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.

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.

Solitary Waves for Cubic-Quintic Nonlinear Schroedinger Equation with Variable Coefficients

The cubic-quintic nonlinear Schroedinger equation （CQNLS） plays important parts in the optical fiber and the nuclear hydrodynamics. By using the homogeneous balance principle, the bell type, kink type, algebraic solitary waves, and trigonometric traveling waves for the cubic-quintic nonlinear Schroedinger equation with variable coefficients （vCQNLS） are derived with the aid of a set of subsidiary high-order ordinary differential equations （sub-equations for short）. The method used in this paper might help one to derive the exact solutions for the other high-order nonlinear evolution equations, and shows the new application of the homogeneous balance principle.

"Nonlinear" characteristics of the static earth pressure coefficient in thick alluvium

Exact calculations of the static earth pressure from a thick alluvium require accurate/Co values. These calculations influence the sinking cost and the safety of the freezing method. The static earth pressure coefficient （K0） of thick and deep soil was analyzed using laboratory tests. The results show that the static earth pressure coefficient of thick and deep soils is nonlinear and different from that of superficial soils. The constant of superficial soils is usually invariant and the total stress or incremental stress definitions used in traditional geo-meehanics give the same value. The influence of load increments when calculating for superficial soil is ignored. The difference in values of K0 for thick alluvium defimed by the total stress or the incremental stress methods is over 10%. The effects of the thick alluvium on K0 should be considered during the design of frozen shaft projects. Such things as the frozen shaft thickness and the excavated section height should be chosen to assure the rationality of the design and to avoid potential faults and accidents.

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article, we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients. The authors use a new method introduced by Duzaar and Grotowski, to prove partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation and directly establish the optimal HSlder exponent for the derivative of a weak solution on its regular set.

Trial function method and exact solutions to the generalized nonlinear Schrdinger equation with time-dependent coefficient

In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.

Remaining useful life prediction based on nonlinear random coefficient regression model with fusing failure time data

Remaining useful life(RUL) prediction is one of the most crucial elements in prognostics and health management(PHM). Aiming at the imperfect prior information, this paper proposes an RUL prediction method based on a nonlinear random coefficient regression(RCR) model with fusing failure time data.Firstly, some interesting natures of parameters estimation based on the nonlinear RCR model are given. Based on these natures,the failure time data can be fused as the prior information reasonably. Specifically, the fixed parameters are calculated by the field degradation data of the evaluated equipment and the prior information of random coefficient is estimated with fusing the failure time data of congeneric equipment. Then, the prior information of the random coefficient is updated online under the Bayesian framework, the probability density function(PDF) of the RUL with considering the limitation of the failure threshold is performed. Finally, two case studies are used for experimental verification. Compared with the traditional Bayesian method, the proposed method can effectively reduce the influence of imperfect prior information and improve the accuracy of RUL prediction.

Water inflow forecasting for tunnel considering nonlinear variation of permeability coefficient

To assess the water inflow which is more suitable to the actual conditions of tunnel,an empirical correlation about the permeability coefficient changing with depth is introduced.Supposing that the surrounding rock is heterogeneous isotropy,the formula for calculating water inflow of tunnel with the nonlinear variation of permeability coefficient is deduced.By the contrast analysis with the existing formulas,the presented method has the similar value to them;moreover,the presented method has more simple form and easy to use.Due to parameter analysis,the water inflow decreases after considering the nonlinear variation of permeability coefficient.When the attenuation coefficient a>0,the water inflow increases first till reaches the maximum at a certain depth,then decreases and is close to 0 finally if deep enough.Thus,it is better to keep away from the certain depth where it is with the maximum water inflow for safe operation and economical construction,and reduce the water damage.Based on the analysis,the radius of tunnel has less impact on the amount of water inflow,and the water inflow just increases by 6.7% when the radius of tunnel increases by 1 m.

