Dynamics of a viscous ball rolling down on a rigid staircase

We theoretically investigate the motion of a ball rolling down on a periodical staircase. Our research is restricted in the case of completely inelastic collision when the ball falls down on the surface of the stairs. The ball is accelerated when it rolls cross the edge of the stair, while it is decelerated when it rolls on the horizontal surface due to the rolling friction. The competition between them causes two different regimes according to the parameters of the system. One is the steady moving regime in which the ball keeps moving forever, and the other is the still regime in which the ball finally stops after rolling on a finite number of stairs. The diagram of these two regimes is given in the reduced parameter space. The tendency that smaller scale of the staircase can keep moving on smaller inclined angle is found.     

Rolling friction for hard cylinder and sphere on viscoelastic solid

We calculate the friction force acting on a hard cylinder or spherical ball rolling on a flat surface of a viscoelastic solid. The rolling-friction coefficient depends non-linearly on the normal load and the rolling velocity. For a cylinder rolling on a viscoelastic solid characterized by a single relaxation time Hunter has obtained an exact result for the rolling friction, and our result is in very good agreement with his result for this limiting case. The theoretical results are also in good agreement with experiments of Greenwood and Tabor. We suggest that measurements of rolling friction over a wide range of rolling velocities and temperatures may constitute a useful way to determine the viscoelastic modulus of rubber-like materials.     

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.     

Can surfactant be present at pinch-off of a liquid filament?

Surfactants lower surface tension and are used to facilitate breakup and spreading. How much surfactant remains where a filament of initial radius R breaks is set by the ratio of convection, which sweeps surfactant away, to diffusion, which replenishes it, or Peclet number Pe proportional, variantR. Thus, as is well known, surfactant concentration Gamma-->0 when a macroscale filament breaks. Here theory and simulation are used to investigate pinch-off of microscopic filaments. At breakup, Gamma is shown to be nonzero but uniform on a filament of negligible Pe. Since R must be finite, the zero-Pe limit is transitory and yields to a final regime. Two such regimes with distinct dynamics characterized by different scaling exponents are reported.     

Friction through dynamical formation and rupture of molecular bonds

We introduce a model for friction in a system of two rigid plates connected by bonds (springs) and experiencing an external drive. The macroscopic frictional properties of the system are shown to be directly related to the rupture and formation dynamics of the microscopic bonds. Different regimes of motion are characterized by different rates of rupture and formation relative to the driving velocity. In particular, the stick-slip regime is shown to correspond to a cooperative rupture of the bonds. Moreover, the notion of static friction is shown to be dependent on the experimental conditions and time scales. The overall behavior can be described in terms of two Deborah numbers.     

Influence of ultrasonic surface acoustic waves. on local friction studied by lateral force microscopy

We studied dynamic friction phenomena introduced by ultrasonic surface acoustic waves using a scanning force microscope in the lateral force mode and a scanning acoustic force microscope. An effect of friction reduction was found when applying surface acoustic waves to the micro-mechanical tip-sample contact. Employing standing acoustic wave fields, the wave amplitude dependent friction variation can be visualized within a microscopic area. At higher wave amplitudes, a regime was found where friction vanishes completely. This behavior is explained by the mechanical diode effect, where the tip's rest position is shifted away from the surface in response to ultrasonic waves.     

Uphill anomalous transport in a deterministic system with speed-dependent friction coefficient

We investigate the transport of a deterministic Brownian particle theoretically, which moves in simple onedimensional, symmetric periodic potentials under the influence of both a time periodic and a static biasing force. The physical system employed contains a friction coefficient that is speed-dependent. Within the tailored parameter regime, the absolute negative mobility, in which a particle can travel in the direction opposite to a constant applied force, is observed.This behavior is robust and can be maximized at two regimes upon variation of the characteristic factor of friction coefficient. Further analysis reveals that this uphill motion is subdiffusion in terms of localization(diffusion coefficient with the form D(t) ~t~(-1) at long times). We also have observed the non-trivially anomalous subdiffusion which is significantly deviated from the localization; whereas most of the downhill motion evolves chaotically, with the normal diffusion.     

Tribological properties of silicate materials on nano and microscale

We studied the friction properties of four model silicate materials at the nanoscale and microscale. From nanotribology, we characterized the tribological properties at single asperity contact scale and from microtribology, we characterized the tribological properties at multi asperity contact scale. First, for each material we measured chemical composition by XPS, Young's modulus by acoustical microscopy and roughness σ by atomic force microscopy (AFM). Second, we measured the nanofriction coefficients with an AFM and the microfriction coefficients with a ball probe tribometer, for three hardnesses of the ball probe. We identified one friction mechanism at the nanoscale (sliding friction) and two friction mechanisms at the microscale (sliding friction and yielding friction). Comparison of the nano and microfriction coefficients at the same sliding friction regime shown, that the tribological properties of these materials didn’t depend on roughness.     

