Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Particle residence time distribution and axial dispersion coefficient in a pressurized circulating fluidized bed by using multiphase particle-in-cell simulation

The particle residence time distribution(RTD)and axial dispersion coefficient are key parameters for the design and operation of a pressurized circulating fluidized bed(PCFB).In this study,the effects of pressure(0.1-0.6 MPa),fluidizing gas velocity(2-7 m·s^(-1)),and solid circulation rate(10-90 kg·m^(-2)·s^(-1))on particle RTD and axial dispersion coefficient in a PCFB are numerically investigated based on the multiphase particle-in-cell(MP-PIC)method.The details of the gas-solid flow behaviors of PCFB are revealed.Based on the gas-solid flow pattern,the particles tend to move more orderly under elevated pressures.With an increase in either fluidizing gas velocity or solid circulation rate,the mean residence time of particles decreases while the axial dispersion coefficient increases.With an increase in pressure,the core-annulus flow is strengthened,which leads to a wider shape of the particle RTD curve and a larger mean particle residence time.The back-mixing of particles increases with increasing pressure,resulting in an increase in the axial dispersion coefficient.

A nonparametric spectrum estimation method for dispersion and attenuation analysis of borehole acoustic measurements

Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures,or stresses.In this paper,we propose a nonparametric spectrum estimation method to get phase dispersion characteristics and attenuation coefficient.By designing an appropriate vector filter,phase velocity,attenuation coefficient and amplitude can be inverted from the waveform recorded by the receiver array.Performance analysis of this algorithm is compared with Extended Prony Method(EPM)and Forward and Backward Matrix Pencil(FBMP)method.Based on the analysis results,the proposed method is capable of achieving high resolution and precision as the parametric spectrum estimation methods.At the meantime,it also keeps high stability as the other nonparametric spectrum estimation methods.At last,applications to synthetic waveforms modeled using finite difference method and real data show its efficiency.The real data processing results show that the P-wave attenuation log is more sensitive to oil formation compared to S-wave;and the S-wave attenuation log is more sensitive to shale formation compared to P-wave.

High-pressure phonon dispersion of copper by using the modified analytic embedded atom method

By using the Born-von Kfirmfin theory of lattice dynamics and the modified analytic embedded atom method, we reproduce the experimental results of the phonon dispersion in fcc metal Cu at zero pressure along three high symmetry directions and four oft-symmetry directions, and then simulate the phonon dispersion curves of Cu at high pressures of 50, 100, and 150 GPa. The results show that the shapes of dispersion curves at high pressures are very similar to that at zero pressure. All the vibration frequencies of Cu in all vibration branches at high pressures are larger than the results at zero pressure, and increase correspondingly as pressure reaches 50, 100, and 150 GPa sequentially. Moreover, on the basis of phonon dispersion, we calculate the values of specific heat of Cu at different pressures. The prediction of thermodynamic quantities lays a significant foundation for guiding and judging experiments of thermodynamic properties of solids under high pressures.

Preparation of natural brucite nanofibers by the dispersion method

The preparation of natural brucite nanofibers through dispersion by the wet process is described. The test results indicate that brucite fibers can be well dispersed by using sodium dioctyl sulfosuccinate （OT） as the dispersant at a dispersant/fiber mass ratio of 0.15：1, dispersing for 30 min at a water/solid mass ratio of 20：1. The prepared nanofibers were characterized with X-ray diffraction （XRD）, scanning electron microscope （SEM）, and transmission electron microscope （TEM）. It is shown that the prepared single brucite nanofiber is around 30 nm in diameter and the talus of the nonsingle brucite nanofibers is about 50-150 nm in diameter. Natural brucite mineral fibers were treated by the dispersion method to obtain nanomaterials. These fibers have significant advantages over artificial nanofibers both in yield and in cost.

A Solution of the Burger’s Equation Arising in the Longitudinal Dispersion Phenomenon in Fluid Flow through Porous Media by Mixture of New Integral Transform and Homotopy Perturbation Method

The main aim of the paper is to examine the concentration of the longitudinal dispersion phenomenon arising in fluid flow through porous media. These phenomenon yields a partial differential equation namely Burger’s equation, which is solved by mixture of the new integral transform and the homotopy perturbation method under suitable conditions and the standard assumption. This method provides an analytical approximation in a rapidly convergent sequence with in exclusive manner computed terms. Its rapid convergence shows that the method is trustworthy and introduces a significant improvement in solving nonlinear partial differential equations over existing methods. It is concluded that the behaviour of concentration in longitudinal dispersion phenomenon is decreases as distance x is increasing with fixed time t > 0 and slightly increases with time t.