A new variable coefficient algebraic method and non-travelling wave solutions of nonlinear equations

In this paper, a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the validity and the advantages of the method, （2＋1）-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained. This algorithm can also be applied to other nonlinear differential equations.

Prediction of Coefficient of Restitution for Impact Elastoplastic Spheres Considering Finite Plate Thickness

Collisions between objects are a relatively common phenomenon in nature.Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts.The coefficient of restitution is a critical parameter in the analysis of collision processes.Many experiments have shown that the coefficient of restitution is closely related to the plate thickness,and the smaller the plate thickness,the more inaccurate the coefficient of restitution predicted by the existing model,which seriously affects the process of collision analysis.To remedy this shortcoming,this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable.The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness.Finally,the validity of the new model is verified using a large amount of experimental data.

ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS

We study equations in divergence form with piecewise Cαcoefficients.The domains contain corners and the discontinuity surfaces are attached to the edges of the corners.We obtain piecewise C^(1,α) estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.

Global stability coefficient of large underground caverns under static loading and earthquake wave condition

Underground energy and resource development,deep underground energy storage and other projects involve the global stability of multiple interconnected cavern groups under internal and external dynamic disturbances.An evaluation method of the global stability coefficient of underground caverns based on static overload and dynamic overload was proposed.Firstly,the global failure criterion for caverns was defined based on its band connection of plastic-strain between multi-caverns.Then,overloading calculation of the boundary geostress and seismic intensity on the caverns model was carried out,and the critical unstable state of multi-caverns can be identified,if the plastic-strain band appeared between caverns during these overloading processes.Thus,the global stability coefficient for the multi-caverns under static loading and earthquake was obtained based on the corresponding overloading coefficient.Practical analysis for the Yingliangbao(YLB)hydraulic caverns indicated that this method can not only effectively obtain the global stability coefficient of caverns under static and dynamic earthquake conditions,but also identify the caverns’high-risk zone of local instability through localized plastic strain of surrounding rock.This study can provide some reference for the layout design and seismic optimization of underground cavern group.

Comparison of transport coefficients before and after density pump-out induced by resonant magnetic perturbation using a BOUT++ six-field model on the EAST tokamak

Many experiments have demonstrated that resonant magnetic perturbation(RMP) can affect the turbulent transport at the edge of the tokamak. Through the Experimental Advanced Superconducting Tokamak(EAST) density modulation experiment, the particle transport coefficients were calculated using the experimental data, and the result shows that the particle transport coefficients increase with RMP. In this study, the six-field two-fluid model in BOUT++ is used to simulate the transport before and after density pump-out induced by RMP,respectively referred as the case without RMP and the case with RMP. In the linear simulations,the instabilities generally decreases for cases with RMP. In the nonlinear simulation, ELM only appears in the case without RMP. Additionally, the particle transport coefficient was analyzed,and the result shows that the particle transport coefficient becomes larger for the case with RMP,which is consistent with the experimental conclusion. Moreover, its magnitude is comparable to the results calculated from experimental data.

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients

In this paper, the extended symmetry transformation of （3＋1）-dimensional （3D） generalized nonlinear Schrodinger （NLS） equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.

Molecular Dynamics, Diffusion Coefficients and Activation Energy of the Electrolyte (Anode) in Lithium (Li and Li+), Sodium (Na and Na+) and Potassium (K and K+)

This work is a simulation modelling with the LAMMPS calculation code of an electrode based on alkali metals (lithium, sodium and potassium) using the MEAM potential. For different multiplicities, two models were studied;with and without gap. In this work, we present the structural, physical and chemical properties of the lithium, sodium and potassium electrodes. For the structural properties, the cohesive energy and the mesh parameters were calculated, revealing that, whatever the chemical element selected, the compact hexagonal hcp structure is the most stable, followed by the face-centred cubic CFC structure, and finally the BCC structure. The most stable structure is lithium, with a cohesion energy of -6570 eV, and the lowest bcc-hcp transition energy of -0.553 eV/atom, followed by sodium. For physical properties, kinetic and potential energies were calculated for each of the sectioned chemical elements, with lithium achieving the highest value. Finally, for the chemical properties, we studied the diffusion coefficient and the activation energy. Only potassium followed an opposite order to the other two, with the quantities with lacunae being greater than those without lacunae, whatever the multiplicity. The order of magnitude of the diffusion coefficients is given by the relationship DLi > DNa > Dk for the multiplicity 6*6*6, while for the activation energy the order is reversed.

