattern of the velocity variation of the loop arcade strongly suggests that the failure of the eruption be caused by the strapping effect of the overlying loop arcade.

physics.space-ph↗

arXiv2014

When and how does a prominence-like jet gain kinetic energy?

A jet is a considerable amount of plasma being ejected from the chromosphere or lower corona into the higher corona and is a common phenomenon. Usually, a jet is triggered by a brightening or a flare, which provides the first driving force to push plasma upward. In this process, magnetic reconnection is thought to be the mechanism to convert magnetic energy into thermal, nonthermal, and kinetic energies. However, most jets could reach an unusual high altitude and end much later than the end of its associated flare. This fact implies that there is another way to continuously transfer magnetic energy into kinetic energy even after the reconnection. The picture described above is well known in the community, but how and how much magnetic energy is released through a way other than reconnection is still unclear. By studying a prominence-like jet observed by SDO/AIA and STEREO-A/EUVI, we find that the continuous relaxation of the post-reconnection magnetic field structure is an important process for a jet to climb up higher than it could through only reconnection. The kinetic energy of the jet gained through the relaxation is 1.6 times that gained from the reconnection. The resultant energy flux is hundreds of times larger than the flux required for the local coronal heating, suggesting that such jets are a possible source to keep the corona hot. Furthermore, rotational motions appear all the time during the jet. Our analysis suggests that torsional Alfvén waves induced during reconnection could not be the only mechanism to release magnetic energy and drive jets.

astro-ph.SR↗

arXiv2013

Feature Selection Based on Term Frequency and T-Test for Text Categorization

Much work has been done on feature selection. Existing methods are based on document frequency, such as Chi-Square Statistic, Information Gain etc. However, these methods have two shortcomings: one is that they are not reliable for low-frequency terms, and the other is that they only count whether one term occurs in a document and ignore the term frequency. Actually, high-frequency terms within a specific category are often regards as discriminators. This paper focuses on how to construct the feature selection function based on term frequency, and proposes a new approach based on $t$-test, which is used to measure the diversity of the distributions of a term between the specific category and the entire corpus. Extensive comparative experiments on two text corpora using three classifiers show that our new approach is comparable to or or slightly better than the state-of-the-art feature selection methods (i.e., $χ^2$, and IG) in terms of macro-$F_1$ and micro-$F_1$.

cs.LG↗

arXiv2013

Waiting Times of Quasi-homologous Coronal Mass Ejections from Super Active Regions

Why and how may some active regions (ARs) frequently produce coronal mass ejections (CMEs)? It is one of the key questions to deepen our understanding of the mechanisms and processes of energy accumulation and sudden release in ARs and to improve our capability of space weather prediction. Although some case studies have been made, the question is still far from fully answered. This issue is now being tried to address statistically through an investigation of waiting times of quasi-homologous CMEs from super ARs in solar cycle 23. It is found that the waiting times of quasi-homologous CMEs have a two-component distribution with a separation at about 18 hours. The first component is a Gaussian-like distribution with a peak at about 7 hours, which indicates a tight physical connection between these quasi-homologous CMEs. The likelihood of occurrences of two or more CMEs faster than 1200 km s-1 from the same AR within 18 hours is about 20%. Furthermore, the correlation analysis among CME waiting times, CME speeds and CME occurrence rates reveals that these quantities are independent to each other, suggesting that the perturbation by preceding CMEs rather than free energy input be the direct cause of quasi-homologous CMEs. The peak waiting time of 7 hours probably characterize the time scale of the growth of instabilities triggered by preceding CMEs. This study uncovers more clues from a statistical perspective for us to understand quasi-homologous CMEs as well as CME-rich ARs.

astro-ph.SR↗

arXiv2012

Generalized-Lush Spaces and the Mazur-Ulam Property

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable $C$-rich subspaces of $C(K)$), and even the two-dimensional space with hexagonal norm. We obtain that the space $C(K,E)$ of the vector-valued continuous functions is a GL-space whenever $E$ is, and show that the GL-space is stable under $c_0$-, $l_1$- and $l_\infty$-sums. As an application, we prove that the Mazur-Ulam property holds for a larger class of Banach spaces, called local-GL-spaces, including all lush spaces and GL-spaces. Furthermore, we generalize the stability properties of GL-spaces to local-GL-spaces. From this, we can obtain many examples of Banach spaces having the Mazur-Ulam property.

math.FA↗

arXiv2012

Slow Magneto-acoustic Waves Observed above Quiet-Sun Region in a Dark Cavity

Waves play a crucial role in diagnosing the plasma properties of various structures in the solar corona and coronal heating. Slow magneto-acoustic (MA) waves are one of the important magnetohydrodynamic waves. In past decades, numerous slow MA waves were detected above the active regions and coronal holes, but rarely found elsewhere. Here, we investigate a `tornado'-like structure consisting of quasi-periodic streaks within a dark cavity at about 40--110 Mm above the quiet-Sun region on 2011 September 25. Our analysis reveals that these streaks are actually slow MA wave trains. The properties of these wave trains, including the phase speed, compression ratio, kinetic energy density, etc., are similar to those of the reported slow MA waves, except that the period of these waves is about 50 s, much shorter than the typical reported values (3--5 minutes).

