Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Strong synergy between physical and chemical properties:Insight into optimization of atomically dispersed oxygen reduction catalysts

Atomically dispersed catalysts exhibit significant influence on facilitating the sluggish oxygen reduction reaction(ORR)kinetics with high atom economy,owing to remarkable attributes including nearly 100%atomic utilization and exceptional catalytic functionality.Furthermore,accurately controlling atomic physical properties including spin,charge,orbital,and lattice degrees of atomically dispersed catalysts can realize the optimized chemical properties including maximum atom utilization efficiency,homogenous active centers,and satisfactory catalytic performance,but remains elusive.Here,through physical and chemical insight,we review and systematically summarize the strategies to optimize atomically dispersed ORR catalysts including adjusting the atomic coordination environment,adjacent electronic orbital and site density,and the choice of dual-atom sites.Then the emphasis is on the fundamental understanding of the correlation between the physical property and the catalytic behavior for atomically dispersed catalysts.Finally,an overview of the existing challenges and prospects to illustrate the current obstacles and potential opportunities for the advancement of atomically dispersed catalysts in the realm of electrocatalytic reactions is offered.

Tunable dispersion relations manipulated by strain in skyrmion-based magnonic crystals

We theoretically investigate the propagation characteristics of spin waves in skyrmion-based magnonic crystals. It is found that the dispersion relation can be manipulated by strains through magneto-elastic coupling. Especially, the allowed bands and forbidden bands in dispersion relations shift to higher frequency with strain changing from compressive to tensile,while shifting to lower frequency with strain changing from tensile to compressive. We also confirm that the spin wave with specific frequency can pass the magnonic crystal or be blocked by tuning the strains. The result provides an advanced platform for studying the tunable skyrmion-based spin wave devices.

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

Reconstructions of time-evolving sound-speed fields perturbed by deformed and dispersive internal solitary waves in shallow water

The high-fidelity reconstruction of sound speeds is crucial for predicting acoustic propagation in shallow water where internal solitary waves(ISWs)are prevalent.Mapping temperatures from time series to spatial fields is an approach widely used to reproduce the sound speed perturbed by deformed internal waves.However,wave-shape distortions are inherent in the modeling results.This paper analyzes the formation mechanism and dynamic behavior of the distorted waveform that is shown to arise from the mismatch between the modeled and real propagation speeds of individual solitons within an ISW packet.To mitigate distortions,a reconstruction method incorporating the dispersion property of an ISW train is proposed here.The principle is to assign each soliton a real speed observed in the experiment.Then,the modeled solitons propagate at their intrinsic speeds,and the packet disperses naturally with time.The method is applied to reconstruct the sound speed perturbed by ISWs in the South China Sea.The mean and median of the root-mean-square error between the reconstructed and measured sound speeds are below 2 m/s.The modeled shape deformations and packet dispersion agree well with observations,and the waveform distortion is reduced compared with the original method.This work ensures the high fidelity of waveguide-environment reconstructions and facilitates the investigation of sound propagation in the future.

Effects of Nano-CaCO_(3)Addition on Properties of Corundum-based Dispersive Purging Plugs

In order to improve the properties of corundum based dispersive purging plugs,dispersive purging plug specimens were prepared using tabular corundum(1-0.15 and≤0.15 mm)as the aggregates,tabular corundum(≤0.044 mm)andα-Al_(2)O_(3)micropowder(d_(50)=0.6μm)as the matrix,Secar 71 cement as the binder,introducing different amounts of nano-CaCO_(3),casting into shapes,and firing at different temperatures(1200 or 1600℃)for 4 h.The effects of the nano-CaCO_(3) extra-addition(0,0.5%,1.0%,1.5%and 2.0%,by mass)on the consistency of the castables as well as the properties and microstructure of the dispersive purging plug specimens were studied.The results show that:(1)with the fixed water addition,the consistency of the corundum castables decreases as the nano-CaCO_(3)addition increases;(2)with the increasing nano-CaCO_(3)addition,the bulk density of the specimens fired at different temperatures for 4 h decreases,the apparent porosity,the cold strength and the hot modulus of rupture all increase,the gas permeability does not change significantly;(3)the specimens fired at 1600℃ for 4 h have obviously better cold comprehensive performance than those fired at 1200℃for 4 h;(4)when the nano-CaCO_(3)addition is 1.5%,the comprehensive performance of the specimen is the optimal.

