Searcharxiv⌕ Search

arXiv subjects

Rui Liu

Publications and source records attributed to Rui Liu.

At least 505 records · Page 28Linked to original sources

Upper Beurling Density of Systems formed by Translates of finite Sets of Elements in $L^p(\R^d)$

In this paper, we prove that if a finite disjoint union of translates $\bigcup_{k=1}^n\{f_k(x-γ)\}_{γ\inΓ_k}$ in $L^p(\R^d)$ $(1<p<\infty)$ is a $p'$-Bessel sequence for some $1<p'<\infty$, then the disjoint union $Γ=\bigcup_{k=1}^nΓ_k$ has finite upper Beurling density, and that if $\bigcup_{k=1}^n\{f_k(x-γ)\}_{γ\inΓ_k}$ is a $(C_q)$-system with $1/p+1/q=1$, then $Γ$ has infinite upper Beurling density. Thus, no finite disjoint union of translates in $L^p(\R^d)$ can form a $p'$-Bessel $(C_q)$-system for any $1< p'<\infty$. Furthermore, by using techniques from the geometry of Banach spaces, we obtain that, for $1<p\le2$, no finite disjoint union of translates in $L^p(\R^d)$ can form an unconditional basis.

math.FA↗

The Occurrence and Speed of CMEs Related to Two Characteristic Evolution Patterns of Helicity Injection in Their Solar Source Regions

Long-term (a few days) variation of magnetic helicity injection was calculated for 28 solar active regions which produced 47 CMEs to find its relationships with the CME occurrence and speed using SOHO/MDI line-of-sight magnetograms. As a result, we found that the 47 CMEs can be categorized into two different groups by two characteristic evolution patterns of helicity injection in their source active regions which appeared for about 0.5-4.5 days before their occurrence: (1) a monotonically increasing pattern with one sign of helicity (Group A; 30 CMEs in 23 active regions) and (2) a pattern of significant helicity injection followed by its sign reversal (Group B; 17 CMEs in 5 active regions). We also found that CME speed has a correlation with average helicity injection rate with linear correlation coefficients of 0.85 and 0.63 for Group A and Group B, respectively. In addition, these two CME groups show different characteristics as follows: (1) the average CME speed of Group B (1330km/s) is much faster than that of Group A (870km/s), (2) the CMEs in Group A tend to be single events, whereas those in Group B mainly consist of successive events, and (3) flares related to the CMEs in Group B are relatively more energetic and impulsive than those in Group A. Our findings therefore suggest that the two CME groups have different pre-CME conditions in their source active regions and different CME characteristics.

astro-ph.SR↗

Upper and lower estimates for schauder frames and atomic decompositions

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable infinite dimensional Banach space has a Schauder frame, then it also has a Schauder frame which is not shrinking.

math.FA↗

Response of the Photospheric Magnetic Field to the X2.2 Flare on 2011 February 15

It is well known that the long-term evolution of the photospheric magnetic field plays an important role in building up free energy to power solar eruptions. Observations, despite being controversial, have also revealed a rapid and permanent variation of the photospheric magnetic field in response to the coronal magnetic field restructuring during the eruption. The Helioseismic and Magnetic Imager instrument (HMI) on board the newly launched Solar Dynamics Observatory (SDO) produces seeing-free full-disk vector magnetograms at consistently high resolution and high cadence, which finally makes possible an unambiguous and comprehensive study of this important back-reaction process. In this study, we present a near disk-center, GOES -class X2.2 flare, which occurred in NOAA AR 11158 on 2011 February 15. Using the magnetic field measurements made by HMI, we obtained the first solid evidence of a rapid (in about 30 minutes) and irreversible enhancement in the horizontal magnetic field at the flaring magnetic polarity inversion line (PIL) by a magnitude of ~30%. It is also shown that the photospheric field becomes more sheared and more inclined. This field evolution is unequivocally associated with the flare occurrence in this sigmoidal active region, with the enhancement area located in between the two chromospheric flare ribbons and the initial conjugate hard X-ray footpoints. These results strongly corroborate our previous conjecture that the photospheric magnetic field near the PIL must become more horizontal after eruptions, which could be related to the newly formed low-lying fields resulted from the tether-cutting reconnection.

astro-ph.SR↗

Rapid Changes of Photospheric Magnetic Field after Tether-Cutting Reconnection and Magnetic Implosion