Design and Numerical Analysis of Ultra-High Negative Dispersion, Highly Birefringent Nonlinear Single Mode Core-Tune Photonic Crystal Fiber (CT-PCF) over Communication Bands

This paper presents the development of a highly efficient CT-PCF (Core-Tune Photonic Crystal Fiber) with substantial birefringence, tailored for applications in high-bit-rate communication and sensing while minimizing signal loss. The design incorporates a modified broadband dispersion compensating structure, optimized for operation across the E, S, C, and L communication bands within a wavelength range spanning 1360 nm to 1625 nm. Notably, the CT-PCF demonstrates a remarkable birefringence of 2.372 × 10-2 at 1550 nm, surpassing traditional PCF structures. Single-mode performance is evaluated using the Higher Order Mode Extinction Ratio (HOMER) method, revealing a peak HOMER value of 104 at 1550 nm. Furthermore, at 1550 nm, the CT-PCF exhibits exceptional nonlinear characteristics, featuring a high nonlinearity of 50.74 W-1⋅Km-1 for y polarization. In comparison to existing designs, the proposed CT-PCF exhibits superior performance metrics and optical characteristics. Additionally, the y polarization dispersion coefficient of the CT-PCF at 1550 nm is measured at -3534 ps/(nm⋅km). Overall, the CT-PCF represents a significant advancement, outperforming established systems in terms of performance metrics and optical properties.

Microstructures and properties of Al_2O_3 dispersion-strengthened copper alloys prepared through different methods

Al2O3 dispersion copper alloy powder was prepared by intemal oxidation, and three consolidation methods--high-velocity compaction （HVC）, hot pressing （HP）, and hot extrusion （HE）--were used to prepare Al2O3 dispersion-strengthened copper （Cu-Al2O3） alloys. The microstructures and properties of these alloys were investigated and compared. The results show that the alloys prepared by the HP and HE methods exhibited the coarsest and finest grain sizes, respectively. The alloy prepared by the HVC method exhibited the lowest relative density （98.3% vs. 99.5% for HP and 100% for HE）, which resulted in the lowest electrical conductivity （81% IACS vs. 86% IACS for HP and 87% IACS for HE）. However, this alloy also exhibited the highest hardness （77 HRB vs. 69 HRB for HP and 70 HRB for HE）, the highest compressive strength （443 MPa vs. 386 MPa for I/P and 378 MPa for HE）, and the best hardness retention among the investigated alloys. The results illustrate that the alloy prepared by the HVC method exhibits high softening temperature and good mechanical properties at high temperatures, which imply long service life when used as spot-welding electrodes.

Preparation of Thermosensitive Microcapsules Containing Water Soluble Powder by Melting Dispersion Cooling Method

It was tried to prepare the thermosensitive microcapsules containing the water soluble solid powder by the melting dispersion cooling method and to establish the optimum preparation conditions. As a model water soluble solid powder, sodium hydrogen carbonate was adopted in order to generate carbon dioxide gas and as a thermosensitive shell material, olefin resin with the melting point of ca. 40°C was used. In the experiment, the concentration of olefin resin in the shell material solution was mainly changed together with the concentrations of the oil soluble surfactant species and the α-tocopherol as a modifier of shell. Addition of α-tocopherol into the shell material solution could prevent the core from breaking away during the microencapsulation process and result in the higher microencapsulation efficiency, because the dispersion stability of solid powder in the shell material solution could be increased due to the increase in affinity between the shell material solution and solid powder. Also, the microencapsulation efficiency increased with the concentration of olefin resin, became maximum at 50 wt% and then, decreased. The microcapsules were found to begin melting at 36°C and to generate carbon dioxide gas.

In-situ Characterization of Non-aqueous Nano-dispersion Systems by Freeze-etching TEM and Comparative Study with Laser Scattering Method

In-situ characterization of non-aqueous nano-dispersion systems（NANDS） by freeze-etching transmission electron microscope（FETEM） was reported.To improve just-for-once successive rate of specimen preparation and get good characterization results,an improving specimen preparation method of freezing etching was developed.Size,distribution and morphology of NANDS were directly visualized.Some information of particle dispersion feature and particle density can also be obtained.Reproductivity of the FETEM characterization is excellent.Comparing with laser scattering method,which is liable to give positive error especially for small size particle anchoring disperser,FETEM characterization can give more accurate measurement of particle size.Moreover,FETEM can give dispersion feature of nanoparticle in non-aqueous medium.

GALERKIN METHOD FOR COMPRESSIBLE FLOW OF CONTAMINATION FROM NUCLEAR WASTE WITH MOLECULAR DIFFUSION AND DISPERSION

Abstract A system of quasilinear coupled equations which arise from simulation of contamination of geologic nulear waste in porous media is studied. We’ll discuss Galerkin method for the model of compressible flow with molecular diffusion and dispersion. Some new techniques are introcued to error analysis. Only one dimensional case is considered. The optimal error estimate in both L^2 and H^1 is proved. A contribution of this paper is how the dispersion term can be handled,

LOCAL DISCONTINUOUS GALERKIN METHOD FOR RADIAL POROUS FLOW WITH DISPERSION AND ADSORPTION

Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e., the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.

ADAPTIVE FINITE ELEMENT METHOD FOR ANALYSIS OF POLLUTANT DISPERSION IN SHALLOW WATER

A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts ： （ 1 ） computation of the velocity flow field and water surface elevation, and （2） computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.

