arXiv subjects
Publications and source records attributed to Hui Li.
We prove convergence of critical points $u^h$ of the nonlinear elastic energies $E^h$ of thin incompressible plates $Ω^h=Ω\times (-h/2, h/2)$, which satisfy the von Kármán scaling: $E^h(u^h)\leq Ch^4$, to critical points of the appropriate limiting (incompressible von Kármán) functional.
Non-thermal radio emission from cosmic ray electrons in the vicinity of merging galaxy clusters is an important tracer of cluster merger activity, and is the result of complex physical processes that involve magnetic fields, particle acceleration, gas dynamics, and radiation. In particular, objects known as radio relics are thought to be the result of shock-accelerated electrons that, when embedded in a magnetic field, emit synchrotron radiation in the radio wavelengths. In order to properly model this emission, we utilize the adaptive mesh refinement simulation of the magnetohydrodynamic evolution of a galaxy cluster from cosmological initial conditions. We locate shock fronts and apply models of cosmic ray electron acceleration that are then input into radio emission models. We have determined the thermodynamic properties of this radio-emitting plasma and constructed synthetic radio observations to compare to observed galaxy clusters. We find a significant dependence of the observed morphology and radio relic properties on the viewing angle of the cluster, raising concerns regarding the interpretation of observed radio features in clusters. We also find that a given shock should not be characterized by a single Mach number. We find that the bulk of the radio emission comes from gas with T>5x10^7, ρ~10^(-28)-10^(-27) g/cm^3, with magnetic field strengths of 0.1-1.0 μG and shock Mach numbers of M~3-6. We present an analysis of the radio spectral index which suggests that the spatial variation of the spectral index can mimic synchrotron aging. Finally, we examine the polarization fraction and position angle of the simulated radio features, and compare to observations.
Consider an effective Hamiltonian circle action on a compact symplectic $2n$-dimensional manifold $(M, ω)$. Assume that the fixed set $M^{S^1}$ is {\em minimal}, in two senses: it has exactly two components, $X$ and $Y$, and $\dim(X) + \dim(Y) = \dim(M) - 2$. We prove that the integral cohomology ring and Chern classes of $M$ are isomorphic to either those of $\CP^n$ or (if $n \neq 1$ is odd) to those of $\Gt_2(\R^{n+2})$, the Grassmannian of oriented two-planes in $\R^{n+2}$. In particular, $H^i(M;\Z) = H^i(\CP^n;\Z)$ for all $i$, and the Chern classes of $M$ are determined by the integral cohomology {\em ring}. We also prove that the fixed set data of $M$ agrees exactly with the fixed set data for one of the standard circle actions on one of these two manifolds. In particular, we show that there are no points with stabilizer $\Z_k$ for any $k > 2$. The same conclusions hold when $M^{S^1}$ has exactly two components and the even Betti numbers of $M$ are minimal, that is, $b_{2i}(M) = 1$ for all $i \in \{0,...,1/2\dim(M)\}$. This provides additional evidence that very few symplectic manifolds with minimal even Betti numbers admit Hamiltonian actions.
Let $G$ be a connected compact Lie group, and let $M$ be a connected Hamiltonian $G$-manifold with equivariant moment map $ϕ$. We prove that if there is a simply connected orbit $G\cdot x$, then $π_1(M)\congπ_1(M/G)$; if additionally $ϕ$ is proper, then $π_1(M)\congπ_1(ϕ^{-1}(G\cdot a))$, where $a=ϕ(x)$. We also prove that if a maximal torus of $G$ has a fixed point $x$, then $π_1(M)\congπ_1(M/K)$, where $K$ is any connected subgroup of $G$; if additionally $ϕ$ is proper, then $π_1(M)\congπ_1(ϕ^{-1}(G\cdot a))\congπ_1(ϕ^{-1}(a))$, where $a=ϕ(x)$. Furthermore, we prove that if $ϕ$ is proper, then $π_1\big(M/\Gh\big)\congπ_1\big(ϕ^{-1}(G\cdot a)/\Gh\big)$ for all $a\inϕ(M)$, where $\Gh$ is any connected subgroup of $G$ which contains the identity component of each stabilizer group. In particular, $π_1(M/G)\congπ_1(ϕ^{-1}(G\cdot a)/G)$ for all $a\inϕ(M)$.
Hadronic gamma-ray emission from supernova remnants (SNRs) is an important tool to test shock acceleration of cosmic ray protons. Tycho is one of nearly a dozen Galactic SNRs which are suggested to emit hadronic gamma-ray emission. Among them, however, it is the only one in which the hadronic emission is proposed to arise from the interaction with low-density (~0.3 cm^{-3}) ambient medium. Here we present an alternative hadronic explanation with a modest conversion efficiency (of order 1%) for this young remnant. With such an efficiency, a normal electron-proton ratio (of order 10^{-2}) is derived from the radio and X-ray synchrotron spectra and an average ambient density that is at least one-order-of-magnitude higher is derived from the hadronic gamma-ray flux. This result is consistent with the multi-band evidence of the presence of dense medium from the north to the east of the Tycho SNR. The SNR-cloud association, in combination with the HI absorption data, helps to constrain the so-far controversial distance to Tycho and leads to an estimate of 2.5 kpc.
