arXiv subjects

Xuefeng Liu

Publications and source records attributed to Xuefeng Liu.

85 records · Page 5Linked to original sources

arXiv2019

Optimal estimation for the Fujino-Morley interpolation error constants

The quantitative estimation for the interpolation error constants of the Fujino-Morley interpolation operator is considered. To give concrete upper bounds for the constants, which is reduced to the problem of providing lower bounds for eigenvalues of bi-harmonic operators, a new algorithm based on the finite element method along with verified computation is proposed. In addition, the quantitative analysis for the variation of eigenvalues upon the perturbation of the shape of triangles is provided. Particularly, for triangles with longest edge length less than one, the optimal estimation for the constants is provided. An online demo with source codes of the constants calculation is available at http://www.xfliu.org/onlinelab/.

math.NA↗

arXiv2018

Test of Covariance and Correlation Matrices

Based on a generalized cosine measure between two symmetric matrices, we propose a general framework for one-sample and two-sample tests of covariance and correlation matrices. We also develop a set of associated permutation algorithms for some common one-sample tests, such as the tests of sphericity, identity and compound symmetry, and the $K$-sample tests of multivariate equality of covariance or correlation matrices. The proposed method is very flexible in the sense that it does not assume any underlying distributions and data generation models. Moreover, it allows data to have different marginal distributions in both the one-sample identity and $K$-sample tests. Through real datasets and extensive simulations, we demonstrate that the proposed method performs well in terms of empirical type I error and power in a variety of hypothesis testing situations in which data of different sizes and dimensions are generated using different distributions and generation models.

stat.ME↗

arXiv2018

Guaranteed eigenvalue bounds for the Steklov eigenvalue problem

To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive definiteness of bilinear forms in the formulation of eigenvalue problems. In practical eigenvalue estimation, the Crouzeix--Raviart finite element method (FEM) along with quantitative error estimation is adopted. Numerical experiments for eigenvalue problems defined on a square domain and an L-shaped domain are provided to validate the precision of computed eigenvalue bounds.

math.NA↗

arXiv2018

Explicit Estimation of Error Constants Appearing in Non-conforming Linear Triangular Finite Element

The non-conforming linear ($P_1$) triangular FEM can be viewed as a kind of the discontinuous Galerkin method, and is attractive in both theoretical and practical senses. Since various error constants must be quantitatively evaluated for its accurate a priori and a posteriori error estimates, we derive their theoretical upper bounds and some computational results. In particular, the Babu$\check{s}$ka-Aziz maximum angle condition is required just as in the case of the conforming $P_1$ triangle. Some applications and numerical results are also illustrated to see the validity and effectiveness of our analysis.

math.NA↗

arXiv2018

Explicit Finite Element Error Estimates for Nonhomogeneous Neumann problems

The paper develops an explicit a priori error estimate for finite element solution to nonhomogeneous Neumann problems. For this purpose, the hypercircle equation over finite element spaces is constructed and the explicit upper bound of the constant in the trace theorem is given. Numerical examples are shown in the final section, which implies the proposed error {estimate} has the convergence rate as $0.5$.

math.NA↗

arXiv2017

Dynamical Anisotropic Response of Black Phosphorus under Magnetic Field

Black phosphorus (BP) has emerged as a promising material candidate for next generation electronic and optoelectronic devices due to its high mobility, tunable band gap and highly anisotropic properties. In this work, polarization resolved ultrafast mid-infrared transient reflection spectroscopy measurements are performed to study the dynamical anisotropic optical properties of BP under magnetic fields up to 9 T. The relaxation dynamics of photoexcited carrier is found to be insensitive to the applied magnetic field due to the broadening of the Landau levels and large effective mass of carriers. While the anisotropic optical response of BP decreases with increasing magnetic field, its enhancement due to the excitation of hot carriers is similar to that without magnetic field. These experimental results can be well interpreted by the magneto-optical conductivity of the Landau levels of BP thin film, based on an effective k*p Hamiltonian and linear response theory. These findings suggest attractive possibilities of multi-dimensional controls of anisotropic response (AR) of BP with light, electric and magnetic field, which further introduces BP to the fantastic magnetic field sensitive applications.

cond-mat.mtrl-sci↗

arXiv2017

Distributed Least-Squares Iterative Methods in Networks: A Survey

Many science and engineering applications involve solving a linear least-squares system formed from some field measurements. In the distributed cyber-physical systems (CPS), often each sensor node used for measurement only knows partial independent rows of the least-squares system. To compute the least-squares solution they need to gather all these measurement at a centralized location and then compute the solution. These data collection and computation are inefficient because of bandwidth and time constraints and sometimes are infeasible because of data privacy concerns. Thus distributed computations are strongly preferred or demanded in many of the real world applications e.g.: smart-grid, target tracking etc. To compute least squares for the large sparse system of linear equation iterative methods are natural candidates and there are a lot of studies regarding this, however, most of them are related to the efficiency of centralized/parallel computations while and only a few are explicitly about distributed computation or have the potential to apply in distributed networks. This paper surveys the representative iterative methods from several research communities. Some of them were not originally designed for this need, so we slightly modified them to suit our requirement and maintain the consistency. In this survey, we sketch the skeleton of the algorithm first and then analyze its time-to-completion and communication cost. To our best knowledge, this is the first survey of distributed least-squares in distributed networks.

cs.DC↗

arXiv2017

Explicit Bound for Quadratic Lagrange Interpolation Constant on Triangular Finite Elements

For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the interpolation constant is obtained by solving an eigenvalue problem along with explicit lower bound for its eigenvalues. The lower bound for interpolation constant can be easily obtained by applying the Rayleigh-Ritz method. Numerical computation is performed to demonstrate the sharpness of lower and upper bounds of the interpolation constants over triangles of different shapes. An online computing demo is available at http://www.xfliu.org/onlinelab/.

