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Hui Yu

Publications and source records attributed to Hui Yu.

At least 109 records · Page 6Linked to original sources
arXiv2021

Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations

In this paper, we design and analyze third order positivity-preserving discontinuous Galerkin (DG) schemes for solving the time-dependent system of Poisson--Nernst--Planck (PNP) equations, which has found much use in diverse applications. Our DG method with Euler forward time discretization is shown to preserve the positivity of cell averages at all time steps. The positivity of numerical solutions is then restored by a scaling limiter in reference to positive weighted cell averages. The method is also shown to preserve steady states. Numerical examples are presented to demonstrate the third order accuracy and illustrate the positivity-preserving property in both one and two dimensions.

math.NA↗
arXiv2021

On the fine regularity of the singular set in the nonlinear obstacle problem

We revisit and sharpen the results from our previous work, where we investigated the regularity of the singular set of the free boundary in the nonlinear obstacle problem. As in the work of Figalli-Serra on the classical obstacle problem, we show that each stratum can be further decomposed into a `good' part and an `anomalous' part, where the former is covered by $C^{1,1-}$ manifolds, and the latter is of lower dimension.

math.AP↗
arXiv2020

Damping of slow surface kink modes in solar photospheric waveguides modeled by one-dimensional inhomogeneities

Given the recent interest in magnetohydrodynamic (MHD) waves in pores and sunspot umbrae, we examine the damping of slow surface kink modes (SSKMs) by modeling solar photospheric waveguides with a cylindrical inhomogeneity comprising a uniform interior, a uniform exterior, and a continuous transition layer (TL) in between. Performing an eigen-mode analysis in linear, resistive, gravity-free MHD, our approach is idealized in that, among other things, our equilibrium is structured only in the radial direction. We can nonetheless address two damping mechanisms simultaneously, one being the Ohmic resistivity, and the other being the resonant absorption of SSKMs in the cusp and Alfv$\acute{\rm e}$n continua. We find that the relative importance of the two mechanisms depends sensitively on the magnetic Reynolds number ($R_{\rm m}$). Resonant absorption is the sole damping mechanism for realistically large values of $R_{\rm m}$, and the cusp resonance in general dominates the Alfv$\acute{\rm e}$n one unless the axial wavenumbers are at the lower end of the observationally relevant range. We also find that the thin-boundary approximation holds only when the TL-width-to-radius ratios are much smaller than nominally expected. The Ohmic resistivity is far more important for realistically small $R_{\rm m}$. Even in this case, SSKMs are only marginally damped, with damping-time-to-period-ratios reaching $\sim 10$ in the parameter range we examine.

astro-ph.SR↗
arXiv2020

On the fully nonlinear Alt-Phillips equation

For a parameter $γ\in(1,2)$, we study the fully nonlinear version of the Alt-Phillips equation, $F(D^2u)=u^{γ-1}$, for $u\ge 0.$ We establish the optimal regularity of the solution, as well as the $C^1$ regularity of the regular part of the free boundary.

math.AP↗
arXiv2020

Meromorphic functions of finite $φ$-order and linear $q$-difference equations

The $φ$-order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of meromorphic functions in the complex plane are investigated in terms of the $φ$-order, which measures the growth of functions between the classical order and the logarithmic order. Several results on value distribution of meromorphic functions are discussed by using the $φ$-order and the $φ$-exponent of convergence. Instead of linear differential equations, the applications in the complex plane lie in linear $q$-difference equations.

math.CV↗
arXiv2020

An outer reflected forward-backward splitting algorithm for solving monotone inclusions

Monotone inclusions have wide applications in solving various convex optimization problems arising in signal and image processing, machine learning, and medical image reconstruction. In this paper, we propose a new splitting algorithm for finding a zero of the sum of a maximally monotone operator, a monotone Lipschitzian operator, and a cocoercive operator, which is called outer reflected forward-backward splitting algorithm. Under mild conditions on the iterative parameters, we prove the convergence of the proposed algorithm. As applications, we employ the proposed algorithm to solve composite monotone inclusions involving monotone Lipschitzian operator, cocoercive operator, and the parallel sum of operators. The advantage of the obtained algorithm is that it is a completely splitting algorithm, in which the Lipschitzian operator and the cocoercive operator are processed via explicit steps and the maximally monotone operators are processed via their resolvents.

math.OC↗
arXiv2020

Diesel Generator Model Parameterization for Microgrid Simulation Using Hybrid Box-Constrained Levenberg-Marquardt Algorithm

Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. This paper presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit.

eess.SY↗
arXiv2020

3D Facial Geometry Recovery from a Depth View with Attention Guided Generative Adversarial Network

