ON CAUCHY PROBLEMS FOR THE RLW EQUATION IN TWO SPACE DIMENSIONS

A cnoidal wave solution of the two dimensional RLW equation of are obtained by elliptic integral method. and the some estimations the uniqueness and the stability of the periodic solution with both x, y to the Cauchy problem are proved by the priori estimations.

CONVERGENCE OF A CONSERVATIVE DIFFERENCE SCHEME FOR THE ZAKHAROV EQUATIONS IN TWO DIMENSIONS

A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in L-2 norm, the convergence of the difference solution is proved in order O(h(2) + r(2)). In the proof, a new skill is used to deal with the term of difference quotient (e(j,k)(n))t. This is necessary, since there is no estimate of E(x, y, t) in L-infinity norm.

Superconvergence Analysis of the Runge-Kutta Discontinuous Galerkin Method with Upwind-Biased Numerical Flux for Two-Dimensional Linear Hyperbolic Equation

In this paper,we shall establish the superconvergence properties of the Runge-Kutta dis-continuous Galerkin method for solving two-dimensional linear constant hyperbolic equa-tion,where the upwind-biased numerical flux is used.By suitably defining the correction function and deeply understanding the mechanisms when the spatial derivatives and the correction manipulations are carried out along the same or different directions,we obtain the superconvergence results on the node averages,the numerical fluxes,the cell averages,the solution and the spatial derivatives.The superconvergence properties in space are pre-served as the semi-discrete method,and time discretization solely produces an optimal order error in time.Some numerical experiments also are given.

A Two-Dimension Time-Domain Comparator for Low Power SAR ADCs

This paper presents a two-dimension time-domain comparator suitable for low power successive-approximation register(SAR)analog-to-digital converters(ADCs).The proposed two-dimension time-domain comparator consists of a ring oscillator collapse-based comparator and a counter.The propagation delay of a voltage controlled ring oscillator depends on the input.Thus,the comparator can automatically change the comparison time according to its input difference,which can adjust the power consumption of the comparator dynamically without any control logic.And a counter is utilized to count the cycle needed to finish a comparison when the input difference is small.Thus,the proposed comparator can not only provide the polarity of the input,but also the amount information of the input,which helps to skip most of the SAR cycles when the initial input is small.Thus,most energy can be saved when the initial input is small.The proposed time-domain comparator is designed in 0.18μm CMOS technology.Simulation results demonstrate that the comparator can not only save power consumption,but also give the design flexibility,and the current is only nA level when the supply voltage is 0.6 V.

Effects of weathering depth and thickness on rock failure:Experimental approach and particle flow code simulation

This study investigated the effects of weathering depth and thickness on the failure mechanisms of rock samples through experimental and numerical methods.The first configuration involved conducting artificial weathering on limestone using the freezing and thawing(F-T)for 40 cycles.The mechanical parameters of the samples were measured at the end of the 40th cycle.In the second configuration,a series of specimens underwent salt crystallization(S-C)tests for 20 cycles.Experimental results were validated using discrete element method(DEM).Next,the weathered limestone model with dimensions of 108 mm54 mm were prepared.The weathering layers were tested at four different thicknesses(i.e.2.5 mm,5 mm,7.5 mm,and 10 mm)and three different positions(at the surface,5 mm under the rock surface,and 10 mm under the rock surface).According to the results,weathering depth and thickness have a considerable effect on the failure process.The results also showed a correlation between the values of compressive strength and failure mechanisms associated with the weathering layer.The numerical results revealed that the tension crack was the dominant factor.Additionally,with increasing weathering thickness,Young's modulus,crack initiation stress,and final strength decreased in constant weathering depth.The results also demonstrated that the failure progress of the numerical models was similar to that observed in the laboratory.

Degenerate States in Nonlinear Sigma Model with SU(2) Symmetry

Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.

Investigation of Rotor Radial Rotating Error upon AMB System

This paper first suggests the use of the Fourier frequency transmission method of two dimensions function （ 2D FFT） to analyze radial rotating errors that occurred in a rotor. Based on this method a magnetic rotor is measured. The authors point out that the main cause to affect radial rotating accuracy of the rotating shaft at a high speed is the dynamic imbalance of the shaft itself. Finally the feedforward control scheme is suggested to improve the accuracy of the shaft in an active magnetic bearing （ AMB ） system.

Highly efficient fluoride removal from water using 2D metal-organic frameworks MIL-53(Al)with rich Al and O adsorptive centers

In this study,metal-organic framework MIL-53(Al)was synthesized and studied to understand the different mechanisms between normal MIL-53(Al)and 2D metal-organic framework MIL-53(Al)for removing fluoride.Comparatively,the 2D MIL-53(Al)had two-dimensional linear morphology rather than block shape,indicating more expose adsorptive sites than normal MIL-53(Al).The batch adsorption experiments were applied to investigate the performance of 2D MIL-53(Al),including pH,adsorption kinetics,and thermodynamics.The 2D MIL-53(Al)(75.50 mg/g)showed better adsorption capacity than normal MIL-53(Al)(35.63 mg/g).The adsorption process of 2D MIL-53(Al)followed the pseudo-firstorder model and Langmuir model.The adsorption mechanism of this material was further studied by using experimental characterization and density functional theory calculations in detail.The main adsorptive sites were Al and O in the 2D MIL-53(Al),and the relationship between fluoride binding with Al and O was HF^(-)_(2)>HF>F^(-).The species of fluoride were HF2
,HF,F at different pH and concentrations.Hence,this study provides a significant way on the application of two-dimensional materials for removing fluoride.

A Cloud Detection Method for Landsat 8 Satellite Remote Sensing Images Based on Improved CDNet Model

Cloud detection in remote sensing images is a crucial task in various applications,such as meteorological disaster prediction and earth resource exploration,which require accurate cloud identi¯cation.This work proposes a cloud detection model based on the Cloud Detection neural Network(CDNet),incorporating a fusion mechanism of channel and spatial attention.Depthwise separable convolution is adopted to achieve a lightweight network model and enhance the e±ciency of network training and detection.In addition,the Convolutional Block Attention Module(CBAM)is integrated into the network to train the cloud detection model with attention features in channel and spatial dimensions.Experiments were conducted on Landsat 8 imagery to validate the proposed improved CDNet.Averaged over all testing images,the overall accuracy(OA),mean Pixel Accuracy(mPA),Kappa coe±cient and Mean Intersection over Union(MIoU)of improved CDNet were 96.38%,81.18%,96.05%,and 84.69%,respectively.Those results were better than the original CDNet and DeeplabV3+.Experiment results show that the improved CDNet is e®ective and robust for cloud detection in remote sensing images.