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.

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.

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.

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.

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.

Rate Coefficients of Roaming Reaction H+MgH Using Ring Polymer Molecular Dynamics

The ring-polymer molecular dynamics(RPMD)was used to calculate the thermal rate coefficients of the multi-channel roaming reaction H+MgH→Mg+H_(2).Two reaction channels,tight and roaming,are explicitly considered.This is a pioneering attempt of exerting RPMD method to multichannel reactions.With the help of a newly developed optimization-interpolation protocol for preparing the initial structures and adaptive protocol for choosing the force constants,we have successfully obtained the thermal rate coefficients.The results are consistent with those from other theoretical methods,such as variational transition state theory and quantum dynamics.Especially,RPMD results exhibit negative temperature dependence,which is similar to the results from variational transition state theory but different from the ones from ground state quantum dynamics calculations.

Effect of Ionic Liquids on Organic Reactions Based on Activity Coefficients at Infinite Dilution

It is important to know how ILs(ionic liquids)influence organic reaction.In this paper,activity coefficients at infinite dilution of more than 80 organic compounds in ILs are collected and analyzed systematically.Through the study on typical organic reactions happened in ILs,such as Diels-Alder,esterification and Friedel-Crafts reaction,the ratio of activity coefficients at infinite dilution of products and reactants is employed to estimate different effects of different structural ILs on the rate and selectivity of reactions.

Dynamics of the Au+H2 reaction by time-dependent wave packet and quasi-classical trajectory methods

Dynamics of the Au + H2 reaction are studied using time-dependent wave packet(TDWP) and quasi-classical trajectory(QCT) methods based on a new potential energy surface [Int. J. Quantum Chem. 118 e25493(2018)]. The dynamic properties such as reaction probability, integral cross section, differential cross section and the distribution of product are studied at state-to-state level of theory. Furthermore, the present results are compared with the theoretical studies available.The results indicate that the complex-forming reaction mechanism is dominated in the reaction in the low collision energy region and the abstract reaction mechanism plays a dominant role at high collision energies. Different from previous theoretical calculations, the side-ways scattering signals are found in the present work and become more and more apparent with increasing collision energy.

Time-Dependent Quantum Wave Packet Calculation for Reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S) on Ab Initio Potential Energy Surface

The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S-(^(2)P)+H_(2)(^(1)∑_(g)^(+))→SH-(^(1)∑)+H(^(2)S)based on the electronic ground state(^(2)A′)potential energy surface of the SH_(2)-ionic molecule.The collision energy dependent reaction probabilities and integral cross sections are obtained.The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies.The vibrational excitation and rotational excitation of the diatomic reagent H_(2) promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j=0,2,4,6,8,10,and the vibrational quantum number v=0,1,2,3,4.The numerical integral cross sections are quite consistent with the experimental data reported in previous work.

Fusion Reaction Rate Coefficient for Different Beam and Target Scenarios

Fusion power output is proportional not only to the fuel particle number densities participating in reaction but also to the fusion reaction rate coefficient （or reactivity）, which is dependent on reactant velocity distribution functions. They are usuMly assumed to be dual Maxwellian distribution functions with the same temperature for thermal nuclear fusion circumstances. However, if high power neutral beam injection and minority ion species ICRF plasma heating, or multi-pinched plasma beam head-on collision, in a converging region are required and investigated in future large scale fusion reactors, then the fractions of the injected energetic fast ion tail resulting from ionization or charge exchange will be large enough and their contribution to the non-Maxwellian distribution functions is not negligible, hence to the fusion reaction rate coefficient or calculation of fusion power. In such cases, beam-target, and beam-beam reaction enhancement effect contributions should play very important roles. In this paper, several useful formulae to calculate the fusion reaction rate coefticient for different beam and target combination scenarios are derived in detail

Bending the Foundation Beam on Elastic Base by Two Reaction Coefficient of Winkler’s Subgrade

A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.

