arXiv subjects
Publications and source records attributed to Xi Chen.
Adaptive grid generation is an active research topic for numer- ical solution of differential equations. In this paper, we propose a variational method which generates transformations with prescribed Jacobian determinant and curl. Then we use this transformation to achieve adaptive grid generation task, and show the importance of curl in a transformation.
We investigate the fast transport of an atom or a packet of atoms by different kinds of non-harmonic traps including power-law traps. The study is based on the reverse engineering method. Exact results are obtained and applied to design robust transport protocols. The optimization of the transport trajectory is performed with classical trajectories, and remains valid for the transport of a wave packet.
We consider the Laplacian $Δ$ on an asymptotically hyperbolic manifold $X$, as defined by Mazzeo and Melrose. We give pointwise bounds on the spectral measure for the operator $(Δ- n^2/4)_+^{1/2}$ on such manifolds, under the assumptions that $X$ is nontrapping and there is no resonance at the bottom of the spectrum. This uses the construction of the resolvent given by Mazzeo and Melrose (valid when the spectral parameter lies in a compact set), Melrose, Sá Barreto and Vasy (high energy estimates for a perturbation of the hyperbolic metric) and the present authors (see also the work by Yiran Wang) in the general high-energy case. Under the additional assumption that $X$ has negative curvature everywhere, we give two applications of the spectral measure estimates. The first, following work due to Guillarmou and Sikora with the second author in the asymptotically conic case, is a restriction theorem, that is, a $L^p(X) \to L^{p'}(X)$ operator norm bound on the spectral measure. The second is a spectral multiplier result, that is, a bound on functions $F((Δ- n^2/4)_+^{1/2})$ of the square root of the Laplacian, in terms of norms of the function $F$. Compared to the asymptotically conic case, our spectral multiplier result is weaker, but the restriction estimate is stronger. In both cases, the difference can be traced to the exponential volume growth at infinity for asymptotically hyperbolic manifolds, as opposed to polynomial growth in the asymptotically conic setting. The pointwise bounds on the spectral measure established here will also be applied to Strichartz estimates in another work by the first author.
In this paper, we explore the multiple source localisation problem in the cerebral cortex using magnetoencephalography (MEG) data. We model neural currents as point-wise dipolar sources which dynamically evolve over time, then model dipole dynamics using a probabilistic state space model in which dipole locations are strictly constrained to lie within the cortex. Based on the proposed models, we develop a Bayesian particle filtering algorithm for localisation of both known and unknown numbers of dipoles. The algorithm consists of a region of interest (ROI) estimation step for initial dipole number estimation, a Gibbs multiple particle filter (GMPF) step for individual dipole state estimation, and a selection criterion step for selecting the final estimates. The estimated results from the ROI estimation are used to adaptively adjust particle filter's sample size to reduce the overall computational cost. The proposed models and the algorithm are tested in numerical experiments. Results are compared with existing particle filtering methods. The numerical results show that the proposed methods can achieve improved performance metrics in terms of dipole number estimation and dipole localisation.
This is the first in a series of papers in which we investigate the resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds with applications to the restriction theorem, spectral multiplier results and Strichartz estimates. In this first paper, we use semiclassical Lagrangian distributions and semiclassical intersecting Lagrangian distributions, along with Mazzeo-Melrose 0-calculus, to construct the high energy resolvent on general non- trapping asymptotically hyperbolic manifolds, generalizing the work due to Melrose, Sa Barreto and Vasy. We note that there is an independent work by Y. Wang which also constructs the high-energy resolvent.
The Stein-Tomas restriction theorem on Euclidean space says one can meaningfully restrict $\hat{f}$ to the unit sphere of $\mathbb{R}^n$ provided $f \in L^p(\mathbb{R}^n)$ with $1 < p < 2$. This result can be rewritten in terms of the estimates for the spectral measure of Laplacian. Guillarmou, Hassell and Sikora formulated a sufficient condition of the restriction theorem, via spectral measure, on abstract metric measure spaces. But they only proved the result in a special case. The present note aims to give a complete proof. In the end, it will be applied to the restriction theorem on asymptotically conic manifolds.
The expansion of a harmonic potential that holds a quantum particle may be realized without any final particle excitation but much faster than adiabatically via "shortcuts to adiabaticity" (STA). While ideally the process time can be reduced to zero, practical limitations and constraints impose minimal finite times for the externally controlled time-dependent frequency protocols. We examine the role of different time-averaged energies (total, kinetic, potential, non-adiabatic) and of the instantaneous power in characterizing or selecting different protocols.Specifically, we prove a virial theorem for STA processes, set minimal energies for specific times or viceversa, and discuss their realizability by means of Dirac impulses or otherwise.
