arXiv subjects
Publications and source records attributed to Shuo Zhang.
This paper is devoted to the convergence analysis of the Adini element scheme for the fourth order problem in arbitrary dimension. We prove that, the Adini element scheme is $\mathcal{O}(h^2)$ order convergent in energy norm provided the exact solution is in $H^4$, and the convergence rate in $L^2$ norm can not be nontrivially higher than $\mathcal{O}(h^2)$ order. Numerical verifications are presented.
The efficient cooling of the nanomechanical resonators is essential to exploration of quantum properties of the macroscopic or mesoscopic systems. We propose such a laser-cooling scheme for a nanomechanical cantilever, which works even for the low-frequency mechanical mode and under weak cooling lasers. The cantilever is attached by a diamond nitrogen-vacancy center under a strong magnetic field gradient and the cooling is assisted by a dynamical Stark-shift gate. Our scheme can effectively enhance the desired cooling efficiency by avoiding the off-resonant and unexpected carrier transitions, and thereby cool the cantilever down to the vicinity of the vibrational ground state in a fast fashion.
We propose a scheme for generating the Schrödinger cat state based on geometric operations by a nanomechanical resonator coupled to a superconducting charge qubit. The charge qubit, driven by two strong classical fields, interacts with a high-frequency phonon mode of the nanomechanical resonator. During the operation, the charge qubit undergoes no real transitions, while the phonon mode of the nanomechanical resonator is displaced along different paths in the phase space, dependent on the states of the charge qubit, which yields the Schrödinger cat state. The robustness of the scheme is justified by considering noise from environment, and the feasibility of the scheme is discussed.
Experimental evidences from transport, magnetic, and magneto-optical (MO) image measurements confirmed that arsenic (As) vapor annealing was another effective way to induce bulk superconductivity with isotropic, large, and homogenous superconducting critical current density (Jc) in Fe1+yTe0.6Se0.4 single crystal. Since As is an exotic and easily detectable heavy element to Fe1+yTe0.6Se0.4 single crystal, As vapor annealing is very advantageous for the study of annealing mechanism. Detailed micro-structural and elemental analyses exclude the possibility that intercalating or doping effect may happen in the other post-annealing methods, proving that Fe reacts with As on the surface of the crystal and the reaction itself acts as a driving force to drag excess Fe out. The removal of excess Fe results in the good superconductivity performance.
In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present paper together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases.
Sagittarius A* harbors the supermassive black hole that lies at the dynamical center of our Galaxy. Sagittarius A* spends most of its time in a low luminosity emission state but flares frequently in the infrared and X-ray, increasing up to a few hundred fold in brightness for up to a few hours at a time. The physical processes giving rise to the X-ray flares are uncertain. Here we report the detection with the NuSTAR observatory in Summer and Fall 2012 of four low to medium amplitude X-ray flares to energies up to 79 keV. For the first time, we clearly see that the power-law spectrum of Sagittarius A* X-ray flares extends to high energy, with no evidence for a cut off. Although the photon index of the absorbed power-law fits are in agreement with past observations, we find a difference between the photon index of two of the flares (significant at the 95% confidence level). The spectra of the two brightest flares (~55 times quiescence in the 2-10 keV band) are compared to simple physical models in an attempt to identify the main X-ray emission mechanism, but the data do not allow us to significantly discriminate between them. However, we confirm the previous finding that the parameters obtained with synchrotron models are, for the X-ray emission, physically more reasonable than those obtained with inverse-Compton models. One flare exhibits large and rapid (< 100 s) variability, which, considering the total energy radiated, constrains the location of the flaring region to be within ~10 Schwarzschild radii of the black hole.
