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Xu Zhang

Publications and source records attributed to Xu Zhang.

At least 505 records · Page 28Linked to original sources
arXiv2015

Hyperbolic Metamaterial Feasible for Fabrication with Direct Laser Writing Processes

Stimulated emission depletion microscopy inspired direct laser writing (STED-DLW) processes can offer diffraction-unlimited fabrication of 3D-structures, not possible with traditional electron-beam or optical lithography. We propose a hyperbolic metamaterial for fabrication with STED-DLW. First, we design meandering wire structures with three different magnetic dipoles which can be excited under different incidences of light. Then, based on effective parameters corresponding to normal incidence and lateral incidence, we find that the hyperbolic dispersion relation for five-layer structure appears between 15THz to 20THz. Finally, we investigate the influence of imaginary parts of the effective parameters on the metamaterial dispersion. The proposed metamaterial structure has also potential for three-dimensionally isotropic permeability despite geometric anisotropy.

physics.optics↗
arXiv2015

Deep Transfer Network: Unsupervised Domain Adaptation

Domain adaptation aims at training a classifier in one dataset and applying it to a related but not identical dataset. One successfully used framework of domain adaptation is to learn a transformation to match both the distribution of the features (marginal distribution), and the distribution of the labels given features (conditional distribution). In this paper, we propose a new domain adaptation framework named Deep Transfer Network (DTN), where the highly flexible deep neural networks are used to implement such a distribution matching process. This is achieved by two types of layers in DTN: the shared feature extraction layers which learn a shared feature subspace in which the marginal distributions of the source and the target samples are drawn close, and the discrimination layers which match conditional distributions by classifier transduction. We also show that DTN has a computation complexity linear to the number of training samples, making it suitable to large-scale problems. By combining the best paradigms in both worlds (deep neural networks in recognition, and matching marginal and conditional distributions in domain adaptation), we demonstrate by extensive experiments that DTN improves significantly over former methods in both execution time and classification accuracy.

cs.CV↗
arXiv2015

Chaotic polynomial maps

This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange attractors, and shows that some maps are chaotic in the sense of Li-Yorke or Devaney. This type of maps includes both the Logistic map and the Hénon map. For some maps in three-dimensional spaces under certain conditions, if the expansion dimension is equal to one or two, it is shown that there exist a Smale horseshoe and a uniformly hyperbolic invariant set on which the system is topologically conjugate to the two-sided fullshift on finite alphabet; if the system is expanding, then it is verified that there is an forward invariant set on which the system is topologically semi-conjugate to the one-sided fullshift on eight symbols. For three types of high-dimensional polynomial maps with degree two, the existence of Smale horseshoe and the uniformly hyperbolic invariant sets are studied, and it is proved that the map is topologically conjugate to the two-sided fullshift on finite alphabet on the invariant set under certain conditions. Some interesting maps with chaotic attractors and positive Lyapunov exponents in three-dimensional spaces are found by using computer simulations. In the end, two examples are provided to illustrate the theoretical results.

nlin.CD↗
arXiv2015

A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods

In this paper, we derive a priori error estimates for a class of interior penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE) functions for a classic second-order elliptic interface problem. The error estimation shows that these methods can converge optimally in a mesh-dependent energy norm. The combination of IFEs and DG formulation in these methods allows local mesh refinement in the Cartesian mesh structure for interface problems. Numerical results are provided to demonstrate the convergence and local mesh refinement features of these DG-IFE methods.

math.NA↗
arXiv2015

Partially Penalized Immersed Finite Element Methods for Elliptic Interface Problems

This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods contain extra stabilization terms introduced only at interface edges for penalizing the discontinuity in IFE functions. With the enhanced stability due to the added penalty, not only these IFE methods can be proven to have the optimal convergence rate in the H1-norm provided that the exact solution has sufficient regularity, but also numerical results indicate that their convergence rates in both the H1-norm and the L2-norm do not deteriorate when the mesh becomes finer which is a shortcoming of the classic IFE methods in some situations. Trace inequalities are established for both linear and bilinear IFE functions that are not only critical for the error analysis of these new IFE methods, but also are of a great potential to be useful in error analysis for other IFE methods.

math.NA↗
arXiv2014

Birefringence of Muscovite Mica Plate Temperature Effect in the Ultraviolet and Visible Spectrum

We developed a method to measure the phase retardation and birefringence of muscovite mica plate in the temperature range of 223K to 358K within the spectrum of 300 to 700 nm. The phase retardation data is gained through the standard transmission ellipsometry using spectroscopic ellipsometer. With the phase retardation and thickness of the mica plate we can calculate its birefringence dispersion. Our results give abundant phase retardation and birefringence data of muscovite mica in the ultraviolet and visible spectrum from 223K to 358K. From the experimental data, the phase retardation and birefringence will drop down at the fixed wavelength when the temperature rises. The accuracy of the birefringence of mica plate is better than 3.5e-5.

physics.optics↗
arXiv2014

Isospectral operators

For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known knowledge on the spectrum (or the estimation of the principal eigenvalue) from a smaller class of operators to a much larger one. In particular, an open problem about the positivity of the principal eigenvalue for birth--death processes is solved in the paper.

