arXiv subjects

Xiangliang Kong

Publications and source records attributed to Xiangliang Kong.

At least 55 records · Page 3Linked to original sources

arXiv2021

Harmonic elctron-cyclotron maser emissions driven by energetic electrons of the horseshoe distribution with application to solar radio spikes

Content. Electron-cyclotron maser emission (ECME) is the favored mechanism for solar radio spikes and has been investigated extensively since the 1980s. Most studies relevant to solar spikes employ a loss-cone-type distribution of energetic electrons, generating waves mainly in the fundamental X/O mode (X1/O1), with a ratio of plasma oscillation frequency to electron gyrofrequency ($ω_ {pe}/Ω_{ce}$) lower than 1. Despite the great progress made in this theory, one major problem is how the fundamental emissions pass through the second-harmonic absorption layer in the corona and escape. This is generally known as the escaping difficulty of the theory. Aims. We study the harmonic emissions generated by ECME driven by energetic electrons with the horseshoe distribution to solve the escaping difficulty of ECME for solar spikes. Methods. We performed a fully kinetic electromagnetic PIC simulation with $ω_ {pe}/Ω_{ce}$ = 0.1, corresponding to the strongly magnetized plasma conditions in the flare region, with energetic electrons characterized by the horseshoe distribution. We also varied the density ratio of energetic electrons to total electrons ($n_e/n_0$) in the simulation. Results. We obtain efficient amplification of waves in Z and X2 modes, with a relatively weak growth of O1 and X3. With a higher-density ratio, the X2 emission becomes more intense, and the rate of energy conversion from energetic electrons into X2 modes can reach $\sim$0.06% and 0.17%, with $n_e/n_0$= 5% and 10%, respectively. Conclusions. We find that the horseshoe-driven ECME can lead to an efficient excitation of X2 and X3 with a low value of $ω_ {pe}/Ω_{ce}$, providing novel means for resolving the escaping difficulty of ECME when applied to solar radio spikes. The simultaneous growth of X2 and X3 can be used to explain some harmonic structures observed in solar spikes.

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arXiv2021

New bounds and constructions for constant weighted $X$-codes

As a crucial technique for integrated circuits (IC) test response compaction, $X$-compact employs a special kind of codes called $X$-codes for reliable compressions of the test response in the presence of unknown logic values ($X$s). From a combinatorial view point, Fujiwara and Colbourn \cite{FC2010} introduced an equivalent definition of $X$-codes and studied $X$-codes of small weights that have good detectability and $X$-tolerance. An $(m,n,d,x)$ $X$-code is an $m\times n$ binary matrix with column vectors as its codewords. The parameters $d,x$ correspond to the test quality of the code. In this paper, bounds and constructions for constant weighted $X$-codes are investigated. First, we obtain a general result on the maximum number of codewords $n$ for an $(m,n,d,x)$ $X$-code of weight $w$, and we further improve this lower bound for the case with $x=2$ and $w=3$ through the probabilistic method. Then, using tools from additive combinatorics and finite fields, we present some explicit constructions for constant weighted $X$-codes with $d=3,7$ and $x=2$, which are optimal for the case when $d=3, w=4$ and nearly optimal for the case when $d=3,w=3$. We also consider a special class of $X$-codes introduced in \cite{FC2010} and improve the best known lower bound on the maximum number of codewords for this kind of $X$-codes.

