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Hui Yu

Publications and source records attributed to Hui Yu.

At least 145 records · Page 8Linked to original sources
arXiv2016

Improve the Evaluation of Fluency Using Entropy for Machine Translation Evaluation Metrics

The widely-used automatic evaluation metrics cannot adequately reflect the fluency of the translations. The n-gram-based metrics, like BLEU, limit the maximum length of matched fragments to n and cannot catch the matched fragments longer than n, so they can only reflect the fluency indirectly. METEOR, which is not limited by n-gram, uses the number of matched chunks but it does not consider the length of each chunk. In this paper, we propose an entropy-based method, which can sufficiently reflect the fluency of translations through the distribution of matched words. This method can easily combine with the widely-used automatic evaluation metrics to improve the evaluation of fluency. Experiments show that the correlations of BLEU and METEOR are improved on sentence level after combining with the entropy-based method on WMT 2010 and WMT 2012.

cs.CL↗
arXiv2016

Impulsively generated sausage waves in coronal tubes with transversally continuous structuring

The frequency dependence of the longitudinal group speeds of trapped sausage waves plays an important role in determining impulsively generated wave trains, which have often been invoked to account for quasi-periodic signals in coronal loops. We examine how the group speeds ($v_{\rm gr}$) depend on angular frequency ($ω$) for sausage modes in pressureless coronal tubes with continuous transverse density distributions by solving the dispersion relation pertinent to the case where the density inhomogeneity of arbitrary form takes place in a transition layer of arbitrary thickness. We find that in addition to the transverse lengthscale $l$ and density contrast $ρ_{\rm i}/ρ_{\rm e}$, the group speed behavior depends also on the detailed form of the density inhomogeneity. For parabolic profiles, $v_{\rm gr}$ always decreases with $ω$ first before increasing again, as happens for the much studied top-hat profiles. For linear profiles, however, the behavior of the $ω-v_{\rm gr}$ curves is more complex. When $ρ_{\rm i}/ρ_{\rm e} \lesssim 6$, the curves become monotonical for large values of $l$. On the other hand, for higher density contrasts, a local maximum $v_{\rm gr}^{\rm max}$ exists in addition to a local minimum $v_{\rm gr}^{\rm min}$ when coronal tubes are diffuse. With time-dependent computations, we show that the different behavior of group speed curves, the characteristic speeds $v_{\rm gr}^{\rm min}$ and $v_{\rm gr}^{\rm max}$ in particular, is reflected in the temporal evolution and Morlet spectra of impulsively generated wave trains. We conclude that the observed quasi-periodic wave trains not only can be employed to probe such key parameters as density contrasts and profile steepness, but also have the potential to discriminate between the unknown forms of the transverse density distribution.

astro-ph.SR↗
arXiv2016

Fast sausage modes in magnetic tubes with continuous transverse profiles: effects of a finite plasma beta

While standing fast sausage modes in flare loops are often invoked to interpret quasi-periodic pulsations (QPPs) in solar flares, it is unclear as to how they are influenced by the combined effects of a continuous transverse structuring and a finite internal plasma beta ($β_{\rm i}$). We derive a generic dispersion relation (DR) governing linear sausage waves in straight magnetic tubes for which plasma pressure is not negligible and the density and temperature inhomogeneities of essentially arbitrary form take place in a layer of arbitrary width. Focusing on fast modes, we find that $β_{\rm i}$ only weakly influences $k_{\rm c}$, the critical longitudinal wavenumber separating the leaky from trapped modes. Likewise, for both trapped and leaky modes, the periods $P$ in units of the transverse fast time depend only weakly on $β_{\rm i}$, which is compatible with the fact that the effective wavevectors of fast sausage modes are largely perpendicular to the background magnetic field. However, a weak $β_{\rm i}$ dependence of the damping times $τ$ is seen only when the length-to-radius ratio $L/R$ is $\sim 50\%$ larger than some critical value $π/(k_{\rm c} R)$, which itself rather sensitively depends on the density contrast, profile steepness as well as on how the transverse structuring is described. In the context of QPPs, we conclude that the much simpler zero-beta theory can be employed for trapped modes, as long as one sees the deduced internal Alfvén speed as actually being the fast speed. In contrast, effects due to a finite beta in flare loops should be considered when leaky modes are exploited.

