Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrodinger system in an inhomogeneous optical fiber

Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

EXPLICIT SOLUTIONS TO THE COUPLED KdV EQUATIONS WITH VARIABLE COEFFICIENTS

By means of sn-function expansion method and cn-function expansion method, several kinds of explicit solutions to the coupled KdV equations with variable coefficients are obtained, which include three sets of periodic wave-like solutions. These solutions degenerate to solitary wave-like solutions at a certain limit. Some new solutions are presented.

Impacts of Surface Exchange Coefficients on Simulations of Super Typhoon Megi(2010)Using a Coupled Ocean-Atmosphere-Wave Model

In this study,the effects of surface exchange coefficients on simulations of Super Typhoon Megi(2010)are investigated using a fully coupled ocean-atmosphere-wave model.Several experiments are conducted using different parameterization schemes for the drag(C_(D))and enthalpy exchange(C_(K))coefficients.For the selected case,considering only the leveling-off of C_(D)at high wind speeds does not effectively improve the simulated typhoon track,intensity,or size.We found that increasing C_(K)monotonically with wind speed(Komori et al.,2018)yields stronger winds and deeper pressures by enhancing latent and sensible heat fluxes,but typhoon intensity remains underestimated.We propose a new higher C_(K)than that from Komori et al.(2018)based on the theory of Emanuel(1995).This approach produces a greater modeled typhoon intensity that is in good agreement with the best track data and effectively improves the track error for the simulation.Improved accuracy for modeled typhoon intensity is achieved with the new coefficient because C_(K)/C_(D)reaches the threshold of about 0.75 predicted by Emanuel(1995).The new proposed C_(K)also results in a reasonably accurate modeled sea surface temperature.However,typhoon size and surface wave height are overestimated.This finding implies that more numerical tests for tropical cyclones of different nature(such as strong,weak,dissipating,rapidly intensifying,or weakening tropical cyclones)should be studied,and more physical processes should be explored in future coupled models.

Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

Auto-Backlund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation

In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.

Influence of water coupling coefficient on the blasting effect of red sandstone specimens

This study investigates the impact of different water coupling coefficients on the blasting effect of red sandstone.The analysis is based on the theories of detonation wave and elastic wave,focusing on the variation in wall pressure of the blasting holes.Using DDNP explosive as the explosive load,blasting tests were conducted on red sandstone specimens with four different water coupling coefficients:1.20,1.33,1.50,and 2.00.The study examines the morphologies of the rock specimens after blasting under these different water coupling coefficients.Additionally,the fractal dimensions of the surface cracks resulting from the blasting were calculated to provide a quantitative evaluation of the extent of rock damage.CT scanning and 3D reconstruction were performed on the post-blasting specimens to visually depict the extent of damage and fractures within the rock.Additionally,the volume fractal dimension and damage degree of the post-blasting specimens are calculated.The findings are then combined with numerical simulation to facilitate auxiliary analysis.The results demonstrate that an increase in the water coupling coefficient leads to a reduction in the peak pressure on the hole wall and the crushing zone,enabling more of the explosion energy to be utilized for crack propagation following the explosion.The specimens exhibited distinct failure patterns,resulting in corresponding changes in fractal dimensions.The simulated pore wall pressure–time curve validated the derived theoretical results,whereas the stress cloud map and explosion energy-time curve demonstrated the buffering effect of the water medium.As the water coupling coefficient increases,the buffering effect of the water medium becomes increasingly prominent.

A Coupled Variable Coefficient Modified KdV Equation Arising from a Two-Layer Fluid System

A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityreductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed.Some exact solutions of the coupled equations are also presented.

