Walking of spider on water surface studied from its leg shadows

Different from sculling forward of water striders with their hairy water-repellent legs, water spiders walked very quickly on water surfaces. By using a shadow method, the walking of water spiders had been studied. The three-dimensional trajectories and the supporting forces of water spider legs during walking forward were achieved. Results showed that the leg movement could be divided into three phases： slap, stroke, and retrieve. Employing an effective strategy to improving walking efficiency, the sculling legs supported most of its body weight while other legs were lifted to reduce the lateral water resistance, which was similar to the strategy of water striders. These findings could help guiding the design of water walking robots with high efficiency.

Measurement Method of Compressibility and Thermal Expansion Coefficients for Density Standard Liquid at 2329 kg/m^3 based on Hydrostatic Suspension Principle

The accurate measurement on the compressibility and thermal expansion coefficients of density standard liquid at 2329kg/m3（DSL-2329） plays an important role in the quality control for silicon single crystal manufacturing. A new method is developed based on hydrostatic suspension principle in order to determine the two coefficients with high measurement accuracy. Two silicon single crystal samples with known density are immersed into a sealed vessel full of DSL-2329. The density of liquid is adjusted with varying liquid temperature and static pressure, so that the hydrostatic suspension of two silicon single crystal samples is achieved. The compression and thermal expansion coefficients are then calculated by using the data of temperature and static pressure at the suspension state. One silicon single crystal sample can be suspended at different state, as long as the liquid temperature and static pressure function linearly according to a certain mathematical relationship. A hydrostatic suspension experimental system is devised with the maximal temperature control error ±50 μK; Silicon single crystal samples can be suspended by adapting the pressure following the PID method. By using the method based on hydrostatic suspension principle, the two key coefficients can be measured at the same time, and measurement precision can be improved due to avoiding the influence of liquid surface tension. This method was further validated experimentally, where the mixture of 1, 2, 3-tribromopropane and 1,2-dibromoethane is used as DSL-2329. The compressibility and thermal expansion coefficients were measured, as 8.5′10–4 K–1 and 5.4′10–10 Pa–1, respectively.

From the second gradient operator and second class of integral theorems to Gaussian or spherical mapping invariants

By combining of the second gradient operator, the second class of integral theorems, the Gaussian-curvature-based integral theorems and the Gaussian （or spherical） mapping, a series of invariants or geometric conservation quantities under Gaussian （or spherical） mapping are revealed. From these mapping invariants important transformations between original curved surface and the spherical surface are derived. The potential applications of these invariants and transformations to geometry are discussed

Shape gradient and classical gradient of curvatures:driving forces on micro/nano curved surfaces

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.

Numerical and Experimental Study of the Roughness Effects on Mechanical Properties of AISI316L by Nanoindentation

Surface roughness is a commonly used criterion for characterization of surface quality in a machining operation. In the study of micro-scale mechanical properties of machined surface and cutting tool using nanoindentation method, perfect surface finish on the specimen is often required for the reliable indentation result. However, the perfect surface finish is often difficult to obtain from the machining operation due to the dynamic behavior of the machining and the limitation of the cutting tool geometry. In the presented paper, the effect of surface roughness on the nanoindentation measurements is investigated by using finite element method. A 3D finite element model with seven levels of surface roughness is developed to simulate the load-displacement behavior in an indentation process with a Berkovich indenter. The material used in the simulation is AISI 316 L stainless steel, modeled as an elastic-plastic material. The mechanical properties were calculated by combining simulations with the Oliver-Pharr method. The hardness and reduced modulus from the simulation were found to decrease with an increase of roughness. The study showed that the scatter of the load-depth curves and the deviation of the hardness and the reduced modulus are significant affected by the variation of roughness. It was also found that the height of pile-up was little affected by the surface roughness from the simulation. The combined effect of indenter tip radius and surface roughness was also investigated. The study was complemented with experimental tests and the results from these tests support the results from the simulation.

