Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Anion type-dependent confinement effect on glass transitions of solutions of LiTFSI and LiFSI

We present findings on the effect of nanometer-sized silica-based pores on the glass transition of aqueous solutions of lithium bis(trifluoromethane)sulfonimide(LiTFSI)and lithium difluorosulfimide(LiFSI),respectively.Our experimental results demonstrate a clear dependence of the confinement effect on the anion type,particularly for water-rich solutions,in which the precipitation of crystalized ice under cooling process induces the formation of freeze-concentrated phase confined between pore wall and core ice.As this liquid layer becomes thinner,the freeze-concentrated phase experiences glass transition at increasingly higher temperatures in solutions of LiTFSI.However,differently,for solutions of LiFSI and LiCl,this secondary confinement has a negligible effect on the glass transition of solutions confined wherein.These different behaviors emphasize the obvious difference in the dynamic properties’response of LiTFSI and LiFSI solutions to spatial confinement and particularly to the presence of the hydrophilic pore wall.

Classroom Management in Young Learners English Teaching——Typical Problems and Effective Solutions

Classroom management is the orchestration of classroom life:planning curriculum,organizing procedures and resources,arranging the environment to maximize efficiency,monitoring progress,dealing with existent problems.Successful classroom management looked like magic shows because students in these classrooms seem to glide from one activity to the next.Successful classroom management contributes to students ' good achievement.Effective classroom management is one of the key elements of importance for efficient school education.However,almost all English teachers face a same problem——classroom management.In this paper,some typical problems and effective solutions in classroom management will be described,defined,or characterized.

Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

Effect of solute concentration on the serrated flow in solution-treated Al-4%Cu alloys

In order to compare with annealed Al-4%Cu alloys, the influence of solute concentration on the serrated flow is investigated by solution treatment. In this paper, some dynamic parameters, such as critical time and the ultimate tensile strength are obtained. Moreover, the change of the strain rate range for serrated flow in Al-4%Cu alloys prepared by annealing and quenching heat treatments is reported too. The difference between them is attributed to the increasing solute concentration in the bulk of the solution treated materials.

Rare Earth Doping Effects on Properties of Ceria-Zirconia Solid Solution

Ce0.6Zr0.3RE0.1O2(RE = Y, La, Pr, Tb)solid solutions were prepared by co-precipitation technique and characterized by a series of methods. XRD and FT-Raman results show that Ce0.6Zr0.3RE0.1O2 has cubic fluorite structure. The different dopant ion radii bring different effect on the cell parameter of Ce0.6Zr0.3RE0 1O2. The X-ray photoelectron spec-troscopy (XPS) results show that the binding energy of Ce3d, Zr3d and O1s for Ce0.6Zr0.3RE0.1O2 rises compared with that for Ce0.6Zr0.4O2, indicating that dopant elements change chemistry environment of solid solutions which is available to improve redox performance. Compared with Pd/Ce0.6Zr0.4O2, doping Y and La does not change air/fuel (A/F) characteristic of TWCs, but doping Pr and Tb widens A/F operating window and makes HC, CO and NO have higher conversion. The light-off temperature of Pd/Ce0.6Zr0.3La0.1O2 is corresponding to that of Pd/Ce0.6Zr0.4O2. However, the light-off temperatures of Pd/Ce0.6Zr0.3M0.1O2(M = Y, Pr, Tb) are lower than that of Pd/Ce0.6Zr0.4O2, which keep much lower after high temperature treatments. Among Pd/Ce0.6Zr0.3RE0.1 O2, Pd/Ce0.6Zr0.3Tb0.1 O2 represents wider A/F operating window, higher conversion, lower light-off temperature and better high-temperature resistance.

ANALYTICAL SMOOTHING EFFECT OF SOLUTION FOR THE BOUSSINESQ EQUATIONS

In this article, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H^1 -solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equations admit exactly same smoothing effect properties of incompressible Navier-Stokes equations.