Reconstruction of Emission Coefficients for a Non-axisymmetric Coupling Arc Based on MALDONADO's Method

The reconstruction of emission coefficient is a key factor for the calculation of temperature field.However,most of the researches for determining arc plasmas are based on axisymmetric sources,little has been done to study non-axisymmetric arc plasmas.In order to reveal temperatures of a non-axisymmetric coupling arc,the distribution of emission coefficients must be reconstructed in advance.In this paper,the argon atomic line intensities of the coupling arc are obtained by using the imaging system that involves a high speed camera in conjunction with a neutral and a narrow-band filter.The converted programme between emission coefficients and emitted intensities is programmed based on MALDONADO＇s method.A displaced Gaussian model is used for evaluating the validity of the converted programme.Then,the emission coefficients of a free burning arc are reconstructed by MALDONADO＇s method and an Abel inversion,respectively,and good agreement is obtained.Finally,the emission coefficient profiles of the coupling arc are achieved.The results show that the distribution of emission coefficient for the coupling arc is non-axisymmetric.The emission coefficient profile is similar to an ellipse,and the short axis of the ellipse is in the direction that the two electrodes are arranged along.The peak temperature of the coupling arc is in the middle of both electrodes.There is a strong interaction between both arcs within the coupling arc.The proposed research solves difficulties for determining asymmetric arcs and enlarges the application scope of spectroscopic techniques.

STUDY ON THE DIFFUSION OF Cu^(2+)-H^+ COUPLE IN A CATION EXCHANGE MEMBRANE——A RAPID METHOD TO DETERMINE SELF-DIFFUSION COEFFICIENTS OF COUNTER-IONS WITH UNEQUAL VALENCE

1 INTRODUCTIONKnowledge of the basic transport phenomena of ions in an ion exchange membrane isimportant for the application of such a membrane.Various studies on the developmentof mathematical models for predicting and correlating membrane transport rate havebeen published in recent years.More exact estimation of the diffusion coefficientshas been the subject of chief concern in many of these papers.For a bi-ionic systemwith the same valence,Sato et al.gave a method for estimating diffusion coefficients

Effects of Different Time-Dependent Couplings on Two-Atom Entanglement

The effects of different time-independent and time-dependent couplings on two-atom entanglement are studied. The results show that the effects depend on the initial state. For the initial state ｜eeO〉, it is found that different time-independent couplings make the case without entanglement exhibit entanglement, and time-dependent couplings turn the irregular entanglement regions into regular one. Under the case of decay, for the initial state ｜eg0〉, the different time-dependent couplings have disbenefit.

Calculations of the Spin-Lattice Coupling Coefficients Fij and Zij for MgO:Co2+Crystal

According to a uniform and simple method of calculating spin-lattice coupling coefficients and the pert1rbation formulas of gi factors and hyperfine structure constants Ai based on the cluster approach for 3d7 ions in cubic,tetragonal and trigonal octahedral crystal fields, the spin-lattice coupling coefficients Fij (F11, Fl2, F44), Zij (Z11, Z12,Z44) and also g factor and hyperfine constant A for MgO:Co2+ are calculated by using the parameters obtained from the optical spectra without adjustable parameters. The calculated results show good agreement with the observed values.The difiiculty in explaining the coeficients Fij and Zij is therefore removed.

Variable Coefficient KdV Equation for Amplitude of Nonlinear Solitary Rossby Waves in a Sort of Time-Dependent Zonal Flow

On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.

On the Couplings between Chebyshev Coefficients as Derived from the Monthly Mean Geopotential Fields at 500 hPa over East Asia and the Southern Oscillation

The first six Chebyshev polynomial coefficients (i.e., A00, A01, A10, A11, A02, A20) were derived from monthly mean geopotential height over East Asia for the period 1951-1983. Spectral analysis of these coefficients reveals relative maxima of power in the frequency bands of 200 months (- 16.7 years), 25 months (the quasi-biennial oscillation), 5-6 months, and 2-3 months. Cross-spectral characteristics between Chebyshev coefficients and the Southern Oscillation Index (SOI) were also explored. Coherence spectrum for the zonal and meridional circulation index (A01 and A 10) with the SOI was significant near 4 years, the QBO, and 2-3 months. Some physical explanations were offered for the spatial linkages (i.e., teleconnections) between the SO and atmospheric circulation anomalies overEast Asia.