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arXiv2021

Inverse problems of the Erdős-Ko-Rado type theorems for families of vector spaces and permutations

Ever since the famous Erdős-Ko-Rado theorem initiated the study of intersecting families of subsets, extremal problems regarding intersecting properties of families of various combinatorial objects have been extensively investigated. Among them, studies about families of subsets, vector spaces and permutations are of particular concerns. Recently, the authors proposed a new quantitative intersection problem for families of subsets: For $\mathcal{F}\subseteq {[n]\choose k}$, define its \emph{total intersection number} as $\mathcal{I}(\mathcal{F})=\sum_{F_1,F_2\in \mathcal{F}}|F_1\cap F_2|$. Then, what is the structure of $\mathcal{F}$ when it has the maximal total intersection number among all families in ${[n]\choose k}$ with the same family size? In \cite{KG2020}, the authors studied this problem and characterized extremal structures of families maximizing the total intersection number of given sizes. In this paper, we consider the analogues of this problem for families of vector spaces and permutations. For certain ranges of family size, we provide structural characterizations for both families of subspaces and families of permutations having maximal total intersection numbers. To some extent, these results determine the unique structure of the optimal family for some certain values of $|\mathcal{F}|$ and characterize the relation between having maximal total intersection number and being intersecting. Besides, we also show several upper bounds on the total intersection numbers for both families of subspaces and families of permutations of given sizes.

math.CO↗

arXiv2020

New Constructions of Optimal Locally Repairable Codes with Super-Linear Length

As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the research of LRCs, bounds and constructions of the corresponding optimal codes are of particular concerns. In this work, codes with $(r,δ)$-locality which have optimal minimal distance w.r.t. the bound given by Prakash et al. \cite{Prakash2012Optimal} are considered. Through parity check matrix approach, constructions of both optimal $(r,δ)$-LRCs with all symbol locality ($(r,δ)_a$-LRCs) and optimal $(r,δ)$-LRCs with information locality ($(r,δ)_i$-LRCs) are provided. As a generalization of a work of Xing and Yuan \cite{XY19}, these constructions are built on a connection between sparse hypergraphs and optimal $(r,δ)$-LRCs. With the help of constructions of large sparse hypergraphs, the length of codes constructed can be super-linear in the alphabet size. This improves upon previous constructions when the minimal distance of the code is at least $3δ+1$. As two applications, optimal H-LRCs with super-linear length and GSD codes with unbounded length are also constructed.

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arXiv2020

Dynamical modulation of solar flare electron acceleration due to plasmoid-shock interactions in the looptop region

A fast-mode shock can form in the front of reconnection outflows and has been suggested as a promising site for particle acceleration in solar flares. Recent development of magnetic reconnection has shown that numerous plasmoids can be produced in a large-scale current layer. Here we investigate the dynamical modulation of electron acceleration in the looptop region when plasmoids intermittently arrive at the shock by combining magnetohydrodynamics simulations with a particle kinetic model. As plasmoids interact with the shock, the looptop region exhibits various compressible structures that modulate the production of energetic electrons. The energetic electron population varies rapidly in both time and space. The number of 5$-$10 keV electrons correlates well with the area with compression, while that of $>$50 keV electrons shows good correlation with strong compression area but only moderate correlation with shock parameters. We further examine the impacts of the first plasmoid, which marks the transition from a quasi-steady shock front to a distorted and dynamical shock. The number of energetic electrons is reduced by $\sim 20\%$ at 15$-$25 keV and nearly 40\% for 25$-$50 keV, while the number of 5$-$10 keV electrons increases. In addition, the electron energy spectrum above 10 keV evolves softer with time. We also find double or even multiple distinct sources can develop in the looptop region when the plasmoids move across the shock. Our simulations have strong implications to the interpretation of nonthermal looptop sources, as well as the commonly observed fast temporal variations in flare emissions, including the quasi-periodic pulsations.

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arXiv2020

Measurement of magnetic field and relativistic electrons along a solar flare current sheet

In the standard model of solar flares, a large-scale reconnection current sheet is postulated as the central engine for powering the flare energy release and accelerating particles. However, where and how the energy release and particle acceleration occur remain unclear due to the lack of measurements for the magnetic properties of the current sheet. Here we report the measurement of spatially-resolved magnetic field and flare-accelerated relativistic electrons along a current-sheet feature in a solar flare. The measured magnetic field profile shows a local maximum where the reconnecting field lines of opposite polarities closely approach each other, known as the reconnection X point. The measurements also reveal a local minimum near the bottom of the current sheet above the flare loop-top, referred to as a "magnetic bottle". This spatial structure agrees with theoretical predictions and numerical modeling results. A strong reconnection electric field of ~4000 V/m is inferred near the X point. This location, however, shows a local depletion of microwave-emitting relativistic electrons. These electrons concentrate instead at or near the magnetic bottle structure, where more than 99% of them reside at each instant. Our observations suggest that the loop-top magnetic bottle is likely the primary site for accelerating and/or confining the relativistic electrons.