关于狮子盘球力学原理的注记——论内力与外力的关系

以人在球体上走动引起球体向前滚动为例,利用牛顿定律说明人-球系统中内力、外力与运动之间的关系.尽管阻碍球体滚动的地面摩擦是人-球系统向前运动的必要条件,且作为外力与系统动量变化率相等,但从运动的因果关系考察,人与球体之间的竖直作用力才是系统运动的真正动力.     

Frictional coupling between sliding and spinning motion

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.     

The ANAIS billiard experiment

The problem on the motion of a homogeneous ball on a horizontal plane is considered. The existence of the vector first integral independent of the friction character and the motion of the support plane in the horizontal directions is shown. In particular, the velocities of the ball center are identical at the moments of rolling on a motionless plane, which corresponds to experiments with the ANAIS billiard table.     

Low-dimensional systems: Quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems

This review is concerned with quantum confinement effects in low-dimensional semiconductor systems. The emphasis is on the optical properties, including luminescence, of nanometre-sized microcrystallites, also referred to as zerodimensional systems. There is some discussion on certain of the two-dimensional systems, such as thin films and layer structures. The increase in energy of excitation peaks (blue shift) as the radius R of a microcrystallite is reduced is treated theoretically, and experimental data when they are available are used to assess the reliability of the different models that have been used. These experiments normally make use of microcrystallites dispersed in a large-bandgap matrix such as glass, rocksalt, polymers, zeolites or liquids. Exciton binding energies E b are larger than for bulk semiconductors, and oscillator strengths are higher for the microcrystallites. The regimes of direct interest are as follows. Firstly there is the so-called weak-confinement regime where R is greater than the bulk exciton Bohr radius a B . Experimentally, semiconductors such as CuCl with a B , 7 Å, are suitable for study in this case. Secondly there is the moderate-confinement regime, where R , a B , and a h < R < a e , a h and a e being the hole and electron Bohr radii, respectively. Finally there is the strong-confinement regime, with R < a B , and R < a h , a e . For this case we are concerned with a ladder of discrete energy levels, as in molecular systems, rather than energy bands. The electrons and holes are treated as independent particles, and for excited states we refer to electron-hole pairs rather than excitons. Suitable materials for investigation in this regime are the II-VI semiconductors, and also GaAs and Ge, for which a B is relatively large. Although a number of different theoretical models have been used, none can be described as completely first-principles calculations, and there is room for improvement on this aspect. However, useful expressions have been developed by Brus and by Lippens and Lannoo, giving the energy of excited states as a function of R , in terms of the bulk energy gap, kinetic energy, Coulomb energy and correlation energy. Other phenomena discussed are firstly biexciton formation by the use of high intensity laser beams and secondly nonlinear optical effects. Strong nonlinearities and short decay times for excited states have been predicted, and the models developed cover both the resonant and the non-resonant cases. The possibility of using microcrystallites embedded at reasonable concentrations in a glass matrix in the field of optical communications and optical switching is also considered.     

The method of reduction of dimensionality and its application to simulation of elastomer friction under complex dynamic loads

The paper reports on basic ideas of the method of reduction of dimensionality and demonstrates its efficiency in simulation of friction of elastomers having arbitrary linear rheology and a rigid rough surface with fractal relief. The fixation time of elastomer on a rigid surface before the onset of tangential motion is studied as a parameter affecting the static friction coefficient. It is also studied how the friction coefficient in steady-state sliding is affected by harmonic oscillations of normal pressing force.     

Frictionless flow in a binary polariton superfluid

We study the properties of a binary microcavity polariton superfluid coherently injected by two lasers at different momenta and energies. The crossover from the supersonic to the subsonic regime, where motion is frictionless, is described by evaluating the linear response of the system to a weak defect potential. We show that the coupling between the two components requires that either both components flow without friction or both scatter against the defect, though scattering can be small when the two fluids are weakly coupled. By analyzing the drag force exerted on a defect, we give a recipe to experimentally address the crossover from the supersonic to the subsonic regime.     

滚球混沌运动演示实验

以滚球在3个凹形槽上的受力体现作用的非线性,导轨由电机推动作简谐振动,滚球在导轨上作受迫(滚动)振动,可以把导轨作简谐振动的频率或振幅作为调整参量.当受迫振动的滚球振幅小时,滚球只在1个凹形槽中作简谐振动;当振幅渐渐增大时,可呈现周期倍增和渐至混沌状态.通过观察安装在同一振动滑板上的2套导轨上的滚球的运动,则可以演示混沌运动对初值的敏感性.     

Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence

We studied a magnetic turbulence axisymmetric around the unperturbed magnetic field for cases having different ratios l( ||)/l( perpendicular). We find, in addition to the fact that a higher fluctuation level deltaB/B(0) makes the system more stochastic, that by increasing the ratio l( ||)/l( perpendicular) at fixed deltaB/B(0), the stochasticity increases. It appears that the different transport regimes can be organized in terms of the Kubo number R=(deltaB/B(0))(l( ||)/l( perpendicular)). The simulation results are compared with the two analytical limits, that is the percolative limit and the quasilinear limit. When R<1 weak chaos, closed magnetic surfaces, and anomalous transport regimes are found. When R approximately 1 the diffusion regime is Gaussian, and the quasilinear scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(2) is recovered. Finally, for R>1 the percolation scaling of the diffusion coefficient D( perpendicular) approximately (deltaB/B(0))(0.7) is obtained.     

纳米级随机粗糙表面微观滑动摩擦力的计算研究

表面形貌很大程度上决定了摩擦副的摩擦性能, 而所有的表面都不可能是绝对光滑的.由于摩擦表面形貌的随机性, 决定了实际的摩擦过程具有随机性的特点, 因此为了获得与随机形貌对应的摩擦特性, 建立合理的随机摩擦模型是必要的. 本文基于Lennard-Jones势能建立了纳米级随机粗糙表面和原子级光滑的刚性平面间的随机摩擦模型; 模型中, 界面势能由法向载荷和界面间平衡距离决定.通过数值计算的方法, 推导了微观滑动摩擦力的计算公式和摩擦力与法向载荷之间的关系. 研究结果表明摩擦力随着法向载荷的增加而增加, 但不是线性增长. 结果也说明界面间的表面势能可能是微观摩擦力的本质起源. 关键词： 随机粗糙表面 Lennard-Jones势能 微滑动摩擦力 微摩擦     

Modeling of the rough spherical nanoparticles manipulation on a substrate based on the AFM nanorobot

In this paper, dynamic behavior of the rough spherical micro/nanoparticles during pulling/pushing on the flat substrate has been investigated and analyzed. For this purpose, at first, two hexagonal roughness models (George and Cooper) were studied and then evaluations for adhesion force were determined for rough particle manipulation on flat substrate. These two models were then changed by using of the Rabinovich theory. Evaluations were determined for contact adhesion force between rough particle and flat substrate; depth of penetration evaluations were determined by the Johnson–Kendall–Roberts contact mechanic theory and the Schwartz method and according to Cooper and George roughness models. Then, the novel contact theory was used to determine a dynamic model for rough micro/nanoparticle manipulation on flat substrate. Finally, simulation of particle dynamic behavior was implemented during pushing of rough spherical gold particles with radii of 50, 150, 400, 600, and 1,000 nm. Results derived from simulations of particles with several rates of roughness on flat substrate indicated that compared to results for flat particles, inherent roughness on particles might reduce the rate of critical force needed for sliding and rolling given particles. Given a fixed radius for roughness value and increased roughness height, evaluations for sliding and rolling critical forces showed greater reduction. Alternately, the rate of critical force was shown to reduce relative to an increased roughness radius. With respect to both models, based on the George roughness model, the predicted rate of adhesion force was greater than that determined in the Cooper roughness model, and as a result, the predicted rate of critical force based on the George roughness model was closer to the critical force value of flat particle.     

Interactions of flame balls

Flame ball interactions are numerically investigated in a reaction–diffusion system characterized by single-step Arrhenius kinetics and radiative heat losses. It is found that the interactions of two neighbouring flame balls are characterized by two distinct regimes – a repulsion regime and an attraction regime, depending upon the separation distance. The two regimes join at a critical separation distance, which corresponds to an unstable equilibrium state. For supercritical separation distances, the two flame balls repel and drift apart from each other; whereas for sub-critical separation distances, they move towards each other and eventually merge into a single stationary flame ball. In this connection, flame ball interactions are found to exhibit a qualitatively reverse character in comparison with the well-known van der Waals curve which characterizes intermolecular forces.     

Solids Movement in Rotary Kilns in the Slumping Regime: Model Using a Control Plane Parallel to the Steepest Descent

A new approach is proposed to model the bulk movement of solids in rotary drums operating at low rotation speeds, in slumping and rolling regimes. The model yields an equation similar to Saeman's equation, but which is valid also for the slumping regime and active area in the rolling regime. The model was developed for constant depth using a control surface containing the steepest descent direction, so that any contribution from sliding particles to flow rate can be neglected. By considering an appropriate virtual kiln, the model is extended to the more general, variable depth situation.