arXiv subjects
Publications and source records attributed to Lei Ni.
In this paper we prove classification results for gradient shrinking Ricci solitons under two invariant conditions, namely nonnegative orthogonal bisectional curvature and weakly PIC1, without any curvature bound. New results on ancient solutions for the Ricci and Kähler-Ricci flow are also obtained. The main new feature is that no curvature upper bound is assumed.
Magnetic reconnection is the most likely mechanism responsible for the high temperature events that are observed in strongly magnetized locations around the temperature minimum in the low solar chromosphere. This work improves upon our previous work ["Magnetic Reconnection in Strongly Magnetized Regions of the Low Solar Chromosphere", The Astrophysical Journal 852, 95 (2018) ] by using a more realistic radiative cooling model computed from the OPACITY project and the CHIANTI database. We find that the rate of ionization of the neutral component of the plasma is still faster than recombination within the current sheet region. For low $β$ plasmas, the ionized and neutral fluid flows are well-coupled throughout the reconnection region resembling the single-fluid Sweet-Parker model dynamics. Decoupling of the ion and neutral inflows appears in the higher $β$ case with $β_0=1.46$, which leads to a reconnection rate about three times faster than the rate predicted by the Sweet-Parker model. In all cases, the plasma temperature increases with time inside the current sheet, and the maximum value is above $2\times10^4$~K when the reconnection magnetic field strength is greater than $500$~G. While the more realistic radiative cooling model does not result in qualitative changes of the characteristics of magnetic reconnection, it is necessary for studying the variations of the plasma temperature and ionization fraction inside current sheets in strongly magnetized regions of the low solar atmosphere. It is also important for studying energy conversion during the magnetic reconnection process when the hydrogen-dominated plasma approaches full ionization.
We numerically study magnetic reconnection on different spatial scales and at different heights in the weakly ionized plasma of the low solar atmosphere (around $300-800$~km above the solar surface) within a reactive 2.5 D multi-fluid plasma-neutral model. We consider a strongly magnetized plasma ($β\sim 6\% $) evolving from a force-free magnetic configuration and perturbed to initialize formation of a reconnection current sheet. On large scales, the resulting current sheets are observed to undergo a secondary 'plasmoid' instability. A series of simulations at different scales demonstrate a cascading current sheet formation process that terminates for current sheets with width of ~2m and length of $\sim100$~m, corresponding to the critical current sheet aspect ratio of $\sim50$. We also observe that the plasmoid instability is the primary physical mechanism accelerating the magnetic reconnection in this plasma parameter regime. After plasmoid instabilities appear, the reconnection rate sharply increases to a value of $\sim$ 0.035, observed to be independent of the Lundquist number. These characteristics are very similar to magnetic reconnection in fully ionized plasmas. In this low $β$ guide field reconnection regime, both the recombination and collisionless effects are observed to have a small contribution to the reconnection rate. The simulations show that it is difficult to heat the dense weakly ionized photospheric plasmas to above $2\times10^4$~K during the magnetic reconnection process. However, the plasmas in the low solar chromosphere can be heated above $3\times10^4$~K with reconnection magnetic fields of $500$~G or stronger.
This work studies a beamforming design for downlink transmission of a multi-user multiple-input single-output (MISO) system where each legitimate user employs a power splitting (PS) based simultaneous wireless information and power transfer (SWIPT) technique. The transmitter intends to send confidential information to its legitimate users in the presence of purely unknown eavesdroppers. Since the transmitter does not have any knowledge of the eavesdroppers' channel state information (CSI), we consider an artificial noise (AN) approach to establishing secure communication. This beamforming design is developed by maximizing the AN power to interfere with the eavesdropper as much as possible. Based on the assumption of imperfect CSI of legitimate users at the transmitter, two robust design approaches for the joint beamforming and PS ratio have been studied to maximize the AN power under both energy harvesting (EH) and signal-to-interference-plus-noise ratio (SINR) requirements at each legitimate user. In the first robust design, we consider the bounded channel uncertainties, and employ semidefinite relaxation (SDR) and a linear matrix inequality (LMI) representation to transform the original problem into a semidefinite program (SDP). In the second robust design, we consider the statistical channel uncertainties, and show that the proposed problem can be reformulated into another form of SDP through both SDR and Bernstein-type inequality. In addition, the non-linear energy harvesting (EH) model is incorporated in this work as it could reflect the characteristics of practical radio frequency(RF)-EH conversion circuit. Simulation results have been provided to demonstrate the performance of our proposed robust designs.