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arXiv2020

On an inverse problem of the Erdős-Ko-Rado type theorems

A family of subsets $\mathcal{F}\subseteq {[n]\choose k}$ is called intersecting if any two of its members share a common element. Consider an intersecting family, a direct problem is to determine its maximal size and the inverse problem is to characterize its extremal structure and its corresponding stability. The famous Erdős-Ko-Rado theorem answered both direct and inverse problems and led the era of studying intersection problems for finite sets. In this paper, we consider the following quantitative intersection problem which can be viewed an inverse problem for Erdős-Ko-Rado type theorems: For $\mathcal{F}\subseteq {[n]\choose k}$, define its \emph{total intersection} as $\mathcal{I}(\mathcal{F})=\sum_{F_1,F_2\in \mathcal{F}}|F_1\cap F_2|$. Then, what is the structure of $\mathcal{F}$ when it has the maximal total intersection among all families in ${[n]\choose k}$ with the same family size? Using a pure combinatorial approach, we provide two structural characterizations of the optimal family of given size that maximizes the total intersection. As a consequence, for $n$ large enough and $\mathcal{F}$ of proper size, these characterizations show that the optimal family $\mathcal{F}$ is indeed $t$-intersecting ($t\geq 1$). To a certain extent, this reveals the relationship between properties of being intersecting and maximizing the total intersection. Also, we provide an upper bound on $\mathcal{I}(\mathcal{F})$ for several ranges of $|\mathcal{F}|$ and determine the unique optimal structure for families with sizes of certain values.

math.CO↗

arXiv2019

The Acceleration and Confinement of Energetic Electrons by a Termination Shock in a Magnetic Trap: An Explanation for Nonthermal Loop-top Sources during Solar Flares

Nonthermal loop-top sources in solar flares are the most prominent observational signature that suggests energy release and particle acceleration in the solar corona. Although several scenarios for particle acceleration have been proposed, the origin of the loop-top sources remains unclear. Here we present a model that combines a large-scale magnetohydrodynamic simulation of a two-ribbon flare with a particle acceleration and transport model for investigating electron acceleration by a fast-mode termination shock at the looptop. Our model provides spatially resolved electron distribution that evolves in response to the dynamic flare geometry. We find a concave-downward magnetic structure located below the flare termination shock, induced by the fast reconnection downflows. It acts as a magnetic trap to confine the electrons at the looptop for an extended period of time. The electrons are energized significantly as they cross the shock front, and eventually build up a power-law energy spectrum extending to hundreds of keV. We suggest that this particle acceleration and transport scenario driven by a flare termination shock is a viable interpretation for the observed nonthermal loop-top sources.

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arXiv2019

The Acceleration of Energetic Particles at Coronal Shocks and Emergence of a Double Power Law Feature in Particle Energy Spectra

We present numerical modelling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that the location on the shock where the high-energy particle intensity is the largest, depends on the energy of the particles and on time. The acceleration of particles to more than 100 MeV mainly occurs in the shock-streamer interaction region, due to perpendicular shock geometry and the trapping effect of closed magnetic fields. A comparison of the particle spectra to that in a radial magnetic field shows that the intensity at 100 MeV (200 MeV) is enhanced by more than one order (two orders) of magnitude. This indicates that the streamer-like magnetic field can be an important factor in producing large solar energetic particle events. We also show that the energy spectrum integrated over the simulation domain consists of two different power laws. Further analysis suggests that it may be a mixture of two distinct populations accelerated in the streamer and open field regions, where the acceleration rate differs substantially. Our calculations also show that the particle spectra are affected considerably by a number of parameters, such as the streamer tilt angle, particle spatial diffusion coefficient, and shock compression ratio. While the low-energy spectra agree well with standard diffusive shock acceleration theory, the break energy ranges from $\sim$1 MeV to $\sim$90 MeV and the high-energy spectra can extend to $\sim$1 GeV with a slope of $\sim$2-3.

