The Second Variation of the Functional L of Symplectic Critical Surfaces in Kähler Surfaces

Let M be a complete Kähler surface andbe a symplectic surface which is smoothly immersed in M.Letαbe the Kähler angle ofin M.In the previous paper Han and Li(JEMS 12:505–527,2010)2010,we study the symplectic critical surfaces,which are critical points of the functional L=1 cosαdμin the class of symplectic surfaces.In this paper,we calculate the second variation of the functional L and derive some consequences.In particular,we show that,if the scalar curvature of M is positive,is a stable symplectic critical surface with cosα≥δ>0,whose normal bundle admits a holomorphic section X∈L2(),thenis holomorphic.We construct symplectic critical surfaces in C2.We also prove a Liouville theorem for symplectic critical surfaces in C2.

Upper bound of Kahler angles on the β-symplectic critical surfaces

Let(M,g)be a Kähler surface andΣbe aβ-symplectic critical surface in M.If L_(q)(Σ)is bounded for some q>3,then we give a uniform upper bound for the Kähler angle onΣ.This bound only depends on M,q,βand the Lq functional ofΣ.For q>4,this estimate is known and we extend the scope of q.

A Simple Monte Carlo Method for Locating the Three-dimensional Critical Slip Surface of a Slope

Based on the assumption of the plain-strain problem, various optimization or random search methods have been developed for locating the critical slip surfaces in slope-stability analysis, but none of such methods is applicable to the 3D case. In this paper, a simple Monte Carlo random simulation method is proposed to identify the 3D critical slip surface. Assuming the initial slip to be the lower part of a slip ellipsoid, the 3D critical slip surface is located by means of a minimized 3D safety factor. A column-based 3D slope stability analysis model is used to calculate this factor. In this study, some practical cases of known minimum safety factors and critical slip surfaces in 2D analysis are extended to 3D slope problems to locate the critical slip surfaces. Compared with the 2D result, the resulting 3D critical slip surface has no apparent difference in terms of only cross section, but the associated 3D safety factor is definitely higher.

Near-zero-adhesion-enabled intact wafer-scale resist-transfer printing for high-fidelity nanofabrication on arbitrary substrates

There is an urgent need for novel processes that can integrate different functional nanostructures onto specific substrates,so as to meet the fast-growing need for broad applications in nanoelectronics,nanophotonics,and fexible optoelectronics.Existing direct-lithography methods are difficult to use on fexible,nonplanar,and biocompatible surfaces.Therefore,this fabrication is usually accomplished by nanotransfer printing.However,large-scale integration of multiscale nanostructures with unconventional substrates remains challenging because fabrication yields and quality are often limited by the resolution,uniformity,adhesivity,and integrity of the nanostructures formed by direct transfer.Here,we proposed a resist-based transfer strategy enabled by near-zero adhesion,which was achieved by molecular modification to attain a critical surface energy interval.This approach enabled the intact transfer of wafer-scale,ultrathin-resist nanofilms onto arbitrary substrates with mitigated cracking and wrinkling,thereby facilitating the in situ fabrication of nanostructures for functional devices.Applying this approach,fabrication of three-dimensional-stacked multilayer structures with enhanced functionalities,nanoplasmonic structures with~10 nm resolution,and MoS2-based devices with excellent performance was demonstrated on specific substrates.These results collectively demonstrated the high stability,reliability,and throughput of our strategy for optical and electronic device applications.

Optics-based metaheuristic approach to assess critical failure surfaces in both circular and non-circular failure modes for slope stability analysis

In many construction projects,a proactive slope stability evaluation is a prerequisite.Although many deterministic or non-deterministic approaches have been commonly used,metaheuristic approaches have resulted in high precision and significant outcomes for slope stability analysis problems.The current work focuses on the reliable assessment of critical failure surfaces associated with the least factor of safety value in both homogeneous and non-homogeneous slopes using a new simplified meta-heuristic approach called optics-inspired optimization(OIO).The algorithm utilizes six different LEM methods as a fitness function for deriving the factor of safety.Experimental analysis over three benchmark studies has been performed to demonstrate the algorithm's robustness and effectiveness.The implementation found more robust results as compared to previous studies.Meanwhile,the algorithm's statistical implication is conducted using the ANOVA test,which inferred better outcomes.With this interpretation,the approach claims to be suitable and efficient for slope stability analysis.