First principle based prediction of mean flow quantities of wall-bounded turbulent flows (channel, pipe, and turbulent boundary layer - TBL) is of great importance from both physics and engineering standpoints. Here (Part I), we present a symmetry-based approach which derives analytic expressions governing the mean velocity profile (MVP) from an innovative Lie-group analysis. The new approach begins by identifying a set of order functions (e.g. stress length, shear-induced eddy length), in analogy with the order parameter in Landau's mean-field theory, which aims at capturing symmetry aspects of the fluctuations (e.g. Reynolds stress, dissipation). The order functions are assumed to satisfy a dilation group invariance - representing the effects of the wall on fluctuations - which allows us to postulate three new kinds of invariant solutions of the mean momentum equation (MME), focusing on group invariants of the order functions (rather than those of the mean velocity as done in previous studies). The first - a power law solution - gives functional forms for the viscous sublayer, the buffer layer, the log-layer, and a newly identified central `core' (for channel and pipe, but non-existent for TBL). The second - a defect power law of form $1-r^{m}$ ($r$ being the distance from the center line) - describes the `bulk zone' (the region of balance between production and dissipation). The third - a relation between the group invariants of the stress length function and its first derivative - describes scaling transition between adjacent layers. A combination of these three expressions yields a multi-layer formula covering the entire flow domain, identifying three important parameters: scaling exponent, layer thickness, and transition sharpness. All three kinds of invariant solutions are validated, individually and in combination, by data from direct numerical simulations (DNS).
Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi$_2$Se$_3$ ultrathin films. At two-dimensional limit, bulk electrons becomes quantized and the quantization can be controlled by film thickness at single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of phase relaxation length $l_ϕ$ and inelastic scattering lifetime $τ$ of topological surface-state electrons. We find that $τ$ exhibits a remarkable $(E-E_F)^{-2}$ energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.
A finite-size quasi two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and balanced, effectively one-dimensional, Rashba-Dresselhaus one. In both cases spin-dependent "anomalous" velocity, proportional to the spin-orbit coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wavepackets, reducing the total condensate density. Depending on the spin-orbit coupling strength, interatomic attraction, and the initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus, extending the domain of existence of condensates of attracting atoms.
We investigate the possibility of constraining the sin i degeneracy of alpha Cen B b -- with orbital period P=3.24 d; a = 0.042 AU; msini = 1.1 M_earth -- to estimate the true mass of the newly reported terrestrial exoplanet in the nearest stellar system to our Sun. We present detailed numerical simulations of the dynamical stability of the exoplanet in the alpha Cen AB binary system for a range of initial inclinations, eccentricities, and semi-major axes. The system represents a benchmark case for the interplay of the Kozai mechanism, general relativistic and tidal forces. From our simulations, there is only a small boundary in initial inclinations and initial semi-major axes that result in the migration via the Kozai mechanism of alpha Cen B b to its present location. Inside this boundary, the planet orbit is stable for up to 1 Gyr against the Kozai mechanism, and outside this boundary the planet collides with alpha Cen B or is ejected. In our three simulations where the planet migrates in towards the star via the Kozai mechanism, the final inclination is 46-53 degrees relative to the AB orbital plane, lower than the initial inclination of 75 degrees in each case. We discuss inclination constraints from the formation of alpha Cen B b in situ at its present location, migration in a proto-planetary disk, or migration in resonance with additional planets. We conclude that alpha Cen B b probably has a mass of less than 2.7 M_earth, implying a likely terrestrial composition warranting future confirmation.
The stoichiometric "111" iron-based superconductor, LiFeAs, has attacted great research interest in recent years. For the first time, we have successfully grown LiFeAs thin film by molecular beam epitaxy (MBE) on SrTiO3(001) substrate, and studied the interfacial growth behavior by reflection high energy electron diffraction (RHEED) and low-temperature scanning tunneling microscope (LT-STM). The effects of substrate temperature and Li/Fe flux ratio were investigated. Uniform LiFeAs film as thin as 3 quintuple-layer (QL) is formed. Superconducting gap appears in LiFeAs films thicker than 4 QL at 4.7 K. When the film is thicker than 13 QL, the superconducting gap determined by the distance between coherence peaks is about 7 meV, close to the value of bulk material. The ex situ transport measurement of thick LiFeAs film shows a sharp superconducting transition around 16 K. The upper critical field, Hc2(0)=13.0 T, is estimated from the temperature dependent magnetoresistance. The precise thickness and quality control of LiFeAs film paves the road of growing similar ultrathin iron arsenide films.