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arXiv2019

Multi-part cross-intersecting families

Let $\mathcal{A}\subseteq{[n]\choose a}$ and $\mathcal{B}\subseteq{[n]\choose b}$ be two families of subsets of $[n]$, we say $\mathcal{A}$ and $\mathcal{B}$ are cross-intersecting if $A\cap B\neq \emptyset$ for all $A\in\mathcal{A}$, $B\in\mathcal{B}$. In this paper, we study cross-intersecting families in the multi-part setting. By characterizing the independent sets of vertex-transitive graphs and their direct products, we determine the sizes and structures of maximum-sized multi-part cross-intersecting families. This generalizes the results of Hilton's and Frankl--Tohushige's on cross-intersecting families in the single-part setting.

math.CO↗

arXiv2019

Effect of the Temperature of Background Plasma and the Energy of Energetic Electrons on Z-Mode Excitation

It has been suggested that the Z-mode instability driven by energetic electrons with a loss-cone type velocity distribution is one candidate process behind the continuum and zebra pattern of solar type-IV radio bursts. Both the temperature of background plasma ($T_0$) and the energy of energetic electrons ($v_e$) are considered to be important to the variation of the maximum growth rate ($γ_{max}$). Here we present a detailed parameter study on the effect of $T_0$ and $v_e$, within a regime of the frequency ratio ($10 \leq \frac{ω_{pe}}{Ω_{ce}} \leq 30$). In addition to $γ_{max}$, we also analyze the effect on the corresponding wave frequency ($ω^r_{max}$) and propagation angle ($θ_{max}$). We find that (1) $γ_{max}$ in-general decreases with increasing $v_e$, while its variation with $T_0$ is more complex depending on the exact value of $v_e$; (2) with increasing $T_0$ and $v_e$, $ω^r_{max}$ presents step-wise profiles with jumps separated by gradual or very-weak variations, and due to the warm-plasma effect on the wave dispersion relation $ω^r_{max}$ can vary within the hybrid band (the harmonic band containing the upper hybrid frequency) and the band higher; (3) the propagation is either perpendicular or quasi-perpendicular, and $θ_{max}$ presents variations in line with those of $ω^r_{max}$, as constrained by the resonance condition. We also examine the profiles of $γ_{max}$ with $\frac{ω_{pe}}{Ω_{ce}}$ for different combinations of $T_0$ and $v_e$ to clarify some earlier calculations which show inconsistent results.

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arXiv2019

New Bounds on the Field Size for Maximally Recoverable Codes Instantiating Grid-like Topologies

In recent years, the rapidly increasing amounts of data created and processed through the internet resulted in distributed storage systems employing erasure coding based schemes. Aiming to balance the tradeoff between data recovery for correlated failures and efficient encoding and decoding, distributed storage systems employing maximally recoverable codes came up. Unifying a number of topologies considered both in theory and practice, Gopalan et al. \cite{Gopalan2017} initiated the study of maximally recoverable codes for grid-like topologies. In this paper, we focus on the maximally recoverable codes that instantiate grid-like topologies $T_{m\times n}(1,b,0)$. To characterize the property of codes for these topologies, we introduce the notion of \emph{pseudo-parity check matrix}. Then, using the Combinatorial Nullstellensatz, we establish the first polynomial upper bound on the field size needed for achieving the maximal recoverability in topologies $T_{m\times n}(1,b,0)$. And using hypergraph independent set approach, we further improve this general upper bound for topologies $T_{4\times n}(1,2,0)$ and $T_{3\times n}(1,3,0)$. By relating the problem to generalized \emph{Sidon sets} in $\mathbb{F}_q$, we also obtain non-trivial lower bounds on the field size for maximally recoverable codes that instantiate topologies $T_{4\times n}(1,2,0)$ and $T_{3\times n}(1,3,0)$.