We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$ isometrically from the simply-connected Kähler manifold with nonnegative bisectional curvature and a linear growth holomorphic function) of L.-F. Tam and the author. The second set of results concerns the so-called $k$-hyperbolicity and its connection with the negativity of the $k$-scalar curvature (when $k=1$ they are the negativity of holomorphic sectional curvature and Kobayashi hyperbolicity) introduced recently by F. Zheng and the author. We lastly prove a new Schwarz Lemma type estimate in terms of {\it only the holomorphic sectional curvatures of both domain and target manifolds}.
In this paper we study the class of compact Kähler manifolds with positive orthogonal Ricci curvature: $Ric^\perp>0$. First we illustrate examples of Kähler manifolds with $Ric^\perp>0$ on Kähler C-spaces, and construct ones on certain projectivized vector bundles. These examples show the abundance of Kähler manifolds which admit metrics of $Ric^\perp>0$. Secondly we prove some (algebraic) geometric consequences of the condition $Ric^\perp>0$ to illustrate that the condition is also quite restrictive. Finally this last point is made evident with a classification result in dimension three and a partial classification in dimension four.
In this paper, we consider orthogonal Ricci curvature $Ric^{\perp}$ for Kähler manifolds, which is a curvature condition closely related to Ricci curvature and holomorphic sectional curvature. We prove comparison theorems and a vanishing theorem related to these curvature conditions, and construct various examples to illustrate their subtle relationship.
The Kelvin-Hemholtz (K-H) instability in the corona EUV jet is studied via 2.5 MHD numerical simulations. The jet results from magnetic reconnection due to the interation of the new emerging magnetic field and the pre-existing magnetic field in the corona. Our results show that the Alfven Mach number along the jet is about 5-14 just before the instability occurs, and it is even higher than 14 at some local areas. During the K-H instability process, several vortex-like plasma blobs of high temperature and high density appear along the jet, and magnetic fields have also been rolled up and the magnetic configuration including anti-parallel magnetic fields forms, which leads to magnetic reconnection at many X-points and current sheet fragments inside the vortex-like blob. After magnetic islands appear inside the main current sheet, the total kinetic energy of the reconnection outflows decreases, and cannot support the formation of the vortex-like blob along the jet any longer, then the K-H instability eventually disappears. We also present the results about how the guide field and the flux emerging speed affect the K-H instability. We find that the strong guide field inhibits the shock formation in the reconnection upward outflow regions but helps secondary magnetic islands appear earlier in the main current sheet, and then apparently suppresses the K-H instability. As the speed of the emerging magnetic field decreases, the K-H instability appears later, the highest temperature inside the vortex blob gets lower and the vortex structure gets smaller.
Solid evidence of magnetic reconnection is rarely reported within sunspots, the darkest regions with the strongest magnetic fields and lowest temperatures in the solar atmosphere. Using the world's largest solar telescope, the 1.6-meter Goode Solar Telescope, we detect prevalent reconnection through frequently occurring fine-scale jets in the H$α$ line wings at light bridges, the bright lanes that may divide the dark sunspot core into multiple parts. Many jets have an inverted Y-shape, shown by models to be typical of reconnection in a unipolar field environment. Simultaneous spectral imaging data from the Interface Region Imaging Spectrograph show that the reconnection drives bidirectional flows up to 200~km~s$^{-1}$, and that the weakly ionized plasma is heated by at least an order of magnitude up to $\sim$80,000 K. Such highly dynamic reconnection jets and efficient heating should be properly accounted for in future modeling efforts of sunspots. Our observations also reveal that the surge-like activity previously reported above light bridges in some chromospheric passbands such as the H$α$ core has two components: the ever-present short surges likely to be related to the upward leakage of magnetoacoustic waves from the photosphere, and the occasionally occurring long and fast surges that are obviously caused by the intermittent reconnection jets.
