arXiv subjects

Cheng Wang

Publications and source records attributed to Cheng Wang.

At least 415 records · Page 23Linked to original sources

arXiv2019

Convergence analysis of a numerical scheme for the porous medium equation by an energetic variational approach

The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et al, J. Comput. Phys., 385 (2019) 13-32], where the trajectory equation can be obtained and two numerical schemes have been developed based on different dissipative energy laws. It is also proved that the nonlinear scheme, based on $f \log f$ as the total energy form of the dissipative law, is uniquely solvable on an admissible convex set and preserves the corresponding discrete dissipation law. Moreover, under certain smoothness assumption, we have also obtained the second order convergence in space and the first order convergence in time for the scheme. In this paper, we provide a rigorous proof of the error estimate by a careful higher order asymptotic expansion and two step error estimates. The latter technique contains a rough estimate to control the highly nonlinear term in a discrete $W^{1,\infty}$ norm, and a refined estimate is applied to derive the optimal error order.

math.NA↗

arXiv2019

PointNLM: Point Nonlocal-Means for vegetation segmentation based on middle echo point clouds

Middle-echo, which covers one or a few corresponding points, is a specific type of 3D point cloud acquired by a multi-echo laser scanner. In this paper, we propose a novel approach for automatic segmentation of trees that leverages middle-echo information from LiDAR point clouds. First, using a convolution classification method, the proposed type of point clouds reflected by the middle echoes are identified from all point clouds. The middle-echo point clouds are distinguished from the first and last echoes. Hence, the crown positions of the trees are quickly detected from the huge number of point clouds. Second, to accurately extract trees from all point clouds, we propose a 3D deep learning network, PointNLM, to semantically segment tree crowns. PointNLM captures the long-range relationship between the point clouds via a non-local branch and extracts high-level features via max-pooling applied to unordered points. The whole framework is evaluated using the Semantic 3D reduced-test set. The IoU of tree point cloud segmentation reached 0.864. In addition, the semantic segmentation network was tested using the Paris-Lille-3D dataset. The average IoU outperformed several other popular methods. The experimental results indicate that the proposed algorithm provides an excellent solution for vegetation segmentation from LiDAR point clouds.

cs.CV↗

arXiv2019

Ultrabroadband Nonlinear Optics in Nanophotonic Periodically Poled Lithium Niobate Waveguides

Quasi-phasematched interactions in waveguides with quadratic nonlinearities enable highly efficient nonlinear frequency conversion. In this article, we demonstrate the first generation of devices that combine the dispersion-engineering available in nanophotonic waveguides with quasi-phasematched nonlinear interactions available in periodically poled lithium niobate (PPLN). This combination enables quasi-static interactions of femtosecond pulses, reducing the pulse energy requirements by several orders of magnitude, from picojoules to femtojoules. We experimentally demonstrate two effects associated with second harmonic generation. First, we observe efficient quasi-phasematched second harmonic generation with <100 fJ of pulse energy. Second, in the limit of strong phase-mismatch, we observe spectral broadening of both harmonics with as little as 2-pJ of pulse energy. These results lay a foundation for a new class of nonlinear devices, in which co-engineering of dispersion with quasi-phasematching enables efficient nonlinear optics at the femtojoule level.

physics.optics↗

arXiv2019

Limited-budget output consensus for descriptor multiagent systems with energy constraints

The current paper deals with limited-budget output consensus for descriptor multiagent systems with two types of switching communication topologies; that is, switching connected ones and jointly connected ones. Firstly, a singular dynamic output feedback control protocol with switching communication topologies is proposed on the basis of the observable decomposition, where an energy constraint is involved and protocol states of neighboring agents are utilized to derive a new two-step design approach of gain matrices. Then, limited-budget output consensus problems are transformed into asymptotic stability ones and a valid candidate of the output consensus function is determined. Furthermore, sufficient conditions for limited-budget output consensus design for two types of switching communication topologies are proposed, respectively. Finally, two numerical simulations are shown to demonstrate theoretical conclusions.

cs.MA↗

arXiv2019

Convergence properties of detonation simulations

We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen-oxygen mixture using the Pencil Code and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10-30, a certain amount of shock viscosity is needed in the Pencil Code to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width $δx$ like $δx^{-1.4}$ down to $δx=0.2μ$m. With the WENO scheme, solutions are smooth at $δx=10μ$m, but no detonation is obtained for $δx=5μ$m. This is argued to be an artifact of a decoupling between pressure and reaction fronts.