math.AP↗
arXiv2014

Phase Retardation and Birefringence of the Crystalline Quartz Plate in the Ultraviolet and Visible Spectrum

A method for measuring the phase retardation and birefringence of crystalline quartz wave plate in the ultraviolet and visible spectrum is demonstrated using spectroscopic ellipsometer. After the calibration of the crystalline quartz plate, the experimental data are collected by the photodetector and sent to the computer. According to the outputted data, the retardation can be obtained in the range of 190 to 770 nm. With the retardation data, the birefringence for the quartz can be calculated in the same spectrum with an accuracy of better than . The birefringence results enrich the crystalline quartz birefringence data especially in the ultraviolet spectrum.

physics.optics↗
arXiv2014

Planar Hall effect in Y3Fe5O12(YIG)/IrMn films

The planar Hall effect of IrMn on an yttrium iron garnet (YIG = Y3Fe5O12) was measured in the magnetic field rotating in the film plane. The magnetic field angle dependence of planar Hall resistance (PHR) has been observed in YIG/IrMn bilayer at different temperatures, while the GGG/IrMn (GGG= Gd3Ga5O12) shows constant PHR for different magnetic field angles at both 10 K and 300 K. This provides evidence that IrMn has interfacial spins which can be led by FM in YIG/IrMn structure. A hysteresis can be observed in PHR-magnetic field angle loop of YIG/IrMn films at 10 K, indicating the irreversible switching of IrMn interfacial spins at low temperature.

cond-mat.mtrl-sci↗
arXiv2014

Pointwise second-order necessary conditions for stochastic optimal controls, Part I: The case of convex control constraint

This paper is the first part of our series work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, both drift and diffusion terms may contain the control variable but the control region is assumed to be convex. Under some assumptions in terms of Malliavin calculus, we establish the desired necessary condition for stochastic singular optimal controls in the classical sense.

math.OC↗
arXiv2014

Some results on pointwise second-order necessary conditions for stochastic optimal controls

The purpose of this paper is to derive some pointwise second-order necessary conditions for stochastic optimal controls in the general case that the control variable enters into both the drift and the diffusion terms. When the control region is convex, a pointwise second-order necessary condition for stochastic singular optimal controls in the classical sense is established; while when the control region is allowed to be nonconvex, we obtain a pointwise second-order necessary condition for stochastic singular optimal controls in the sense of Pontryagin-type maximum principle. It is found that, quite different from the first-order necessary conditions, the correction part of the solution to the second-order adjoint equation appears in the pointwise second-order necessary conditions whenever the diffusion term depends on the control variable, even if the control region is convex.

math.OC↗
arXiv2014

Prometheus: LT Codes Meet Cooperative Transmission in Cellular Networks

Following fast growth of cellular networks, more users have drawn attention to the contradiction between dynamic user data traffic and static data plans. To address this important but largely unexplored issue, in this paper, we design a new data plan sharing system named Prometheus, which is based on the scenario that some smartphone users have surplus data traffic and are willing to help others download data. To realize this system, we first propose a mechanism that incorporates LT codes into UDP. It is robust to transmission errors and encourages more concurrent transmissions and forwardings. It also can be implemented easily with low implementation complexity. Then we design an incentive mechanism using a Stackelberg game to choose assistant users ($AUs$), all participants will gain credits in return, which can be used to ask for future help when they need to download something. Finally real environment experiments are conducted and the results show that users in our Prometheus not only can manage their surplus data plan more efficiently, but also achieve a higher speed download rate.

cs.NI↗
arXiv2014

Transposition Method for Backward Stochastic Evolution Equations Revisited, and Its Application

The main purpose of this paper is to improve our transposition method to solve both vector-valued and operator-valued backward stochastic evolution equations with a general filtration. As its application, we obtain a general Pontryagin-type maximum principle for optimal controls of stochastic evolution equations in infinite dimensions. In 1articular, we drop the technical assumption appeared in [Q. Lü and X. Zhang, Springer Briefs in Mathematics,Springer, New York, 2014, Theorem 9.1].

math.OC↗
arXiv2014

Efficient classification using parallel and scalable compressed model and Its application on intrusion detection

In order to achieve high efficiency of classification in intrusion detection, a compressed model is proposed in this paper which combines horizontal compression with vertical compression. OneR is utilized as horizontal com-pression for attribute reduction, and affinity propagation is employed as vertical compression to select small representative exemplars from large training data. As to be able to computationally compress the larger volume of training data with scalability, MapReduce based parallelization approach is then implemented and evaluated for each step of the model compression process abovementioned, on which common but efficient classification methods can be directly used. Experimental application study on two publicly available datasets of intrusion detection, KDD99 and CMDC2012, demonstrates that the classification using the compressed model proposed can effectively speed up the detection procedure at up to 184 times, most importantly at the cost of a minimal accuracy difference with less than 1% on average.

cs.LG↗
arXiv2013

Multibump solutions of a class of second-order discrete Hamiltonian systems

For a class of second-order discrete Hamiltonian systems $Δ^2x(t-1)-L(t)x(t)+V'_x(t,x(t))=0$, we investigate the existence of homoclinic orbits by applying variational method, where $L$ and $V(\cdot,x)$ are periodic functions. Further, we show that there exist either uncountable many homoclinic orbits or multibump solutions under certain conditions.

math.DS↗