We report the first detection of high-energy X-ray (E>10 keV) emission from the Galactic Center non-thermal filament G359.89-0.08 (Sgr A-E) using data acquired with the Nuclear Spectroscopic Telescope Array (NuSTAR). The bright filament was detected up to ~50 keV during a NuSTAR Galactic Center monitoring campaign. The featureless power-law spectrum with a photon index of ~2.3 confirms a non-thermal emission mechanism. The observed flux in the 3-79 keV band is ~ 2.0e-12 erg/cm^2/s, corresponding to an unabsorbed X-ray luminosity of ~2.6e34 erg/s assuming a distance of 8.0 kpc. Based on theoretical predictions and observations, we conclude that Sgr A-E is unlikely to be a pulsar wind nebula (PWN) or supernova remnant-molecular cloud (SNR-MC) interaction, as previously hypothesized. Instead, the emission could be due to a magnetic flux tube which traps TeV electrons. We propose two possible TeV electron sources: old PWNe (up to ~100 kyr) with low surface brightness and radii up to ~30 pc or molecular clouds (MCs) illuminated by cosmic rays (CRs) from CR accelerators such as SNRs or Sgr A*.
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction is commonly defined as the solution of an inverse problem, which is regularized by a priori assumptions about the object. While practical realizations have hitherto been surprisingly successful, strong assumptions about the continuity of image features may affect the temporal fidelity of the estimated images. Here we propose a novel approach for the reconstruction of serial real-time MRI data which integrates the deformations between nearby frames into the data consistency term. The method is not required to be affine or rigid and does not need additional measurements. Moreover, it handles multi-channel MRI data by simultaneously determining the image and its coil sensitivity profiles in a nonlinear formulation which also adapts to non-Cartesian (e.g., radial) sampling schemes. Experimental results of a motion phantom with controlled speed and in vivo measurements of rapid tongue movements demonstrate image improvements in preserving temporal fidelity and removing residual artifacts.
We propose an efficient optical electromagnetically induced transparency (EIT) cooling scheme for a cantilever with a nitrogen-vacancy center attached in a non-uniform magnetic field using dynamical Zeeman effect. In our scheme, the Zeeman effect combined with the quantum interference effect enhances the desired cooling transition and suppresses the undesired heating transitions. As a result, the cantilever can be cooled down to nearly the vibrational ground state under realistic experimental conditions within a short time. This efficient optical EIT cooling scheme can be reduced to the typical EIT cooling scheme under special conditions.
We report the unambiguous detection of non-thermal X-ray emission up to 30 keV from the Cannonball, a few-arcsecond long diffuse X-ray feature near the Galactic Center, using the NuSTAR X-ray observatory. The Cannonball is a high-velocity (vproj~500 km/s) pulsar candidate with a cometary pulsar wind nebula (PWN) located ~2' north-east from Sgr A*, just outside the radio shell of the supernova remnant Sagittarius A (Sgr A) East. Its non-thermal X-ray spectrum, measured up to 30 keV, is well characterized by a Gamma~1.6 power-law, typical of a PWN, and has an X-ray luminosity of L(3-30 keV)=1.3e34 erg/s. The spectral and spatial results derived from X-ray and radio data strongly suggest a runaway neutron star born in the Sgr A East supernova event. We do not find any pulsed signal from the Cannonball. The NuSTAR observations allow us to deduce the PWN magnetic field and show that it is consistent with the lower limit obtained from radio observations.
In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex associated with that finite element pair. The finite element spaces involved consist of piecewise polynomials only, and the divergence-free condition is imposed in a primal formulation. Combined with some existing results, these constructions can be generated onto grids that consist of both triangular and quadrilateral cells.
We designed and implemented a signal generator that can simulate the output of the NaI (Tl)CsI (Na) detectors pre amplifier onboard the Hard X ray Modulation Telescope (HXMT). Using the development of FPGA (Field Programmable Gate Array) with VHDL language and adding random constituent, we have finally produced the double exponential random pulse signal generator. The statistical distribution of signal amplitude is programmable. The occurrence time intervals of adjacent signals content negative exponential distribution statistically.