Study of road tunnel threshold zone lighting reduction coefficient

The luminance in the road tunnel threshold zone attracts broad attention due to its enormous energy consumption and direct influence on tunnel transportation security.Current lighting design methods in threshold zones mostly adopt the reduction coefficient method.However,the determination of reduction coefficient k simply considers tunnel design speed and flow rate,while excluding outside tunnel luminance and threshold zone color temperature and luminance,which have a major impact on driver visual adaptation.Existing problems in the determination of k value are analyzed;a visual performance experiment is utilized;and the reaction time of drivers in changeable outside tunnel luminance and threshold zone color temperature and luminance conditions is obtained;thus,the equations concerning reduction coefficient variation law are derived.In the end,a comparative analysis is made of the k values of the reduction coefficient stipulated by various norms under different color temperature conditions.

Calculation of activity coefficients for components in ternary Ti alloys and intermetallics as matrix of composites

Based on Kohler’s ternary solution model and Miedema’s model for calculating the formation heat of binary solution, the integral equation was established for calculating the activity coefficients in ternary alloys and intermetallics. The activity coefficients for components in alloy Ti-5Al-2.5Sn, Ti-6Al-4V and intermetallics TiAl, Ti3Al and Ti2AlNb were calculated with the equations. The calculated data coincide well with the experimental ones found in literatures. According to the calculated activity coefficients and activities, it can be predicted that the interfacial reaction in SiC/Ti3Al composite is more severe than that in composites SiC/Ti2AlNb and SiC/TiAl.

Time-dependent density functional theoretical studies on the photo-induced dynamics of an HCI molecule encapsulated in C60 under femtosecond laser pulses

By using first-principles simulations based on time-dependent density functional theory, the chemical reaction of an HCl molecule encapsulated in C60 induced by femtosecond laser pulses is observed. The H atom starts to leave the Cl atom and is reflected by the C60 wall. The coherent nuclear dynamic behaviors of bond breakage and recombination of the HCl molecule occurring in both polarized parallel and perpendicular to the H-Cl bond axis are investigated. The radial oscillation is also found in the two polarization directions of the laser pulse. The relaxation time of the H-Cl bond lengths in transverse polarization is slow in comparison with that in longitudinal polarization. Those results are important for studying the dynamics of the chemical bond at an atomic level.

Experimental Evaluation of the Heat Output/Input and Coefficient of Performance Characteristics of a Chemical Heat Pump in the Periodic Operation of CaCl₂Hydration

We herein evaluate the use of a chemical heat pump (CHP) for upgrading waste heat. CaCl2 was used in the system of CHP. We evaluated the heat storage and heat releasing of CHP, and confirmed the practicality from the experimental results. The reactor module employed was an aluminum plate-tube heat exchanger with corrugated fins, and the CaCl2 powder was in the form of a packed bed. Heat storage operation and heat dissipation operation are performed at the same time and supplied to the heat demand destination. At this time, an environmental heat source can be used during the heat radiation operation, and the heat output can release more heat than the heat input during heat storage. The heat discharging and charging characteristics of the reactor module were evaluated experimentally. The coefficient of performance (COP) was calculated for the heat upgrading cycle, and the heat output in the system was determined. A COP of 1.42 and output of 650 W/L, based on the heat exchanger volume, were obtained using a 600 s change time for the heat pump.

