Multi-Waves,Breathers,Periodic and Cross-Kink Solutions to the(2+1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation

The present article deals with multi-waves and breathers solution of the(2+1)-dimensional variable-coefficient CaudreyDodd-Gibbon-Kotera-Sawada equation under the Hirota bilinear operator method.The obtained solutions for solving the current equation represent some localized waves including soliton,solitary wave solutions,periodic and cross-kink solutions in which have been investigated by the approach of the bilinear method.Mainly,by choosing specific parameter constraints in the multi-waves and breathers,all cases the periodic and cross-kink solutions can be captured from the 1-and 2-soliton.The obtained solutions are extended with numerical simulation to analyze graphically,which results in 1-and 2-soliton solutions and also periodic and cross-kink solutions profiles.That will be extensively used to report many attractive physical phenomena in the fields of acoustics,heat transfer,fluid dynamics,classical mechanics,and so on.We have shown that the assigned method is further general,efficient,straightforward,and powerful and can be exerted to establish exact solutions of diverse kinds of fractional equations originated in mathematical physics and engineering.We have depicted the figures of the evaluated solutions in order to interpret the physical phenomena.

Multi-wave amplitude-preserved AVO modeling considering wave propagation effects

Traditional AVO forward modeling only considers the impact of reflection coefficients at the interface on seismic wave field amplitude and ignores various propagation effects. Introducing wave propagation effects including geometric spreading, transmission loss, attenuation into seismic wave propagation, multi-wave amplitude-preserved AVO forward modeling for horizontally layered media based on ray theory is proposed in this paper. We derived the multi-wave geometric spreading correction formulas for horizontally layered media in order to describe the geometric spreading effect of multi-wave propagation. Introducing the complex traveltime directly, we built the relationship between complex traveltime and quality factor without the help of complex velocity to describe the attenuation of viscoelastic media. Multi-wave transmission coefficients, obtained by solving the Zoeppritz equations directly, is used to describe the transmission loss. Numerical results show that the effects of geometric spreading, attenuation, and transmission loss on multi-wave amplitude varies with offset and multi-wave amplitude-preserved AVO forward modeling should consider the reconstructive effect of wave propagation on reflection amplitude.

Reservoir prediction using multi-wave seismic attributes

The main problems in seismic attribute technology are the redundancy of data and the uncertainty of attributes, and these problems become much more serious in multi-wave seismic exploration. Data redundancy will increase the burden on interpreters, occupy large computer memory, take much more computing time, conceal the effective information, and especially cause the ＂curse of dimension＂. Uncertainty of attributes will reduce the accuracy of rebuilding the relationship between attributes and geological significance. In order to solve these problems, we study methods of principal component analysis （PCA）, independent component analysis （ICA） for attribute optimization and support vector machine （SVM） for reservoir prediction. We propose a flow chart of multi-wave seismic attribute process and further apply it to multi-wave seismic reservoir prediction. The processing results of real seismic data demonstrate that reservoir prediction based on combination of PP- and PS-wave attributes, compared with that based on traditional PP-wave attributes, can improve the prediction accuracy.

STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the Riemann problem in the flow direction, consisting of two shocks, one vortex sheet, and one entropy wave, which is one of the core multi-wave configurations for the two-dimensional Euler equations. It is proved that such steady four-wave configurations in supersonic flow are stable in structure globally, even under the BV perturbation of the incoming flow in the flow direction. In order to achieve this, we first formulate the problem as the Cauchy problem （initial value problem） in the flow direction, and then develop a modified Glimm difference scheme and identify a Glimm-type functional to obtain the required BV estimates by tracing the interactions not only between the strong shocks and weak waves, but also between the strong vortex sheet/entropy wave and weak waves. The key feature of the Euler equations is that the reflection coefficient is always less than 1, when a weak wave of different family interacts with the strong vortex sheet/entropy wave or the shock wave, which is crucial to guarantee that the Glimm functional is decreasing. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution, close to the background solution of steady four-wave configuration.

Monitoring the change in horizontal stress with multi-wave time-lapse seismic response based on nonlinear elasticity theory

Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO_(2)) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.

Research on model testing of a new ultrasonic multi-wav detecting method

The traditional crack exploring method with echo （reflected wave） in metals is called the ＂single-wave detecting method＂ that uses a probe of single weight. This method is not able to detect directly the size and shape of the crack and the result can only be obtained by relative comparison, that is to compare the echo amplitudes of the unknown quantity （crack） with the known quantity （regular artificial crack） to determine the equivalent size and shape of a certain crack.

An ultrasonic multi-wave focusing and imaging method for linear phased arrays

To overcome the inherent limits of traditional single wave imaging for nondestructive testing,the multi-wave focusing and imaging method is thoroughly studied.This method makes the compressional waves and shear waves focused in both emission and reception processes,which strengthens the focusing energy and improves the signal-to-noise ratio of received signals.A numerical model is developed to study the characteristics of a multi-wave focusing field.It is shown that the element width approaching 0.8 wavelengths of shear waves can keep a balance between the radiation energy of two waves,which can achieve a desirable multi-wave focusing performance.And an experiment using different imaging methods for a linear phased array is performed.It can be concluded that due to the combination of the propagation and reflection characteristics of two waves,the multi-wave focusing and imaging method can significantly improve the imaging distinguishability of defects and expand the available sweeping range to a sector of-650 to 65°.