astro-ph.SR↗
arXiv2016

Small perturbation solutions for nonlocal elliptic equations

We present a small perturbation result for nonlocal elliptic equations, which says that for a class of nonlocal operators, the solutions are in $C^{σ+α}$ for any $α\in (0,1)$ as long as the solutions are small. This is a nonlocal generalization of a celebrated result of Savin in the case of second order equations.

math.AP↗
arXiv2016

Smooth Solutions to a Class of Nonlocal Fully Nonlinear Elliptic Equations

We show that a certain class of fully nonlinear nonlocal equations have smooth solutions as long as the right-hand side is nice and the boundary datum is bounded. To this end we follow the classical strategy. We first show that solutions are $C^{σ+α}$ continuous, then develop a bootstrap argument robust enough for operators that may depend on the solution and its σ-derivatives.

math.AP↗
arXiv2016

Self-Organized Hydrodynamics with nonconstant velocity

Motivated by recent experimental and computational results that show a motility-induced clustering transition in self-propelled particle systems, we study an individual model and its corresponding Self-Organized Hydrodynamic model for collective behaviour that incorporates a density-dependent velocity, as well as inter-particle alignment. The modal analysis of the hydrodynamic model elucidates the relationship between the stability of the equilibria and the changing velocity, and the formation of clusters. We find, in agreement with earlier results for non-aligning particles, that the key criterion for stability is $(ρv(ρ))'> 0$, i.e. a non-rapid decrease of velocity with density. Numerical simulation for both the individual and hydrodynamic models with a velocity function inspired by experiment demonstrates the validity of the theoretical results.

nlin.AO↗
arXiv2016

A Dirichlet problem for nonlocal degenerate elliptic operators with internal nonlinearity

We study a Dirichlet problem in the entire space for some nonlocal degenerate elliptic operators with internal nonlinearities. With very mild assumptions on the boundary datum, we prove existence and uniqueness of the solution in the viscosity sense. If we further assume uniform ellipticity then the solution is shown to be classical, and even smooth if both the operator and the boundary datum are smooth.

math.AP↗
arXiv2016

$W^{σ,ε}$-estimates for nonlocal elliptic equations

We prove that the fractional derivatives of solutions to a class of nonlocal fully nonlinear elliptic equations are epsilon-integrable. We follow Fanghua Lin's original approach to the analogous problem for second order equations, by first proving a potential estimate, then combining this estimate with the ABP-type estimate by N. Guillen and R. Schwab to control the size of the superlevel sets of the fractional derivatives of solutions.

math.AP↗
arXiv2016

Period ratios for standing kink and sausage modes in magnetized structures with siphon flow on the Sun

Standing oscillations with multiple periods were found in a number of atmospheric structures on the Sun. The ratio of the period of the fundamental to twice the one of its first overtone, $P_1/2P_2$, is important in applications of solar magneto-seismology. We examine how field-aligned flows impact $P_1/2P_2$ of standing modes in solar magnetic cylinders. For coronal loops, the flow effects are significant for both fast kink and sausage modes. For kink ones, they reduce $P_1/2P_2$ by up to 17\% relative to the static case even when the density contrast between the loop and its surroundings approaches infinity. For sausage modes, the reduction in $P_1/2P_2$ due to flow is typically $\lesssim 5.5\%$ compared with the static case. However, the threshold aspect ratio, only above which can trapped sausage modes be supported, may increase dramatically with the flow magnitude. For photospheric tubes, the flow effect on $P_1/2P_2$ is not as strong. However, when applied to sausage modes, introducing field-aligned flows offers more possibilities in interpreting the multiple periods recently measured. We conclude that field-aligned flows should be taken into account to help better understand what causes the departure of $P_1/2P_2$ from unity.

