Shear resistance characteristics and influencing factors of root-soil composite on an alpine metal mine dump slope with different recovery periods

Artificial vegetation restoration is the main measure for vegetation restoration and soil and water conservation in alpine mine dumps on the Qinghai-Tibet Plateau,China.However,there are few reports on the dynamic changes and the influencing factors of the soil reinforcement effect of plant species after artificial vegetation restoration under different recovery periods.We selected dump areas of the Delni Copper Mine in Qinghai Province,China to study the relationship between the shear strength and the peak displacement of the root-soil composite on the slope during the recovery period,and the influence of the root traits and soil physical properties on the shear resistance characteristics of the root-soil composite via in situ direct shear tests.The results indicate that the shear strength and peak displacement of the rooted soil initially decreased and then increased with the increase of the recovery period.The shear strength of the rooted soil and the recovery period exhibited a quadratic function relationship.There is no significant function relationship between the peak displacement and the recovery period.Significant positive correlations(P<0.05)exists between the shear strength of the root-soil composite and the root biomass density,root volume density,and root area ratio,and they show significant linear correlations(P<0.05).There are no significant correlations(P>0.05)between the shear strength of the root-soil composite and the root length density,and the root volume ratio of the coarse roots to the fine roots.A significant negative linear correlation(P<0.05)exists between the peak displacement of the rooted soil and the coarse-grain content,but no significant correlations(P>0.05)with the root traits,other soil physical property indices(the moisture content and dry density of the soil),and slope gradient.The coarse-grain content is the main factor controlling the peak displacement of the rooted soil.

Predicting dynamic compressive strength of frozen-thawed rocks by characteristic impedance and data-driven methods

In cold regions,the dynamic compressive strength(DCS)of rock damaged by freeze-thaw weathering significantly influences the stability of rock engineering.Nevertheless,testing the dynamic strength under freeze-thaw weathering conditions is often both time-consuming and expensive.Therefore,this study considers the effect of characteristic impedance on DCS and aims to quickly determine the DCS of frozen-thawed rocks through the application of machine-learning techniques.Initially,a database of DCS for frozen-thawed rocks,comprising 216 rock specimens,was compiled.Three external load parameters(freeze-thaw cycle number,confining pressure,and impact pressure)and two rock parameters(characteristic impedance and porosity)were selected as input variables,with DCS as the predicted target.This research optimized the kernel scale,penalty factor,and insensitive loss coefficient of the support vector regression(SVR)model using five swarm intelligent optimization algorithms,leading to the development of five hybrid models.In addition,a statistical DCS prediction equation using multiple linear regression techniques was developed.The performance of the prediction models was comprehensively evaluated using two error indexes and two trend indexes.A sensitivity analysis based on the cosine amplitude method has also been conducted.The results demonstrate that the proposed hybrid SVR-based models consistently provided accurate DCS predictions.Among these models,the SVR model optimized with the chameleon swarm algorithm exhibited the best performance,with metrics indicating its effectiveness,including root mean square error(RMSE)﹦3.9675,mean absolute error(MAE)﹦2.9673,coefficient of determination(R^(2))﹦0.98631,and variance accounted for(VAF)﹦98.634.This suggests that the chameleon swarm algorithm yielded the most optimal results for enhancing SVR models.Notably,impact pressure and characteristic impedance emerged as the two most influential parameters in DCS prediction.This research is anticipated to serve as a reliable reference for estimating the DCS of rocks subjected to freeze-thaw weathering.

The Study of Root Subspace Decomposition between Characteristic Polynomials and Minimum Polynomial

Let Abe the linear transformation on the linear space V in the field P, Vλibe the root subspace corresponding to the characteristic polynomial of the eigenvalue λi, and Wλibe the root subspace corresponding to the minimum polynomial of λi. Consider the problem of whether Vλiand Wλiare equal under the condition that the characteristic polynomial of Ahas the same eigenvalue as the minimum polynomial (see Theorem 1, 2). This article uses the method of mutual inclusion to prove that Vλi=Wλi. Compared to previous studies and proofs, the results of this research can be directly cited in related works. For instance, they can be directly cited in Daoji Meng’s book “Introduction to Differential Geometry.”

EXTRACTION OF CHARACTERISTIC ROOTS ON BESSEL-NEUMANN’S MIXED EQUATIONS

This paper discusses the problem of the extraction of characteristic roots on Bessel-Neumann's mixed equations. It gives the expressions and the evaluation of the minimum root. The advantage of the method has no use for the table of the multi-figure number Bessel function and it does not need computer but can calculate all the characteristic roots The precision of these roots is still high.

Matlab Methods for Roots of Characteristic Equation of Cylindrical Bessel Equation Eigenvalue Problems on General Interval

Root of characteristic equation for cylindrical Bessel equation eigenvalue problems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.