Optical Multi-wave Mixing Process Based on Electromagnetically InducedTransparency

In this paper, we propose and analyze an optical multi-wave mixing scheme for the generation of coherent light in a five-level atomic system in the context of electromagnetically induced transparency. A detailed semiclassical study of the propagation of generated mixing and probe fields is demonstrated. The analytical dependence of the generated mixing field on the probe field and the respective detuning is predicted. Such a nonlinear optical process can be used for generating short-wavelength radiation at low pump intensities.

Dressed multi-wave mixing in a V-type four-level atomic system

The dressed four- and six-wave mixings in a V-type four-level system are considered. Under two different dressed conditions, two- and three-photon resonant Autler-Townes splittings, accompanied by enhancement and suppression of wave mixing signal, are obtained analytically. Meanwhile, an electromagnetic induced transparency of multi-wave mixing is presented, which shows multiple peaks and asymmetric effects caused by one-photon, two-photon and three-photon resonances, separately. The slow light propagation multiple region of multi-wave mixing signal is also obtained.

Multi-wave forward modeling of a reservoir and AVO analysis

In the process of accurate interpretation of multi-wave seismic data,we wanted to solve the problem of multi-wave information recognition.Based on techniques of elastic wave forwarding,targeting the geological model of a reservoir of an oil field exploration area,we used a high-order staggered-grid difference technology to simulate many shots of seismic records of nonzero offset shots,implemented multi-wave seismic data processing to acquire the CMP of P waves and converted waves,NMO traces of CCP pre stacks,including AVA information and superposition profiles.Based on the AVA calculation of the model,the layer parameters of the model and the forwarding wave field relations of the P-S wave,we also compared and studied the correspondence between P waves and converted waves.The results of our analysis show that the results from simulation and from the AVO analysis are consistent.Significant wave field differences between P waves and converted waves in the same reservoir were found,which are helpful in recognizing and interpreting the multi-wave information in this area.We made use of the multi-wave data to provide the important guidelines for reservoir prediction.

An Analysis of the Impact of Stay-at-Home Measures on the Occurrence of Vaccine Shortages

COVID-19, a contagious respiratory disease, presents immediate and unforeseen challenges to people worldwide. Moreover, its transmission rapidly extends globally due to its viral transmissibility, emergence of novel strains (variants), absence of immunity, and human unawareness. This framework introduces a revised epidemic model, drawing upon mathematical principles. This model incorporates a modified vaccination and lockdown approach to comprehensively depict an epidemics transmission, containment, and decision-making processes within a community. This study aims to provide policymakers with precise information on real-world situations to assist them in making informed decisions about the implementation of lockdown strategies, maintenance variables, and vaccine availability. The suggested model has conducted stability analysis, strength number analysis, and first and second-order derivative analysis of the Lyapunov function and has established the existence and uniqueness of solutions of the proposed models. We examine the combined effects of an effective vaccination campaign and non-pharmaceutical measures such as lockdowns and states of emergency. We rely on the results of this research to assist policymakers in various countries in eradicating the illness by developing more innovative measures to control the outbreak.

Prediction of Subtle Thin Gas Reservoir in the Loess Desert Area in the North of Ordos Basin

For thin gas reservoir of low-porosity and low-permeability in the loess desert area, a suite of lateral reservoir prediction techniques has been developed by Changqing Oil Company and the excellent effects achieved in exploration and exploitation in the areas such as Yulin, Wushenqi,Suligemiao, Shenmu etc., so that the Upper Paleozoic gas reserve has been stably increasing for eight years in Changqing Oilfield. The paper analyzed the effects and experience of the application of these techniques in detail.

Multiwave Amplitude Compensation and Its SensitivityAnalysis to AVO Inversion in Viscoelastic Media

We derive formulae of correction for multi-wave geometric spreading and absorption in layered viscoelastic media, this provides the theoretical foundation for true amplitude compensation of field data and for our sensitivity analysis. The imaging matrix at a plane reflector between viscoelastic media can be determined in the frequency domain using linearized reflection coefficients through Born approximation. We quantitatively analyze the sensitivity by studying eigenvalues and eigenvectors of the imaging matrix. The results show that two linear combinations of petrophysical parameters can be determined from the multi-wave AVO inversion in the case of amplitude compensation. Multi-wave AVO contains the information of attenuation in the media. However, the sensitivity of multi-wave AVO inversion to attenuation is small.