Magnetic reconnection in strongly magnetized regions around the temperature minimum region of the low solar atmosphere is studied by employing MHD-based simulations of a partially ionized plasma within a reactive 2.5D multi-fluid model. It is shown that in the absence of magnetic nulls in a low $β$ plasma the ionized and neutral fluid flows are well-coupled throughout the reconnection region. However, non-equilibrium ionization-recombination dynamics play a critical role in determining the structure of the reconnection region, lead to much lower temperature increases and a faster magnetic reconnection rate as compared to simulations that assume plasma to be in ionization-recombination equilibrium. The rate of ionization of the neutral component of the plasma is always faster than recombination within the current sheet region even when the initial plasma $β$ is as high as $β_0=1.46$. When the reconnecting magnetic field is in excess of a kilogauss and the plasma $β$ is lower than 0.0145, the initially weakly ionized plasmas can become fully ionized within the reconnection region and the current sheet can be strongly heated to above $2.5\times10^4$~K, even as most of the collisionally dissipated magnetic energy is radiated away. The Hall effect increases the reconnection rate slightly, but in the absence of magnetic nulls it does not result in significant asymmetries or change the characteristics of the reconnection current sheet down to meter scales.
In this paper we prove a gap theorem for Kähler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for plurisubharmonic functions on such a manifolds, which generalizes a previous result of L.-F. Tam and the first author.
We perform two-dimensional resistive magnetohydrodynamic simulations of coronal jets driven by flux emergence along the lower boundary. The reconnection layers are susceptible the formation of blobs that are ejected in the jet. Our simulation with low plasma $β$ (Case I) shows that magnetic islands form easily and propagate upwards in the jet. These islands are multithermal and thus are predicted to show up in hot channels (335 Å\, and 211 Å) and the cool channel (304 Å) in observations by the Atmospheric Imaging Assembly (AIA) on the \emph{Solar Dynamics Observatory}. The islands have maximum temperatures of 8 MK, lifetimes of 120 s, diameters of 6 Mm, and velocities of 200 km s$^{-1}$. These parameters are similar to the properties of blobs observed in EUV jets by AIA\@. The Kelvin-Helmholtz instability develops in our simulation with moderately high plasma $β$ (Case II), and leads to the formation of bright vortex-like blobs above the multiple high magneto-sonic Mach number regions that appear along the jet. These vortex-like blobs can also be identified in the AIA channels. However, they eventually move downward and disappear after the high magneto-sonic Mach number regions disappear. In the lower plasma $β$ case, the lifetime for the jet is shorter, the jet and magnetic islands are formed with higher velocities and temperatures, the current sheet fragments are more chaotic, and more magnetic islands are generated. Our results show that the plasmoid instability and Kelvin-Helmholtz instability along the jet are both possible causes of the formation of blobs observed at extreme ultraviolet (EUV) wavelengths.
We simulate several magnetic reconnection processes in the low solar chromosphere/photosphere, the radiation cooling, heat conduction and ambipolar diffusion are all included. Our numerical results indicate that both the high temperature($ \gtrsim 8\times10^4$~K) and low temperature($\sim 10^4$~K) magnetic reconnection events can happen in the low solar atmosphere ($100\sim600$~km above the solar surface). The plasma $β$ controlled by plasma density and magnetic fields is one important factor to decide how much the plasma can be heated up. The low temperature event is formed in a high $β$ magnetic reconnection process, Joule heating is the main mechanism to heat plasma and the maximum temperature increase is only several thousand Kelvin. The high temperature explosions can be generated in a low $β$ magnetic reconnection process, slow and fast-mode shocks attached at the edges of the well developed plasmoids are the main physical mechanisms to heat the plasma from several thousand Kelvin to over $8\times10^4$~K. Gravity in the low chromosphere can strongly hinder the plasmoind instability and the formation of slow-mode shocks in a vertical current sheet. Only small secondary islands are formed; these islands, however, are not well developed as those in the horizontal current sheets. This work can be applied for understanding the heating mechanism in the low solar atmosphere and could possibly be extended to explain the formation of common low temperature EBs ($\sim10^4$~K) and the high tenperature IRIS bombs ($\gtrsim 8\times10^4$) in the future.