Rigorous back analysis of shear strength parameters of landslide slip

A rigorous back analysis of shear strength parameters of landslide slip was presented. Kinematical element method was adopted to determine factor of safety and critical failure surface, which overcomes the disadvantage of limit equilibrium method. The theoretical relationship between the combination of shear strength parameters and stability state was studied. The results show that the location of critical slip surface, F/tan f and F/c depend only on the value of c/tan f. The failure surface moves towards the inside of slope as c/tan f increases. According to the information involving factor of safety and critical failure surface in a specific cross-section, strength parameters can be back calculated based on the above findings. Three examples were given for demonstrating the validity of the present method. The shear strength parameters obtained by back analysis are almost consistent with their correct solutions or test results.

A Generalized Limit Equilibrium Method for the Solution of Active Earth Pressure on a Retaining Wall

In this paper, a generalized limit equilibrium method of solving the active earth pressure problem behind a retaining wall is proposed.Differing from other limit equilibrium methods, an arbitrary slip surface shape without any assumptions of pre-defined shapes is needed in the current framework, which is verified to find the most probable failure slip surface. Based on the current computational framework, numerical comparisons with experiment, discrete element method and other methods are carried out. In addition, the influences of the inclination of the wall, the soil cohesion, the angle of the internal friction of the soil, the slope inclination of the backfill soil on the critical pressure coefficient of the soil, the point of application of the resultant earth pressure and the shape of the slip surface are also carefully investigated. The results demonstrate that limit equilibrium solution from predefined slip plane assumption, including Coulomb solution, is a special case of current computational framework. It is well illustrated that the current method is feasible to evaluate the characteristics of earth pressure problem.

Back analysis of general slope under earthquake forces using upper bound theorem

Long time monitoring is acquired to obtain the displacement data for displacement-based geotechnical material back analysis, and these data are hard to be measured under some special condition, such as earthquake. For a simple homogeneous slope, the position of a critical failure surface is determined by value of c/tan ~b. Utilizing upper bound theorem of limit analysis, the external work rate and internal energy for normal slope under earthquake forces are given, and the formula for minimum safety factor is derived. On this basis, the equation of slip surface and the surface depth of a given position are solved. In this way, the strength parameter can be analyzed by known slip surface depth. For practical use, the surface depth for a given slope under varying strength parameter is presented. Finally, two examples are given to show its simplicity and effectiveness.

Determination of critical slip surface of fractured rock slopes based on fracture orientation data

The critical slip surface of a fractured rock slope tends to extend along the fractures.Thus,fracture orientation plays a critical role in determining the critical slip surface.Based on fracture orientation data,this paper examines the critical slip surfaces of fractured rock slopes.Given that the surface of a fractured rock slope extends along the fracture surfaces,or the wedges,with each composed of two arbitrary fractures,the critical slip surface is determined via stochastic dynamics.In addition,a fracture frequency method is proposed as a means of analyzing the critical slip surface.According to this method,the critical slip surface slips in whichever direction has the lowest fracture frequency.Based on the stochastic dynamics method and the fracture frequency method,the critical slip surface of the slope is finally determined,that is,the critical slip surface takes the form of a plane passing the slope toe with a dip of 120° and a dip angle of 45°.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional(3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

Study on the critical submergence of surface vortices and the design of anti-vortex intakes

Surface vortex behavior in front of the tunnel intake was investigated in this paper.The critical submergence of vortex was discussed based on the concept of 'critical spherical sink surface'(CSSS).The vortex formation and evolution at the tunnel intake were analyzed based on the theory of CSSS considering the effect of circulation.A theory was proposed to explain the surface vortex.The theoretical development was verified by the physical model experiments of Xiluodu hydropower station.The radial velocity and vortex circulation were considered as the main factors that influence the formation and evolution of surface vortex.Finally,an anti-vortex intake configuration was proposed to weaken the air-core vortex in front of the tunnel intakes of the hydraulic structures.