We present to recover the complete 3D facial geometry from a single depth view by proposing an Attention Guided Generative Adversarial Networks (AGGAN). In contrast to existing work which normally requires two or more depth views to recover a full 3D facial geometry, the proposed AGGAN is able to generate a dense 3D voxel grid of the face from a single unconstrained depth view. Specifically, AGGAN encodes the 3D facial geometry within a voxel space and utilizes an attention-guided GAN to model the illposed 2.5D depth-3D mapping. Multiple loss functions, which enforce the 3D facial geometry consistency, together with a prior distribution of facial surface points in voxel space are incorporated to guide the training process. Both qualitative and quantitative comparisons show that AGGAN recovers a more complete and smoother 3D facial shape, with the capability to handle a much wider range of view angles and resist to noise in the depth view than conventional methods

cs.CV↗
arXiv2020

Real-time 3D Facial Tracking via Cascaded Compositional Learning

We propose to learn a cascade of globally-optimized modular boosted ferns (GoMBF) to solve multi-modal facial motion regression for real-time 3D facial tracking from a monocular RGB camera. GoMBF is a deep composition of multiple regression models with each is a boosted ferns initially trained to predict partial motion parameters of the same modality, and then concatenated together via a global optimization step to form a singular strong boosted ferns that can effectively handle the whole regression target. It can explicitly cope with the modality variety in output variables, while manifesting increased fitting power and a faster learning speed comparing against the conventional boosted ferns. By further cascading a sequence of GoMBFs (GoMBF-Cascade) to regress facial motion parameters, we achieve competitive tracking performance on a variety of in-the-wild videos comparing to the state-of-the-art methods, which require much more training data or have higher computational complexity. It provides a robust and highly elegant solution to real-time 3D facial tracking using a small set of training data and hence makes it more practical in real-world applications.

cs.CV↗
arXiv2020

PIoU Loss: Towards Accurate Oriented Object Detection in Complex Environments

Object detection using an oriented bounding box (OBB) can better target rotated objects by reducing the overlap with background areas. Existing OBB approaches are mostly built on horizontal bounding box detectors by introducing an additional angle dimension optimized by a distance loss. However, as the distance loss only minimizes the angle error of the OBB and that it loosely correlates to the IoU, it is insensitive to objects with high aspect ratios. Therefore, a novel loss, Pixels-IoU (PIoU) Loss, is formulated to exploit both the angle and IoU for accurate OBB regression. The PIoU loss is derived from IoU metric with a pixel-wise form, which is simple and suitable for both horizontal and oriented bounding box. To demonstrate its effectiveness, we evaluate the PIoU loss on both anchor-based and anchor-free frameworks. The experimental results show that PIoU loss can dramatically improve the performance of OBB detectors, particularly on objects with high aspect ratios and complex backgrounds. Besides, previous evaluation datasets did not include scenarios where the objects have high aspect ratios, hence a new dataset, Retail50K, is introduced to encourage the community to adapt OBB detectors for more complex environments.

cs.CV↗
arXiv2020

QoS-Based Source and Relay Secure Optimization Design with Presence of Channel Uncertainty

In this letter, we study relay-aided networks with presence of single eavesdropper. We provide joint beamforming design of the source and relay that can minimize the overall power consumption while satisfying our predefined quality-of-service (QoS) requirements. Additionally, we investigate the case that the channel between relay and eavesdropper suffers from channel uncertainty. Finally, simulation results are provided to verify the effectiveness of our algorithm.

eess.SP↗
arXiv2020

Robust Beamforming Design for Sum Secrecy Rate Optimization in MU-MISO Networks

This paper studies the beamforming design problem of a multi-user downlink network, assuming imperfect channel state information known to the base station. In this scenario, the base station is equipped with multiple antennas, and each user is wiretapped by a specific eavesdropper where each user or eavesdropper is equipped with one antenna. It is supposed that the base station employs transmit beamforming with a given requirement on sum transmitting power. The objective is to maximize the sum secrecy rate of the network. Due to the uncertainty of the channel, it is difficult to calculate the exact sum secrecy rate of the system. Thus, the maximum of lower bound of sum secrecy rate is considered. The optimization of the lower bound of sum secrecy rate still makes the considered beamforming design problem difficult to handle. To solve this problem, a beamforming design scheme is proposed to transform the original problem into a convex approximation problem, by employing semidefinite relaxation and first-order approximation technique based on Taylor expansion. Besides, with the advantage of low complexity, a zero-forcing based beamforming method is presented in the case that base station is able to nullify the eavesdroppers' rate. When the base station doesn't have the ability, user selection algorithm would be in use. Numerical results show that the former strategy achieves better performance than the latter one, which is mainly due to the ability of optimizing beamforming direction, and both outperform the signal-to-leakage-and-noise ratio based algorithm.