In many wireless communication systems, radios are subject to a duty cycle constraint, that is, a radio only actively transmits signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This work studies the capacity of scalar discrete-time Gaussian channels subject to duty cycle constraint as well as average transmit power constraint. An idealized duty cycle constraint is first studied, which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword. A unique discrete input distribution is shown to achieve the channel capacity. In many situations, numerically optimized on-off signaling can achieve much higher rate than Gaussian signaling over a deterministic transmission schedule. This is in part because the positions of nontransmissions in a codeword can convey information. Furthermore, a more realistic duty cycle constraint is studied, where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is no longer independent over time and is hard to compute. A lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first-order Markov input process, the distribution of which is also discrete and can be computed efficiently. The results in this paper suggest that, under various duty cycle constraints, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain.
Radio observations of galaxy clusters show that there are $μ$G magnetic fields permeating the intra-cluster medium (ICM), but it is hard to accurately constrain the strength and structure of the magnetic fields without the help of advanced computer simulations. We present qualitative comparisons of synthetic VLA observations of simulated galaxy clusters to radio observations of Faraday Rotation Measure (RM) and radio halos. The cluster formation is modeled using adaptive mesh refinement (AMR) magneto-hydrodynamic (MHD) simulations with the assumption that the initial magnetic fields are injected into the ICM by active galactic nuclei (AGNs) at high redshift. In addition to simulated clusters in Xu et al. (2010, 2011), we present a new simulation with magnetic field injections from multiple AGNs. We find that the cluster with multiple injection sources is magnetized to a similar level as in previous simulations with a single AGN. The RM profiles from simulated clusters, both $|RM|$ and the dispersion of RM ($σ_{RM}$), are consistent at a first-order with the radial distribution from observations. The correlations between the $σ_{RM}$ and X-ray surface brightness from simulations are in a broad agreement with the observations, although there is an indication that the simulated clusters could be slightly over-dense and less magnetized with respect to those in the observed sample. In addition, the simulated radio halos agree with the observed correlations between the radio power versus the cluster X-ray luminosity and between the radio power versus the radio halo size. These studies show that the cluster wide magnetic fields that originate from AGNs and are then amplified by the ICM turbulence (Xu et al. 2010) match observations of magnetic fields in galaxy clusters.
We statistically study the property of emerging flux regions (EFRs) and the upper solar atmosphere response to the flux emergence by using data from the Helioseismic and Magnetic Imager (HMI) and the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Parameters including the total emerged flux, the flux growth rate, the maximum area, the duration of the emergence and the separation speed of the opposite polarities are adopted to delineate the property of the EFRs. The response of the upper atmosphere is addressed by the response of the atmosphere at different wavelengths (and thus at different temperatures). According to our results, the total emerged fluxes are in the range of (0.44 -- 11.2)$\times10^{19}$ Mx while the maximum area ranges from 17 to 182 arcsec$^2$. The durations of the emergence are between 1 and 12 hours, which are positively correlated to both the total emerged flux and the maximum area. The maximum distances between the opposite polarities are 7 -- 25 arcsec and are also correlated to the duration positively. The separation speeds are from 0.05 to 1.08 km s$^{-1}$, negatively correlated to the duration. The derived flux growth rates are (0.1 -- 1.3)$\times10^{19}$ Mx hr$^{-1}$, which are positively correlated to the total emerging flux. The upper atmosphere responds to the flux emergence in the 1600Å chromospheric line first, and then tens and hundreds of seconds later, in coronal lines, such as the 171Å (T=10$^{5.8}$ K) and 211Å (T=10$^{6.3}$ K) lines almost simultaneously, suggesting the successively heating of atmosphere from the chromosphere to the corona.
One of the most promising explanations for the origin of the billion solar mass black holes (BHs) inferred to power quasars at redshifts z > 6 is that supermassive stars (SMSs) with masses > 10,000 solar masses collapse to form the seed BHs from which they grow. Here we review recent theoretical advances which provide support for this scenario. Firstly, given sufficiently high accretion rates of gas into the cores of primordial protogalaxies, it appears that neither the high energy radiation emitted from the stellar surface nor the limited lifetime of SMSs can prevent their growth to masses of up to > 100,000 solar masses. Secondly, recent cosmological simulations suggest that the high fluxes of molecule-dissociating radiation which may be required in order to achieve such high accretion rates may be more common in the early universe than previously thought. We conclude that the majority of supermassive BHs may originate from SMSs at high redshifts.
