A COMBINED REFRACTION-DIFFRACTION-DISSIPATION MODEL OF WAVE PROPAGATION

A numerical model based on the mild-slope equation of water wave propagation over complicated bathymetry,taking into account the combined effects of refraction,diffraction and dissipation due to wavebreaking is presented.Wave breaking is simulated by modifying the wave height probability density func-tion and the wave energy dissipation mechanism is parameterized according to that of the hydraulic jumpformulation.Solutions of the wave height,phase function,and the wave direction at every grid point areobtained by finite difference approximation of the governing equations,using Gauss-Seidel Iterative Method(GSIM)row by row.Its computational convenience allows it to be applied to large coast regions tostudy the wave transformation problem.Several case studies have been made and the results compare verywell with the experiment data and other model solutions.The capability and utility of the model forreal coast areas are illustrated by application to a shallow bay of northeast Australia.

Water Wave Refraction and Diffraction over Frictional Topography

This paper considers the effect of wave energy dissipation induced by sea-bottom friction on the computational results of water wave refraction and diffraction with the parabolic equation method. The presented results show that the friction factor formula adopted in this paper is of higher numerical accuracy than that introduced by Dalrymphe (1984), and it can be used to compute wave propagation over large open areas.

Numerical Modeling of Wave Diffraction-Refraction in Water of Varying Current and Topography

A numerical model for wave diffracrion-refraction in water of varying current and topography is proposed, and time-dependent wave mild-slope equation with a dissipation term and corresponding equivalent: governing equations are presented. Two different expressions of parabolic approximations for the case of the absence of current are also given and analyzed. The influence of current on the results of simulation of waves is discussed. Some examples show that the present model is better than others in simulating wave transformation in large water areas. And they also show that the influence of current should be taken into account, on numerical modeling of wave propagation in water of strong current and coastal areas, otherwise the modeling results will be largely distorted.

Mathematical Models for Combined Refraction-Diffraction of Waves on Non-Uniform Current and Depth

Two mathematical models for combined refraction-diffraction of regular and irregular waves on non-uniform current in water of slowly varying topography are presented in this paper. Model I is derived by wave theory and variational principle separately. It has two kinds of expressions including the dissipation term. Model n is based on the energy conservation equation with energy flux through the wave crest lines in orthogonal curvilinear coordinates and the wave kinematic conservation equation. The analysis and comparison and special cases of these two models are also given.

Numerical Simulation for Refraction-Diffraction of Waves in Water of Slowly Varying Current and Topography

A new numerical finite difference iteration method for refraction-diffraction of waves ia water of slowly varying current and topography is developed in this paper. And corresponding theoretical model including the dissipation term is briefly described, together with some analysis and comparison of computational results of the model with measurements in a hydraulic scale model (Berkhoff et al., 1982). An example of practical use of the method is given, showing that the present model is useful to engineering practice.

Computation of Wave Refraction-Diffraction with Error Vector Propagation Method

After modifying the basic computation model made by Panchang (1988), the error vector propagation (EVP) method has been adopted to compute the combined effects of water wave refraction and diffraction in the presence of reflection boundary. The results show that the present method is successful in restraining the noise in Panchang's solution. Compared to other numerical methods for the mild-slope wave equation, EVP method can both consider the influence of reflection and save computer memory and computing time.

Combined refraction and diffraction models for sea waves over complicated topography and with currents in shallow water

-Combined refraction and diffraction models in the form of linear parabolic approximation are derived through smallparameter method. More strictly theoretical basis and more accuracy in the models than Lozano's (1980) are obtained. Some theoretical defects in Liu's model (1985) with consideration of current are not only found but also eliminated. More strict and accurate models are, therefore, presented in this paper.The calculation results and analysis in applying the models to actual wave field with consideration of bottom friction will be given in the following paper.

Wave Refraction-Diffraction in the Presence of a Current

-Wave refraction-diffraction due to a large ocean structure and topography in the presence of a 'current are studied numerically. The mathematical model is the mild-slope equation developed by Kirby (1984). This equation is solved using a finite and boundary element method. The physical domain is devid-ed into two regions: a slowly varying topography region and a constant water depth region. For waves propagating in the constant water depth region, without current interfering, the mild- slope equation is then reduced to the Helmholtz equation which is solved by boundary element method. In varying topography region, this equation will be solved by finite element method. Conservation of mass and energy flux of the fluid between these two regions is required for composition of these two numerical methods. The numerical scheme proposed here is capable of dealing with water wave problems of different water depths with the main characters of these two methods.

