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Fei Xu

Publications and source records attributed to Fei Xu.

At least 127 records · Page 7Linked to original sources
arXiv2017

An Efficient Multigrid Method for Ground State Solution of Bose-Einstein Condensates

An efficient multigrid method is proposed to compute the ground state solution of Bose-Einstein condensations by the finite element method based on the combination of the multigrid method for nonlinear eigenvalue problem and an efficient implementation for the nonlinear iteration. The proposed numerical method not only has the optimal convergence rate, but also has the asymptotically optimal computational work which is independent from the nonlinearity of the problem. The independence from the nonlinearity means that the asymptotic estimate of the computational work can reach almost the same as that of solving the corresponding linear boundary value problem by the multigrid method. Some numerical experiments are provided to validate the efficiency of the proposed method.

math.NA↗
arXiv2017

Finite Element Methods For Wave Propagation With Debye Polarization In Nonlinear Dielectric Materials

In this paper, we consider the wave propagation with Debye polarization in nonlinear dielectric materials. For this model, the Rother's method is employed to derive the well-posedness of the electric fields and the existence of the polarized fields by monotonicity theorem as well as the boundedness of the two fields are established. Then, the time errors are derived for the semi-discrete solutions by the order $O(Δt)$. Subsequently, decoupled the full-discrete scheme of the Euler in time and Raviart-Thomas-N$\acute{e}$d$\acute{e}$lec element $k\geq 2$ in spatial is established. Based on the truncated error, we present the convergent analysis with the order $O(Δt+h^s) $ under the technique of a-prior $L^\infty$ assumption. For the $k=1$, we employ the superconvergence technique to ensure the a-prior $L^\infty$ assumption. In the end, we give some numerical examples to demonstrate our theories.

math.NA↗
arXiv2017

Complete orbital angular momentum Bell-state measurement and superdense coding

Quantum protocols require access to large-scale entangled quantum states, due to the requirement of channel capacity. As a promising candidate, the high-dimensional orbital angular momentum (OAM) entangled states have been implemented, but only one of four OAM Bell states in each individual subspace can be distinguished. Here we demonstrate the first realization of complete OAM Bell-state measurement (OAM-BSM) in an individual subspace, by seeking the suitable unitary matrix performable using only linear optics and breaking the degeneracy of four OAM Bell states in ancillary polarization dimension. We further realize the superdense coding via our complete OAMBSM with the average success probability of ~82% and the channel capacity of ~1.1(4) bits. This work opens the window for increasing the channel capacity and extending the applications of OAM quantum states in quantum information in future.

quant-ph↗
arXiv2017

A Full Multigrid Method For Semilinear Elliptic Equation

A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as the linear solver for solving boundary value problems. The optimality of the computational work is also proved. Compared with the existing multigrid methods which need the bounded second order derivatives of the nonlinear term, the proposed method only needs the Lipschitz continuation in some sense of the nonlinear term.

math.NA↗
arXiv2017

Local Representation Theory of Transporter Categories

We attempt to generalize the $p$-modular representation theory of finite groups to finite transporter categories, which are regarded as generalized groups. We shall carry on our tasks through modules of transporter category algebras, a type of Gorenstein skew group algebras. The Kan extensions, upgrading the induction and co-induction, are our main tools to establish connections between representations of a transporter category and of its transporter subcategories. Some important constructions and theorems in local representation theory of finite groups are generalized.

math.RT↗
arXiv2016

Dynamical Coulomb blockade theory of plasmon-mediated light emission from a tunnel junction

Inelastic tunneling of electrons can generate the emission of photons with energies intuitively limited by the applied bias voltage. However, experiments indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission with overbias energies. We recently proposed a model of this observation in Phys. Rev. Lett. \textbf{113}, 066801 (2014), in analogy to the dynamical Coulomb blockade, originally developed for treating the electromagnetic environment in mesoscopic circuits. This model describes the correlated tunneling of two electrons interacting with a local plasmon-polariton mode, represented by a resonant circuit, and shows that the overbias emission is due to the non-Gaussian fluctuations. Here we extend our model to study the overbias emission at finite temperature. We find that the thermal smearing strongly masks the overbias emission. Hence, the detection of the correlated tunneling processes requires temperatures $k_BT$ much lower than the bias energy $eV$ and the plasmon energy $\hbarω_0$, a condition which is fortunately realized experimentally.