Energy-dispersive X-ray Spectroscopy for the Quantitative Analysis of Pyrite Thin Specimens

To explore ways to improve the accuracy of quantitative analysis of samples in the micrometer to nanometer range of magnitudes,we adopted analytical transmission electron microscopy(AEM/EDS)for qualitative and quantitative analysis of pyrite materials.Additionally,the k factor of pyrite is calculated experimentally.To develop an appropriate non-standard quantitative analysis model for pyrite materials,the experimentally calculated k factor is compared with that estimated from the non-standard quantitative analytical model of the instrument software.The experimental findings demonstrate that the EDS attached to a TEM can be employed for precise quantitative analysis of micro-and nanoscale regions of pyrite materials.Furthermore,it serves as a reference for improving the results of the EDS quantitative analysis of other sulfides.

Patterns and drivers of avian taxonomic and phylogenetic beta diversity in China vary across geographical backgrounds and dispersal abilities

Geographical background and dispersal ability may strongly influence assemblage dissimilarity;however,these aspects have generally been overlooked in previous large-scale beta diversity studies.Here,we examined whether the patterns and drivers of taxonomic beta diversity(TBD)and phylogenetic beta diversity(PBD)of breeding birds in China vary across(1)regions on both sides of the Hu Line,which demarcates China’s topographical,climatic,economic,and social patterns,and(2)species with different dispersal ability.TBD and PBD were calculated and partitioned into turnover and nestedness components using a moving window approach.Variables representing climate,habitat heterogeneity,and habitat quality were employed to evaluate the effects of environmental filtering.Spatial distance was considered to assess the impact of dispersal limitation.Variance partitioning analysis was applied to assess the relative roles of these variables.In general,the values of TBD and PBD were high in mountainous areas and were largely determined by environmental filtering.However,different dominant environmental filters on either side of the Hu Line led to divergent beta diversity patterns.Specifically,climate-driven species turnover and habitat heterogeneity-related species nestedness dominated the regions east and west of the line,respectively.Additionally,bird species with stronger dispersal ability were more susceptible to environmental filtering,resulting in more homogeneous assemblages.Our results indicated that regions with distinctive geographical backgrounds may present different ecological factors that lead to divergent assemblage dissimilarity patterns,and dispersal ability determines the response of assemblages to these ecological factors.Identifying a single universal explanation for the observed pattern without considering these aspects may lead to simplistic or incomplete conclusions.Consequently,a comprehensive understanding of large-scale beta diversity patterns and effective planning of conservation strategies necessitate the consideration of both geographical background and species dispersal ability.

Modeling Analysis of Factors Influencing Wind-Borne Seed Dispersal: A Case Study on Dandelion

A weed is a plant that thrives in areas of human disturbance, such as gardens, fields, pastures, waysides, and waste places where it is not intentionally cultivated. Dispersal affects community dynamics and vegetation response to global change. The process of seed disposal is influenced by wind, which plays a crucial role in determining the distance and probability of seed dispersal. Existing models of seed dispersal consider wind direction but fail to incorporate wind intensity. In this paper, a novel seed disposal model was proposed in this paper, incorporating wind intensity based on relevant references. According to various climatic conditions, including temperate, arid, and tropical regions, three specific regions were selected to establish a wind dispersal model that accurately reflects the density function distribution of dispersal distance. Additionally, dandelions growth is influenced by a multitude of factors, encompassing temperature, humidity, climate, and various environmental variables that necessitate meticulous consideration. Based on Factor Analysis model, which completely considers temperature, precipitation, solar radiation, wind, and land carrying capacity, a conclusion is presented, indicating that the growth of seeds is primarily influenced by plant attributes and climate conditions, with the former exerting a relatively stronger impact. Subsequently, the remaining two plants were chosen based on seed weight, yielding consistent conclusion.

Discontinuities of Banana Integrals in Dispersion Relation Representation

We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic integrals,these identities enable the reduction of various p-DOBIs to be a linear combination of some fundamental ones.We present a practical application of p-DOBIs for deriving the Picard–Fuchs operator.Then we establish the expression of generalized dispersion relation,which enables us to obtain the dispersion relation representation of arbitrary banana integrals.Moreover,we propose a hypothesis for generalized dispersion relation and p-DOBIs,which provides a simple way to calculate the discontinuities and transform dispersion relation representation to p-DOBIs.

