arXiv subjects
Publications and source records attributed to Xiaopeng Zhao.
In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{β-1}u$ ($β>1$) in $\mathbb{R}^3$.
Music is older than language, and for most of human history music holds our culture together. The pipe instrument is one of the most popular musical instruments of all time. Built on the foundation of previous flute and flute-like acoustic metamaterial models, we herein report the experimental results of the inverse Doppler effects discovered in two common pipe instruments - recorder and clarinet. Our study shows that the inverse Doppler effects can be detected at all seven pitches of an ascending musical scale when there is a relative motion between a microphone (observer) and abovementioned two pipe instruments (source). The calculated effective refractive indices of these two pipe instruments are negative and varying across a set of pitches, exhibiting a desired characteristic of broadband acoustic metamaterials. This study suggests that recorder and clarinet may be the earliest man-made acoustic metamaterials known so far, offering a new explanation why pipe instruments have enjoyed wide popularity in Europe and Asia over the past hundreds and thousands years. This newly discovered phenomenon would also offer a clue into designing next-generation smart broadband double-negative acoustic metamaterials with varying refractive index.
In this paper, we consider the Fourier spectral method for numerically solving the 2D convective Cahn-Hilliard equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error bound are also considered.
In this paper, on the basis of the Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for a generalized Cahn-Hilliard equation with biological applications.
In this paper, the existence of weak solutions of a convective Cahn-Hilliard equation with degenerate mobility is studied. We first define a notion of weak solutions and establish a regularized problems. The existence of such solutions is obtained by considered the limits of the regularized problems.
The critical temperature (TC) of MgB2, one of the key factors limiting its application, is highly desired to be improved. On the basis of the meta-material structure, we prepared a smart meta-superconductor structure consisting of MgB2 micro-particles and inhomogeneous phases by an ex situ process. The effect of inhomogeneous phase on the TC of smart meta-superconductor MgB2 was investigated. Results showed that the onset temperature (Ton C) of doping samples was lower than those of pure MgB2. However, the offset temperature (Toff C) of the sample doped with Y2O3:Eu3+ nanosheets with a thickness of 2~3 nm which is much less than the coherence length of MgB2 is 1.2 K higher than that of pure MgB2. The effect of the applied electric field on the TC of sample was also studied. Results indicated that with the increase of current, Ton C is slightly increased in the samples doping with different inhomogeneous phases. When increasing current, the Toff C of the samples doped with nonluminous inhomogeneous phases was decreased. However, the Toff C of the luminescent inhomogeneous phase doping samples increased and then decreased as increasing current.
Brain-Machine Interaction (BMI) system motivates interesting and promising results in forward/feedback control consistent with human intention. It holds great promise for advancements in patient care and applications to neurorehabilitation. Here, we propose a novel neurofeedback-based BCI robotic platform using a personalized social robot in order to assist patients having cognitive deficits through bilateral rehabilitation and mental training. For initial testing of the platform, electroencephalography (EEG) brainwaves of a human user were collected in real time during tasks of imaginary movements. First, the brainwaves associated with imagined body kinematics parameters were decoded to control a cursor on a computer screen in training protocol. Then, the experienced subject was able to interact with a social robot via our real-time BMI robotic platform. Corresponding to subject's imagery performance, he/she received specific gesture movements and eye color changes as neural-based feedback from the robot. This hands-free neurofeedback interaction not only can be used for mind control of a social robot's movements, but also sets the stage for application to enhancing and recovering mental abilities such as attention via training in humans by providing real-time neurofeedback from a social robot.
Brain computer interface (BCI) provides promising applications in neuroprosthesis and neurorehabilitation by controlling computers and robotic devices based on the patient's intentions. Here, we have developed a novel BCI platform that controls a personalized social robot using noninvasively acquired brain signals. Scalp electroencephalogram (EEG) signals are collected from a user in real-time during tasks of imaginary movements. The imagined body kinematics are decoded using a regression model to calculate the user-intended velocity. Then, the decoded kinematic information is mapped to control the gestures of a social robot. The platform here may be utilized as a human-robot-interaction framework by combining with neurofeedback mechanisms to enhance the cognitive capability of persons with dementia.
We demonstrated a 2D helical chiral metamaterial that exhibits broadband strong optical activity resulting nonresonant Drude-like response. The strong chirality leads to broadband negative refractive index with high figure of merit (>90) and extremely low loss (<2% per layer). The optical activity are insensitive to the angles of incident electromagnetic waves, thereby enabling more flexibility in polarization manipulation applicaitons.
The manipulation of visible light is important in science and technology research. Metasurfaces can enable flexible and effective regulation of the phase, polarization, and propagation modes of an electromagnetic wave. Metasurfaces have become a research hotspot in optics and electromagnetics, and cross-polarization conversion is an important application for visible-light manipulation using a metasurface. A metasurface composed of nano-antenna arrays and bilayer plasma can reportedly convert the direction of linear polarized light efficiently. However, the metasurface of cross-polarization conversion operating in short-wavelength visible light is problematic. In addition, previous metasurfaces prepared using the top-down etching method is unsuitable for practical applications because of the necessary harsh experimental conditions and the high construction cost of preparation. In the present work, we suggest a dendritic cell-cluster metasurface achieve cross-polarization in transmission mode within 550, 570, 590 and 610 nm wavelength. Preparation is accomplished using a bottom-up electrochemical deposition method, which is easy and low cost. The dendritic cell-cluster metasurface is an important step in cross-polarization conversion research and has broad application prospects and development potential.
