Measurement of Random Surface Parameters of Weak Scatterers using the Speckle Contrast Method

Theoretical analysis shows that the deviation roughness ωand the lateral correlation length ξ of a weak scattering object determine the different properties of the contrast of the speckles in the image plane of a 4f system.Experimentally,we have measured the data of the speckle contrast versus the radius R of the variable filtering aperture.By fitting the theoretical results to these data,we extract the parameters ω and ξ of the random surfaces with Gaussian correlation.This method can determine the two parameters simultaneously and independently,and pre-calibrations are not needed.     

Calculation of Free Energy of the Integrable Landau—Lifshitz model

The generalized Bethe-ansatz method of thermodynamic analysis of integrable systems was employed to compute the free energy of a classical integrable model,i.e.the Landau-Lifshitz model.Using the action-angle variables of the model and by imposing a periodic boundary condition.we derive a phase-shifted density of states for the excitations of the system.The free energy,in the thermodynamic limit,can be expressed analytic in terms of two coupled nonlinear integral equations of the finie temperature excited energy for effective phonons and kinks (antikinks).we solve these equations iteratively for a special case that the model is in the limit of anisotropic strong yz coupling.     

First-principles study of the （001） surface of cubic PbHfO3 and BaHfO3

Using first-principles techniques,we investigate the(001) surfaces of cubic PbHfO3(PHO) and BaHfO3(BHO) terminated with both AO(A=Pb and Ba) and HfO2.Surface structure,partial density of states,band structure,and surface energy are obtained.The BaO surface is found to be similar to its counterpart in BHO.For the HfO2-terminated surface of cubic PHO,the largest relaxation appears on the second-layer atoms but not on the first-layer ones.The analysis of the structure relaxation parameters reveals that the rumpling of the(001) surface for PHO is stronger than that for BHO.The surface thermodynamic stability is explored,and it is found that both the PbO-and the BaO-terminated surfaces are more stable than the HfO2-terminated surfaces for PHO and BHO,respectively.The surface energy calculations show that the(001) surface of PHO is more easily constructed than that of BHO.     

New amplitude equation of single—mode laser

The white-gain model and the white-loss model of a single-mode laser are investigated in the presence of cross-correlations between the real and imaginary parts of quantum noise as well as pump noise. It was found that, like the white cubic model (2001 Chin. Phys. Lett. 18 370), the amplitude equations are all decoupled from the phase equations for the two models, and the same novel term appears in the amplitude equations of the two models. So we can put the amplitude equations of all the models into a general form, that is, the new amplitude equation. We further use this new amplitude equation to study specifically the stationary properties of the laser intensity for the white-gain model.     

Mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence

Main mathematical concepts and their physical foundation in the nonstandard analysis theory of turbulence are presented and discussed. The underlying fact is that there does not exist the absolute zero fluid-volume. Therefore, the physical object corresponding to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-particle corresponds to the uniform monad, while the nonuniform fluid-particle to the nonuniform monad. There are two kinds of the differentiations, one is based on the absolute point, and the other based on the monad. The former is adopted in the Navier--Stokes equations, and the latter in the fundamental equations presented in this paper for the nonstandard analysis theory of turbulence. The continuity of fluid is elucidated by virtue of the concepts of the fluid-particle and fluid-particle at a lower level. Furthermore, the characters of the continuity in two cases, i.e. in the standard and nonstandard analyses, are presented in this paper. And the difference in discretization between the Navier--Stokes equations and the fundamental equations given herein is also pointed out.     

On Light-Like Extremal Surfaces in Curved Spacetimes

In this paper, we find that under a diffeomorphic of nonlinear geodesic equations are concerned with light-like extremal surfaces in curved spaeetimes. It is interesting to transformation of variables, the light-like extremal surfaces can be described by a system Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.     

Elastic wave scattering from rough free surfaces of solids

Elastic wave scattering by a rough free surface of solids is analyzed. The analysis is based on the concept of scattering amplitude (SA) and perturbation approximation. The SA method is very convenient for rough surface scattering problems. By solving the boundary equations, the first and the second order solutions of approximate scattering amplitude are obtained. The general solutions are used for, as an example, the wave scattering by rough surfaces with Gaussian distribution. The mean field and variance are given. Finally, an experiment is designed to verifv the theoretical predications.     