astro-ph.SR↗
arXiv2015

Inferring flare loop parameters with measurements of standing sausage modes

Standing fast sausage modes in flare loops were suggested to account for a considerable number of quasi-periodic pulsations (QPPs) in the light curves of solar flares. This study continues our investigation into the possibility to invert the measured periods $P$ and damping times $τ$ of sausage modes to deduce the transverse Alfvén time $R/v_{\rm Ai}$, density contrast $ρ_{\rm i}/ρ_{\rm e}$, and the steepness of the density distribution transverse to flare loops. A generic dispersion relation (DR) governing linear sausage modes is derived for pressureless cylinders where density inhomogeneity of arbitrary form takes place within the cylinder. We show that in general the inversion problem is under-determined for QPP events where only a single sausage mode exists, be the measurements spatially resolved or unresolved. While $R/v_{\rm Ai}$ can be inferred to some extent, the range of possible steepness parameters may be too broad to be useful. However, for spatially resolved measurements where an additional mode is present, it is possible to deduce self-consistently $ρ_{\rm i}/ρ_{\rm e}$, the profile steepness, and the internal Alfvén speed $v_{\rm Ai}$. We show that at least for a recent QPP event that involves a fundamental kink mode in addition to a sausage one, flare loop parameters are well constrained, even if the specific form of the transverse density distribution remains unknown. We conclude that spatially resolved, multi-mode QPP measurements need to be pursued for inferring flare loop parameters.

astro-ph.SR↗
arXiv2015

Kink and Sausage Modes in Nonuniform Magnetic Slabs with Continuous Transverse Density Distributions

We examine the influence of a continuous density structuring transverse to coronal slabs on the dispersive properties of fundamental standing kink and sausage modes supported therein. We derive generic dispersion relations (DRs) governing linear fast waves in pressureless straight slabs with general transverse density distributions, and focus on the cases where the density inhomogeneity takes place in a layer of arbitrary width and in arbitrary form. The physical relevance of the solutions to the DRs is demonstrated by the corresponding time-dependent computations. For all profiles examined, the lowest-order kink modes are trapped regardless of longitudinal wavenumber $k$. A continuous density distribution introduces a difference to their periods of $\lesssim 13\%$ when $k$ is the observed range, relative to the case where the density profile takes a step-function form. Sausage modes and other branches of kink modes are leaky at small $k$, and their periods and damping times are heavily influenced by how the transverse density profile is prescribed, the lengthscale in particular. These modes have sufficiently high quality to be observable only for physical parameters representative of flare loops. We conclude that while the simpler DR pertinent to a step-function profile can be used for the lowest-order kink modes, the detailed information on the transverse density structuring needs to be incorporated into studies of sausage modes and higher-order kink modes.

astro-ph.SR↗
arXiv2015

A continuum model for nematic alignment of self-propelled particles

A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field kinetic equation. The resulting perturbation problem is solved thanks to the concept of generalized collision invariants. It yields a hyperbolic but non-conservative system of equations for the nematic mean direction of the flow and the densities of particles flowing parallel or anti-parallel to this mean direction. Diffusive terms are introduced under a weakly non-local interaction assumption and the diffusion coefficient is proven to be positive. An application to the modeling of myxobacteria is outlined.

math.AP↗
arXiv2015

Standing Sausage Modes In Nonuniform Magnetic Tubes: An Inversion Scheme For Inferring Flare Loop Parameters

Standing sausage modes in flare loops are important for interpreting quasi-periodic pulsations (QPPs) in solar flare lightcurves. We propose an inversion scheme that consistently uses their periods $P$ and damping times $τ$ to diagnose flare loop parameters. We derive a generic dispersion relation governing linear sausage waves in pressure-less straight tubes, for which the transverse density inhomogeneity takes place in a layer of arbitrary width $l$ and is of arbitrary form. We find that $P$ and $τ$ depend on the combination of $[R/v_{\rm Ai}, L/R, l/R, ρ_{\rm i}/ρ_{\rm e}]$, where $R$ is the loop radius, $L$ is the looplength, $v_{\rm Ai}$ is the internal Alfvén speed, and $ρ_{\rm i}/ρ_{\rm e}$ is the density contrast. For all the density profiles examined, $P$ and $τ$ experience saturation when $L/R \gg 1$, yielding an inversion curve in the $[R/v_{\rm Ai}, l/R, ρ_{\rm i}/ρ_{\rm e}]$ space with a specific density profile when $L/R$ is sufficiently large. When applied to a spatially unresolved QPP event, the scheme yields that $R/v_{\rm Ai}$ is the best constrained, whereas $l/R$ corresponds to the other extreme. For spatially resolved QPPs, while $L/R \gg 1$ cannot be assumed beforehand, an inversion curve remains possible due to additional geometrical constraints. When a spatially resolved QPP event involves another mode, as is the case for a recent event, the full set of $[v_{\rm Ai}, l, ρ_{\rm i}/ρ_{\rm e}]$ can be inferred. We conclude that the proposed scheme provides a useful tool for magneto-seismologically exploiting QPPs.

