Construction of modulated amplitude waves via averaging in collisionally inhomogeneous Bose-Einstein condensates

We apply the averaging method to analyze spatio-temportal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with the scattering length varying periodically in spatial and crossing zero. Infinitely many (positive measure set) modulated amplitude waves (periodic and quasi-periodic), which are instable, can be proved to exist by adjusting the intergration constant c on some open interval. Finally, some numerical simulations support our results.Comment: 13 pages, 2 figure

Multitask Deep Learning with Spectral Knowledge for Hyperspectral Image Classification

In this letter, we propose a multitask deep learning method for classification of multiple hyperspectral data in a single training. Deep learning models have achieved promising results on hyperspectral image classification, but their performance highly rely on sufficient labeled samples, which are scarce on hyperspectral images. However, samples from multiple data sets might be sufficient to train one deep learning model, thereby improving its performance. To do so, we trained an identical feature extractor for all data, and the extracted features were fed into corresponding Softmax classifiers. Spectral knowledge was introduced to ensure that the shared features were similar across domains. Four hyperspectral data sets were used in the experiments. We achieved higher classification accuracies on three data sets (Pavia University, Pavia Center, and Indian Pines) and competitive results on the Salinas Valley data compared with the baseline. Spectral knowledge was useful to prevent the deep network from overfitting when the data shared similar spectral response. The proposed method tested on two deep CNNs successfully shows its ability to utilize samples from multiple data sets and enhance networks' performance.Comment: Accepted by IEEE GRS

Sobolev inequalities on product Sierpinski spaces

On fractals, different measures (mutually singular in general) are involved to measure volumes of sets and energies of functions. Singularity of measures brings difficulties in (especially non-linear) analysis on fractals. In this paper, we prove a type of Sobolev inequalities, which involve different and possibly mutually singular measures, on product Sierpinski spaces. Sufficient and necessary conditions for the validity of these Sobolev inequalities are given. Furthermore, we compute the sharp exponents which appears in the sufficient and necessary conditions for the product Kusuoka measure, i.e. the reference energy measure on Sierpinski spaces.Comment: 23 page

Nonequilibrium Effects and Self Heating in Single Electron Coulomb Blockade Devices

We present a comprehensive investigation of nonequilibrium effects and self heating in single electron transfer devices based primarily on the Coulomb blockade effect. During an electron trapping process, a hot electron may be deposited in a quantum dot or metal island, with an extra energy usually on the order of the Coulomb charging energy, which is much higher than the temperature in typical experiments. The hot electron may relax through three channels: tunneling back and forth to the feeding lead (or island), emitting phonons, and exciting background electrons. Depending on the magnitudes of the rates in the latter two channels relative to the device operation frequency and to each other, the system may be in one of three different regimes: equilibrium, non-equilibrium, and self heating (partial equilibrium). In the quilibrium regime, a hot electron fully gives up its energy to phonons within a pump cycle. In the nonequilibrium regime, the relaxation is via tunneling with a distribution of characteristic rates; the approach to equilibrium goes like a power law of time (frequency) instead of an exponential. This channel is plagued completely in the continuum limit of the single electron levels. In the self heating regime, the hot electron thermalizes quickly with background electrons, whose temperature $T_e$ is elevated above the lattice temperature $T_l$. We have calculated the coefficient in the well known $T^5$ law of energy dissipation rate, and compared the results to experimental values for aluminum and copper islands and for a two dimensional semiconductor quantum dot. Moreover, we have obtained different scaling relations between the electron temperature and operation frequency and device size for various types of devices.Comment: The abstract for an earlier post is incomplete. The correct one is given here. No revision for the content of the paper. 39 pages, latex, 6 figures available upon request. To appear in "Physics Report

Generation and complete nondestructive analysis of hyperentanglement assisted by nitrogen-vacancy centers in resonators

We present two efficient schemes for the deterministic generation and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom (DOFs) of two-photon systems, assisted by the nitrogen-vacancy (NV) centers in diamonds coupled to microtoroidal resonators as a result of cavity quantum electrodynamics (QED). With the input-output process of photons, two-photon polarization-spatial hyperentangled Bell states can be generated in a deterministic way and their complete nondestructive analysis can be achieved. These schemes can be generalized to generate and analyze hyperentangled Greenberger-Horne-Zeilinger states of multi-photon systems as well. Compared with previous works, these two schemes relax the difficulty of their implementation in experiment as it is not difficult to obtain the $\pi$ phase shift in single-sided NV-cavity systems. Moreover, our schemes do not require that the transmission for the uncoupled cavity is balanceable with the reflectance for the coupled cavity. Our calculations show that these schemes can reach a high fidelity and efficiency with current technology, which may be a benefit to long-distance high-capacity quantum communication with two DOFs of photon systems