变系数辅助方程法与广义Hirota-Satsuma coupled KdV系统的行波解

利用变系数辅助方程法讨论了广义Hirota-Satsuma coupled KdV方程组的精确行波解.根据齐次平衡原理又借助Maple软件计算工具获得了新的精确行波解,并且通过所得结果可以获得系统无穷多组精确行波解,丰富了该方程组的解系.

Principle of Cross Coupling Between Vertical Heat Turbulent Transport and Vertical Velocity and Determination of Cross Coupling Coefficient

It has been proved that there exists a cross coupling between vertical heat turbulent transport and vertical velocity by using linear thermodynamics. This result asserts that the vertical component of heat turbulent transport flux is composed of both the transport of the vertical potential temperature gradient and the coupling transport of the vertical velocity. In this paper, the coupling effect of vertical velocity on vertical heat turbulent transportation is validated by using observed data from the atmospheric boundary layer to determine cross coupling coefficients, and a series of significant properties of turbulent transportation are opened out. These properties indicate that the cross coupling coefficient is a logarithm function of the dimensionless vertical velocity and dimensionless height, and is not only related to the friction velocity u., but also to the coupling roughness height zwo and the coupling temperature Two of the vertical velocity. In addition, the function relations suggest that only when the vertical velocity magnitude conforms to the limitation IW/u. I # 1, and is above the level zwo, then the vertical velocity leads to the cross coupling effect on the vertical heat turbulent transport flux. The cross coupling theory and experimental results provide a challenge to the traditional turbulent K closure theory and the Monin-Obukhov similarity theory.

Numerical analysis of dynamic response of vehicle–bridge coupled system on long-span continuous girder bridge

To systematically study the vehicle-bridge coupled dynamic response and its change rule with different parameters, a vehicle model with seven degrees of freedom was built and the total potential energy of vehicle space vibration system was deduced. Considering the stimulation of road roughness, the dynamic response equation of vehicle-bridge coupled system was established in accordance with the elastic system principle of total potential energy with stationary value and the ＂set-in-right-position＂ rule. On the basis of the self-compiled Fortran program and bridge engineering, the dynamic response of long- span continuous girder bridge under vehicle load was studied. This study also included the calculation of vehicle impact coefficient, evaluation of vibration comfort, and analysis of dynamic response parameters. Results show the impact coefficient changes with lane number and is larger than the value calculated by the ＂general code for design of highway bridges and culverts （China）＂. The Dieckmann index of bridge vibration is also related to lane number, and the vibration comfort evaluation is good in normal conditions. The relevant conclusions from parametric analyses have practical significance to dynamic design and daily operation of long-span continuous girder bridges in expressways. Safety and comfort are expected to improve significantly with further control of the vibration of vehicle-bridge system.

Mode stability analysis in the beam-wave interaction process for a three-gap Hughes-type coupled cavity chain

Based on space-charge wave theory, the formulae of the beam-wave coupling coefficient and the beam-loaded conductance are given for the beam-wave interaction in an N-gap Hughes-type coupled cavity chain. The ratio of the nonbeam-loaded quality factor of the coupled cavity chain to the beam quality factor is used to determine the stability of the beam-wave interaction. As an example, the stabilities of the beam-wave interaction in a three-gap Hughes-type coupled cavity chain are discussed with the formulae and the CST code for the operations of the 2π, π, and π/2 modes, respectively. The results show that stable operation of the 2π, π, and π/2 modes may all be realized in an extended-interaction klystron with the three-gap Hughes-type coupled cavity chain.

Estimation of Mutual Coupling Coefficient of the Array by Simulated Annealing Algorithm

We propose a method for estimating the mutual coupling coefficient among antennas in this paper which is based on the principle of signal subspace and the simulated annealing （SA） algorithm. The computer simulation has been conducted to illustrate the＇ excellent performance of this method and to demonstrate that it is statistically efficient. The benefit of this new method is that calibration signals and unknown signals can be received simultaneously, during the course of calibration.