Research on dynamic characteristics of arc under electrode relative motion

The relative motion of the electrodes is a typical feature of sliding electrical contact systems.The system fault caused by the arc is the key problem that restricts the service life of the sliding electrical contact system.In this paper,an arcing experimental platform that can accurately control the relative speed and distance of electrodes is built,and the influence of different electrode speeds and electrode distances on arc motion characteristics is explored.It is found that there are three different modes of arc root motion:single arc root motion mode,single and double arc roots alternating motion mode,and multiple arc roots motion mode.The physical process and influence mechanism of different arc root motion modes are further studied,and the corresponding relationship between arc root motion modes and electrode speed is revealed.In addition,to further explore the distribution characteristics of arc temperature and its influencing factors,an arc magnetohydrodynamic model under the relative motion of electrodes is established,and the variation law of arc temperature under the effect of different electrode speeds and electrode distances is summarized.Finally,the influence mechanism of electrode speed and electrode distance on arc temperature,arc root distance,and arc root speed is clarified.The research results enrich the research system of arc dynamic characteristics in the field of sliding electrical contact,and provide theoretical support for restraining arc erosion and improving the service life of the sliding electrical contact system.

Effects of Antimony Stress on Root Growth,Antimony Accumulation and Physiological Characteristics of Ramie(Boehmeria nivea(L.) Gaudich.)

[Objectives]This study was conducted to investigate the toxicity of heavy metal antimony(Sb) to ramie(Boehmeria nivea(L.) Gaudich.) and the tolerance response in ramie. [Methods] A pot experiment was conducted to study the effects of Sb stress on root growth and Sb accumulation and transport of the root system of cultivated ramie Zhongzhu No.1, as well as on the physiological characteristics of ramie leaves. [Results] The plant height and root dry weight and volume of Zhongzhu No.1 showed an effect of "promoting at low concentrations and inhibiting at high concentrations" with the increase of Sb concentration, and decreased significantly at the concentration of 4 000 mg/kg, but no obvious toxic growth symptoms were observed. The content of Sb in roots(289.7-508.6 mg/kg) and the root-shoot transfer factor(0.09-0.57) of Zhongzhu No.1 increased with the increase of soil Sb concentration, but the change of Sb bioconcentration factor in roots was opposite, indicating that high concentrations of Sb in soil could promote the absorption of Sb in roots and the transport of Sb to the aboveground part, but the Sb enrichment capacity of roots was relatively reduced with the increase of soil Sb. Sb stress had a certain impact on the physiological characteristics of ramie leaves. With the increase of Sb treatment concentration, MDA, POD and SOD showed a change trend of "first increasing and then decreasing", while CAT gradually increased, indicating that Sb stress caused changes in the physiological characteristics of ramie leaves, thereby affecting plant growth and development. [Conclusions] This study provides a theoretical basis for ecological restoration of ramie in mining areas.

Fine Root Distribution Characteristics of Populus cathayana Plantations at Different Ages in Alpine Sandy Land

[Objectives]The paper was to study the fine root distribution characteristics of Populus cathayana plantations at different ages in alpine sandy land.[Methods]With 5,10,15,20,and 25 years old P.cathayana plantation in the eastern margin of Gonghe Basin,Qinghai Province as the research objects,fine roots were collected by root core drilling method,and the differences of fine root biomass,root length density,average diameter and root tip number at the soil depths of 0-20,20-40,40-60,60-80 and 80-100 cm were analyzed.[Results]The total biomass density of P.cathayana plantation was mainly distributed in the soil layer of 0-60 cm,accounting for 76%of the entire soil layer,and its value increased with the increase in forest age.With the increase in different forest ages,the root length density,average diameter and root tip number of living fine roots in the soil layer of 0-60 cm accounted for 74%-81%of the entire soil layer,and the proportions in the soil layers of 60-80 and 80-100 cm were 9%-11%.The biomass density,root length density,average diameter and root tip number of living and dead fine roots of P.cathayana plantation increased with the increase of forest age.The root length density,average diameter and root tip number of P.cathayana fine roots showed a linear function change trend with the growth of forest age,which could be described by the linear function equation y=ax+b(a>0).The analysis results showed that the root length density,average diameter and root tip number of P.cathayana were significantly correlated with the total biomass density of fine roots,and the root length density and average diameter had an extremely positive correlation with the total biomass density.[Conclusions]In the future,P.cathayana plantation should be properly tended to promote the development of fine roots and maximize its ecological benefits.

CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.

Derivation of lattice Boltzmann equation via analytical characteristic integral

A lattice Boltzmann(LB) theory, the analytical characteristic integral(ACI) LB theory, is proposed in this paper.ACI LB theory takes the Bhatnagar–Gross–Krook(BGK)-Boltzmann equation as the exact kinetic equation behind Navier–Stokes continuum and momentum equations and constructs an LB equation by rigorously integrating the BGK-Boltzmann equation along characteristics. It is a general theory, supporting most existing LB equations including the standard lattice BGK(LBGK) equation inherited from lattice-gas automata, whose theoretical foundation had been questioned. ACI LB theory also indicates that the characteristic parameter of an LB equation is collision number, depicting the particle-interaction intensity in the time span of the LB equation, instead of the traditionally assumed relaxation time, and the over-relaxation time problem is merely a manifestation of the temporal evolution of equilibrium distribution along characteristics under high collision number, irrelevant to particle kinetics. In ACI LB theory, the temporal evolution of equilibrium distribution along characteristics is the determinant of LB method accuracy and we numerically prove this.