Upper Bound Solution of Soil Slope Stability under Coupling Effect of Rainfall and Earthquake

Based on the limit analysis upper bound method,a new model of soil slope collapse has been proposed which consists of two rigid block zones and a plastic shear zone.Soil slope was induced failure by coupling effect of rainfall and earthquake,and these blocks were also incorporated horizontal earthquake force and vertical gravitate.The velocities and forces were analyzed in three blocks,and the expression of velocity discontinuities was obtained by the principle of incompressibility.The external force work for the blocks,the internal energy of the plastic shear zone and the velocity discontinuous were solved.The present stability ratios are compared to the prevenient research,which shows the superiority of the mechanism and rationality of the analysis.The critical height of the soil slope can provide theoretical basis for slope support and design.

Nontrivial Homoclinic Solutions for Second-Order p-Laplacian Differential System with Impulsive Effects

The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.

PERIODIC AND ALMOST PERIODIC SOLUTIONS FOR A NON-AUTONOMOUS RESPIRATORY DISEASE MODEL WITH A LAG EFFECT

This paper studies a kind of non-autonomous respiratory disease model with a lag effect.First of all,the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques.Second,it assumes that all coefficients of the system are periodic.The existence of positive periodic solutions of the system is proven,based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines.In the meantime,the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem.In addition,the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time.Finally,the theoretical derivation is verified by a numerical simulation.

A Review on Chemical Effects in Aqueous Solution induced by Plasma with Glow Discharge

Chemical effects in different aqueous solutions induced by plasma with glow discharge electrolysis (GDE) and contact glow discharge electrolysis (CGDE) are described in this paper. The experimental and discharge characteristics are also reviewed. These are followed by a discussion of their mechanisms of both anodic and cathodic CGDE..

RARE EARTH DISSOLVED IN SOLID SOLUTION OF STEEL AND ITS EFFECT ON MICROSTRUCTURE

The amounts of rare earth in the solid solution in steel 16Mn were determined by means of inductive coupling plasma(ICP)spectroscopy.While the RE/S ratio was less than 1.9,the amounts of rare earth in solid solution were not more than 8 ppm,which rised slightly with the increase of the rare earth content in the steel.While the RE/S was more than 1.9,MnS disappeared completely in the steel and the amounts of rare earth in solid solution increased rapidly with the increasing of the rare earth content.The solubility of cerium in steel 16 Mn(St 52)is less than 0.011 wt% at room temperature.The results also indicate that rare earth in solid solution can reduce the amount of pearlite and increase that of ferrite and its mierohardness.The rela- tionship between microhardness(Hv)and the amount of rare earth in solid solution can be expressed by the equation of Hv=117+7 RE(ppm).

Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect

This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries.The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle,of which the non-Darcian effect is characterized by Izbash’s equation.The solutions are derived by Boltzmann and dimensionless transformations.Then,the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution.The results show that the aquifer boundaries have non-negligible effects on pumping,and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping.The higher the degree of non-Darcian,the smaller the drawdown.

Numerical investigation on electron effects in the mass transfer of the plasma species in aqueous solution

The objective of this work is to contribute an understanding of the effects of electrons in the plasmas on the mass transfer of plasma species in aqueous solution by means of the numerical simulation based on a one-dimensional diffusion-reaction model.The plasma species are divided into two groups,i.e.electrons and the other species,and the mass transfer in the three scenarios has been simulated,including the systematic calculations of the depth distributions of five major reactive species,OH,O3,HO2,O2^-,and H2O2.In the three scenarios,the particles considered to enter into aqueous solution are all the plasma species(the scenario Ⅰ,where the mass transfer of plasma species is a result due to the synergy of the electrons and the other plasma species),the other species(the scenario Ⅱ),and only electrons in plasma species(the scenario Ⅲ),respectively.The detailed analyses on the difference between the depth distributions of each reactive species in these three scenarios show the following conclusions.The electrons play an important role in the mass transfer of plasma species in aqueous solution and the synergy of the electrons and the other plasma species(the electron-species synergy)presents its different effects on the mass transfer.The vast majority of H2O2 are generated from a series of the electronrelated reactions in aqueous solution,which is hardly affected by the electron-species synergy.Compared to the results when only the electrons enter into the liquid region,the electron-species synergy evidently weakens the generation of O2^-,O3,and OH,but promotes to produce HO2.