Refraction-Diffraction Mathematical Model for Waves With Lateral Energy Transmission Mechanism and Its Verification

To solve problems concerning wave elements and wave propagation, an effective way is the wave energy balance equation, which is widely applied in oceanography and ocean dynamics for its simple computation. The present papaer advances wave energy balance equations considering lateral energy transmission and energy loss as the governing equation for the study of wave refraction-diffraction. For the mathematical model, numerical simulation is made by means of difference method, and the result is verified with two examples.

Microstructures and micromechanical behaviors of high -entropy alloys investigated by synchrotron X-ray and neutron diffraction techniques: A review

High-entropy alloys(HEAs)possess outstanding features such as corrosion resistance,irradiation resistance,and good mechan-ical properties.A few HEAs have found applications in the fields of aerospace and defense.Extensive studies on the deformation mech-anisms of HEAs can guide microstructure control and toughness design,which is vital for understanding and studying state-of-the-art structural materials.Synchrotron X-ray and neutron diffraction are necessary techniques for materials science research,especially for in situ coupling of physical/chemical fields and for resolving macro/microcrystallographic information on materials.Recently,several re-searchers have applied synchrotron X-ray and neutron diffraction methods to study the deformation mechanisms,phase transformations,stress behaviors,and in situ processes of HEAs,such as variable-temperature,high-pressure,and hydrogenation processes.In this review,the principles and development of synchrotron X-ray and neutron diffraction are presented,and their applications in the deformation mechanisms of HEAs are discussed.The factors that influence the deformation mechanisms of HEAs are also outlined.This review fo-cuses on the microstructures and micromechanical behaviors during tension/compression or creep/fatigue deformation and the application of synchrotron X-ray and neutron diffraction methods to the characterization of dislocations,stacking faults,twins,phases,and intergrain/interphase stress changes.Perspectives on future developments of synchrotron X-ray and neutron diffraction and on research directions on the deformation mechanisms of novel metals are discussed.

Relative peripheral refraction in school children with different refractive errors using a novel multispectral refraction topographer

AIM:To compare relative peripheral refraction(RPR)in Chinese school children with different refractive errors using multispectral refraction topography(MRT).METHODS:A total of 713 eyes of primary school children[172 emmetropia(E),429 low myopia(LM),80 moderate myopia(MM),and 32 low hypermetropia(LH)]aged 10 to 13y were analyzed.RPRs were measured using MRT without mydriasis.MRT results showed RPR at 0-15°(RPR 0-15),15°-30°(RPR 15-30),and 30°-45°(RPR 30-45)annular in the inferior(RPR-I),superior(RPR-S),nasal(RPR-N),and temporal(RPR-T)quadrants.Spherical equivalent(SE)was detected and calculated using an autorefractor.RESULTS:There were significant differences of RPR 15-30 between groups MM[0.02(-0.12;0.18)]and LH[-0.13(-0.36;0.12)](P<0.05),MM and E[-0.06(-0.20;0.10)](P<0.05),and LM[-0.02(-0.15;0.15)]and E(P<0.05).There were also significant differences of RPR 30-45 between groups MM[0.45(0.18;0.74)]and E[0.29(-0.09;0.67)](P<0.05),and LM[0.44(0.14;0.76)]and E(P<0.001).RPR values increased from the hyperopic to medium myopic group in each annular.There were significant differences of RPR-S between groups MM[-0.02(-0.60;0.30)]and E[-0.44(-0.89;-0.04)](P<0.001),and LM[-0.28(-0.71;0.12)]and E(P<0.05).There were also significant differences of RPR-T between groups MM[0.37(0.21;0.78)]and LH[0.14(-0.52;0.50)](P<0.05),LM[0.41(0.06;0.84)]and LH(P<0.05),and LM and E[0.29(-0.10;0.68),P<0.05].A Spearman’s correlation analysis showed a negative correlation between RPR and SE in the 15°-30°(P=0.005),30°-45°(P<0.05)annular(P=0.002),superior(P<0.001),and temporal(P=0.001)quadrants.CONCLUSION:Without pupil dilation,values for RPR 15-30,30-45,RPR-S,and T shows significant differences between myopic eyes and emmetropia,and the differences are negatively correlated with SE.