A three-dimensional nonlinear reduced-order predictive joint model

Mechanical joints can have significant effects on the dynamics of assembled structures.However,the lack of efficacious predictive dynamic models tot joints hinders accurate prediction of their dynamic behavior.The goal of our work is to develop physics-based,reduced-order,finite element models that are capable of replicating the effects of joints on vi- brating structures.The authors recently developed the so-called two-dimensional adjusted lwan beam element(2-D AIBE) to simulate the hysteretic behavior of bolted joints in 2-D beam structures.In this paper,2-D AIBE is extended to three-di- mensional cases by formulating a three-dimensional adjusted lwan beam element(3-D AIBE).hupulsive loading experi- ments are applied to a jointed frame structure and a beam structure containing the same joint.The frame is subjected to ex- citation out of plane so that the joint is under rotation and single axis bending.By assuming that the rotation in the joint is linear elastic,the parameters of the joint associated with bending in the flame are identified from acceleration responses of the jointed beam structure,using a multi-layer teed-torward neural network(MLFF).Numerieal simulation is then per- formed on the frame structure using the identified parameters.The good agreement between the simulated and experimental impulsive acceleration responses of the frame structure validates the efficacy of the presented 3-D AIBE,and indicates that the model can potentially be applied to more complex structural systems with joint parameters identified from a relatively simple structure.

Performance assisted enhancement based on change point detection and Kalman filtering

A performance assisted enhancement Kalman filtering algorithm(PAE-KF) for GPS/INS integration navigation in urban areas was presented in this work. The aim of this PAE-KF algorithm was to prevent "deep contamination" caused by error GPS data. This filtering algorithm effectively combined fault estimation of raw GPS data and nonholonomic constraint of vehicle. In fault estimation, a change point detection algorithm based on abrupt change model was proposed. Statistical tool was then used to infer the future bound of GPS data, which can detect faults in GPS raw data. If any kinds of faults were detected, dead reckoning mechanism begins to compute current position. Nonholonomic constraint condition of vehicle was used to estimate velocity of vehicle and change point detection was added into classic Kalman filtering structure. Experiment on vehicle shows that even when the GPS signals are unavailable for a period of time, this method can also output high accuracy data.

Fractal growth kinematics abstracted from snowflakes:topological evolution

Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.

Fractal geometry and topology abstracted from hair fibers

Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.

Multiple-cell elements and regular multifractals

Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper： First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the con- struction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed.

Growth kinematics of fractal super snowflakes

Based on the recent research progress in fractal super fibers,the growth kinematics(or pattern kinematics) of(6+1) -circle fractal super fiber with snowflake-like cross section(abbreviated as"fractal super snowflake") is explored.The following results are obtained.(1) The fractal super snowflake obeys simply the straight-line growth mode.(2) At a given movement,the growth speed of the snowflake distributes uniformly in space.At a given point in space,the growth speed decreases along with the time.(3) The growth kinematics of the fractal super snowflake is intensively influenced by the self-similar ratio:If and only if the self-similar ratio is equal to 1/3,the macro speed equals to the micro speed,and the macro density equals to the micro density.If the self-similar ratio is smaller than 1/3,the micro speed is larger than the macro speed,and the micro density is larger than the macro density.If the self-similar ratio is larger than 1/3,the macro speed is larger than the micro speed,and the macro density is larger than the micro density.These results provide references for us to understand the complicated fractal growing phenomena in nature.