Chebyshev Pseudo-Spectral Method for Solving Fractional Advection-Dispersion Equation

Fractional differential equations have recently been applied in various areas of engineering, science, finance, applied mathematics, bio-engineering and others. However, many researchers remain unaware of this field. In this paper, an efficient numerical method for solving the fractional Advection-dispersion equation (ADE) is considered. The fractional derivative is described in the Caputo sense. The method is based on Chebyshev approximations. The properties of Chebyshev polynomials are used to reduce ADE to a system of ordinary differential equations, which are solved using the finite difference method (FDM). Moreover, the convergence analysis and an upper bound of the error for the derived formula are given. Numerical solutions of ADE are presented and the results are compared with the exact solution.

Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media

Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.

Adjoint Method-Based Algorithm for Calculating the Relative Dispersion Ratio in a Hydrodynamic System

Relative dispersion ratio(RDR)can be used to quantify the deviation behavior of a water parcel’s trajectory caused by a disturbance in a hydrodynamic system.It can be calculated by using a standard method for determining relative dispersion(RD),which accounts for the growth of the deviation of a cluster of particles from a specific initial time.However,the standard method for computing RD is time consuming.It involves numerous computations on tracing many water parcels.In this study,a new method based on the adjoint method is proposed to acquire a series of RDR fields in one round of tracing.Through this method,the continuous variation in the RDR corresponding to a time series of the disturbance time t can be obtained.The consistency and efficiency of the new method are compared with those of the standard method by applying it to a double-gyre flow and an unsteady Arnold-Beltrami-Childress flow field.Results show that the two methods have good consistency in a finite time span.The new method has a notable speedup for evaluating the RDR at multiple t.

Suppress numerical dispersion in reversetime migration of acoustic wave equation using optimal nearly analytic discrete method

Using staggered-grid finite difference method to solve seismic wave equation,large spatial grid and high dominant frequency of source cause numerical dispersion,staggeredgrid finite difference method,which can reduce the step spatial size and increase the order of difference,will multiply the calculation amount and reduce the efficiency of solving wave equation.The optimal nearly analytic discrete(ONAD)method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition.In this study,the ONAD method is introduced into the field of reverse-time migration(RTM)for performing forward-and reverse-time extrapolation of a two-dimensional acoustic equation,and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition,effectively suppressed the numerical dispersion and improved the imaging accuracy.Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM,and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2 nd and space order 4 th,results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records,and archive accurate imaging of complex geological structures especially the fine structure,and the migration sections of the measured data show that ONAD method has practical application value.

Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension

In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

Preparation of Microcapsules Containing Aqueous Solution of Azur B with Melting Dispersion Cooling Method and Application to DNA Amplification Detector

Microcapsules containing the aqueous solution of Azur B of a water soluble dye were prepared with the melting dispersion cooling method and applied to the amplification detector of plant DNA. Paraffin wax with melting temperature of 75°C was used as the shell material. In the experiment, the aqueous solution (W) of Azur B as the core material was dispersed in the melted paraffin wax (O) to form the (W/O) emulsion and then, the (W/O) emulsion was dispersed in the silicon oil (O’) as the continuous phase to form the (W/O)/O’ emulsion at 85°C. After formation of the (W/O)/O’ emulsion, the microcapsules were prepared by cooling the (W/O)/O’ emulsion to 50°C. The microcapsules were prepared by changing the concentration of oil soluble surfactant in the (W/O) emulsion and the volume of the (W/O) emulsion in the (W/O)/O’ emulsion. The microencapsulation efficiency increased with the concentration of oil soluble surfactant and finally became 100% under the optimum conditions. Furthermore, the microcapsules were melted down at temperature of 85°C to reveal the sharp thermal responsibility and to release the aqueous solution of Azur B. As a result, it was found that the microcapsules were able to be applied to the amplification detector of plant DNA by utilizing the reaction between DNA and Azur B.

Gap States of ZnO Thin Films by New Methods:Optical Spectroscopy,Optical Conductivity and Optical Dispersion Energy

The optical reflectance and transmittance spectra in the wavelength range of 300-2500 nm are used to compute the absorption coefficient of zinc oxide films annealed at different post-annealing temperatures 400, 500 and 600°C.The values of the cross point between the curves of the real and imaginary parts of the optical conductivity ɑ_1 and ɑ_1 with energy axis of films exhibit values that correspond to optical gaps and are about 3.25-3.3 eV. The maxima of peaks in plots dR/dλ and dT/dλ versus wavelength of films exhibit optical gaps at about 3.12-3.25 eV.The values of the fundamental indirect band gap obtained from the Tauc model are at about 3.14-3.2 eV. It can be seen that films annealed at 600°C have the minimum indirect optical band gap at about 3.15 eV. The films annealed at 600°C have Urbach＇s energy minimum of 1.38 eV and hence have minimum disorder. The dispersion energy d of films annealed at 500°C has the minimum value of 43 eV.