We report an improved test of the weak equivalence principle by using a simultaneous $^{85}$Rb-$^{87}$Rb dual-species atom interferometer. We propose and implement a four-wave double-diffraction Raman transition scheme for the interferometer, and demonstrate its ability in suppressing common-mode phase noise of Raman lasers after their frequencies and intensity ratios are optimized. The statistical uncertainty of the experimental data for Eötvös parameter $η$ is $0.8\times10^{-8}$ at 3200 s. With various systematic errors corrected the final value is $η=(2.8\pm3.0)\times10^{-8}$. The major uncertainty is attributed to the Coriolis effect.
We report transport studies on (Bi,Sb)2Te3 topological insulator thin films with tunable electronic band structure. We find a doping and temperature regime in which the Hall coefficient is negative indicative of electron-type carriers, whereas the Seebeck coefficient is positive indicative of hole-type carriers. This sign anomaly is due to the distinct transport behaviors of the bulk and surface states: the surface Dirac fermions dominate magnetoelectric transport while the thermoelectric effect is mainly determined by the bulk states. These findings may inspire new ideas for designing topological insulator-based high efficiency thermoelectric devices.
We investigate the effect of slow spring-constant drifts of the trap used to shuttle two ions of different mass. We design transport protocols to suppress or mitigate the final excitation energy by applying invariant-based inverse engineering, perturbation theory, and a harmonic dynamical normal-mode approximation. A simple, explicit trigonometric protocol for the trap trajectory is found to be robust with respect to the spring-constant drifts.
Online social networks (OSNs) are changing the way in which the information spreads throughout the Internet. A deep understanding of the information spreading in OSNs leads to both social and commercial benefits. In this paper, we characterize the dynamic of information spreading (e.g., how fast and widely the information spreads against time) in OSNs by developing a general and accurate model based on the Interactive Markov Chains (IMCs) and mean-field theory. This model explicitly reveals the impacts of the network topology on information spreading in OSNs. Further, we extend our model to feature the time-varying user behaviors and the ever-changing information popularity. The complicated dynamic patterns of information spreading are captured by our model using six key parameters. Extensive tests based on Renren's dataset validate the accuracy of our model, which demonstrate that it can characterize the dynamic patterns of video sharing in Renren precisely and predict future spreading tendency successfully.
We have detected emission from both the 4_{-1}-3_{0} E (36.2~GHz) class I and 7_{-2}-8_{-1} E (37.7~GHz) class II methanol transitions towards the centre of the closest ultra-luminous infrared galaxy Arp 220. The emission in both the methanol transitions show narrow spectral features and have luminosities approximately 8 orders of magnitude stronger than that observed from typical class I methanol masers observed in Galactic star formation regions. The emission is also orders of magnitude stronger than the expected intensity of thermal emission from these transitions and based on these findings we suggest that the emission from the two transitions are masers. These observations provides the first detection of a methanol megamaser in the 36.2 and 37.7 GHz transitions and represents only the second detection of a methanol megamaser, following the recent report of an 84 GHz methanol megamaser in NGC1068. We find the methanol megamasers are significantly offset from the nuclear region and arise towards regions where there is Ha emission, suggesting that it is associated with starburst activity. The high degree of correlation between the spatial distribution of the 36.2 GHz methanol and X-ray plume emission suggests that the production of strong extragalactic class I methanol masers is related to galactic outflow driven shocks and perhaps cosmic rays. In contrast to OH and H2O megamasers which originate close to the nucleus, methanol megamasers provide a new probe of feedback (e.g. outflows) processes on larger-scales and of star formation beyond the circumnuclear starburst regions of active galaxies.
It is crucial for the studies of the transport properties and quantum effects related to Dirac surface states of three-dimensional topological insulators (3D TIs) to be able to simultaneously tune the chemical potentials of both top and bottom surfaces of a 3D TI thin film. We have realized this in molecular beam epitaxy-grown thin films of 3D TIs, as well as magnetic 3D TIs, by fabricating dual-gate structures on them. The films could be tuned between n-type and p-type by each gate alone. Combined application of two gates can reduce the carrier density of a TI film to a much lower level than with only one of them and enhance the film resistance by 10000 %, implying that Fermi level is tuned very close to the Dirac points of both top and bottom surface states without crossing any bulk band. The result promises applications of 3D TIs in field effect devices.