The Characteristic Function Method and Its Application to (1 + 1)-Dimensional Dispersive Long Wave Equation

In this paper, the characteristic function method is applied to seek traveling wave solutions of nonlinear partial differential equations in a unified way. We consider the Wu-Zhang equation (which describes (1 + 1)-dimensional disper-sive long wave). The equations governing the wave propagation consist of a pair of non linear partial differential equations. The characteristic function method reduces the system of nonlinear partial differential equations to a system of nonlinear ordinary differential equations which is solved via the shooting method, coupled with Rungekutta scheme. The results include kink-profile solitary wave solutions, periodic wave solutions and rational solutions. As an illustrative example, the properties of some soliton solutions for Wu-Zhang equation are shown by some figures.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

Canonical Characteristic Relation for Two Dimensional Euler Equations

We propose a new way of rewriting the two dimensional Euler equations and derive an original canonical characteristic relation based on the characteristic theory of hyperbolic systems. This relation contains the derivatives strictly along the bicharacteristic directions, and can be viewed as the 2D extension of the characteristic relation in 1D case.

Characteristic-based finite volume scheme for 1D Euler equations

In this paper, a high-order finite-volume scheme is presented for the one- dimensional scalar and inviscid Euler conservation laws. The Simpson＇s quadrature rule is used to achieve high-order accuracy in time. To get the point value of the Simpson＇s quadrature, the characteristic theory is used to obtain the positions of the grid points at each sub-time stage along the characteristic curves, and the third-order and fifth-order central weighted essentially non-oscillatory （CWENO） reconstruction is adopted to estimate the cell point values. Several standard one-dimensional examples are used to verify the high-order accuracy, convergence and capability of capturing shock.

Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations （PDEs） with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu＇s method, in differential equations.

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING'S EQUATION

The 1/3 sub-harmonic solution for the Duffing＇s with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.

MIXED FINITE ELEMENT METHODS FOR THE SHALLOW WATER EQUATIONS INCLUDING CURRENT AND SILT SEDIMENTATION (Ⅱ)——THE DISCRETE-TIME CASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation system consisting of water dynamics equations,silt transport equation,and the equation of bottom topography change were derived.A fully discrete MFE scheme for the discrete_time along characteristics is presented and error estimates are established.The existence and convergence of MFE solution of the discrete current velocity,elevation of the bottom topography,thickness of fluid column,and mass rate of sediment is demonstrated.

Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity

A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity, the characteristic equation which the characteristic general solution vectors must satisfy is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced ad- joint matrices of the differential operator matrix, the corresponding fundamental analyt- ical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin （B-G） solutions, modified Papkovich-Neuber solutions proposed by Min-zhong WANG （P-N-W）, and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial func- tions used in numerical methods.

Morphological Characteristics and Nutrient Content of Fine Roots of 2-Year-Old and 3-Year-Old Eucalyptus grandis Plantation

[ Objective] This study aimed to explore the morphological characteristics and nutrient content of f＇me roots of 2-year-old and 3-year-old Euca/yptus grand/s plantation and investigate the correlation. [ Method] Fine roots of 2-year-old and 3-year-old Eucalyptus grandis plantation were collected as experimental materials, to determine the root diameter （D）, root length （L）, specific root length （SRL） and contents of major nutrient elements N, P, K, Ca, Mg and C of fine roots （level 1 -5）, study the morphological characteristics and major nutrient element content and investigate the correlation. [ Result] The results showed that morphological differences of fine roots （ level 1 - 5 ） of Eucalyptus grandis plantation were great with the increase of root order, to be specific, D and L increased and SRL decreased with the increasing root order; SRL, L and D of 3-year-old Eucalyptus grauclis plantation were greater than those of 2-year-old Euca/yptus grand/s plantation. Contents of N, Ca, Mg and C of fine roots of 2-year-old and 3-year-old Eucalyptus grandis plantation showed consistent orders with the increase of root order： N and Mg contents were reduced, while Ca and C contents were enhanced; P and K contents varied with different forest ages; both 2-year-old and 3-year- old Eucalyptus grandis showed an order of C 〉 K 〉 Ca （Mg） 〉 N. Major nutrient element content and morphological characteristics of Eucalyptus grand/s fine roots （level 1 -5 ） were extremely significantly correlated （P 〈0.01 ）, SRL, L and D could be adopted as reference indices to evaluate nutrient status of Eucalyptus grand/s. Required nutrients and fine root morphology of Eucalyptus grandis plantation changed with the increase of forest age, and the nutrient cycling and energy flow patterns also changed; major nutrient dements in fine roots of 2-year-old and 3-year-old Eucalyptus grandis plantation transferred in a different order from the growth order, therefore N fertilizer could be applied to improve the growth of fine roots. [ Condusion] This study laid the foundation for understanding the fine root morphology and nutrient variation pattern of Eucalyptus grandis plantation and enriching the response and adaptation mechanism theory of roots to environment, pos- sessing important reference significance for the sustainable development of Eucalyptus grand/s plantation.