A simple atomization approach enables monolayer dispersion of nano graphenes in cementitious composites with excellent strength gains

Carbon nano additives(CNAs)are critical to achieving the unique properties of functionalized composites,however,controlling the dispersion of CNAs in material matrix is always a challenging task.In this study,a simple atomization approach was successfully developed to promote the dispersion efficiency of graphene nanoplatelets(GNPs)in cement composites.This atomization approach can be integrated with the direct,indirect and combined ultrasonic stirrings in a homemade automatic stirring-atomization device.Mechanical and microstructure tests were performed on hardened cement pastes blended with GNPs in different stirring and mixing approaches.Results show that the direct ultrasonic stirrings enabled more homogeneous dispersions of GNP particles with a smaller size for a longer duration.The atomized droplets with the mean size of~100μm largely mitigated GNPs’agglomerations.Monolayer GNPs were observed in the cement matrix with the strength gain by up to 54%,and the total porosity decrease by 21%in 0.3 wt%GNPs dosage.The greatly enhanced dispersion efficiency of GNPs in cement also raised the cement hydration.This work provides an effective and manpower saving technique toward dispersing CNAs in engineering materials with great industrialization prospects.

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.

Real-time data processing method for CO_(2) dispersion interferometer on EAST

A real-time data processing system is designed for the carbon dioxide dispersion interferometer(CO_(2)-DI)on EAST.The system utilizes the parallel and pipelining capabilities of an fieldprogrammable gate array(FPGA)to digitize and process the intensity of signals from the detector.Finally,the real-time electron density signals are exported through a digital-to-analog converter(DAC)module in the form of analog signals.The system has been successfully applied in the CO_(2)-DI system to provide low-latency electron density input to the plasma control system on EAST.Experimental results of the latest campaign with long-pulse discharges on EAST(2022–2023)demonstrate that the system can respond effectively in the case of rapid density changes,proving its reliability and accuracy for future electron density calculation.

CFD-PBM coupled modeling of the liquid-liquid dispersion characteristics and structure optimization for Kenics static mixer

Kenics static mixers(KSM)are extensively used in industrial mixing-reaction processes by virtue of high mixing efficiency,low power homogenization and easy continuous production.Resolving liquid droplet size and its distribution and thus revealing the dispersion characteristics are of great significance for structural optimization and process intensification in the KSM.In this work,a computational fluid dynamics-population balance model(CFD-PBM)coupled method is employed to systematically investigate the effects of operating conditions and structural parameters of KSM on droplet size and its distribution,to further reveal the liquid-liquid dispersion characteristics.Results indicate that higher Reynolds numbers or higher dispersed phase volume fractions increase energy dissipation,reducing Sauter mean diameter(SMD)of dispersed phase droplets and with a shift in droplet size distribution(DSD)towards smaller size.Smaller aspect ratios,greater blade twist and assembly angles amplify shear rate,leading to smaller droplet size and a narrower DSD in the smaller range.The degree of impact exerted by the aspect ratio is notably greater.Notably,mixing elements with different spin enhance shear and stretching efficiency.Compared to the same spin,SMD becomes 3.7-5.8 times smaller in the smaller size range with a significantly narrower distribution.Taking into account the pressure drop and efficiency in a comprehensive manner,optimized structural parameters for the mixing element encompass an aspect ratio of 1-1.5,a blade twist angle of 180°,an assembly angle of 90°,and interlaced assembly of adjacent elements with different spin.This work provides vital theoretical underpinning and future reference for enhancing KSM performance.

Effect of trigger system on experimental dispersion characteristics of active surface wave testing

A trigger system is typically employed in active seismic testing to trigger and synchronize multichannel surface wave data acquisition.The effect of the trigger system on the dispersion image of surface waves is empirically known to be negligible,however,theoretical explanation regarding the effect of the trigger system is insufficient.This study systematically examines the theory for surface wave dispersion analysis and proves that the effect of the trigger system on a dispersion image is negligible via a solid theoretical explanation.Subsequently,based on the new theoretical explanation,an alternative method that uses only the relative phase difference between sensors to extract dispersion characteristics with better conceptual clarity is proposed.Two active surface wave testing cases are considered to validate the theory and method.The results indicate that(1)an accurate trigger system is not necessary for surface wave data acquisition,and(2)it is unnecessary to assume that the impact point is the generation point of the surface waves for the experimental dispersion analysis.

A nonlocal dispersal and time delayed HIV infection model with general incidences

Biologically,because of the impact of reproduction period and nonlocal dispersal of HIV-infected cells,time delay and spatial heterogeneity should be considered.In this paper,we establish an HIV infection model with nonlocal dispersal and infection age.Moreover,applying the theory of Fourier transformation and von Foerster rule,we transform the model to an integrodifferential equation with nonlocal time delay and dispersal.The well-posedness,positivity,and boundedness of the solution for the model are studied.