We report the discovery of 3.76-s pulsations from a new burst source near Sgr A* observed by the NuSTAR Observatory. The strong signal from SGR J1745-29 presents a complex pulse profile modulated with pulsed fraction 27+/-3 % in the 3-10 keV band. Two observations spaced 9 days apart yield a spin-down rate of Pdot = (6.5+/-1.4)x10^{-12}. This implies a magnetic field B = 1.6x10^14 G, spin-down power Edot = 5x10^33 erg/s, and characteristic age P/2Pdot = 9x10^3 yr, for the rotating dipole model. However, the current Pdot may be erratic, especially during outburst. The flux and modulation remained steady during the observations and the 3-79 keV spectrum is well fitted by a combined blackbody plus power-law model with temperature kT_BB = 0.96+/-0.02 keV and photon index = 1.5+/-0.4, respectively. The neutral hydrogen column density (nH ~ 1.4x10^23 cm^{-2}) measured by NuSTAR and Swift suggests that SGR J1745-29 is located at or near the Galactic Center. The lack of an X-ray counterpart in the published Chandra survey catalog sets a quiescent 2-8 keV luminosity limit of Lx ~< 10^32 erg/s. The bursting, timing, and spectral properties indicate a transient magnetar undergoing an outburst with 2-79 keV luminosity up to 3.5x10^35 erg/s for a distance of 8 kpc. SGR J1745-29 joins a growing subclass of transient magnetars, indicating that many magnetars in quiescence remain undetected in the X-ray band or have been detected as high-B radio pulsars. The peculiar location of SGR J1745-29 has important implications for the formation and dynamics of neutron stars in the Galactic Center region.
This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of size $N$ on an arbitrary polygoanl domain. Several preconditioners are presented, and the conjugate gradient methods applied with these preconditioners are proven to converge uniformly with respect to the size of the preconditioned linear system. One main ingredient of the optimal preconditioners is a mixed-form discretization of the fourth-order problem. Such a mixed-form discretization leads to a non-desirable ---either non-optimal or non-convergent--- approximation of the original solution, but it provides optimal preconditioners for the direct finite element problem. It is further shown that the implementation of the preconditioners can be reduced to the solution of several discrete Poisson equations. Therefore, any existing optimal or nearly optimal solver, such as geometric or algebraic multigrid methods, for Poisson equations would lead to a nearly optimal solver for the discrete fourth-order system. A number of nonstandard Sobolev spaces and their discretizations defined on the boundary of polygonal domains are carefully studied and used for the analysis of those preconditioners.
Based on the first-principles calculations, we have investigated the geometry, binding properties, density of states and band structures of the novel superconductor LaFe1-xCoxAsO and its parent compounds with the ZrCuSiAs structure. We demonstrate that La-O bond and TM-As (TM=Fe or Co) bond are both strongly covalent, while the LaO and TMAs layers have an almost ionic interaction through the Bader charge analysis. Partial substitution of iron with cobalt modify the Fermi level from a steep edge to a flat slope, which explains why in this system Co doping suppresses the spin density wave (SDW) transition.
The alkali halides have been studied very frequently for their simple structures and interesting properties, for example, the high-pressure induced transition$^1$. There are several successful models that can be employed. The most famous model of them is the Tosi-Fumi interionic potential$^2$ which is an empirical potential derived from the experimental data. Whereas, here we developed a new potential model based on the Möbius lattice inversion method$^{3,4}$, which can be derived directly from the cohesive energy curve without any experimental data and is more effective than the ab initial calculation. With the Möbius interionic potentials, we calculated the structural and elastic properties of RbCl crystal. The results are in good agreement with experiments. We also studied the high-pressure induced B1-B2 transition of RbCl crystal and estimated approximately the transition-point which is about 1.09GPa. Further more, we used this potential model to simulate the RbCl melting with molecular dynamics. The calculated melt-point is approximately 990K$\sim$995K, close to the experimental data.