On the construction of nested space-filling designs

Nested space-filling designs are nested designs with attractive low-dimensional stratification. Such designs are gaining popularity in statistics, applied mathematics and engineering. Their applications include multi-fidelity computer models, stochastic optimization problems, multi-level fitting of nonparametric functions, and linking parameters. We propose methods for constructing several new classes of nested space-filling designs. These methods are based on a new group projection and other algebraic techniques. The constructed designs can accommodate a nested structure with an arbitrary number of layers and are more flexible in run size than the existing families of nested space-filling designs. As a byproduct, the proposed methods can also be used to obtain sliced space-filling designs that are appealing for conducting computer experiments with both qualitative and quantitative factors.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1229 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic spreading of interacting species with multiple fronts II: Exponentially decaying initial data

This is part two of our study on the spreading properties of the Lotka-Volterra competition-diffusion systems with a stable coexistence state. We focus on the case when the initial data are exponential decaying. By establishing a comparison principle for Hamilton-Jacobi equations, we are able to apply the Hamilton-Jacobi approach for Fisher-KPP equation due to Freidlin, Evans and Souganidis. As a result, the exact formulas of spreading speeds and their dependence on initial data are derived. Our results indicate that sometimes the spreading speed of the slower species is nonlocally determined. Connections of our results with the traveling profile due to Tang and Fife, as well as the more recent spreading result of Girardin and Lam, will be discussed

Estimate of the charmed 0-- hybrid meson spectrum from quenched lattice QCD

We compute from quenched lattice QCD the ground state masses of the charmed hybrid mesons cbar c g, with exotic quantum numbers JPC=1-+, 0+- and 0--. The 0-- hybrid meson spectrum has never been provided by lattice simulations due to the difficulties to extract high gluonic excitations from noise. We employ improved gauge and fermion actions on the anisotropic lattice, which reduce greatly the lattice artifacts, and lead to very good signals. The data are extrapolated to the continuum limit, with finite size effects under well control. For 1-+ and 0+- hybrid mesons, the ground state masses are 4.405(38) GeV and 4.714(52) GeV. We predict for the first time from lattice QCD, the ground state mass of 0-- to be 5.883(146) GeV.Comment: Version accepted for publication in Physical Review

Gluonic excitation of non-exotic hybrid charmonium from lattice QCD

The ground and first excited states of the hybrid charmonium ${\bar c} c g$, with non-exotic quantum numbers $J^{PC}=0^{-+}$, $1^{--}$ and $1^{++}$ are investigated using quenched lattice QCD. They are completely ignored in the literature, only because their ground states are degenerate with $\eta_c$, $J/\psi$, and $\chi_{c1}$, and are difficult to be distinguished from these conventional charmonium mesons in experiment. However, we observe strong gluonic radial excitations in the first excited states; We predict that their masses are 4.352(225)GeV, 4.379(149)GeV and 7.315(257)GeV, completely different from the first excited states of the corresponding conventional charmonium. Their relevance to the recent discovery of the Y(4260) state and future experimental search for other states are also discussed.Comment: Different analysis methods were used for a cross check, leading to consistent result

Inertial Migration of Aerosol Particles in Confined Microfluidic Channels

In recent years, manipulation of particles by inertial microfluidics has attracted significant attention. Most studies focused on inertial focusing of particles suspended within liquid phase, in which the ratio of the density of the particle to that of the medium is O(1). the investigation on manipulation of aerosol particles in an inertial microfluidics is very limited. In this study, we numerically investigate the aerosol particle motion in a 3D straight microchannel with rectangular cross section by fully resolved simulation of the particle-air flow based on the contiuum model. The air flow is modeled by the Navier-Stokes equations, and particle's motions, including transition and rotation, are governed, respectively, by the Newton's second law and the Euler equations without using any approximation models for the lift and drag forces. The coupled mathematical model is numerically solved by combining immersed boundary with lattice Boltzmann method (IB-LBM). We find that the Reynolds numer, the particle's initial position, particle's density, and particle's diameter are the influential parameters in this process. the equilibrium positions and their stabilities of aerosols are different form those suspended in liquid.Comment: 21pages, 13figure