Ionization Balance in Non-Local-Thermodynamic-Equilibrium Plasmas

A collisional-radiative model is developed for population calculations of plasmas in non-local thermodynamic equilibrium. The rate equations in detailed configuration accounting are solved to obtain ion populations. The configuration averaged rate coefficients are used in the rate equations. The cross sections are calculated based on the first perturbation theory. Wavefunctions required in cross section calculations are obtained by the Hartree-Fock-Slater self-consistent-field model. This kinetic model is applied to low- and medium-Z as well as high-Zplasmas. The results are compared with those of other theoretical models and experiments. The comparisons show that the present results of the mean charge statetheoretical ones, while for high-Z elements, the presentthe experimental ones.for low- and medium-Z elements agree well with other theoretical ones, while for high-Z elements, the present mean ionization stages are about two stages lower than the experimental ones.     

Consensus protocol for heterogeneous multi-agent systems: A Markov chain approach

This paper deals with the consensus problem for heterogeneous multi-agent systems. Different from most existing consensus protocols, we consider the consensus seeking of two types of agents, namely, active agents and passive agents. The objective is to directly control the active agents such that the states of all the agents would achieve consensus. In order to obtain a computational approach, we subtly introduce an appropriate Markov chain to cast the heterogeneous systems into a unified framework. Such a framework is helpful for tackling the constraints from passive agents. Furthermore, a sufficient and necessary condition is established to guarantee the consensus in heterogeneous multi-agent systems. Finally, simulation results are provided to verify the theoretical analysis and the effectiveness of the proposed protocol.     

Research on synthetic aperture radar imaging technology of one-dimensional layered rough surfaces

A quick and exact imaging method for one-dimensional layered rough surfaces is proposed in this paper to study the scattering characteristics of a layered medium that exists widely in nature.The boundary integral equations of layered rough surfaces are solved by using the propagation-inside-layer expansion combined with the forward and backward spectral acceleration method(PILE+FB-SA),and the back scattering data are obtained.Then,a conventional synthetic aperture radar(SAR) imaging procedure called back projection method is used to generate a two-dimensional(2D) image of the layered rough surfaces.Combined with the relative dielectric permittivity of realistic soil,the random rough surfaces with Gauss spectrum are used to simulate the layered medium with rough interfaces.Since the back scattering data are computed by using the fast numerical method,this method can be used to study layered rough surfaces with any parameter,which has a great application value in the detection and remote sensing areas.     

Large Slip Length over a Nanopatterned Surface

A thermodynamic method is employed to analyse the slip length of hydrophobic nanopatterned surface. The maximal slip lengths with respect to the hydrophobicity of the nanopatterned surface are computed. It is found that the slip length reaches more than 50 μm if the nanopatterned surfaces have a contact angle larger than 160°. Such results are expected to find extensive applications in micro-channels and helpful to understand recent experimental observations of the slippage of nanopatterned surfaces.     

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

Speckle fields are the random light wave distributions produced when the light fields are scattered from random surfaces or a random medium. They appear in many optical phenomena that are related to light propagations[1,2] and have found wide appli-cations in a variety of scientific and technical fields. The examples of the recent impor-tant applications of speckles include the analysis of the movement of the granules[3], the three-dimensional imaging for the microstructures of metal nanocryst…     

Quantum Transport and Surface Scattering in Magnetic Metallic Film

Taking into account the quantum size effect and the spin dependence of the electronic band structure, and including the spin dependence of the scattering from bulk impurities and two different sets of surface roughness, we present a theory on the electronic transport in magnetic film, in which the average autocorrelation function （ACF） for surface roughness is described by a Gaussion model. Our result shows that the conductivity is a sensitive function of surface roughness and exchange energy. It is also found that in the thin film limit and in the lower-order approximation of the surface scattering, the total conductivity is given by a sum of conductivities of all the subbands and the two spin channels, for each subband and each spin channel the scattering rates due to the impurities and two surfaces are additive.     

Heat transfer for boundary layers with cross flow

An analysis is presented to study the dual nature of solutions for the forced convective boundary layer flow and heat transfer in a cross flow with viscous dissipation terms in the energy equation. The governing equations are transformed into a set of three self-similar ordinary differential equations by similarity transformations. These equations are solved numerically using the very efficient shooting method. This study reveals that the dual solutions of the transformed similarity equations for velocity and temperature distributions exist for certain values of the moving parameter, Prandtl number, and Eckert numbers. The reverse heat flux is observed for larger Eckert numbers; that is, heat absorption at the wall occurs.     