A seismic elastic moduli module for the measurements of low-frequency wave dispersion and attenuation of fluid-saturated rocks under different pressures

Knowledge about the seismic elastic modulus dispersion,and associated attenuation,in fluid-saturated rocks is essential for better interpretation of seismic observations taken as part of hydrocarbon identification and time-lapse seismic surveillance of both conventional and unconventional reservoir and overburden performances.A Seismic Elastic Moduli Module has been developed,based on the forced-oscillations method,to experimentally investigate the frequency dependence of Young's modulus and Poisson's ratio,as well as the inferred attenuation,of cylindrical samples under different confining pressure conditions.Calibration with three standard samples showed that the measured elastic moduli were consistent with the published data,indicating that the new apparatus can operate reliably over a wide frequency range of f∈[1-2000,10^(6)]Hz.The Young's modulus and Poisson's ratio of the shale and the tight sandstone samples were measured under axial stress oscillations to assess the frequency-and pressure-dependent effects.Under dry condition,both samples appear to be nearly frequency independent,with weak pressure dependence for the shale and significant pressure dependence for the sandstone.In particular,it was found that the tight sandstone with complex pore microstructure exhibited apparent dispersion and attenuation under brine or glycerin saturation conditions,the levels of which were strongly influenced by the increased effective pressure.In addition,the measured Young's moduli results were compared with the theoretical predictions from a scaled poroelastic model with a reasonably good agreement,revealing that the combined fluid flow mechanisms at both mesoscopic and microscopic scales possibly responsible for the measured dispersion.

Overview of computation strategies on the dispersion analysis for explicit finite difference solution of acoustic wave equation

Finite-difference(FD)method is the most extensively employed numerical modeling technique.Nevertheless,when using the FD method to simulate the seismic wave propagation,the large spatial or temporal sampling interval can lead to dispersion errors and numerical instability.In the FD scheme,the key factor in determining both dispersion errors and stability is the selection of the FD weights.Thus,How to obtain appropriate FD weights to guarantee a stable numerical modeling process with minimum dispersion error is critical.The FD weights computation strategies can be classified into three types based on different computational ideologies,window function strategy,optimization strategy,and Taylor expansion strategy.In this paper,we provide a comprehensive overview of these three strategies by presenting their fundamental theories.We conduct a set of comparative analyses of their strengths and weaknesses through various analysis tests and numerical modelings.According to these comparisons,we provide two potential research directions of this field:Firstly,the development of a computational strategy for FD weights that enhances stability;Secondly,obtaining FD weights that exhibit a wide bandwidth while minimizing dispersion errors.

Discussion on“Dispersion characteristics of clayey soils containing waste rubber particles”[J Rock Mech Geotech Eng 15(2023)3050-3058]

We read with great interest the recent article by Erenson(2023)entitled“Dispersion characteristics of clayey soils containing waste rubber particles”.The author has studied the dispersion characteristics of clayey soils containing different percentages of waste rubber particles(WRPs)by performing several tests(viz.consistency limit,linear shrinkage limit,double hydrometer,crumb test and pinhole test)and scanning electron microscopy(SEM)analysis on five clayey(viz.Na-activated bentonite,refined ball clay,Ukrainian kaolin,Avanos kaolin and Afyon clay)samples containing 0%,5%,10%and 15%WRPs.It should be noted that Erenson(2023)has presented some interesting observations,but there are some serious issues that we want to share through this discussion and request the author of the original paper to address them to avoid their persistence in the scientific literature.

Study on concentration distribution and detonation characteristics for non-axisymmetric fuel dispersal

The study of non-axisymmetric fuel dispersal and detonation can provide reference for the prevention of industrial cloud explosion accidents and the design of fuel air explosive(FAE).The concentration and detonation fields of 85 kg cylindrical and fan-shaped fuel are investigated by experiments and numerical simulations.A dynamic model of the whole process for fuel dispersal and detonation is built.The concentration distribution of fuel is used as the initial condition to calculate the detonation stage,thus solving the initial value problem of detonation field.The phase and component changes of fuel cloud at different locations are compared.The fuel cloud is divided into directions of 0°,90°,135°and 180°.The results show that the maximum cloud radius is 20.94 m in 135°and the minimum is 12.04 m in 0°.The diameter of the detonation fireball is 53.6 m,and the peak temperature is 3455 K.The highest peak overpressure is 3.44 MPa in 0°and the lowest is 2.97 MPa in 135°.The proportion of liquid phase in 0°is22.90%,and the fuel loss is 11.8% and 9% higher than that in 135°and cylindrical charge,respectively.The stable propagation distance of blast wave in 135°is 42.50% longer than 0°and 28.37% longer than cylindrical charge.