Nano-friction phenomenon of Frenkel-Kontorova model under Gaussian colored noise

The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova model under Gaussian colored noise is investigated by using the molecular dynamic simulation method. The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method. Via the stochastic Runge-Kutta algorithm, the relationship between different parameter values of the Gaussian colored noise (the noise intensity and the correlation time) and the nano-friction phenomena such as hysteresis, the maximum static friction force is separately studied here. Similar results are obtained from the two geometrically opposed ideal cases: incommensurate and commensurate interfaces. It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force, the introduction of noise can accelerate the motion of the system, making the atoms escape from the substrate potential well more easily. Interestingly, suitable correlation time and noise intensity give rise to super-lubricity. It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the Incommensurate interface.

Tuning of a shunted electromagnetic vibration absorber based on the maximisation of the electrical power dissipated

This paper investigates a local tuning approach for a shunted electromagnetic vibration absorber, which is based on the maximisation of the electrical power dissipated by the coil and shunt components. The study considers a simplified problem with a single-degree-of-freedom mechanical hosting system, which is excited by a white noise stochastic force. The hosting system is equipped with a coil-magnet seismic transducer, which is connected to a resistive-inductive shunt. The study examines the effectiveness of the shunted electromagnetic vibration absorber with respect to the following cost functions. Firstly, the reference cost function, which is based on the minimisation of the time-averaged kinetic energy of the hosting system. Secondly, the local cost functions, which are based on: the maximisation of the time-averaged vibration power absorbed by the shunted electromagnetic vibration absorber; the maximisation of the time-averaged mechanical power dissipated by the electromagnetic transducer and the maximisation of the time-averaged electrical power dissipated by the coil and the shunt. The study shows that, provided the transducer is lightly damped, the local cost function based on the maximisation of the electrical power dissipated by the coil and the shunt gives the same optimal tuning parameters than the reference cost function. Therefore, provided the electromagnetic transducer is properly designed, the shunt can be suitably tuned by maximising the time-averaged electrical power dissipated by the coil and shunt. This is a rather appealing practical solution since it can be implemented locally without the need of measuring the response of the hosting system and also it can be implemented in the shunt circuit without the need of extra sensors.

Escape dynamics of active particles in multistable potentials

Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state theory and in particular by Kramers’ dynamical framework. Its predictions, however, do not apply to systems that feature non-conservative forces or correlated noise histories. An important class of such systems are active particles, prominent in both biology and nanotechnology. Here, we study the active escape dynamics of a silica nanoparticle trapped in a bistable potential. We introduce activity by applying an engineered stochastic force that emulates self-propulsion. Our experiments, supported by a theoretical analysis, reveal the existence of an optimal correlation time that maximises the transition rate. We discuss the origins of this active turnover, reminiscent of the much celebrated Kramers turnover. Our work establishes a versatile experimental platform to study single particle dynamics in non-equilibrium settings.

Development of a Model of Crack Propagation in Multilayer Hard Coatings under Conditions of Stochastic Force Impact

The article deals with the problems of cracking in the structure of multilayered coatings under the conditions of stochastic loading process. A mathematical model has been proposed in order to predict the crack propagation velocity in the coating while taking the influence of interlayer interfaces into account. A technique for calculating the probability density distribution of the coating fracture (failure rate) has been developed. The probability of a change in the crack growth direction is compared with the experimental data that were obtained as a result of the studies focused on the pattern of cracking in the Zr,Nb-(Zr,Nb)N-(Zr,Nb,Al)N and Ti-TiN-(Ti,Cr,Al)N coatings under the conditions of the real stochastic loading of cutting tools during the turning. The influence of the crystalline structure of the coating on the cracking pattern has been studied. The investigation has found the significant effect of the crystalline structure of the coating layers on the cracking pattern.

Existence and uniqueness result for an hyperbolic scalar conservation law with a stochastic force using a finite volume approximation

We are interested in multi-dimensional nonlinear scalar conservation laws forced by a multiplicative stochastic noise with a general time and space dependent flux-function. We address simultaneously theoretical and numerical issues in a general framework and consider a larger class of flux functions in comparison to the one in the literature. We establish existence and uniqueness of a stochastic entropy solution together with the convergence of a finite volume scheme. The novelty of this paper is the use of a numerical approximation (instead of a viscous one) in order to get, both, the existence and the uniqueness of solutions. The quantitative bounds in our uniqueness result constitute a preliminary step toward the establishment of strong error estimates. We also provide an [Formula: see text] stability result for the stochastic entropy solution.

Perturbation dynamics in Keplerian flow under external stochastic forcing

ABSTRACT We investigate the dynamics of linear perturbations in Keplerian flow under external stochastic force. To abstract from the details of flow structure and boundary conditions, we consider the problem in the shearing box approximation. An external force is assumed to have zero mean, even so, induced perturbations form a steady state, which provides angular momentum transfer to the periphery of the flow. The most effective scenario is based on the transient amplification of induced vortices with the following emission of a shearing sound wave, wherein the maximum of the flux linearly depends on Reynolds number. Thus such a mechanism is significant for astrophysical flows, for which enormous Reynolds numbers are typical. At the same time, addressing the problem analytically, we find that for incompressible fluid in the shearing box approximation stochastic forcing does not lead to average angular momentum transfer. Thus the compressibility of the fluid plays an important role here, and one cannot neglect it.

Contrasting Age Effects on Complexity of Tracking Force and Force Fluctuations During Monorhythmic Contraction

This study contrasted the stochastic force component between young and older adults, who performed pursuit tracking/compensatory tracking by exerting in-phase/antiphase forces to match a sinusoidal target. Tracking force was decomposed into the force component containing the target frequency and the nontarget force fluctuations (stochastic component). Older adults with inferior task performance had higher complexity (entropy across time; p = .005) in total force. For older adults, task errors were negatively correlated with force fluctuation complexity (pursuit tracking: r = −.527 to −.551; compensatory tracking: r = −.626 to −.750). Notwithstanding an age-related increase in total force complexity (p = .004), older adults exhibited lower complexity of the stochastic force component than young adults did (low frequency: p = .017; high frequency: p = .035). Those older adults with a higher complexity of stochastic force had better task performance due to the underlying use of a richer gradation strategy to compensate for impaired oscillatory control.