math.NA↗

arXiv2017

Ultrafast Relaxation Dynamics of Photoexcited Dirac Fermion in The Three Dimensional Dirac Semimetal Cadmium Arsenide

Three dimensional (3D) Dirac semimetals which can be seen as 3D analogues of graphene have attracted enormous interests in research recently. In order to apply these ultrahigh-mobility materials in future electronic/optoelectronic devices, it is crucial to understand the relaxation dynamics of photoexcited carriers and their coupling with lattice. In this work, we report ultrafast transient reflection measurements of the photoexcited carrier dynamics in cadmium arsenide (Cd3As2), which is one of the most stable Dirac semimetals that have been confirmed experimentally. By using low energy probe photon of 0.3 eV, we probed the dynamics of the photoexcited carriers that are Dirac-Fermi-like approaching the Dirac point. We systematically studied the transient reflection on bulk and nanoplate samples that have different doping intensities by tuning the probe wavelength, pump power and lattice temperature, and find that the dynamical evolution of carrier distributions can be retrieved qualitatively by using a two-temperature model. This result is very similar to that of graphene, but the carrier cooling through the optical phonon couplings is slower and lasts over larger electron temperature range because the optical phonon energies in Cd3As2 are much lower than those in graphene.

cond-mat.mes-hall↗

arXiv2016

Ultrafast Broadband Photodetectors based on Three-dimensional Dirac Semimetal Cd3As2

The efforts to pursue photo detection with extreme performance in terms of ultrafast response time, broad detection wavelength range, and high sensitivity have never been exhausted as driven by its wide range of optoelectronic and photonic applications such as optical communications, interconnects, imaging and remote sensing1. 2D Dirac semimetal graphene has shown excellent potential toward high performance photodetector with high operation speed, broadband response and efficient carrier multiplications benefiting from its linear dispersion band structure with high carrier mobility and zero bandgap2-4. As the three dimensional analogues of graphene, Dirac semimetal Cd3As2 processes all advantages of graphene as a photosensitive material but potentially has stronger interaction with light as bulk material and thus enhanced responsivity5,6, which promises great potential in improving the performance of photodetector in various aspects . In this work, we report the realization of an ultrafast broadband photodetector based on Cd3As2. The prototype metal-Cd3As2-metal photodetector exhibits a responsivity of 5.9 mA/W with response time of about 6.9 ps without any special device optimization. Broadband responses from 0.8 eV to 2.34 eV are measured with potential detection range extendable to far infrared and terahertz. Systematical studies indicate that the photo-thermoelectric effect plays important roles in photocurrent generation, similar to that in graphene. Our results suggest this emerging class of exotic quantum materials can be harnessed for photo detection with high sensitivity and high speed (~145 GHz) in challenging middle/far-infrared and THz range.

cond-mat.mes-hall↗

arXiv2016

Several Classes of Negabent Functions over Finite Fields

Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over finite fields. First, by using the compositional inverses of certain binomial and trinomial permutations, we present several classes of negabent functions of the form $f(x)=\Tr_1^n(λx^{2^k+1})+\Tr_1^n(ux)\Tr_1^n(vx)$, where $λ\in \F_{2^n}$, $2\leq k\leq n-1$, $(u,v)\in \F^*_{2^n}\times \F^*_{2^n}$, and $\Tr_1^n(\cdot)$ is the trace function from $\F_{2^n}$ to $\F_{2}$. Second, by using Kloosterman sum, we prove that the condition for the cubic monomials given by Zhou and Qu (Cryptogr. Commun., to appear, DOI 10.1007/s12095-015-0167-0.) to be negabent is also necessary. In addition, a conjecture on negabent monomials whose exponents are of Niho type is given.

cs.IT↗

arXiv2014

Ultrafast Terahertz Probe of Transient Evolution of Charged and Neutral Phase of Photoexcited Electron-hole Gas in Monolayer Semiconductor

We investigate the dynamical formation of excitons from photoexcited electron-hole plasma and its subsequent decay dynamics in monolayer MoS2 grown by chemical vapor deposition using ultrafast pump and terahertz probe spectroscopy. Different photoexcited electron-hole states are resolved based on their distinct responses to THz photon and decay lifetime. The observed transient THz transmission can be fit with two decay components: a fast component with decay lifetime of 20 ps, which is attributed to exciton life time including the exciton formation and subsequent intraexciton relaxation; a slow component with extremely long decay lifetime of several ns due to either localized exciton state or a long live dark exciton state which is uncovered for the first time. The relaxation dynamics is further verified by temperature and pump fluence dependent studies of the decay time constants.

cond-mat.mtrl-sci↗

arXiv2012

Verified eigenvalue evaluation for Laplacian over polygonal domain of arbitrary shape

The finite element method(FEM) is applied to bound leading eigenvalues of Laplace operator over polygonal domain. Compared with classical numerical methods, most of which can only give concrete eigenvalue bounds over special domain of symmetry, our proposed algorithm can provide concrete eigenvalue bounds for domain of arbitrary shape, even in the case that eigenfunction has singularity. The problem of eigenvalue estimation is solved in two steps. First, we construct computable a priori error estimation for FEM solution of Poisson's problem even for non-convex domain with re-entrant corner. Second, a new computable lower and upper bounds is developed for eigenvalues. As the interval arithmetic is implemented in the FEM computation, the desired eigenvalue bounds can be expected to be mathematically correct. The Lehmann's theorem is also adopted to sharpen the eigenvalue bounds with high precision. At the end of this paper, we illustrate several computation examples, such as the case of L-shaped domain and crack domain, to demonstrate the efficiency and flexibility of proposed method.

math.NA↗