astro-ph.SR↗

arXiv2012

A Note on The Mazur-Ulam Property of Almost-CL-spaces

We introduce the (T)-property, and prove that every Banach space with the (T)-property has the Mazur-Ulam property (briefly MUP). As its immediate applications, we obtain that almost-CL-spaces admitting a smooth point(specially, separable almost-CL-spaces) and a two-dimensional space whose unit sphere is a hexagon has the MUP. Furthermore, we discuss the stability of the spaces having the MUP by the $c_0$- and $\ell_1$-sums, and show that the space $C(K,X)$ of the vector-valued continuous functions has the the MUP, where $X$ is a separable almost-CL-space and $K$ is a compact metric space.

math.FA↗

arXiv2012

Slow Rise and Partial Eruption of a Double-Decker Filament. I Observations and Interpretation

We study an active-region dextral filament which was composed of two branches separated in height by about 13 Mm. This "double-decker" configuration sustained for days before the upper branch erupted with a GOES-class M1.0 flare on 2010 August 7. Analyzing this evolution, we obtain the following main results. 1) During hours before the eruption, filament threads within the lower branch were observed to intermittently brighten up, lift upward, and then merge with the upper branch. The merging process contributed magnetic flux and current to the upper branch, resulting in its quasi-static ascent. 2) This transfer might serve as the key mechanism for the upper branch to lose equilibrium by reaching the limiting flux that can be stably held down by the overlying field or by reaching the threshold of the torus instability. 3) The erupting branch first straightened from a reverse S shape that followed the polarity inversion line and then writhed into a forward S shape. This shows a transfer of left-handed helicity in a sequence of writhe-twist-writhe. The fact that the initial writhe is converted into the twist of the flux rope excludes the helical kink instability as the trigger process of the eruption, but supports the occurrence of the instability in the main phase, which is indeed indicated by the very strong writhing motion. 4) A hard X-ray sigmoid, likely of coronal origin, formed in the gap between the two original filament branches in the impulsive phase of the associated flare. This supports a model of transient sigmoids forming in the vertical flare current sheet. 5) Left-handed magnetic helicity is inferred for both branches of the dextral filament. 6) Two types of force-free magnetic configurations are compatible with the data, a double flux rope equilibrium and a single flux rope situated above a loop arcade.

astro-ph.SR↗

arXiv2012

Contracting and Erupting Components of Sigmoidal Active Regions

It is recently noted that solar eruptions can be associated with the contraction of coronal loops that are not involved in magnetic reconnection processes. In this paper, we investigate five coronal eruptions originating from four sigmoidal active regions, using high-cadence, high-resolution narrowband EUV images obtained by the Solar Dynamic Observatory (SDO}). The magnitudes of the flares associated with the eruptions range from the GOES-class B to X. Owing to the high-sensitivity and broad temperature coverage of the Atmospheric Imaging Assembly (AIA) onboard SDO, we are able to identify both the contracting and erupting components of the eruptions: the former is observed in cold AIA channels as the contracting coronal loops overlying the elbows of the sigmoid, and the latter is preferentially observed in warm/hot AIA channels as an expanding bubble originating from the center of the sigmoid. The initiation of eruption always precedes the contraction, and in the energetically mild events (B and C flares), it also precedes the increase in GOES soft X-ray fluxes. In the more energetic events, the eruption is simultaneous with the impulsive phase of the nonthermal hard X-ray emission. These observations confirm the loop contraction as an integrated process in eruptions with partially opened arcades. The consequence of contraction is a new equilibrium with reduced magnetic energy, as the contracting loops never regain their original positions. The contracting process is a direct consequence of flare energy release, as evidenced by the strong correlation of the maximal contracting speed, and strong anti-correlation of the time delay of contraction relative to expansion, with the peak soft X-ray flux. This is also implied by the relationship between contraction and expansion, i.e., their timing and speed.

astro-ph.SR↗

arXiv2012

Operator-Valued Measures, Dilations, and the Theory of Frames

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known results from the theory of frames and framings.

math.OA↗

arXiv2012

Hilbert-Schauder Frame Operators

We introduce a new concept of frame operators for Banach spaces we call a Hilbert-Schauder frame operator. This is a hybird between standard frame theory for Hilbert spaces and Schauder frame theory for Banach spaces. Most of our results involve basic structure properties of the Hilbert-Schauder frame operator. Examples of Hilbert-Schauder frames include standard Hilbert frames and classical bases of $\ell_p$ and $L^p$-spaces with $1< p \le 2$. Finally, we give a new isomorphic characterization of Hilbert spaces.

math.FA↗