Stretching correction for amplitude-preserving vector wavefield reverse-time migration

The migration of multi-wave seismic data is aimed at obtaining the P- and S-wave imaging results of the amplitude preserving. But the P- and S-wave stretching effect produced by the reverse time migration of the elastic wave equation will not only reduce the vertical resolution of the migration results and the amplitude preserving of the large reflection angle. In this paper, the reverse time migration technique of amplitude preserving vector wave-field separating is used. Based on the analysis of the stretch mechanism and the influencing factors of stretch magnitude, the paper gave the stretch correcting factors. Then, realize the stretch correction method at the time that after the reverse extrapolation and before the imaging by solving the problem which is how to calculate the P-wave and Ps-wave propagation directions of imaging points at different times. The stretch correction method can improve the vertical resolution and amplitude fidelity of the imaging results and provide high fidelity input data for seismic data interpretation and inversion.

Cavity-Enhanced Third Harmonic Generation

We derive the analytical expression of microcavity-enhanced factor for third harmonic generation in terms of detunings, linewidths, and the Purcell factors of the relevant microcavity modes. It is suitable for microcavities with any dimensions and arbitrary geometric shapes.

Four-wave mixing and six-wave mixing in a four-level confined atomic system

We have investigated coexisting four-wave mixing and six-wave mixing （SWM） in ultra-thin, micrometre and long vapour cells. There exists competition between Dicke-narrowing features and polarization interference in the micrometre cell. The oscillation behaviour of SWM signal intensities and linewidths results from destructive interference. With a larger destructive interference, the SWM signal in ultra-thin cells shows a narrow spectrum, in contrast to the long cell case. Due to the Dicke-narrowing features, a narrow spectrum can be obtained, and such spectra can be used for high precision measurements and metrological standards.

Application of microspectral luminescent analysis to study the intracellular metabolism in single cells and cell systems

Spectral luminescent analysis of single cells and cellular systems enable us to reveal the initial changes of intracellular metabolism that can followed by human diseases or failure in biocenosis. Two cytodiagnostic systems of de-vices and techniques have been developed: 1) Microspectrofluorimeters registering the fluo-rescent spectra of individual cells or intracellular organelles used for fundamental investigations of cell reactions and for discovering and studying new dimensionless fluorescent characteristic parameters reflecting the biochemical or physiological properties of the cells;2) Double- and multi-wave microfluorimeters for rapid registration of fluorescent characteristic para- meters for many cells to obtain statistical information about cell population. These techni- ques are useful especially in medical and eco-logical investigations.

Deterministic Chaos of Exponential Oscillons and Pulsons

An exact 3-D solution for deterministic chaos of J wave groups with M internal waves governed by the Navier-Stokes equations is presented. Using the Helmholtz decomposition, the Dirichlet problem for the Navier-Stokes equations is decomposed into the Archimedean, Stokes, and Navier problems. The exact solution is derived by the method of decomposition in invariant structures (DIS). A cascade differential algebra is developed for four families of invariant structures: deterministic scalar kinematic (DSK) structures, deterministic vector kinematic (DVK) structures, deterministic scalar dynamic (DSD) structures, and deterministic vector dynamic (DVD) structures. The Helmholtz decomposition of anticommutators, commutators, and directional derivatives is computed in terms of the dot and cross products of the DVK structures. Computation is performed with the help of the experimental and theoretical programming in Maple. Scalar and vector variables of the Stokes problem are decomposed into the DSK and DVK structures, respectively. Scalar and vector variables of the Navier problem are expanded into the DSD and DVD structures, correspondingly. Potentialization of the Navier field is possible since internal vortex forces, which are described by the vector potentials of the Helmholtz decomposition, counterbalance each other. On the contrary, external potential forces, which are expressed via the scalar potentials of the Helmholtz decomposition, superpose together to form the gradient of a dynamic pressure. Various constituents of the kinetic energy and the total pressure are visualized by the conservative, multi-wave propagation and interaction of three-dimensional, nonlinear, internal waves with a two-fold topology, which are called oscillons and pulsons.

Magnetic-field-sensitive multi-wave interference

We report an experimental study of magnetic-field-sensitive multi-wave interference,realized in a three-wave RF-atom system.In the F=1 hyperfine level of the ^(87)Rb 5^(2)S_(1/2) ground state,Ramsey fringes were observed via the spin-selective Raman detection.A decrease in the fringe contrast was observed with increasing free evolution time.The maximum evolution time for observable fringe contrasts was investigated at different atom temperatures,under free-falling and trapped conditions.As the main interest of the Ramsey method,the improvement in magnetic field resolution is observed with an increase of evolution time T up to 3 ms and with the measurement resolution reaching 0.85 nT.This study paves the way for precision magnetic field measurements based on cold atoms.

A simple multi-wave algorithm for the uncapacitated facility location problem

The multi-wave algorithm(Glover, 2016)integrates tabu search and strategic oscillation utilizing repeated waves(nested iterations) of constructive search or neighborhood search. We propose a simple multi-wave algorithm for solving the Uncapacitated Facility Location Problem(UFLP) to minimize the combined costs of selecting facilities to be opened and of assigning each customer to an opened facility in order to meet the customers' demands. The objective is to minimize the overall cost including the costs of opening facilities and the costs of allocations. Our experimental tests on a standard set of benchmarks for this widely-studied class of problems show that our algorithm outperforms all previous methods.