cond-mat.mes-hall↗
arXiv2016

Neutro-Connectedness Cut

Interactive image segmentation is a challenging task and receives increasing attention recently; however, two major drawbacks exist in interactive segmentation approaches. First, the segmentation performance of ROI-based methods is sensitive to the initial ROI: different ROIs may produce results with great difference. Second, most seed-based methods need intense interactions, and are not applicable in many cases. In this work, we generalize the Neutro-Connectedness (NC) to be independent of top-down priors of objects and to model image topology with indeterminacy measurement on image regions, propose a novel method for determining object and background regions, which is applied to exclude isolated background regions and enforce label consistency, and put forward a hybrid interactive segmentation method, Neutro-Connectedness Cut (NC-Cut), which can overcome the above two problems by utilizing both pixel-wise appearance information and region-based NC properties. We evaluate the proposed NC-Cut by employing two image datasets (265 images), and demonstrate that the proposed approach outperforms state-of-the-art interactive image segmentation methods (Grabcut, MILCut, One-Cut, MGC_max^sum and pPBC).

cs.CV↗
arXiv2016

A Multigrid Method for the Ground State Solution of Bose-Einstein Condensates Based on Newton Iteration

In this paper, a new kind of multigrid method is proposed for the ground state solution of Bose-Einstein condensates based on Newton iteration method. Instead of treating eigenvalue $λ$ and eigenvector $u$ respectively, we regard the eigenpair $(λ, u)$ as one element in the composite space $\R \times H_0^1(Ω)$ and then Newton iteration method is adopted for the nonlinear problem. Thus in this multigrid scheme, we only need to solve a linear discrete boundary value problem in every refined space, which can improve the overall efficiency for the simulation of Bose-Einstein condensations.

math.NA↗
arXiv2015

Mechanical Modulation of Hybrid Graphene Microfiber Structure

Recently, the strain engineering of two-dimensional materials such as graphene has attracted considerable attention for its great potential in functional nanodevices. Here, we theoretically and experimentally investigate the strain manipulation of a graphene-integrated microfiber system for the first time. We analyze the influential factors of strain tuning, i.e., the geometrical parameters of the microfiber, the strain magnitude, and the probe-light wavelength. Moreover, we experimentally achieve in-line modulation as high as 30% with a moderate strain of ~5%, which is two orders of magnitude larger than previous results. The dynamic vibration response is also researched. The broadband, polarization-independent, cost-effective, strain-based modulator may find applications in low-speed modulation and strain sensing. Further, we believe that our platform may allow for all-in fiber engineering of graphene-analogue materials and provide new ideas for graphene-integrated flexible device design.

physics.optics↗
arXiv2015

An algorithm for Left Atrial Thrombi detection using Transesophageal Echocardiography

Transesophageal echocardiography (TEE) is widely used to detect left atrium (LA)/left atrial appendage (LAA) thrombi. In this paper, the local binary pattern variance (LBPV) features are extracted from region of interest (ROI). And the dynamic features are formed by using the information of its neighbor frames in the sequence. The sequence is viewed as a bag, and the images in the sequence are considered as the instances. Multiple-instance learning (MIL) method is employed to solve the LAA thrombi detection. The experimental results show that the proposed method can achieve better performance than that by using other methods.

cs.CV↗
arXiv2015

Polarization-dependent all-optical modulator with ultra-high modulation depth based on a stereo graphene-microfiber structure