physics.flu-dyn↗

arXiv2019

A shrinkage estimation for large dimensional precision matrices using random matrix theory

In this paper, a new ridge-type shrinkage estimator for the precision matrix has been proposed. The asymptotic optimal shrinkage coefficients and the theoretical loss were derived. Data-driven estimators for the shrinkage coefficients were also conducted based on the asymptotic results deriving from random matrix theories. The new estimator which has a simple explicit formula is distribution-free and applicable to situation where the dimension of observation is greater than the sample size. Further, no assumptions are required on the structure of the population covariance matrix or the precision matrix. Finally, numerical studies are conducted to examine the performances of the new estimator and existing methods for a wide range of settings.

stat.ME↗

arXiv2019

Raman lasing and soliton modelocking in lithium-niobate microresonators

The recent advancement in lithium niobate on insulator (LNOI) technology is revolutionizing the optoelectronic industry as devices of higher performance, lower power consumption, and smaller footprint can be realized due to the high optical confinement in the structures. The LNOI platform offers both large \c{hi}(2) and \c{hi}(3) nonlinearities along with the power of dispersion engineering, enabling brand new nonlinear photonic devices and applications towards the next generation of integrated photonic circuits. However, the Raman scattering, one of the most important nonlinear phenomena, have not been extensively studied, neither was its influences in dispersion-engineered LNOI nano-devices. In this work, we characterize the Raman radiation spectra in a monolithic lithium niobate (LN) microresonator via selective excitation of Raman-active phonon modes. Remarkably, the dominant mode for Raman oscillation is observed in the backward direction for a continuous-wave pump threshold power of 20 mW with a reportedly highest differential quantum efficiency of 46 %. In addition, we explore the effects of Raman scattering on Kerr optical frequency combs generation. We achieve, for the first time, soliton modelocking on a X-cut LNOI chip through sufficient suppression of the Raman effect via cavity geometry control. Our analysis of the Raman effect provides guidance for the development of future chip-based photonic devices on the LNOI platform.

physics.optics↗

arXiv2019

Magnetotransport properties of granular oxide-segregated CoPtCr films for applications in future magnetic memory technology

Magnetotransport properties of granular oxide-segregated CoPtCr films were studied on both macroscopic and microscopic length scales by performing bulk and point-contact magnetoresistance measurements, respectively. Such a perpendicular magnetic medium is used in state-of-the-art hard disc drives and if combined with magnetoresistive phenomena (for read/write operations) may lead to a novel concept for magnetic recording with high areal density. While the bulk measurements on the films showed only small variations in dc resistance as a function of applied magnetic field (magnetoresistance of less than 0.02 %), the point-contact measurements revealed giant-magnetoresistance-like changes in resistance with up to 50,000 % ratios. The observed magnetorestive effect could be attributed to a tunnel magnetoresistance between CoPtCr grains with different coercivity. The tunneling picture of electronic transport in our granular medium was confirmed by the observation of tunneling-like current-voltage characteristics and bias dependence of magnetoresistance; both the point-contact resistance and magnetoresistance were found to decrease with the applied dc bias.

cond-mat.mes-hall↗

arXiv2019

Microwave-to-optical conversion using lithium niobate thin-film acoustic resonators

We demonstrate conversion of up to 4.5 GHz-frequency microwaves to 1500 nm-wavelength light using optomechanical interactions on suspended thin-film lithium niobate. Our method utilizes an interdigital transducer that drives a free-standing 100 $μ$m-long thin-film acoustic resonator to modulate light travelling in a Mach-Zehnder interferometer or racetrack cavity. Owing to the strong microwave-to-acoustic coupling offered by the transducer in conjunction with the strong photoelastic, piezoelectric, and electro-optic effects of lithium niobate, we achieve a half-wave voltage of $V_π$ = 4.6 V and $V_π$ = 0.77 V for the Mach-Zehnder interferometer and racetrack resonator, respectively. The acousto-optic racetrack cavity exhibits an optomechancial single-photon coupling strength of 1.1 kHz. Our integrated nanophotonic platform coherently leverages the compelling properties of lithium niobate to achieve microwave-to-optical transduction. To highlight the versatility of our system, we also demonstrate a lossless microwave photonic link, which refers to a 0 dB microwave power transmission over an optical channel.