We present and analyze the optical photometric and spectroscopic data of the Be/X-ray binary MXB 0656-072 from 2006 to 2009. A 101.2-day orbital period is found, for the first time, from the present public X-ray data(Swift/BAT and RXTE/ASM). The anti-correlation between the H$α$ emission and the $UBV$ brightness of MXB 0656$-$072 during our 2007 observations indicates that a mass ejection event took place in the system. After the mass ejection, a low-density region might develop around the Oe star. With the outward motion of the circumstellar disk, the outer part of the disk interacted with the neutron star around its periastron passage and a series of the X-ray outbursts were triggered between MJD 54350 and MJD 54850. The PCA--HEXTE spectra during the 2007-2008 X-ray outbursts could be well fitted by a cut-off power law with low energy absorption, together with an iron line around 6.4 keV, and a broad cyclotron resonance feature around 30 keV. The same variability of the soft and hard X-ray colors in 2.3-21 keV indicated that there were no overall changes in the spectral shape during the X-ray outbursts, which might be only connected with the changes of the mass-accretion rate onto the neutron star.
We develop notions of a representation of a topological graph E and of a covariant representation of a topological graph E which do not require the machinery of C*-correspondences and Cuntz-Pimsner algebras. We show that the C*-algebra generated by a universal representation of E coincides with the Toeplitz algebra of Katsura's topological-graph bimodule, and that the C*-algebra generated by a universal covariant representation of E coincides with Katsura's topological graph C*-algebra. We exhibit our results by constructing the isomorphism between the C*-algebra of a row-finite directed graph E with no sources and the C*-algebra of the topological graph arising from the shift map acting on infinite path space E^\infty.
A rapidly growing body of observational results suggests that planet formation takes place preferentially at high metallicity. In the core accretion model of planet formation this is expected because heavy elements are needed to form the dust grains which settle into the midplane of the protoplanetary disk and coagulate to form the planetesimals from which planetary cores are assembled. As well, there is observational evidence that the lifetimes of circumstellar disks are shorter at lower metallicities, likely due to greater susceptibility to photoevaporation. Here we estimate the minimum metallicity for planet formation, by comparing the timescale for dust grain growth and settling to that for disk photoevaporation. For a wide range of circumstellar disk models and dust grain properties, we find that the critical metallicity above which planets can form is a function of the distance r at which the planet orbits its host star. With the iron abundance relative to that of the Sun [Fe/H] as a proxy for the metallicity, we estimate a lower limit for the critical abundance for planet formation of [Fe/H]_crit ~ -1.5 + log(r/1 AU), where an astronomical unit (AU) is the distance between the Earth and the Sun. This prediction is in agreement with the available observational data, and carries implications for the properties of the first planets and for the emergence of life in the early Universe. In particular, it implies that the first Earth-like planets likely formed from circumstellar disks with metallicities Z > 0.1 Z_Sun. If planets are found to orbit stars with metallicities below the critical metallicity, this may be a strong challenge to the core accretion model.
The current study aims to quantify characteristic features of bipolar flux appearance of solar intranetwork (IN) magnetic elements. To attack such a problem, we use the Narrow-band Filter Imager (NFI) magnetograms from the Solar Optical Telescope (SOT) on board \emph{Hinode}; these data are from quiet and an enhanced network areas. Cluster emergence of mixed polarities and IN ephemeral regions (ERs) are the most conspicuous forms of bipolar flux appearance within the network. Each of the clusters is characterized by a few well-developed ERs that are partially or fully co-aligned in magnetic axis orientation. On average, the sampled IN ERs have total maximum unsigned flux of several 10^{17} Mx, separation of 3-4 arcsec, and a lifetime of 10-15 minutes. The smallest IN ERs have a maximum unsigned flux of several 10^{16} Mx, separations less than 1 arcsec, and lifetimes as short as 5 minutes. Most IN ERs exhibit a rotation of their magnetic axis of more than 10 degrees during flux emergence. Peculiar flux appearance, e.g., bipole shrinkage followed by growth or the reverse, is not unusual. A few examples show repeated shrinkage-growth or growth-shrinkage, like magnetic floats in the dynamic photosphere. The observed bipolar behavior seems to carry rich information on magneto-convection in the sub-photospheric layer.