Analytical solution of coal-bed methane migration with slippage effects in hypotonic reservoir

Using theoretical analysis, the single-phase gas seepage mathematical model influenced by slippage effects was established. The results show that the pressure of producing wells attenuates more violently than the wells without slippage effects. The decay rate of reservoir pressure is more violent as the Klinkenherg factor increases. The gas prediction output gradually increases as the Klinenberg factor increases when considering gas slippage effects. Through specific examples, analyzed the law of stope pore pressure and gas output forecast changing in a hypotonic reservoir with slippage effects. The results have great theoretical significance in the study of the law of coal-bed methane migration in hypotonic reservoirs and for the exploitation of coal-bed methane.

The Effect of the pH of Ammonum Nitrate Solution on the Susceptability of Mild Steel to Stress Corrosion Cracking (SCC) and General Corrosion

This work investigates the relative aggressiveness of nitrate solutions at different pH values on mild steel towards stress corrosion cracking (SCC) and general corrosion. Electrochemical behavior and stress corrosion cracking sus-ceptibility measurements were carried out in 52 Wt% ammonium nitrate solutions at 368° K and various pH values ranging from 0.77 to 9.64. Constant load stress corrosion test at 90% yield stress was conducted. Tested specimens were prepared and examined using the scanning electron microscope (SEM). The potentiodynamic polarization curves for different pH values again emphasized the validity of the gravimetric measurements and hence the mechanism of cracking was attributed to the stress that assisted the dissolution process.

Mssbauer Effect in Ultrafine Particles with Fe-C Solid Solution,γ-Fe and Fe_3C Phases

Ultrafine particles prepared by evaporating pure Fe in CH4 atmosphere using arc-dischargeheating method, were found to consist of Fe-C solid solution, γ-Fe and Fe3C phases. EfFect of annealing temperature on phase transformation and hyperfine interactions has been investigated by Mossbauer spectroscopy, X-ray diffraction (XRD), differential thermal analysis and thermogravimetry (DTA-TG), transmission electron microscopy (TEM), oxygen determination and vibrating sample magnetometer (VSM) measurements. It was observed that phase transformation of γ-Fe to α-Fe occurs during annealing in vacuum. The mechanism causing the change of hyperfine interactions with annealing temperature differs for Fe-C solution and interstitial compounds. DifFerence of hyperfine interactions of Fe-C solid solution in the starting sample and its annealed samples is ascribed to the improvement of activation of interstitial carbon atoms. Stress-relieving in structure of annealed Fe3C particle can result in a weak influence on hyperfine interactions. Parameters fitted to the Mossbauer spectra show the existence of superparamagnetism in all the samples. Absorbed and combined oxygen on particle surface of the starting sample were determined.

Effects of Nine Kinds of Household Vase Solutions on Fresh-keeping Effect of Lilium Cut Flowers

[Objective]The paper was to study the effects of nine kinds of household vase solutions on fresh-keeping effect of Lilium cut flowers.[Method]Using Lilium"Sorbonne"as the material,nine kinds of household vase solutions were prepared by edible white granulated sugar,white vinegar,akafen powder and vitamin C tablets,respectively.The morphological and physiological indexes of Lilium cut flowers,including vase life,ornamental grade,flower diameter,fresh weight of flower branches,water balance value,soluble protein content and MDA content of petals,were observed,and the effects of nine kinds of household vase solutions on fresh-keeping effect of Lilium cut flowers were studied.[Result]The household vase solution F8(20 g/L white granated sugar+1 packet/L acafen powder+2 tablets/L vitamin C tablets)had the best fresh-keeping effect on Lilium cut flowers,which was beneficial to prolong the vase life and improve the ornamental value of Lilium cut flowers.[Conclusion]The household vase solution of Lilium cut flowers is optimized,which is not only environmentally friendly but also convenient for ordinary families.

Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.