cs.IT↗

arXiv2018

The Dynamical Behavior of Reconnection-driven Termination Shocks in Solar Flares: Magnetohydrodynamic Simulations

In eruptive solar flares, termination shocks (TSs), formed when high-speed reconnection outflows collide with closed dense flaring loops, are believed to be one of the possible candidates for plasma heating and particle acceleration. In this work, we perform resistive magnetohydrodynamic simulations in a classic Kopp-Pneuman flare configuration to study the formation and evolution of TSs, and analyze in detail the dynamic features of TSs and variations of the shock strength in space and time. This research focuses on the fast reconnection phase when plasmoids form and produce small-scale structures inside the flare current sheet. It is found that the TS emerges once the downward outflow colliding with closed magnetic loops becomes super-magnetosonic, and immediately becomes highly dynamical. The morphology of a TS can be flat, oblique, or curved depending on the detailed interactions between the outflows/plasmoids and the highly dynamic plasma in the looptop region. The TS becomes weaker when a plasmoid is crossing through, or may even be destroyed by well developed plasmoids and then re-constructed above the plasmoids. We also perform detailed statistical analysis on important physical quantities along and across the shock front. The density and temperature ratios range from 1 to 3 across the TS front, and the pressure ratio typically has larger values up to 10. We show that weak guide fields do not strongly affect the Mach number and compression ratios, and the TS length becomes slightly larger in the case with thermal conduction.

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arXiv2018

Gyrosynchrotron emission generated by nonthermal electrons with energy spectra of a broken power law

Latest observational reports of solar flares reveal some uncommon features of microwave spectra, such as unusually hard (or even positive) spectra, and/or a super-high peak frequency. For a better understanding of these features, we conduct a parameter study to investigate the effect of broken-power-law spectra of energetic electrons on microwave emission on the basis of gyrosynchrotron mechanism. The electron broken-power-law energy distribution is characterized by three parameters, the break energy ($E_B$), the power-law indices below ($δ_1$) and above ($δ_2$) the break energy. We find that with the addition of the $δ_2$ component of the electron spectra, the total flux density can increase by several times in the optically-thick regime, and by orders of magnitude in the optically-thin regime; the peak frequency ($ν_p$) also increases and can reach up to tens of GHz; and the degree of polarization ($r_c$) decreases in general. We also find that (1) the variation of the flux density is much larger in the optically-thin regime, and the microwave spectra around the peak frequency manifest various profiles with the softening or soft-hard pattern; (2) the parameters $δ_1$ and $E_B$ affect the microwave spectral index ($α$) and the degree of polarization ($r_c$) mainly in the optically-thick regime, while $δ_2$ mainly affects the optically-thin regime. The results are helpful in understanding the lately-reported microwave bursts with unusual spectral features and point out the demands for a more-complete spectral coverage of microwave bursts, especially, in the high-frequency regime, say, $>10-20$ GHz.

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arXiv2018

Harmonics of Solar Radio Spikes at Metric Wavelengths

This paper presents the latest observations from the newly-built solar radio spectrograph at the \emph{Chashan Solar Observatory}. On July 18 2016, the spectrograph records a solar spike burst event, which has several episodes showing harmonic structures, with the second, third, and fourth harmonics. The lower harmonic radio spike emissions are observed later than the higher harmonic bands, and the temporal delay of the second (third) harmonic relative to the fourth harmonic is about 30\ --\ 40 (10) ms. Based on the electron cyclotron maser emission mechanism, we analyze possible causes of the temporal delay and further infer relevant coronal parameters, such as the magnetic field strength and the electron density at the radio source.