eess.SP↗
arXiv2020

Regularity of the singular set in the fully nonlinear obstacle problem

For the obstacle problem involving a convex fully nonlinear elliptic operator, we show that the singular set in the free boundary stratifies. The top stratum is locally covered by a $C^{1,α}$-manifold, and the lower strata are covered by $C^{1,\log^\varepsilon}$-manifolds. This essentially recovers the regularity result obtained by Figalli-Serra when the operator is the Laplacian.

math.AP↗
arXiv2019

On the number of linearly independent rapid solutions to linear differential and linear difference equations

Assuming that $A_0,\ldots,A_{n-1}$ are entire functions and that $p\in \{0,\ldots,n-1\}$ is the smallest index such that $A_p$ is transcendental, then, by a classical theorem of Frei, each solution base of the differential equation $f^{(n)}+A_{n-1}f^{(n-1)}+\cdots +A_{1}f'+A_{0}f=0$ contains at least $n-p$ entire functions of infinite order. Here, the transcendental coefficient $A_p$ dominates the growth of the polynomial coefficients $A_{p+1},\ldots,A_{n-1}$. By expressing the dominance of $A_p$ in different ways, and allowing the coefficients $A_{p+1},\ldots,A_{n-1}$ to be transcendental, we show that the conclusion of Frei's theorem still holds along with an additional estimation on the asymptotic lower bound for the growth of solutions. At times these new refined results give a larger number of linearly independent solutions of infinite order than the original theorem of Frei. For such solutions, we show that $0$ is the only possible finite deficient value. Previously this property has been known to hold for so-called admissible solutions and is commonly cited as Wittich's theorem. Analogous results are discussed for linear differential equations in the unit disc, as well as for complex difference and complex $q$-difference equations.

math.CV↗
arXiv2019

A brief survey on the obstacle problem

We discuss some regularity issues in the study of the obstacle problem. In particular, we present a recent result by O. Savin and the author on the regularity of the singular set for the obstacle problem with a fully nonlinear elliptic operator. This survey is based on a lecture by the author at the 8th International Congress of Chinese Mathematicians.

math.AP↗
arXiv2019

THIRD ORDER MAXIMUM-PRINCIPLE-SATISFYING DG SCHEMES Third Order Maximum-Principle-Satisfying DG schemes for Convection-Diffusion problems with Anisotropic Diffusivity DIFFUSIVITY

For a class of convection-diffusion equations with variable diffusivity, we construct third order accurate discontinuous Galerkin (DG) schemes on both one and two dimensional rectangular meshes. The DG method with an explicit time stepping can well be applied to nonlinear convection-diffusion equations. It is shown that under suitable time step restrictions, the scaling limiter proposed in [Liu and Yu, SIAM J. Sci. Comput. 36(5): A2296{A2325, 2014] when coupled with the present DG schemes preserves the solution bounds indicated by the initial data, i.e., the maximum principle, while maintaining uniform third order accuracy. These schemes can be extended to rectangular meshes in three dimension. The crucial for all model scenarios is that an effective test set can be identified to verify the desired bounds of numerical solutions. This is achieved mainly by taking advantage of the flexible form of the diffusive flux and the adaptable decomposition of weighted cell averages. Numerical results are presented to validate the numerical methods and demonstrate their effectiveness.

math.NA↗
arXiv2019

High-performance silicon-graphene hybrid plasmonic waveguide photodetectors beyond 1.55 μm

A fast silicon-graphene hybrid plasmonic waveguide photodetectors beyond 1.55 μm is proposed and realized by introducing an ultra-thin wide silicon-on-insulator ridge core region with a narrow metal cap. With this novel design, the light absorption in graphene is enhanced while the metal absorption loss is reduced simultaneously, which helps greatly improve the responsivity as well as shorten the absorption region for achieving fast responses. Furthermore, metal-graphene-metal sandwiched electrodes are introduced to reduce the metal-graphene contact resistance, which is also helpful for improving the response speed. When the photodetector operates at 2 μm, the measured 3dB-bandwidth is >20 GHz (which is limited by the experimental setup) while the 3dB-bandwith calculated from the equivalent circuit with the parameters extracted from the measured S11 is as high as ~100 GHz. To the best of our knowledge, it is the first time to report the waveguide photodetector at 2 μm with a 3dB-bandwidth over 20 GHz. Besides, the present photodetectors also work very well at 1.55 μm. The measured responsivity is about 0.4 A/W under a bias voltage of -0.3 V for an optical power of 0.16 mW, while the measured 3dB-bandwidth is over 40 GHz (limited by the test setup) and the 3 dB-bandwidth estimated from the equivalent circuit is also as high as ~100 GHz, which is one of the best results reported for silicon-graphene photodetectors at 1.55 μm.

physics.app-ph↗