EXOTHERMIC MODEL OF PERCOLATION ZONE IN A GLACIER

During the ablation period, the melt-water on the surface of percolation zone of a glacier percolates down through the snow layer when it cools and freezes, the latent heat released causes the temperature of metres of the snow layer to rise to 0℃. However, at the end of ablation period melting stops, the snow layer through which melt-water permeated begins to release heat to the air and the temperature on the surface of snow layer decreases. As a result, the melt-water in the snow layer

Unified Solution of Conjugate Fluid and Solid Heat Transfer-Part I.Solid Heat Conduction

A unified solution framework is proposed for efficiently solving conjugate fluid and solid heat transfer problems.The unified solution is solely governed by the compressible Navier-Stokes(N-S)equations in both fluid and solid domains.Such method not only provides the computational capability for solid heat transfer simulations with existing successful N-S flow solvers,but also can relax time-stepping restrictions often imposed by the interface conditions for conjugate fluid and solid heat transfer.This paper serves as Part I of the proposed unified solution framework and addresses the handling of solid heat conduction with the nondimensional N-S equations.Specially,a parallel,adaptive high-order discontinuous Galerkin unified solver has been developed and applied to solve solid heat transfer problems under various boundary conditions.

Understanding the multifunctionality in Cu-doped BiVO_4 semiconductor photocatalyst

A visible light-induced, Cu-doped BiVO_4 photocatalyst was synthesized by a microwave hydrothermal method. The photocatalytic efficiency was investigated in the degradation of model water pollutants like Methylene Blue(dye) and ibuprofen(pharmaceuticals), as well as the inactivation of Escherichia coli(bacteria). The Cu-doped BiVO4 samples showed better efficiency than undoped BiVO_4, and the 1 wt.% Cu-doped BiVO_4 sample showed the best efficiency. The degradation of Methylene Blue reached 95%, while the degradation of ibuprofen reached 75%, and the inactivation of E. coli reached 85% in irradiation with visible light. The appearance of additional absorption band shoulders and widening of the optical absorption in the visible range makes the prepared powder an efficient visible light-driven photocatalyst. Moreover, the formation of an in-gap energy state just above the valance band as determined by density functional theory(DFT) first principle calculation, facilitates the wider optical absorption range of the doped system. Similarly, this in-gap energy state also acts as an electron trap, which is favorable for the efficient separation and photoexcited charge carriers' transfer process. The formation of oxygen vacancies due to doping also improved the separation of the charge carrier, which promoted the trapping of electrons and inhibited electron hole recombination, thus increasing the photocatalytic activity. No decrease in the efficiency of the 1 wt.% Cu-doped BiVO_4 photocatalyst in the degradation of ibuprofen over three consecutive cycles revealed the stability of the photocatalyst towards photocorrosion. These findings highlight the multifunctional applications of Cu-doped BiVO_4 in wastewater containing multiple pollutants.

Interaction potential between micro/nano curved surface and a particle located inside the surface (I):driving forces induced by curvatures

This paper focuses on the interaction between a micro/nano curved surface and a particle located inside the surface (hereafter abbreviated as in-surface-particle).Based on the exponential pair potential (namely 1/R2k) between particles,the interaction potential between the micro/nano curved surface and the in-surface-particle is derived.The following results are shown:(a) For an even number of exponents in the pair potential,the interaction potential between the micro/nano curved surface and the in-surface-particle can be expressed as a unified function of the mean curvature and Gaussian curvature of the curved surface;(b) the curvatures and the gradients of curvatures of the micro/nano curved surface are the essential factors that dominate the driving force acting on the particle.

Interaction potential between micro/nano curved surface and a particle located inside the surface (II):Numerical experiment and equipotential surfaces

We verify the accuracy of the curvature-based potential.By means of the idealized numerical experiment,we show that the curvature-based potential is in good agreement with the numerical experiment,and the errors are within a reasonable range.Based on the curvature-based potential,the equipotential surfaces of particles are derived,and the intrinsic relations between the equipotential surfaces and Weingarten helicoids are shown.