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arXiv2017

The acceleration of high-energy protons at coronal shocks: the effect of large-scale streamer-like magnetic field structures

Recent observations have shown that coronal shocks driven by coronal mass ejections can develop and accelerate particles within several solar radii in large solar energetic particle (SEP) events. Motivated by this, we present an SEP acceleration study including the process that a fast shock propagates through a streamer-like magnetic field with both closed and open field lines in the low corona region. The acceleration of protons is modeled by numerically solving the Parker transport equation with spatial diffusion both along and across the magnetic field. We show that particles can be sufficiently accelerated to up to several hundred MeV within 2-3 solar radii. When the shock propagates through a streamer-like magnetic field, particles are more efficiently accelerated compared to the case with a simple radial magnetic field, mainly due to perpendicular shock geometry and the natural trapping effect of closed magnetic fields. Our results suggest that the coronal magnetic field configuration is an important factor for producing large SEP events. We further show that the coronal magnetic field configuration strongly influences the distribution of energetic particles, leading to different locations of source regions along the shock front where most of high energy particles are concentrated. This work may have strong implications to SEP observations. The upcoming Parker Solar Probe will provide in situ observations for the distribution of energetic particles in the coronal shock region, and test the results of the study.

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arXiv2017

EUV and Magnetic Activities Associated with Type-I Solar Radio Bursts

Type-I bursts (i.e. noise storms) are the earliest-known type of solar radio emission at the metre wavelength. They are believed to be excited by non-thermal energetic electrons accelerated in the corona. The underlying dynamic process and exact emission mechanism still remain unresolved. Here, with a combined analysis of extreme ultraviolet (EUV), radio and photospheric magnetic field data of unprecedented quality recorded during a type-I storm on 30 July 2011, we identify a good correlation between the radio bursts and the co-spatial EUV and magnetic activities. The EUV activities manifest themselves as three major brightening stripes above a region adjacent to a compact sunspot, while the magnetic field there presents multiple moving magnetic features (MMFs) with persistent coalescence or cancelation and a morphologically similar three-part distribution. We find that the type-I intensities are correlated with those of the EUV emissions at various wavelengths with a correlation coefficient of 0.7-0.8. In addition, in the region between the brightening EUV stripes and the radio sources there appear consistent dynamic motions with a series of bi-directional flows, suggesting ongoing small-scale reconnection there. Mainly based on the induced connection between the magnetic motion at the photosphere and the EUV and radio activities in the corona, we suggest that the observed type-I noise storms and the EUV brightening activities are the consequence of small-scale magnetic reconnection driven by MMFs. This is in support of the original proposal made by Bentely et al. (Solar Phys. 193, 227, 2000).

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arXiv2016

An Eruptive Hot-Channel Structure Observed at Metric Wavelength as a Moving Type-IV Solar Radio Burst

Hot channel (HC) structure, observed in the high-temperature passbands of the AIA/SDO, is regarded as one candidate of coronal flux rope which is an essential element of solar eruptions. Here we present the first radio imaging study of an HC structure in the metric wavelength. The associated radio emission manifests as a moving type-IV (t-IVm) burst. We show that the radio sources co-move outwards with the HC, indicating that the t-IV emitting energetic electrons are efficiently trapped within the structure. The t-IV sources at different frequencies present no considerable spatial dispersion during the early stage of the event, while the sources spread gradually along the eruptive HC structure at later stage with significant spatial dispersion. The t-IV bursts are characterized by a relatively-high brightness temperature ($\sim$ 10$^{7}$ $-$ 10$^{9}$ K), a moderate polarization, and a spectral shape that evolves considerably with time. This study demonstrates the possibility of imaging the eruptive HC structure at the metric wavelength and provides strong constraints on the t-IV emision mechanism, which, if understood, can be used to diagnose the essential parameters of the eruptive structure.

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