astro-ph.SR↗
arXiv2015

Spatial damping of propagating sausage waves in coronal cylinders

Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere. We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field. Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued longitudinal wavenumber $k$ at given real angular frequencies $ω$. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of $ω_{\rm c}$, the critical angular frequency separating trapped from leaky waves. In contrast to the standing case, propagating sausage waves are allowed for $ω$ much lower than $ω_{\rm c}$. However, while able to direct their energy upwards, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for $ω\lesssim 1.5 v_{\rm Ai}/a$, where $a$ and $v_{\rm Ai}$ are the cylinder radius and the Alfvén speed in the cylinder, respectively. We conclude that if a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.

astro-ph.SR↗
arXiv2015

Periods and damping rates of fast sausage oscillations in multi-shelled coronal loops

Standing sausage modes are important in interpreting quasi-periodic pulsations in the lightcurves of solar flares. Their periods and damping times play an important role in seismologically diagnosing key parameters like the magnetic field strength in regions where flare energy is released. Usually such applications are based on theoretical results neglecting unresolved fine structures in magnetized loops. However, the existence of fine structuring is suggested on both theoretical and observational grounds. Adopting the framework of cold magnetohydrodynamics (MHD), we model coronal loops as magnetized cylinders with a transverse equilibrium density profile comprising a monolithic part and a modulation due to fine structuring in the form of concentric shells. The equation governing the transverse velocity perturbation is solved with an initial-value-problem approach, and the effects of fine structuring on the periods $P$ and damping times $τ$ of global, leaky, standing sausage modes are examined. A parameter study shows that fine structuring, be it periodically or randomly distributed, brings changes of only a few percent to $P$ and $τ$ when there are more than about ten shells. The monolithic part, its steepness in particular, plays a far more important role in determining $P$ and $τ$. We conclude that when measured values of $P$ and $τ$ of sausage modes are used for seismological purposes, it is justified to use theoretical results where the effects due to fine structuring are neglected.

astro-ph.SR↗
arXiv2014

Self-organized Hydrodynamics in an Annular Domain: Modal Analysis and Nonlinear Effects

The Self-Organized Hydrodynamics model of collective behavior is studied on an annular domain. A modal analysis of the linearized model around a perfectly polarized steady-state is conducted. It shows that the model has only pure imaginary modes in countable number and is hence stable. Numerical computations of the low-order modes are provided. The fully non-linear model is numerically solved and nonlinear mode-coupling is then analyzed. Finally, the efficiency of the modal decomposition to analyze the complex features of the nonlinear model is demonstrated.

math-ph↗
arXiv2014

Standing sausage modes in coronal loops with plasma flow

Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops.We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated, its solutions used to construct standing modes. Two transverse profiles are distinguished, one being the generalized Epstein distribution (profile E) and the other (N) proposed recently in Nakariakov et al.(2012). A parameter study is performed on the dependence of the maximum period $P_\mathrm{max}$ and cutoff length-to-radius ratio $(L/a)_{\mathrm{cutoff}}$ in the trapped regime on the density parameters ($ρ_0/ρ_\infty$ and profile steepness $p$) and flow parameters (magnitude $U_0$ and profile steepness $u$). For either profile, introducing a flow reduces $P_\mathrm{max}$ relative to the static case. $P_\mathrm{max}$ depends sensitively on $p$ for profile N but is insensitive to $p$ for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: $(L/a)_{\mathrm{cutoff}}$ may be substantially reduced in the case with flow relative to the static one. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E better describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfvén speed can make coronal loops considerably less likely to support trapped standing sausage modes.

astro-ph.SR↗