高速铁路无砟轨道车辆荷载传递特性研究

为进一步探讨无砟轨道荷载设计参数取值,为我国时速400 km及以上高速铁路建设提供重要理论支撑,通过开展无砟轨道静力分析以及钢轨焊缝、车轮扁疤激励下车辆-轨道动力相互作用,揭示列车静、动力载荷特征及传递规律;同时根据轨道承载特点和无砟轨道设计原理,提出车辆竖向设计荷载取值建议。研究结果表明:(1)高速列车车轮扁疤和钢轨焊缝不平顺将造成显著的轮轨冲击,其轮载动载系数最大可达5.79,远高于现行规范取值;扣件系统对扁疤和焊缝不平顺引起的轮轨力高频成分衰减作用明显,扣件支反力的动载系数最大为2.64;(2)钢轨焊缝不平顺引起的轮轨冲击力随着车速提高以及焊缝不平顺幅值的增大而迅速增大,建议500 km/h及以下高速铁路的钢轨焊缝平直度标准取0.2 mm/m;(3)列车轮载通过扣件支反力作用于轨道板,从传递特性的角度来说,以扣件支反力作为轨道板竖向设计荷载更为合理,其动载系数可取3.0,且能满足400 km/h及以上高速铁路的行车需求。

基坑中软土的水平抗力系数几种确定方法探讨

该文围绕基坑中软土的的水平抗力系数的确定方法开展了探讨,分析了基坑规程中土的水平反力系数的比例系数m值的来源,分析了水平抗力系数确定的理论,罗列了现行规范中软土的水平抗力系数的经验值,最后通过案例分析,将3种土的水平抗力系数的计算方法(m值、k值和c值)的计算结果与实测进行了比较,发现按目前基坑规程公式计算的软土的水平反力系数的比例系数m值偏小的现象。

基于副反应形成配合物浓度的计算公式及应用

配位滴定法,常用的滴定剂为EDTA(Y),体系中常存在各类副反应。本文从副反应系数(α)出发,推导出达到化学计量点时,基于配体Y与其他共存金属离子(N^(n+)),或待测金属离子(M^(n+))与其他配体(L)等副反应形成配位比为1:1的NY或ML浓度的计算公式,所得结果使该配合物浓度的计算问题得到简化。

负温度系数区域内RP-3喷气燃料表征燃料化学反应动力学分析

为探究喷气燃料(RP-3)在不同条件下负温度系数(NTC)区域内的反应路径、敏感反应以及小分子基元团的影响规律,以CRECK小分子详细机理为核心,基于解耦法耦合正十二烷、正丁基环己烷、正丁基苯简化机理,构建得到RP-3多组分表征燃料化学反应动力学详细机理;并在不同压力、燃料/空气质量比工况下对其NTC区域内的燃烧过程进行了敏感性分析、组分含量变化分析以及组分间交互作用路径分析。结果表明:NTC区域内反应H_(2)O_(2)(+M)=2OH(+M)(M为反应中第三体)是最重要的着火促进反应;不同反应条件下O_(2)、CH_(4)、C_(2)H_(4)的陡降时刻与CO_(2)的激增时刻均与燃料的着火延迟期表现出极高的吻合度;压力与燃料/空气质量比的改变仅会影响反应路径的占比。

扩散吸附作用下CO_(2)非混相驱微观渗流特征模拟

利用数值模拟方法建立CO_(2)非混相驱数值模型,使用水平集法模拟扩散吸附作用下CO_(2)非混相驱和近混相驱的微观渗流规律,并对CO_(2)在孔隙中的微观渗流特征及扩散吸附特征进行研究,选取注入速度、扩散系数、吸附反应速率常数等参数研究近混相驱微观渗流特征的影响因素。研究结果表明:①相场法CO_(2)驱数值模拟采出程度为51.29%,水平集法CO_(2)驱数值模拟采出程度为53.60%,因此水平集法更适用于CO_(2)非混相驱的渗流过程模拟。②非混相驱条件下,CO_(2)优先向大孔隙扩散,采收率为87.7%,出口气体体积分数为71.60%,CO_(2)最大表面吸附浓度为3.16×10-4mol/m^(2);近混相驱条件下,CO_(2)更易向小孔隙扩散,采收率为91.1%,出口含气率为97.01%,CO_(2)最大表面吸附浓度为5.81×10-4mol/m^(2)。③近混相驱微观渗流特征受注入速度、扩散系数、吸附反应速率常数等因素影响。注入速度增大,出口含气率和采收率均提高;扩散系数和吸附反应速率常数增大,会使采收率提高,出口含气率下降。