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The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally obtain the {\em nonsymmetric indefinite system} [Chen et al., IMA J. Numer. Anal., (2021)]. In this case, the discrete maximum principle is not satisfied, which might be trickier for the stability analysis of the high-order numerical schemes [D'Elia et al., Acta Numer., (2020); Leng et al., SIAM J. Numer. Anal., (2021)]. Here, we present the modified (shifted-symmetric) piecewise quadratic polynomial collocation for solving the linear nonlocal diffusion model, which has the {\em symmetric positive definite system} and satisfies the discrete maximum principle. Using Faulhaber's formula and Riemann zeta function, the perturbation error for symmetric positive definite system and nonsymmetric indefinite systems are given. Then the detailed proof of the convergence analysis for the nonlocal models with the general horizon parameter $\delta=\mathcal{O}\left(h^\beta\right)$, $\beta\geq0$ are provided. More concretely, the global error is $\mathcal{O}\left(h^{\min\left\{2,1+\beta\right\}}\right)$ if $\delta$ is not set as a grid point, but it shall recover $\mathcal{O}\left(h^{\max\left\{2,4-2\beta\right\}}\right)$ when $\delta$ is set as a grid point. We also prove that the shifted-symmetric scheme is asymptotically compatible, which has the global error $\mathcal{O}\left(h^{\min\left\{2,2\beta\right\}}\right)$ as $\delta,h\rightarrow 0$. The numerical experiments (including two-dimensional case) are performed to verify the convergence., Comment: 23 pages

Optical spin-Hall effect (OSHE) is a spin-dependent transportation phenomenon of light as an analogy to its counterpart in condensed matter physics. Although being predicted and observed for decades, this effect has recently attracted enormous interests due to the development of metamaterials and metasurfaces, which can provide us tailor-made control of the light-matter interaction and spin-orbit interaction. In parallel to the developments of OSHE, metasurface gives us opportunities to manipulate OSHE in achieving a stronger response, a higher efficiency, a higher resolution, or more degrees of freedom in controlling the wave front. Here, we give an overview of the OSHE based on metasurface-enabled geometric phases in different kinds of configurational spaces and their applications on spin-dependent beam steering, focusing, holograms, structured light generation, and detection. These developments mark the beginning of a new era of spin-enabled optics for future optical components.

Following the emergence of many novel two-dimensional (2-D) materials beyond graphene, interest has grown in exploring implications for fundamental physics and practical applications, ranging from electronics, photonics, phononics, to thermal management and energy storage. In this Colloquium, we first summarize and compare the phonon properties, such as phonon dispersion and relaxation time, of pristine 2-D materials with single layer graphene to understand the role of crystal structure and dimension on thermal conductivity. We then compare the phonon properties, contrasting idealized 2-D crystals, realistic 2-D crystals, and 3-D crystals, and synthesizing this to develop a physical picture of how the sample size of 2-D materials affects their thermal conductivity. The effects of geometry, such as number of layers, and nanoribbon width, together with the presence of defects, mechanical strain, and substrate interactions, on the thermal properties of 2-D materials are discussed. Intercalation affects both the group velocities and phonon relaxation times of layered crystals and thus tunes the thermal conductivity along both the through-plane and basal-plane directions. We conclude with a discussion of the challenges in theoretical and experimental studies of thermal transport in 2-D materials. The rich and special phonon physics in 2-D materials make them promising candidates for exploring novel phenomena such as topological phonon effects and applications such as phononic quantum devices., This article has been accepted by Reviews of Modern Physics

Generating and detection coherent high-frequency heat-carrying phonons has been a great topic of interest in recent years. While there have been successful attempts in generating and observing coherent phonons, rigorous techniques to characterize and detect these phonon coherence in a crystalline material have been lagging compared to what has been achieved for photons. One main challenge is a lack of detailed understanding of how detection signals for phonons can be related to coherence. The quantum theory of photoelectric detection has greatly advanced the ability to characterize photon coherence in the last century and a similar theory for phonon detection is necessary. Here, we re-examine the optical sideband fluorescence technique that has been used detect high frequency phonons in materials with optically active defects. We apply the quantum theory of photodetection to the sideband technique and propose signatures in sideband photon-counting statistics and second-order correlation measurement of sideband signals that indicates the degree of phonon coherence. Our theory can be implemented in recently performed experiments to bridge the gap of determining phonon coherence to be on par with that of photons., Comment: 3 Figures