Nonlinear Refractive Index and Absorption Coefficient of Single-Shell Semiconductor Carbon Nanotube

The nonlinear refractive index and absorption coefficient of single\|shell semiconductor carbon nanotubes(CN s ) are calculated based on the two\|band approximation and Genkin\|Mednis approach. The results of nonlinear refractive index and absorption coefficient reach the order of 10 -8 and 10 -4 cm 2\5W -1 separately, which indicates that CN s have wonderful nonlinear optical properties. Taking into account the temperature effect and overlapping of σ and π orbits, the effect of relaxation term and chiral angle is discussed. The results show that the smaller the relaxation term, the larger the nonlinear absorption coefficient and refractive index. At the same time, CN s with different chiral angles have different results due to their different energy gap.

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.

Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement

Measurements of bubble size distribution require the understanding of the acoustic characteristics of the medium.The bubbles show highly nonlinear properties under finite amplitude acoustic excitation,so the acoustic fields from bubble population are easily observed at the second harmonics as well as at the fundamental frequency,which shows that the nonlinear coefficient increases obviously.The inversion method of bubble size distribution based on nonlinear acoustic effects can peel off the influence of complex environment and obtain the size distribution coefficient information of bubbles more accurately.The previous nonlinear inversion methods of bubble size distribution are mostly based on the nonlinear scattering cross-section characteristics of bubbles.However,the stability of inversion is not high enough.In this paper,we introduce a new acoustic inversion method for bubble size distribution,which is based on the nonlinear coefficients of bubble medium.Compared with other inversion methods based on linear or nonlinear scattering cross section,the inversion method based on nonlinear coefficients of bubble medium proposed in this paper shows good robustness in both simulation and experiment.

GCAGA: A Gini Coefficient-Based Optimization Strategy for Computation Offloading in Multi-User-Multi-Edge MEC System

To support the explosive growth of Information and Communications Technology(ICT),Mobile Edge Comput-ing(MEC)provides users with low latency and high bandwidth service by offloading computational tasks to the network’s edge.However,resource-constrained mobile devices still suffer from a capacity mismatch when faced with latency-sensitive and compute-intensive emerging applications.To address the difficulty of running computationally intensive applications on resource-constrained clients,a model of the computation offloading problem in a network consisting of multiple mobile users and edge cloud servers is studied in this paper.Then a user benefit function EoU(Experience of Users)is proposed jointly considering energy consumption and time delay.The EoU maximization problem is decomposed into two steps,i.e.,resource allocation and offloading decision.The offloading decision is usually given by heuristic algorithms which are often faced with the challenge of slow convergence and poor stability.Thus,a combined offloading algorithm,i.e.,a Gini coefficient-based adaptive genetic algorithm(GCAGA),is proposed to alleviate the dilemma.The proposed algorithm optimizes the offloading decision by maximizing EoU and accelerates the convergence with the Gini coefficient.The simulation compares the proposed algorithm with the genetic algorithm(GA)and adaptive genetic algorithm(AGA).Experiment results show that the Gini coefficient and the adaptive heuristic operators can accelerate the convergence speed,and the proposed algorithm performs better in terms of convergence while obtaining higher EoU.The simulation code of the proposed algorithm is available:https://github.com/Grox888/Mobile_Edge_Computing/tree/GCAGA.

INITIAL-OBLIQUE DERIVATIVE PROBLEMS FOR NONLINEAR PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with measurable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for the problems are proved.