Invariants for Parallel Mapping

This paper analyzes the geometric quantities that remain unchanged during parallel mapping （i.e., mapping from a reference curved surface to a parallel surface with identical normal direction）. The second gradient operator, the second class of integral theorems, the Gauss-curvature-based integral theorems, and the core property of parallel mapping are used to derive a series of parallel mapping invariants or geometrically conserved quantities. These include not only local mapping invariants but also global mapping invafiants found to exist both in a curved surface and along curves on the curved surface. The parallel mapping invariants are used to identify important transformations between the reference surface and parallel surfaces. These mapping invariants and transformations have potential applications in geometry, physics, biomechanics, and mechanics in which various dynamic processes occur along or between parallel surfaces.

The Unified Coordinate System in Computational Fluid Dynamics

A fundamental issue in CFD is the role of coordinates and,in particular,the search for“optimal”coordinates.This paper reviews and generalizes the recently developed unified coordinate system(UC).For one-dimensional flow,UC uses a material coordinate and thus coincides with Lagrangian system.For two-dimensional flow it uses a material coordinate,with the other coordinate determined so as to preserve mesh othorgonality(or the Jacobian),whereas for three-dimensional flow it uses two material coordinates,with the third one determined so as to preserve mesh skewness(or the Jacobian).The unified coordinate system combines the advantages of both Eulerian and the Lagrangian system and beyond.Specifically,the followings are shown in this paper.(a)For 1-D flow,Lagrangian system plus shock-adaptive Godunov scheme is superior to Eulerian system.(b)The governing equations in any moving multi-dimensional coordinates can be written as a system of closed conservation partial differential equations(PDE)by appending the time evolution equations–called geometric conservation laws–of the coefficients of the transformation(from Cartesian to the moving coordinates)to the physical conservation laws;consequently,effects of coordinate movement on the flow are fully accounted for.(c)The system of Lagrangian gas dynamics equations is written in conservation PDE form,thus providing a foundation for developing Lagrangian schemes as moving mesh schemes.(d)The Lagrangian system of gas dynamics equations in two-and three-dimension are shown to be only weakly hyperbolic,in direct contrast to the Eulerian system which is fully hyperbolic;hence the two systems are not equivalent to each other.(e)The unified coordinate system possesses the advantages of the Lagrangian system in that contact discontinuities(including material interfaces and free surfaces)are resolved sharply.(f)In using the UC,there is no need to generate a body-fitted mesh prior to computing flow past a body;the mesh is automatically generated by the flow.Numerical examples are given to confirm these properties.Relations of the UC approach with the Arbitrary-Lagrangian-Eulerian(ALE)approach and with various moving coordinates approaches are also clarified.

Steiner minimal trees——the final destinations for lipid nanotube networks with three-way junctions

Through the combination of the minimum energy principle in physics and the Steiner minimal tree (SMT) theory in geometry,this paper proves a universal law for lipid nanotube networks (LNNs):at stable equilibrium state,the network of three-way lipid nanotube junctions is equivalent to a SMT.Besides,an arbitrary (usually non-equilibrium) network of lipid nanotube junctions may fission into a SMT through diffusions and dynamic self-organizations of lipid molecules.Potential applications of the law to the micromanipulations of LNNs are presented.

Gas Kinetic Scheme for Anisotropic Savage-Hutter Model

The gas-kinetic scheme is applied to a depth-integrated continuum model for avalanche flows,namely the Savage-Hutter model.In this method,the continuum fluxes are calculated based on the pseudo particle motions which are relaxed from nonequilibrium to equilibrium states.The processes are described by the Bhatnagar-GrossKrook(BGK)equation.The benefit of this scheme is its capability to resolve shock discontinuities sharply and to handle the vacuum state without special treatments.Because the Savage-Hutter equation bears an anisotropic stress on the tangential space of the topography,the equilibrium distribution function of the microscopic particles are shown to be bi-Maxwellian.These anisotropic stresses are the key to preserve the coordinate objectivity in the Savage-Hutter model.The effect of the anisotropic stress is illustrated by two examples:an axisymmetric dam break and a finite mass sliding on an inclined plane chute.It is found that the propagation of the flow fronts significantly depends on the orientation of the principal axes of the tangential stresses.