Refraction difference value variations in children and adolescents with different refractive errors

AIM:To evaluate the refraction difference value(RDV)variations in children and adolescents with different refractive errors and analyze its correlation with refractive development.METHODS:Participants aged 4-16y with different refractive statuses(hyperopia,emmetropia,myopia)underwent comprehensive eye examinations,including spherical equivalent(SE)refraction,axial length(AL),total RDV(TRDV),and RDVs at various eccentricities(0°-15°,15°-30°,30°-45°)and quadrants(inferior,superior,nasal,temporal).Statistical analysis involved one-way ANOVA for group comparisons and Pearson correlation for examining relationships between SE/AL and RDVs.Paired t-tests compared quadrant-specific RDVs within groups.RESULTS:Significant difference was found in TRDV(P<0.001),RDV15°-30°(P=0.033),RDV30°-45°(P<0.001),RDV-inferior(RDV-I,P<0.001)and RDV-temporal(RDV-T,P<0.001)among hyperopia,emmetropia and myopia group.Pearson correlation analysis revealed a negative correlation of SE with TRDV(P=0.001),RDV30°-45°(P=0.004),RDV-I(P=0.047),and RDV-T(P<0.001).The differences between RDV-superior(RDV-S)and RDV-I were statistically significant in all groups(P<0.001 for all)and between RDV-T and RDV-nasal(RDV-N)were statistically significant in hyperopia group(P<0.001).Within the premyopic group,the analysis revealed a negative correlation of SE with RDV-I(P=0.009).Pearson correlation analysis revealed a positive correlation of AL with TRDV(P=0.036),RDV15°-30°(P=0.004),RDV30°-45°(P<0.001),RDV-S(P=0.003),RDV-I(P<0.001),RDV-T(P<0.001),RDV-N(P=0.022),while revealed a negative correlation of AL with RDV0-15°(P=0.018).CONCLUSION:Our study indicates TRDV,RDV30°-45°,RDV-I,RDV-T may relate to refractive development,and a negative correlation between SE and RDV-I in pre-myopic children.

Direct visualization of laser-driven dynamic fragmentation in tin by in situ x-ray diffraction

We present a novel method for investigating laser-driven dynamic fragmentation in tin using in situ X-ray diffraction.Our experimental results demonstrate the feasibility of the method for simultaneously identifying the phase and temperature of fragments through analysis of the diffraction pattern.Surprisingly,we observe a deviation from the widely accepted isentropic release assumption,with the temperature of the fragments being found to be more than 100 K higher than expected,owing to the release of plastic work during dynamic fragmentation.Our findings are further verified through extensive large-scale molecular dynamics simulations,in which strain energies are found to be transferred into thermal energies during the nucleation and growth of voids,leading to an increase in temperature.Our findings thus provide crucial insights into the impact-driven dynamic fragmentation phenomenon and reveal the significant influence of plastic work on material response during shock release.

Intensity correlation properties of x-ray beams split with Laue diffraction

Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.

Dispersion Relations in Diffraction in Time

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.

Surface diffraction beamline at the SSRF

BL02U2 of the Shanghai Synchrotron Radiation Facility is a surface diffraction beamline with a photon flux of 5.5×10^(12) photons/s at 10 keV and a beam size of 160µm×80µm at the sample site.It is dedicated to studying surfaces(solid-vacuum,solid-gas)and interfaces(solid-solid,solid-liquid,and liquid-liquid)in nanoscience,condensed matter,and soft matter systems using various surface scattering techniques over an energy range of 4.8-28 keV with transmission and reflection modes.Moreover,BL02U2 has a high energy resolution,high angular resolution,and low beam divergence,which can provide excellent properties for X-ray diffraction experiments,such as grazing incident X-ray diffraction,X-ray reflectivity,crystal truncation rods,and liquid X-ray scattering.Diversity of in situ environments can also be provided for the samples studied.This paper describes the setup of the new beamline and its applications in various fields.