Because of the strong inherent resonances, the giant optical activity obtained via chiral metamaterials generally suffers from high dispersion, which has been a big stumbling block to broadband applications. In this paper, we propose a type of chiral metamaterial consisting of interconnected metal helix structures with four-fold symmetry, which exhibits nonresonant Drude-like response and can therefore avoid the highly dispersive optical activity resulting from resonances. It shows that the well-designed chiral metamaterial can achieve nondispersive and pure optical activity with high transmittance in a broadband frequency range. And the optical activity of multi-layer chiral metamaterials is proportional to the layer numbers of single-layer chiral metamaterial. Most remarkably, the broadband behaviors of nondispersive optical activity and high transmission are insensitive to the incident angles of electromagnetic waves and permittivity of dielectric substrate, thereby enabling more flexibility in polarization manipulation.
Enhancing the critical temperature (TC) is important not only to the practical applications but also to the theories of superconductivity. MgB2 is a type II superconductor with a TC of 39 K, which is very close to the McMillan limit. Improving the TC of MgB2 is challenging but significant. Inspired by the metamaterial structure, we designed a smart meta-superconductor that consists of MgB2 microparticles and Y2O3:Eu3+ nanorods. In the local electric field, Y2O3:Eu3+ nanorods will generate electroluminescence (EL) that can excite MgB2 particles, thereby improving the TC by strengthening the electron-phonon interaction. Each MgB2-based superconductor doped with one of the four dopants of different EL intensities was prepared by an ex-situ process. The results showed that the addition of Y2O3:Eu3+ brings about an impurity effect that decreases the TC and an EL exciting effect that increases the TC. Apart from the EL intensity, the micro-morphology and degree of dispersion of the dopants also affected the TC. This smart meta-superconductor provides a new method for increasing TC.
The MgB2 superconductor was doped with electroluminescent Y2O3:Eu, to synthesise a superconducting metamaterial. The temperature dependence of the resistivity of the superconductor indicates that the critical temperature (TC) of samples decrease when increasing the amount of doped Y2O3 nanorods, due to impurity (Y2O3, MgO and YB4). However, the TC of the samples increase with increasing amount of doped Y2O3:Eu3+ nanorods, which are opposite to doped Y2O3 nanorods. Moreover, the transition temperature of the sample doped with 8 wt. % Y2O3:Eu3+ nanorods is higher than those of doped and pure MgB2. The TC of the sample doped with 8 wt. % Y2O3:Eu3+ nanorods is 1.15 K higher than that of the sample doped with 8 wt. % Y2O3. The TC of sample doped with 8 wt. % Y2O3:Eu3+ is 0.4 K higher than that of pure MgB2. Results indicate that doping electroluminescent materials into MgB2 increases the transition temperature; this novel strategy may also be applicable to other superconductors.
We propose a planar composite chiral metamaterial (CCMM) by symmetrically inserting a metallic mesh between two layers of conjugated gammadion resonators. As the elaborate CCMM operates in the frequency region of off-resonance, it therefore presents loss-less and dispersion-free features. It can achieve flat polarization rotation simultaneously accompanied with high transmission and extremely low ellipticity in a broad bandwidth. In the meanwhile, this intriguing CCMM shows more superiorities in polarization rotation power and operating bandwidth than the pure chiral metamaterial just composed of conjugated gammadions. Due to the fascinating properties, the proposed CCMM is greatly appealing for controlling the polarization state of the electromagnetic waves.
This paper reports an experimental observation of broadband reversed Doppler effects using an acoustic metamaterial with seven flute-like double-meta-molecule clusters. Simulations and experiments verify that this locally resonant acoustic metamaterial with simultaneous negative elastic modulus and mass density can realize negative refraction in a broad frequency range. The constructed metamaterial exhibits broadband reversed Doppler effects. The frequency shift increases continuously as the frequency increases. The assembling of double-meta-molecule clusters introduces a new direction in designing double-negative acoustic metamaterials in an arbitrarily broad frequency range and other various applications.
The investigation of metasurface, which is of great current interest, has opened up new degrees of freedom to research metamaterials. In this paper, we propose an ultrathin acoustic metasurface consisting of a series of structurally simple drum-like subunit cells. Eight units with different sizes aer selected to realize discrete transmisson phase shifts ranging from 0 to 360 degrees ar 3.5 KHz. The designed metasurface is capable of manipulating sound waves at will, including anomalous refraction and conversion of propagating waves into surface waves, which can be predicted precisely by the generalized Snell's law. It id worth noting that the total thickness of such planar metasurface is approximately 1/5 of working wavelength, which may be beneficial to the miniaturization and integration of acoustic equipment.
Since the introduction of the artificially designed negative-index metamaterial (NIM) introduced in 2001, its extraordinary electromagnetic properties, which cannot be attained from naturally occurring materials, have continuously attracted many researchers to study them. Various types of NIMs with the resonant frequencies shifted from gigahertz all the way to higher frequencies have been actualized over the past decade. For the actual applications, the most fascinating and significant goal of research on NIMs is to achieve negative refraction at visible wavelengths. According to the effective medium theory, the interior structural unit of NIMs must be on a scale much smaller than the operating wavelength.
We presented an acoustic 'meta-atom' model of hollow steel tube (HST). The simulated and experimental results demonstrated that the resonant frequency is closely related to the length of the HST. Based on the HST model, we fabricated a two-dimensional (2D) acoustic metamaterial (AM) with negative effective mass density, which put up the transmission dip and accompanied inverse phase in experiment. By coupling the HST with split hollow sphere (SHS), another kind of 'meta-atom' with negative effective modulus in the layered sponge matrix, a three-dimensional (3D) AM was fabricated with simultaneously negative modulus and negative mass density. From the experiment, it is shown that the transmission peak similar to the electromagnetic metamaterials exhibited in the double-negative region of the AM. We also demonstrated that this kind of doble-negative AM can faithfully distinguish the acoustic sub-wavelength details (λ/7) at the resonance frequency of 1630Hz.