The rapid, irreversible change of the photospheric magnetic field has been recognized as an important element of the solar flare process. This Letter reports such a rapid change of magnetic fields during the 2011 February 13 M6.6 flare in NOAA AR 11158 that we found from the vector magnetograms of the Helioseismic and Magnetic Imager with 12-min cadence. High-resolution magnetograms of Hinode that are available at ~-5.5, -1.5, 1.5, and 4 hrs relative to the flare maximum are used to reconstruct three-dimensional coronal magnetic field under the nonlinear force-free field (NLFFF) assumption. UV and hard X-ray images are also used to illuminate the magnetic field evolution and energy release. The rapid change is mainly detected by HMI in a compact region lying in the center of the magnetic sigmoid, where the mean horizontal field strength exhibited a significant increase by 28%. The region lies between the initial strong UV and hard X-ray sources in the chromosphere, which are cospatial with the central feet of the sigmoid according to the NLFFF model. The NLFFF model further shows that strong coronal currents are concentrated immediately above the region, and that more intriguingly, the coronal current system underwent an apparent downward collapse after the sigmoid eruption. These results are discussed in favor of both the tether-cutting reconnection producing the flare and the ensuing implosion of the coronal field resulting from the energy release.

astro-ph.SR↗

A Time Series of Filament Eruptions Observed by Three Eyes from Space: From Failed to Successful Eruptions

We present stereoscopic observations of six sequent eruptions of a filament in the active region NOAA 11045 on 2010 Feb 8, with the advantage of the STEREO twin viewpoints in combination with the earth viewpoint from SOHO instruments and ground-based telescopes. The last one of the six eruptions is with a coronal mass ejection, while the others are not. The flare in this successful one is more intensive than in the others. Moreover, the filament material velocity of the successful one is also the largest among them. Interestingly, all the filament velocities are found proportional to their flare powers. We calculate magnetic field intensity at low altitude, the decay indexes of the external field above the filament, and the asymmetry properties of the overlying fields before and after the failed eruptions and find little difference between them, indicating the same coronal confinement for the failed and the successful eruptions. The results suggest that, besides the confinement of coronal magnetic field, the energy released in low corona should be another crucial element for production of a failed or successful filament eruption. That is, only a coronal mass ejection can be launched away if the energy released exceeds some critical value, given the same coronal conditions.

astro-ph.SR↗

A standard-to-blowout jet

The commonly observed jets provide critical information on the small-scale energy release in the solar atmosphere. We report a near disk-center jet on 2010 July 20, observed by the Solar Dynamics Observatory. In this event, the standard interchange magnetic reconnection between an emerging flux spanning 9 x 10^3 km and ambient open fields is followed by a blowout-like eruption. In the "standard" stage, as the emerging negative element approached the nearby positive network fields, a jet with a dome-like base in EUV grew for 30 minutes before the jet spire began to migrate laterally with enhanced flux emergence. In the "blowout" stage, the above converging fields collided and the subsequent cancellation produced a UV microflare lasting seven minutes, in which the dome of the jet seemed to be blown out as (1) the spire swung faster and exhibited an unwinding motion before vanishing, (2) a rising loop and a blob erupted leaving behind cusped structures, with the blob spiraling outward in acceleration after the flare maximum, and (3) ejecting material with a curtain-like structure at chromospheric to transition-region temperatures also underwent a transverse motion. It is thus suggested that the flare reconnection rapidly removes the outer fields of the emerging flux to allow its twisted core field to erupt, a scenario favoring the jet-scale magnetic breakout model as recently advocated by Moore et al. in 2010.

astro-ph.SR↗

Predicting Bugs' Components via Mining Bug Reports

The number of bug reports in complex software increases dramatically. Now bugs are triaged manually, bug triage or assignment is a labor-intensive and time-consuming task. Without knowledge about the structure of the software, testers often specify the component of a new bug wrongly. Meanwhile, it is difficult for triagers to determine the component of the bug only by its description. We dig out the components of 28,829 bugs in Eclipse bug project have been specified wrongly and modified at least once. It results in these bugs have to be reassigned and delays the process of bug fixing. The average time of fixing wrongly-specified bugs is longer than that of correctly-specified ones. In order to solve the problem automatically, we use historical fixed bug reports as training corpus and build classifiers based on support vector machines and Naïve Bayes to predict the component of a new bug. The best prediction accuracy reaches up to 81.21% on our validation corpus of Eclipse project. Averagely our predictive model can save about 54.3 days for triagers and developers to repair a bug. Keywords: bug reports; bug triage; text classification; predictive model

cs.SE↗

First Flare-related Rapid Change of Photospheric Magnetic Field Observed by Solar Dynamics Observatory