Analytical Method for the Wave Diffraction of Asymmetrically Arranged Breakwaters

The layout forms of several breakwater structures can be generalized as asymmetrical arrangements in actual engineering.However,the problem of wave diffraction around asymmetrically arranged breakwaters has not been adequately investigated.In this study,we propose an analytical method of wave diffraction for regular waves passing through asymmetrically arranged breakwaters,and we use the Nyström method to obtain the analytical solution numerically.We compared the results of this method with those of previous analytical solutions and with numerical results to demonstrate the validity of our approach.We also provided diffraction coefficient diagrams of breakwaters with different layout forms.Moreover,we described the analytical expression for the problem of diffraction through long-wave incident breakwaters and presented an analysis of the relationship between the diffraction coefficients and the widths of breakwater gates.The analytical method presented in this study contributes to the limited literature on the theory of wave diffraction through asymmetrically arranged breakwaters.

A novel self-alignment method for high precision silicon diffraction microlens arrays preparation and its integration with infrared focal plane arrays

Silicon(Si)diffraction microlens arrays are usually used to integrating with infrared focal plane arrays(IRFPAs)to improve their performance.The errors of lithography are unavoidable in the process of the Si diffrac-tion microlens arrays preparation in the conventional engraving method.It has a serious impact on its performance and subsequent applications.In response to the problem of errors of Si diffraction microlens arrays in the conven-tional method,a novel self-alignment method for high precision Si diffraction microlens arrays preparation is pro-posed.The accuracy of the Si diffractive microlens arrays preparation is determined by the accuracy of the first li-thography mask in the novel self-alignment method.In the subsequent etching,the etched area will be protected by the mask layer and the sacrifice layer or the protective layer.The unprotection area is carved to effectively block the non-etching areas,accurately etch the etching area required,and solve the problem of errors.The high precision Si diffraction microlens arrays are obtained by the novel self-alignment method and the diffraction effi-ciency could reach 92.6%.After integrating with IRFPAs,the average blackbody responsity increased by 8.3%,and the average blackbody detectivity increased by 10.3%.It indicates that the Si diffraction microlens arrays can improve the filling factor and reduce crosstalk of IRFPAs through convergence,thereby improving the perfor-mance of the IRFPAs.The results are of great reference significance for improving their performance through opti-mizing the preparation level of micro nano devices.

Reconfigurable mechanism-based metamaterials for ternary-coded elastic wave polarizers and programmable refraction control

Elastic metamaterials with unusual elastic properties offer unprecedented ways to modulate the polarization and propagation of elastic waves.However,most of them rely on the resonant structural components,and thus are frequency-dependent and unchangeable.Here,we present a reconfigurable 2D mechanism-based metamaterial which possesses transformable and frequency-independent elastic properties.Based on the proposed mechanism-based metamaterial,interesting functionalities,such as ternarycoded elastic wave polarizer and programmable refraction,are demonstrated.Particularly,unique ternary-coded polarizers,with 1-trit polarization filtering and 2-trit polarization separating of longitudinal and transverse waves,are first achieved.Then,the strong anisotropy of the proposed metamaterial is harnessed to realize positive-negative bi-refraction,only-positive refraction,and only-negative refraction.Finally,the wave functions with detailed microstructures are numerically verified.

A robust triaxial localization method of AE source using refraction path

Acoustic emission(AE)localization algorithms based on homogeneous media or single-velocity are less accurate when applied to the triaxial localization experiments.To the end,a robust triaxial localization method of AE source using refraction path is proposed.Firstly,the control equation of the refraction path is established according to the sensor coordinates and arrival times.Secondly,considering the influence of time-difference-of-arrival(TDOA)errors,the residual of the governing equation is calculated to estimate the equation weight.Thirdly,the refraction points in different directions are solved using Snell’s law and orthogonal constraints.Finally,the source coordinates are iteratively solved by weighted correction terms.The feasibility and accuracy of the proposed method are verified by pencil-lead breaking experiments.The simulation results show that the new method is almost unaffected by the refraction ratio,and always holds more stable and accurate positioning performance than the traditional method under different ratios and scales of TDOA outliers.