An Approach to Biochemical Imaging of Heterogeneity in the Bio—tissue Simultaneously Using the Data of Reflectance and Transmittance of Diffuse—Photon Density Waves

An algorithm for the biochemical imaging of heterogeneity in the bio-tissue with finite parallel-plane geometry simultaneously using the data of reflectance and transmittance of diffuse-photon density waves is presented.In this algorithm,the priori knowledge of heterogeneity is not needed,This algorithm is suitable for the imaging of heterogeneity in the large volume tissue and is small organs.To reduce the errors produced by the algorithm,it is suggested that the experiment should be performed in two steps,at first step the light source should be placed at one boundary to measure the data of reflectance and transmittance,and these data are used to construct the heterogeneous function in the half space close to the light source;at the second step the light source should be placed at another boundary to measure the data of reflectance and transmittance,these data are used to construct the heterogeneous function in another half space closed to the light source;after taking above two steps the heterogeneous function in the whole space is constructed.     

Dynamics of surface motion on a rotating massive homogeneous body

It is of great interest to study the dynamical environment on the surface of non-spherical small bodies, especially for asteroids. This paper takes a simple case of a cube for instance, investigates the dynamics of a particle on the surface of a rotating homogeneous cube, and derives fruitful results. Due to the symmetrical characteristic of the cube, the analysis includes motions on two different types of surfaces. For each surface, both the frictionless and friction cases are considered. (i) Without consideration of friction, the surface equilibria in both of the different surfaces are examined and periodic orbits are derived. The analysis of equilibria and periodic orbits could assist understanding the skeleton of motions on the surface of asteroids. (ii) For the friction cases, the conditions that the particle does not escape from the surface are examined. Due to the effect of the friction, there exist the equilibrium regions on the surface where the particle stays at rest, and the locations of them are found. Finally, the dust collection regions are predicted. Future work will extend to real asteroid shapes.     

The AME 2020 atomic mass evaluation (I). Evaluation of input data,and adjustment procedures

This is the first of two articles(Part I and Part II)that presents the results of the new atomic mass evaluation,Ame2020.It includes complete information on the experimental input data that were used to derive the tables of recommended values which are given in Part II.This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction,decay and mass-spectrometric data which were used in a least-squares fit adjustment in order to determine the recommended mass values and their uncertainties.All input data,including both the accepted and rejected ones,are tabulated and compared with the adjusted values obtained from the least-squares fit analysis.Differences with the previous Ame2016 evaluation are discussed and specific examples are presented for several nuclides that may be of interest to Ame users.     

Scattering from Alpha-Stable Non-Gaussian Distributed Surfaces

The scattering problem of alpha-stable non-Gaussian distributed rough surfaces is studied. The alpha-stable non-Gaussian distribution is used to describe the surfaces that exhibit sharp and sparse peaks, not usually seen in Gaussian distributed surfaces. Then a magnetic field integral equation is formulated to calculate the scattered field and the scattering coefficient. Numerical simulations show that the magnitude distribution of the scattered field is affected significantly by the probability distribution of the surface when the height of the surface changes in a random way. In addition, simulation results are presented as bistatic scattering coefficient for alpha-stable distributed surfaces.     

Exact solutions and residual symmetries of the Ablowitz–Kaup–Newell–Segur system

The residual symmetries of the Ablowitz–Kaup–Newell–Segur(AKNS)equations are obtained by the truncated Painleve′analysis.The residual symmetries for the AKNS equations are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries of a prolonged AKNS system.The local Lie point symmetries of the prolonged AKNS equations are composed of the residual symmetries and the standard Lie point symmetries,which suggests that the residual symmetry method is a useful complement to the classical Lie group theory.The calculation on the symmetries shows that the enlarged equations are invariant under the scaling transformations,the space–time translations,and the shift translations.Three types of similarity solutions and the reduction equations are demonstrated.Furthermore,several types of exact solutions for the AKNS equations are obtained with the help of the symmetry method and the Bcklund transformations between the AKNS equations and the Schwarzian AKNS equation.     

Solutions of the nonlocal(2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy

The(2+1)-dimensional nonlocal breaking solitons AKNS hierarchy and the nonlocal negative order AKNS hierarchy are presented.Solutions in double Wronskian form of these two hierarchies are derived by means of a reduction technique from those of the unreduced hierarchies.The advantage of our method is that we start from the known solutions of the unreduced bilinear equations,and obtain solitons and multiple-pole solutions for the variety of classical and nonlocal reductions.Dynamical behaviors of some obtained solutions are illustrated.It is remarkable that for some real nonlocal equations,amplitudes of solutions are related to the independent variables that are reversed in the real nonlocal reductions.