The collapse of baryons into extremely massive stars with masses exceeding 10^4 M_Sun in a small fraction of protogalaxies at z > 10 is a promising candidate for the origin of supermassive black holes, some of which grow to a billion solar masses by z ~ 7. We determine the maximum masses such stars can attain by accreting primordial gas. We find that at relatively low accretion rates the strong ionizing radiation of these stars limits their masses to M_* ~ 10^3 M_Sun (dM_acc/dt / 10^-3 M_Sun yr^-1)^8/7, where dM_acc/dt is the rate at which the star gains mass. However, at the higher central infall rates usually found in numerical simulations of protogalactic collapse (>~ 0.1 M_Sun yr^-1), the lifetime of the star instead limits its final mass to >~ 10^6 M_Sun. Furthermore, for the spherical accretion rates at which the star can grow, its ionizing radiation is confined deep within the protogalaxy, so the evolution of the star is decoupled from that of its host galaxy. Lyman alpha emission from the surrounding H II region is trapped in these heavy accretion flows and likely reprocessed into strong Balmer series emission, which may be observable by the James Webb Space Telescope. This, along with strong He II 1640 Angstrom and continuum emission, are likely to be the key observational signatures of the progenitors of supermassive black holes at high redshift.
We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512^3) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8,196^3. Three Mach 9 simulations are performed, two super-Alfvénic and one trans-Alfvénic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties similar to non-self-gravitating in this regime, and we examine the effects of varied magnetic field strength on statistical properties: the density probability distribution function is approximately lognormal; velocity power spectral slopes decrease with field strength; alignment between velocity and magnetic field increases with field; the magnetic field probability distribution can be fit to a stretched exponential. The high density state is characterized by self-similar spheres; the density PDF is a power-law; collapse rate decreases with increasing mean field; density power spectra have positive slopes, P(ρ,k) \propto k; thermal-to-magnetic pressure ratios are unity for all simulations; dynamic-to-magnetic pressure ratios are larger than unity for all simulations; magnetic field distribution is a power-law. The high Alfvén Mach numbers in collapsing regions explain recent observations of magnetic influence decreasing with density. We also find that the high density state is found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored.
We have performed extensive two-dimensional magnetohydrodynamic simulations to study the amplification of magnetic fields when a supernova blast wave propagates into a turbulent interstellar plasma. The blast wave is driven by injecting high pressure in the simulation domain. The interstellar magnetic field can be amplified by two different processes, occurring in different regions. One is facilitated by the fluid vorticity generated by the ``rippled" shock front interacting with the background turbulence. The resulting turbulent flow keeps amplifying the magnetic field, consistent with earlier work \citep{Giacalone2007}. The other process is facilitated by the growth of the Rayleigh-Taylor instability at the contact discontinuity between the ejecta and the shocked medium. This can efficiently amplify the magnetic field and tends to produce the highest magnetic field. We investigate the dependence of the amplification on numerical parameters such as grid-cell size and on various physical parameters. We show the magnetic field has a characteristic radial profile that the downstream magnetic field gets progressively stronger away from the shock. This is because the downstream magnetic field needs a finite time to reach the efficient amplification, and will get further amplified in the Rayleigh-Taylor region. In our simulation we do not observe a systematic strong magnetic field within a small distance to the shock. This indicates that if the magnetic-field amplification in supernova remnants indeed occurs near the shock front, other processes such as three-dimensional instabilities, plasma kinetics and/or cosmic ray effect may need to be considered to explain the strong magnetic field in supernova remnants.
Recent observations reveal that spectral breaks at ~GeV are commonly present in Galactic gamma-ray supernova remnants (SNRs) interacting with molecular clouds and that most of them have a spectral ($E^2dF/dE$) "platform" extended from the break to lower energies. In paper I (Li & Chen 2010), we developed an accumulative diffusion model by considering an accumulation of the diffusive protons escaping from the shock front throughout the history of the SNR expansion. In this paper, we improve the model by incorporating finite-volume of MCs, demonstrate the model dependence on particle diffusion parameters and cloud size, and apply it to nine interacting SNRs (W28, W41, W44, W49B, W51C, Cygnus Loop, IC443, CTB 37A, and G349.7+0.2). This refined model naturally explains the GeV spectral breaks and, especially, the "platform"s, together with available TeV data. We find that the index of the diffusion coeffcient δ is in the range of 0.5-0.7, similar to the galactic averaged value, and the diffusion coefficient for cosmic rays around the SNRs is essentially two orders of magnitude lower than the Galactic average, which is a good indication for the suppression of cosmic ray diffusion near SNRs.
Let $n=2m$, $m$ odd, $e|m$, and $p$ odd prime with $p\equiv1\ \mathrm{mod}\ 4$. Let $d=\frac{(p^{m}+1)^{2}}{2(p^{e}+1)}$. In this paper, we study the cross-correlation between a $p$-ary $m$-sequence $\{s_{t}\}$ of period $p^{2m}-1$ and its decimation $\{s_{dt}\}$. Our result shows that the cross-correlation function is six-valued and that it takes the values in $\{-1,\ \pm p^{m}-1,\ \frac{1\pm p^{\frac{e}{2}}}{2}p^{m}-1,\ \frac{(1- p^{e})}{2}p^{m}-1\}$. Also, the distribution of the cross-correlation is completely determined.