We show that a four-dimensional complete gradient shrinking Ricci soliton with positive isotropic curvature is either a quotient of S^4 or a quotient of S^3 cross R. This gives a clean classification result removing the earlier additional assumptions in [13] by Wallach and the second author.
In this paper, we study the energy conversion and spectra in a corona current sheet by 2.5-dimensional MHD numerical simulations. Numerical results show that many Petschek-like fine structures with slow-mode shocks mediated by plasmoid instabilities develop during the magnetic reconnection process. The termination shocks can also be formed above the primary magnetic island and at the head of secondary islands. These shocks play important roles in generating thermal energy in a corona current sheet. For a numerical simulation with initial conditions close to the solar corona environment, the ratio of the generated thermal energy to the total dissipated magnetic energy is around $1/5$ before secondary islands appear. After secondary islands appear, the generated thermal energy starts to increase sharply and this ratio can reach a value about $3/5$. In an environment with a relatively lower plasma density and plasma $β$, the plasma can be heated to a much higher temperature. After secondary islands appear, the one dimensional energy spectra along the current sheet do not behave as a simple power law and the spectrum index increases with the wave number. The average spectrum index for the magnetic energy spectrum along the current sheet is about $1.8$. The two dimensional spectra intuitively show that part of the high energy is cascaded to large $kx$ and $ky$ space after secondary islands appear. The plasmoid distribution function calculated from numerical simulations behaves as a power law closer to $f(ψ) \sim ψ^{-1}$ in the intermediate $ψ$ regime. By using $η_{eff} = v_{inflow}\cdot L$, the effective magnetic diffusivity is estimated about $10^{11}\sim10^{12}$~m$^2$\,s$^{-1}$.
We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $α>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex self-similar contracting solution of the flow. Under additional central symmetry of the initial body we prove that the limit is the round sphere.
Magnetic reconnection in the partially ionized solar chromosphere is studied in 2.5-dimensional magnetohydrodynamic simulations including radiative cooling and ambipolar diffusion. A Harris current sheet with and without a guide field is considered. Characteristic values of the parameters in the middle chromosphere imply a high magnetic Reynolds number of $\sim10^{6}\mbox{--}10^7$ in the present simulations. Fast magnetic reconnection then develops as a consequence of the plasmoid instability without the need to invoke anomalous resistivity enhancements. Multiple levels of the instability are followed as it cascades to smaller scales, which approach the ion inertial length. The reconnection rate, normalized to the asymptotic values of magnetic field and Alfvén velocity in the inflow region, reaches values in the range $\sim0.01\mbox{--}0.03$ throughout the cascading plasmoid formation and for zero as well as for strong guide field. The out-flow velocity reaches $\approx40$~km\,s$^{-1}$. Slow-mode shocks extend from the $X$-points, heating the plasmoids up to $\sim 8\times10^4$~K. In the case of zero guide field, the inclusion of ambipolar diffusion and radiative cooling both cause a rapid thinning of the current sheet (down to $\sim30$~m) and early formation of secondary islands. Both of these processes have very little effect on the plasmoid instability for a strong guide field. The reconnection rates, temperature enhancements, and upward out-flow velocities from the vertical current sheet correspond well to their characteristic values in chromospheric jets.
Viscosity solutions are suitable notions in the study of nonlinear PDEs justified by estimates established via the maximum principle or the comparison principle. Here we prove that the isoperimetric profile functions of Riemannian manifolds with Ricci lower bound are viscosity super-solutions of some nonlinear differential equations. From these one can derive the isoperimetric inequalities of Lévy-Gromov and Bérard-Besson-Gallot, as well as some new comparison results.