physics.app-ph↗

arXiv2019

An efficient ADMM algorithm for high dimensional precision matrix estimation via penalized quadratic loss

The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to solve problems with a very large $p$. In this paper, we propose a very efficient algorithm for precision matrix estimation via penalized quadratic loss functions. Under the high dimension low sample size setting, the computation complexity of our algorithm is linear in both the sample size and the number of parameters. Such a computation complexity is in some sense optimal, as it is the same as the complexity needed for computing the sample covariance matrix. Numerical studies show that our algorithm is much more efficient than other state-of-the-art methods when the dimension $p$ is very large.

stat.CO↗

arXiv2019

Convergence Analysis of A Second-order Semi-implicit Projection Method for Landau-Lifshitz Equation

The numerical approximation for the Landau-Lifshitz equation, the dynamics of magnetization in a ferromagnetic material, is taken into consideration. This highly nonlinear equation, with a non-convex constraint, has several equivalent forms, and involves solving an auxiliary problem in the infinite domain. All these features have posed interesting challenges in developing numerical methods. In this paper, we first present a fully discrete semi-implicit method for solving the Landau-Lifshitz equation based on the second-order backward differentiation formula and the one-sided extrapolation (using previous time-step numerical values). A projection step is further used to preserve the length of the magnetization. Subsequently, we provide a rigorous convergence analysis for the fully discrete numerical solution, with second-order accuracy in both time and space, provided that the spatial step-size is the same order as the temporal step-size. And also, the unique solvability of the numerical solution is theoretically justified, which turns out to be the first such result for the micromagnetics model. All these theoretical properties are verified by numerical examples in both one- and three- dimensional spaces.

math.AP↗

arXiv2019

A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection

In this paper, a stabilized second order in time accurate linear exponential time differencing (ETD) scheme for the no-slope-selection thin film growth model is presented. An artificial stabilizing term $Aτ^2\frac{\partialΔ^2 u}{\partial t}$ is added to the physical model to achieve energy stability, with ETD-based multi-step approximations and Fourier collocation spectral method applied in the time integral and spatial discretization of the evolution equation, respectively. Long time energy stability and detailed $\ell^{\infty}(0,T; \ell^2)$ error analysis are provided based on the energy method, with a careful estimate of the aliasing error. In addition, numerical experiments are presented to demonstrate the energy decay and convergence rate.

math.NA↗

arXiv2019

Second-order semi-implicit projection methods for micromagnetics simulations

Micromagnetics simulations require accurate approximation of the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which is nonlinear, nonlocal, and has a non-convex constraint, posing interesting challenges in developing numerical methods. In this paper, we propose two second-order semi-implicit projection methods based on the second-order backward differentiation formula and the second-order interpolation formula using the information at previous two temporal steps. Unconditional unique solvability of both methods is proved, with their second-order accuracy verified through numerical examples in both 1D and 3D. The efficiency of both methods is compared to that of another two popular methods. In addition, we test the robustness of both methods for the first benchmark problem with a ferromagnetic thin film material from National Institute of Standards and Technology.

physics.comp-ph↗

arXiv2019

An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation

In this paper we propose and analyze an energy stable numerical scheme for the square phase field crystal (SPFC) equation, a gradient flow modeling crystal dynamics at the atomic scale in space but on diffusive scales in time. In particular, a modification of the free energy potential to the standard phase field crystal model leads to a composition of the 4-Laplacian and the regular Laplacian operators. To overcome the difficulties associated with this highly nonlinear operator, we design numerical algorithms based on the structures of the individual energy terms. A Fourier pseudo-spectral approximation is taken in space, in such a way that the energy structure is respected, and summation-by-parts formulae enable us to study the discrete energy stability for such a high-order spatial discretization. In the temporal approximation, a second order BDF stencil is applied, combined with an appropriate extrapolation for the concave diffusion term(s). A second order artificial Douglas-Dupont-type regularization term is added to ensure energy stability, and a careful analysis leads to the artificial linear diffusion coming at an order lower that that of surface diffusion term. Such a choice leads to reduced numerical dissipation. At a theoretical level, the unique solvability, energy stability are established, and an optimal rate convergence analysis is derived in the $\ell^\infty (0,T; \ell^2) \cap \ell^2 (0,T; H_N^3)$ norm. In the numerical implementation, the preconditioned steepest descent (PSD) iteration is applied to solve for the composition of the highly nonlinear 4-Laplacian term and the standard Laplacian term, and a geometric convergence is assured for such an iteration. Finally, a few numerical experiments are presented, which confirm the robustness and accuracy of the proposed scheme.