The direct production of ethanol from dextran industrial waste water was investigated by using Zymomonas mobilis via batch and semi-continuous fermentation mode. In batch fermentation, pretreated waste water (unsterilized and sterilized), pH value (3.8 and 6.0), and Mg2+ (with and without) was compared with OD600, sugar and ethanol concentration. After 24 h fermentation, sugar in the dextran waste water was almost exhausted, and the amount of ethanol accumulated reached 24.33–29.92 g/l, which is nearly 99% of the theoretical yield of ethanol. Kinetic parameters of Z. mobilis in batch fermentation were also investigated. The raw dextran waste water was also used in semi-continuous fermentation. After 48 h fermentation, the production of ethanol was 28.65 g/l. These results indicated that dextran waste water may be used as a candidate substrate and Z. mobilis could convert the raw material into ethanol directly.

A successful start-up enables acceleration of anaerobic digestion (AD) into steady state. The microbial community influences the AD performance during the start-up. To investigate how microbial communities changed during the start-up, microbial dynamics was analyzed via high-throughput sequencing in this study. The results confirmed that the AD was started up within 25 d. Thermophilic methanogens and bacterial members functioning in hydrolysis, acidogenesis, and syntrophic oxidation became predominant during the start-up stage, reflecting a quick adaption of microorganisms to operating conditions. Such predominance also indicated the great contribution of these members to the fast start-up of AD. Redundancy analysis confirmed that the bacterial abundance significantly correlated with AD conditions. The stable ratio of hydrogenotrophic methanogens to aceticlastic methanogens is also important to maintain the stability of the AD process. This work will be helpful to understand the contribution of microbial community to the start-up of AD.

We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear finite elements. Since the discretized error in a suitable norm can be bounded by the sum of interpolation error and its variants in different norms, we replace them by some terms which contain the Hessian matrix of the true solution, convective fields, and the geometric properties such as directed edges and the area of the triangle. Based on this observation, the shape, size and equidistribution requirements are used to derive the corresponding metric tensor and the stabilized parameters. It is easily found from our derivation that the optimal stabilized parameter is coupled with the optimal metric tensor on each element. Some numerical results are also provided to validate the stability and efficiency of the proposed numerical strategy., Comment: 24 pages, 4 figures

Piezoelectricity offers precise and robust conversion between electricity and mechanical force. Here we report the first experimental evidence of piezoelectricity in a single layer of molybdenum disulfide (MoS2) crystal as a result of inversion symmetry breaking of the atomic structure, with measured piezoelectric coefficient e11 = 2.9e-10 C/m. Through the angular dependence of electro-mechanical coupling, we uniquely determined the two-dimensional (2D) crystal orientation. We observed that only MoS2 membranes with odd number of layers exhibited piezoelectricity, in sharp contrast to the conventional materials. The piezoelectricity discovered in single molecular membrane promises scaling down of nano-electro-mechanical systems (NEMS) to single atomic unit cell - the ultimate material limit.

Heat flow control is essential for widespread applications of heating, cooling, energy conversion and utilization. Here we demonstrate the first observation of temperature-gated thermal rectification in vanadium dioxide beams, in which an environment temperature actively modulates asymmetric heat flow. In this three terminal device, there are two switchable states, which can be accessed by global heating: Rectifier state and Resistor state. In the Rectifier state, up to 28% thermal rectification is observed. In the Resistor state, the thermal rectification is significantly suppressed (below 4%). This temperature-gated rectifier can have substantial implications ranging from autonomous thermal management of micro/nanoscale devices to thermal energy conversion and storage.

A uniform strategy to derive metric tensors in two spatial dimension for interpolation errors and their gradients in $L^p$ norm is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in corresponding metric space, with the metric tensor being computed based on a posteriori error estimates in different norms. Numerical results show that the corresponding convergence rates are always optimal., Comment: 19 pages, 24 figures

This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)).

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on a posteriori error estimates proposed in \cite{YinXie}. The new metric tensor explores more comprehensive information of anisotropy for the true solution than those existing ones. Numerical results show that this approach can be successfully applied to deal with poisson and steady convection-dominated problems. The superior accuracy and efficiency of the new metric tensor to others is illustrated on various numerical examples of complex two-dimensional simulations., 18 pages, 18 figures

In this paper, we give a new type of a posteriori error estimators suitable for moving finite element methods under anisotropic meshes for general second-order elliptic problems. The computation of estimators is simple once corresponding Hessian matrix is recovered. Wonderful efficiency indices are shown in numerical experiments., 16 pages, 16 figures