Effect of Inclined Tension Crack on Rock Slope Stability by SSR Technique

The tension cracks and joints in rock or soil slopes affect their failure stability.Prediction of rock or soil slope failure is one of the most challenging tasks in the earth sciences.The actual slopes consist of inhomogeneous materials,complex morphology,and erratic joints.Most studies concerning the failure of rock slopes primarily focused on determining Factor of Safety(FoS)and Critical Slip Surface(CSS).In this article,the effect of inclined tension crack on a rock slope failure is studied numerically with Shear Strength Reduction Factor(SRF)method.An inclined Tension Crack(TC)influences the magnitude and location of the rock slope’s Critical Shear Strength Reduction Factor(CSRF).Certainly,inclined cracks are more prone to cause the failure of the slope than the vertical TC.Yet,all tension cracks do not lead to failure of the slope mass.The effect of the crest distance of the tension crack is also investigated.The numerical results do not show any significant change in the magnitude of CSRF unless the tip of the TC is very near to the crest of the slope.ATC is also replaced with a joint,and the results differ from the corresponding TC.These results are discussed regarding shear stress and Critical Slip Surface(CSS).

Observation of lateral long range order in superconducting FeTe thin films

We find that the superconductivity in the thin films of the formerly believed non-superconducting parent compound FeTe is accompanied by an emergence of second order with a correlation length of 742 nm and 258 nm at 10 K and 300 K, respectively. The structural phase transition found in iron pnictide superconductors, in non-superconducting FeTe bulk samples, and in FeSe superconducting thin films is not observed in the superconducting FeTe thin films. The interplay between superconductivity and long range order may suggest the crucial role of competition between electronic localization and itinerancy which leads to strong quantum fluctuations in the FeTe system.

Quantitative Modeling for Corrosion Behavior in Complex Coupled Environment by Response Surface Methodology

Response surface methodology（RSM） is introduced into corrosion research as a tool to assess the effects of environmental factors and their interactions on corrosion behavior and establish a model for corrosion prediction in complex coupled environment（CCE）. In this study, a typical CCE, that is, the corrosion environment of pipelines in gas field is taken as an example. The effects of environmental factors such as chloride concentration, pH value and pressure as well as their interactions on critical pitting temperature（CPT） were evaluated, and a quadratic polynomial model was developed for corrosion prediction by RSM. The results showed that the model was excellent in corrosion prediction with R2= 0.9949. CPT was mostly affected by single environmental factor rather than interaction, and among the whole factors, chloride concentration was the most influential factor of CPT.

Gradient Flow of the L_(β)-Functional

In this paper,we start to study the gradient flow of the functional L_(β) introduced by Han-Li-Sun in[8].As a first step,we show that if the initial surface is symplectic in a Kähler surface,then the symplectic property is preserved along the gradient flow.Then we show that the singularity of the flow is characterized by the maximal norm of the second fundamental form.When β=1,we derive a monotonicity formula for the flow.As applications,we show that the l-tangent cone of the flow consists of the finite flat planes.

Comparative study of material point method and upper bound limit analysis in slope stability analysis

The upper bound limit analysis(UBLA)is one of the key research directions in geotechnical engineering and is widely used in engineering practice.UBLA assumes that the slip surface with the minimum factor of safety(FSmin)is the critical slip surface,and then applies it to slope stability analysis.However,the hypothesis of UBLA has not been systematically verified,which may be due to the fact that the traditional numerical method is difficult to simulate the large deformation.In this study,in order to systematically verify the assumption of UBLA,material point method(MPM),which is suitable to simulate the large deformation of continuous media,is used to simulate the whole process of the slope failure,including the large-scale transportation and deposition of soil mass after slope failure.And a series of comparative studies are conducted on the stability of cohesive slopes using UBLA and MPM.The proposed study indicated that the slope angle,internal friction angle and cohesion have a remarkable effect on the slip surface of the cohesive slope.Also,for stable slopes,the calculation results of the two are relatively close.However,for unstable slopes,the slider volume determined by the UBLA is much smaller than the slider volume determined by the MPM.In other words,for unstable slopes,the critical slip surface of UBLA is very different from the slip surface when the slope failure occurs,and when the UBLA is applied to the stability analysis of unstable slope,it will lead to extremely unfavorable results.

Catenoidal Layers for the Allen-Cahn Equation in Bounded Domains

This paper presents a new family of solutions to the singularly perturbed Allen-Cahn equation α~2Δu + u(1- u^2) = 0 in a smooth bounded domain Ω R^3, with Neumann boundary condition and α > 0 a small parameter. These solutions have the property that as α→ 0, their level sets collapse onto a bounded portion of a complete embedded minimal surface with finite total curvature intersecting ?Ω orthogonally and that is non-degenerate respect to ?Ω. The authors provide explicit examples of surfaces to which the result applies.