Photospheric magnetic field not only plays important roles in building up free energy and triggering solar eruptions, but also has been observed to change rapidly and permanently responding to the coronal magnetic field restructuring due to coronal transients. The Helioseismic and Magnetic Imager instrument (HMI) on board the newly launched Solar Dynamics Observatory (SDO) produces seeing-free full-disk vector magnetograms at consistently high resolution and high cadence, which finally makes possible an unambiguous and comprehensive study of this important back-reaction process. In this study, we present a near disk-center, GOES-class X2.2 flare occurred at NOAA AR 11158 on 2011 February 15 using the magnetic field measurements made by HMI. We obtained the first solid evidence of an enhancement in the transverse magnetic field at the flaring magnetic polarity inversion line (PIL) by a magnitude of 70%. This rapid and irreversible field evolution is unequivocally associated with the flare occurrence, with the enhancement area located in between the two chromospheric flare ribbons. Similar findings have been made for another two major flare events observed by SDO. These results strongly corroborate our previous suggestion that the photospheric magnetic field near the PIL must become more horizontal after eruptions. In-depth studies will follow to further link the photospheric magnetic field changes with the dynamics of coronal mass ejections, when full Stokes inversion is carried out to generate accurate magnetic field vectors.

astro-ph.SR↗

Sigmoid-to-Flux-Rope Transition Leading to A Loop-Like Coronal Mass Ejection

Sigmoids are one of the most important precursor structures for solar eruptions. In this Letter, we study a sigmoid eruption on 2010 August 1 with EUV data obtained by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory (SDO). In AIA 94 Å (Fe XVIII; 6 MK), topological reconfiguration due to tether-cutting reconnection is unambiguously observed for the first time, i.e., two opposite J-shaped loops reconnect to form a continuous S-shaped loop, whose central portion is dipped and aligned along the magnetic polarity inversion line (PIL), and a compact loop crossing the PIL. A causal relationship between photospheric flows and coronal tether-cutting reconnections is evidenced by the detection of persistent converging flows toward the PIL using line-of-sight magnetograms obtained by the Helioseismic and Magnetic Imager (HMI) on board SDO. The S-shaped loop remains in quasi-equilibrium in the lower corona for about 50 minutes, with the central dipped portion rising slowly at ~10 km s-1. The speed then increases to ~60 km s-1 about 10 minutes prior to the onset of a GOES-class C3.2 flare, as the S-shaped loop speeds up its transformation into an arch-shaped loop, which eventually leads to a loop-like coronal mass ejection (CME). The AIA observations combined with H? filtergrams as well as hard X-ray (HXR) imaging and spectroscopy are consistent with most flare loops being formed by reconnection of the stretched legs of less-sheared J-shaped loops that envelopes the rising flux rope, in agreement with the standard tether-cutting scenario.

astro-ph.SR↗

A Reconnecting Current Sheet Imaged in A Solar Flare

Magnetic reconnection changes the magnetic field topology and powers explosive events in astrophysical, space and laboratory plasmas. For flares and coronal mass ejections (CMEs) in the solar atmosphere, the standard model predicts the presence of a reconnecting current sheet, which has been the subject of considerable theoretical and numerical modeling over the last fifty years, yet direct, unambiguous observational verification has been absent. In this Letter we show a bright sheet structure of global length (>0.25 Rsun) and macroscopic width ((5 - 10)x10^3 km) distinctly above the cusp-shaped flaring loop, imaged during the flare rising phase in EUV. The sheet formed due to the stretch of a transequatorial loop system, and was accompanied by various reconnection signatures that have been dispersed in the literature. This unique event provides a comprehensive view of the reconnection geometry and dynamics in the solar corona.