We report an in-line polarization-dependent all-optical fiber modulator based on a stereo graphene-microfiber structure (GMF) by utilizing the lab-on-rod technique. Owing to the unique spring-like geometry, an ultra-long GMF interaction length can be achieved, and an ultra-high modulation depth (MD) of ~7.5 dB and a high modulation efficiency (ME) of ~0.2 dB/mW were demonstrated for one polarization state. The MD and ME are more than one order larger than those of other graphene-waveguide hybrid all-optical modulators. By further optimizing the transferring and cleaning process, the modulator can quickly switch between transparent and opaque states for both the two polarization states with a maximized MD of tens of decibels. This modulator is compatible with current fiber-optic communication systems and may be applied in the near future to meet the impending need for ultrafast optical signal processing.

physics.optics↗
arXiv2015

A Full Multigrid Method for Nonlinear Eigenvalue Problems

This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient iteration methods for solving boundary value problems can serve as the linear problem solver. We will prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. In this case, this type of iteration scheme certainly improves the overfull efficiency of solving nonlinear eigenvalue problems. Some numerical experiments are presented to validate the efficiency of the new method.

math.NA↗
arXiv2014

Very strong approximation for certain algebraic varieties

Let F be a global field. In this work, we show that the Brauer-Manin condition on adelic points for subvarieties of a torus T over F cuts out exactly the rational points, if either F is a function field or, if F is the field of rational numbers and T is split. As an application, we prove a conjecture of Harari-Voloch over global function fields which states, roughly speaking, that on any rational hyperbolic curve, the local integral points with the Brauer-Manin condition are the global integral points. Finally we prove for tori over number fields a theorem of Stoll on adelic points of zero-dimensional subvarieties in abelian varieties.

math.AG↗
arXiv2014

Reconfigurable optical-force-drive chirp and delay-line in micro/nano-fiber Bragg grating

The emergence of optical micro/nano-fiber (MNF) with a subwavelength diameter, which has ultra-light mass and an intense light field, brings an opportunity for develop fiber based optomechanical systems. In this study, we theoretically show an optomechanical effect in silica MNF Bragg gratings (MNFBGs). The light-induced mechanical effect results in continuously distributed strain along the grating. It is shown that the power-related strain introduces an optically reconfigurable chirp in the grating period. We develop new optomechanical coupled-mode equations and theoretically analyze the influence of the optical-force-induced nonlinearity and chirp on the grating performance. Compared with weak Kerr effect, the optomechanics effect dominated in the properties evolution of MNFBGs and significant group velocity reduction and switching effect have been theoretically demonstrated at medium power level. This kind of optomechanical MNFBG with optically reconfigurable chirp may offer a path toward all-optical tunable bandwidth of Bragg resonance and may lead to useful applications such as all-optical switching and optically controlled dispersion and slow/fast light.

physics.optics↗
arXiv2014

Strong approximation for certain quadric fibrations with compact fibers

In this paper, we will show that strong approximation with Brauer-Manin obstruction holds for certain quadratic fibration such that none of fibers satisfies strong approximation with Brauer-Manin obstruction. Moreover, we develop the representation theory of quadratic Diophantine equations and explain that the representability of quadratic polynomials is equivalent to the classical result of representability of quadratic forms with congruent conditions and extend the classical result over number fields.

math.NT↗
arXiv2014

Platform for enhanced light-graphene interaction length and miniaturizing fiber stereo-devices

Sufficient light-matter interactions are important for waveguide-coupled graphene optoelectronic devices. Using a microfiber-based lab-on-a-rod technique, we present a platform for ultra-long light-graphene interaction and design graphene-integrated helical microfiber (MF) devices. Using this approach, we experimentally demonstrate an in-line stereo polarizer by wrapping an MF on a rod pretreated with a graphene sheet. The device operates as a broadband (450 nm wavelength) polarizer capable of achieving an extinction ratio (ER) as high as ~8 dB/coil in the telecommunication band. Furthermore, we extend this approach to successfully demonstrate a high-Q graphene-based single-polarization resonator, which operates with an ER of ~11 dB with excellent suppression of polarization noise. The fiber-coil resonator shows great potential for sensing applications and gyro-integration. By specializing the rod surface and coil geometry, we believe the preliminary results reported herein could contribute to advancing the research for lab-on-a-rod graphene-MF-integrated devices.

physics.optics↗