math.NA↗

arXiv2019

Accelerating Mini-batch SARAH by Step Size Rules

StochAstic Recursive grAdient algoritHm (SARAH), originally proposed for convex optimization and also proven to be effective for general nonconvex optimization, has received great attention due to its simple recursive framework for updating stochastic gradient estimates. The performance of SARAH significantly depends on the choice of step size sequence. However, SARAH and its variants often employ a best-tuned step size by mentor, which is time consuming in practice. Motivated by this gap, we proposed a variant of the Barzilai-Borwein (BB) method, referred to as the Random Barzilai-Borwein (RBB) method, to calculate step size for SARAH in the mini-batch setting, thereby leading to a new SARAH method: MB-SARAH-RBB. We prove that MB-SARAH-RBB converges linearly in expectation for strongly convex objective functions. We analyze the complexity of MB-SARAH-RBB and show that it is better than the original method. Numerical experiments on standard data sets indicate that MB-SARAH-RBB outperforms or matches state-of-the-art algorithms.

cs.LG↗

arXiv2019

RF-Net: An End-to-End Image Matching Network based on Receptive Field

This paper proposes a new end-to-end trainable matching network based on receptive field, RF-Net, to compute sparse correspondence between images. Building end-to-end trainable matching framework is desirable and challenging. The very recent approach, LF-Net, successfully embeds the entire feature extraction pipeline into a jointly trainable pipeline, and produces the state-of-the-art matching results. This paper introduces two modifications to the structure of LF-Net. First, we propose to construct receptive feature maps, which lead to more effective keypoint detection. Second, we introduce a general loss function term, neighbor mask, to facilitate training patch selection. This results in improved stability in descriptor training. We trained RF-Net on the open dataset HPatches, and compared it with other methods on multiple benchmark datasets. Experiments show that RF-Net outperforms existing state-of-the-art methods.

cs.CV↗

arXiv2019

Phononic band structure engineering for high-Q gigahertz surface acoustic wave resonators on lithium niobate

Phonons at gigahertz frequencies interact with electrons, photons, and atomic systems in solids, and therefore have extensive applications in signal processing, sensing, and quantum technologies. Surface acoustic wave (SAW) resonators that confine surface phonons can play a crucial role in such integrated phononic systems due to small mode size, low dissipation, and efficient electrical transduction. To date, it has been challenging to achieve high quality (Q) factor and small phonon mode size for SAW resonators at gigahertz frequencies. Here, we present a methodology to design compact high-Q SAW resonators on lithium niobate operating at gigahertz frequencies. We experimentally verify out designs and demonstrate Q factors in excess of $2\times10^4$ at room temperature ($6\times10^4$ at 4 Kelvin) and mode area as low as $1.87 λ^2$. This is achieved by phononic band structure engineering, which provides high confinement with low mechanical loss. The frequency-Q products (fQ) of our SAW resonators are greater than $10^{13}$. These high-fQ and small mode size SAW resonators could enable applications in quantum phononics and integrated hybrid systems with phonons, photons, and solid-state qubits.

cond-mat.mes-hall↗

arXiv2019

Fast Regularity-Constrained Plane Reconstruction

Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of algorithmic plane reconstruction of complex scenes. This research leverages a constraint model requiring minimal prior knowledge to implicitly establish relationships among planes. We introduce a method based on energy minimization to reconstruct the planes consistent with our constraint model. The proposed algorithm is efficient, easily to understand, and simple to implement. The experimental results show that our algorithm successfully reconstructs planes under high percentages of noise and outliers. This is superior to other state-of-the-art regularity-constrained plane reconstruction methods in terms of speed and robustness.

cs.CV↗