astro-ph.SR↗

Motions of Hard X-ray Sources During an Asymmetric Eruption

Filament eruptions and hard X-ray (HXR) source motions are commonly observed in solar flares, which provides critical information on the coronal magnetic reconnection. This Letter reports an event on 2005 January 15, in which we found an asymmetric filament eruption and a subsequent coronal mass ejection together with complicated motions of HXR sources during the GOES-class X2.6 flare. The HXR sources initially converge to the magnetic polarity inversion line (PIL), and then move in directions either parallel or perpendicular to the PIL depending on the local field configuration. We distinguish the evolution of the HXR source motion in four phases and associate each of them with distinct regions of coronal magnetic fields as reconstructed using a non-linear force-free field extrapolation. It is found that the magnetic reconnection proceeds along the PIL toward the regions where the overlying field decreases with height more rapidly. It is also found that not only the perpendicular but the parallel motion of the HXR sources correlates well with the HXR lightcurve. These results are discussed in favor of the torus instability as an important factor in the eruptive process.

astro-ph.SR↗

Gradual Inflation of Active-Region Coronal Arcades Building up to Coronal Mass Ejections

The pre-CME structure is of great importance to understanding the origin of CMEs, which, however, has been largely unknown for CMEs originating from active regions. In this paper, selected for studying are 16 active-region coronal arcades whose gradual inflation lead up to CMEs. 12 of them clearly build upon post-eruptive arcades resulting from a preceding eruption. The observed inflation sustains for 8.7 +/- 4.1 h, with the arcade rising from 1.15 +/- 0.06 Rsun to 1.36 +/- 0.07 Rsun within the EIT field of view (FOV). The rising speed is less than 5 km s-1 for most of the time. Only at the end of this quasi-static stage, it increases to tens of kilometers per second over tens of minutes. The arcade then erupts out of the EIT FOV as a CME with similar morphology. This pre-CME structure is apparently unaffected by the flares occurring during its quasi-static inflation phase, but is closely coupled with the flare occurring during its acceleration phase. For four events that were observed on the disk, it is found that the gradual inflation of the arcade is accompanied by significant helicity injection from photosphere. In particular, a swirling structure, which is reminiscent of a magnetic flux rope, was observed in one of the arcades over 4 h prior to the subsequent CME, and the growth of the arcade is associated with the injection of helicity of opposite sense into the active region via flux emergence. We propose a four-phase evolution paradigm for the observed CMEs, i.e., a quasi-static inflation phase which corresponds to the buildup of magnetic free energy in the corona, followed by the frequently observed three-phase paradigm, including an initial phase, an acceleration phase and a gradual phase.

astro-ph.SR↗

A Revisit of the Masuda Flare

We revisit the flare on 1992 January 13, which is now universally termed the "Masuda flare". The revisit is motivated not only by its uniqueness despite accumulating observations of \hxr coronal emission, but also by the improvement of Yohkoh hard X-ray imaging, which was achieved after the intensive investigations on this celebrated event. Through an uncertainty analysis, we show that the hard X-ray coronal source is located much closer to the soft X-ray loop in the re-calibrated HXT images than in the original ones. Specifically, the centroid of the M1-band (23--33 keV) coronal source is above the brightest pixel of the SXT loop by ~5000+/-1000 km (~9600 km in the original data); and above the apex of the 30% brightness contour of the SXT loop by ~2000+/-1000 km (~7000 km in the original data). We suggest that this change may naturally account for the fact that the spectrum of the coronal emission was reported to be extremely hard below ~20 keV in the pre-calibration investigations, whereas it has been considerably softer in the literature since Sato's re-calibration circa 1999. Still, the coronal spectrum is flatter at lower energies than at higher energies, owing to the lack of a similar source in the L-band (14--23 keV), which remains a puzzle.

astro-ph.SR↗

A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.

math.FA↗

Time-Dependent Transport Through Molecular Junctions

We investigate transport properties of molecular junctions under two types of bias--a short time pulse or an AC bias--by combining a solution for the Green functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency AC bias, the electron flow either tracks or leads the bias signal (capacitive or resistive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.

cond-mat.mes-hall↗

Evolution of Filament Barbs

We present a selected few cases in which the sense of chirality of filament barbs changed within as short as hours. We investigate in detail a quiescent filament on 2003 September 10 and 11. Of its four barbs displaying such changes only one overlay a small polarity inversion line inside the EUV filament channel (EFC). No magnetic elements with magnitude above the noise level were detected at the endpoints of all barbs. In particular, a pair of barbs first approached toward and then departed from each other in H-alpha, with the barb endpoints migrating as far as ~10". We conclude that the evolution of the barbs was driven by flux emergence and cancellation of small bipolar units at the EFC border.

astro-ph.SR↗

On Shrinking and Boundedly Complete Schauder Frames of Banach spaces

This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames.

math.FA↗