Friction parameter of an ion near a metal surface

The force on an ion located near a condensed-matter surface determines its Brownian motion along the surface. We have studied the dissipative component of this force using a model in which the ion interacts with a metal while moving parallel with its surface. We recover the known asymptotic form of the force for large separations when only electron-hole excitations are accounted for but find a different form when damping of collective states is included.     

Chains of oscillators with negative stiffness elements

Negative stiffness is not allowed by thermodynamics and hence materials and systems whose global behaviour exhibits negative stiffness are unstable. However the stability is possible when these materials/systems are elements of a larger system sufficiently stiff to stabilise the negative stiffness elements. In order to investigate the effect of stabilisation we analyse oscillations in a chain of n linear oscillators (masses and springs connected in series) when some of the springs? stiffnesses can assume negative values. The ends of the chain are fixed. We formulated the necessary stability condition: only one spring in the chain can have negative stiffness. Furthermore, the value of negative stiffness cannot exceed a certain critical value that depends upon the (positive) stiffnesses of other springs. At the critical negative stiffness the system develops an eigenmode with vanishing frequency. In systems with viscous damping vanishing of an eigenfrequency does not yet lead to instability. Further increase in the value of negative stiffness leads to the appearance of aperiodic eigenmodes even with light damping. At the critical negative stiffness the low dissipative mode becomes non-dissipative, while for the high dissipative mode the damping coefficient becomes as twice as high as the damping coefficient of the system. A special element with controllable negative stiffness is suggested for designing hybrid materials whose stiffness and hence the dynamic behaviour is controlled by the magnitude of applied compressive force.     

Phenomenology of current-induced dynamics in antiferromagnets

We derive a phenomenological theory of current-induced staggered magnetization dynamics in antiferromagnets. The theory captures the reactive and dissipative current-induced torques and the conventional effects of magnetic fields and damping. A Walker ansatz describes the dc current-induced domain-wall motion when there is no dissipation. If magnetic damping and dissipative torques are included, the Walker ansatz remains robust when the domain wall moves slowly. As in ferromagnets, the domain-wall velocity is proportional to the ratio between the dissipative torque and the magnetization damping. In addition, a current-driven antiferromagnetic domain wall acquires a net magnetic moment.     

On the dissipation of mechanical energy in a noncontact dynamic mode of a scanning probe microscope under vacuum

This paper presents a critical review of experiments on the measurement of conservative and dissipative forces in dynamic contacts of nanotips of scanning probe microscopes with surfaces (under high-vacuum conditions). In particular, it is noted that, although the perpendicular and parallel oscillatory motions of tips in the vicinity of the surface of various materials have been investigated experimentally, the question as to the nature of noncontact damping forces at distances ≥0.5 nm remains open. A phenomenological relationship between arbitrary conservative and dissipative forces acting on the tip is proposed. This relationship includes a model parameter characterizing the rate or time of the dissipative process and offers a correct explanation of the observed damping. It is shown that, despite the large differences in the damping coefficients, geometric sizes of tips, and types of conservative interactions in different experiments, the dissipative forces in perpendicular and parallel oscillatory motions of tips are adequately described within the proposed theory.     

A STOCHASTIC OPTIMAL SEMI-ACTIVE CONTROL STRATEGY FOR ER/MR DAMPERS

A stochastic optimal semi-active control strategy for randomly excited systems using electrorheological/magnetorheological (ER/MR) dampers is proposed. A system excited by random loading and controlled by using ER/MR dampers is modelled as a controlled, stochastically excited and dissipated Hamiltonian system with n degrees of freedom. The control forces produced by ER/MR dampers are split into a passive part and an active part. The passive control force is further split into a conservative part and a dissipative part, which are combined with the conservative force and dissipative force of the uncontrolled system, respectively, to form a new Hamiltonian and an overall passive dissipative force. The stochastic averaging method for quasi-Hamiltonian systems is applied to the modified system to obtain partially completed averaged Itô stochastic differential equations. Then, the stochastic dynamical programming principle is applied to the partially averaged Itô equations to establish a dynamical programming equation. The optimal control law is obtained from minimizing the dynamical programming equation subject to the constraints of ER/MR damping forces, and the fully completed averaged Itô equations are obtained from the partially completed averaged Itô equations by replacing the control forces with the optimal control forces and by averaging the terms involving the control forces. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully completed averaged Itô equations of the system. Two examples are given to illustrate the application and effectiveness of the proposed stochastic optimal semi-active control strategy.     

Dynamic force spectroscopy of conservative and dissipative forces in an Al-Au(111) tip-sample system

The conservative and dissipative interaction between an aluminum tip and a gold (111) surface were investigated using dynamic force spectroscopy in UHV. Complete force vs distance curves and friction coefficient vs distance curves were obtained quantitatively. The force curves were compared to the model by Muller, Yushenko, and Derjaguin, and long and short range interactions were subsequently quantified without fit parameters. A short range conservative interaction was separated from longer range van der Waals forces. The long range behavior of the damping coefficient obeys an inverse power law of third order.     

Quantum theory of a dissipative oscillator

The nonlinear equation of dissipative quantum mechanics is considered in the relaxation-time approximation. It is shown that the steady current-free state does not change when dissipation is taken into account; in particular, there is no ground-state damping, and the zero energy is conserved. A solution is obtained to the problem of the excitation of a harmonic oscillator, serving as a model of single-mode radiation in an open resonator; the solution obtained describes the evolution of the oscillator from an arbitrary steady state under the action of a constraining force. Transition probabilities between the oscillator steady states are calculated. The results are found to be in agreement with the classical theory of damping oscillations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 99–105, September, 1978.     

RESPONSE OF NON-LINEAR DISSIPATIVE SHOCK ISOLATORS

In this paper, a simple technique combining the straightforward perturbation method with Laplace transform has been developed to determine the transient response of a single degree-of-freedom system in the presence of non-linear, dissipative shock isolators. Analytical results are compared with those obtained by numerical integration using the classical Runge–Kutta method. Three types of input base excitations, namely, the rounded step, the rounded pulse and the oscillatory step are considered. The effects of nonlinear damping on the response are discussed in detail. Both the positive and negative coefficients of the nonlinear damping term have been considered. It has been shown that a critical value of the positive coefficient maximizes the peak values of relative and absolute displacements. This is true for any power-law damping force with an index greater than 1. On the other hand, the overall performance of a shock isolator improves if the nonlinear damping term is symmetric and quadratic with a negative coefficient.     

Damping of the trapped-particle diocotron mode

The damping mechanism of a recently discovered trapped-particle mode is identified as collisional velocity scattering of marginally trapped particles. The mode exists on non-neutral plasma columns that are partially divided by an electrostatic potential. This damping mechanism is similar to that responsible for damping of the dissipative trapped-ion mode. The damping rate is calculated using a Fokker-Planck analysis and agrees with measurement to within 50%. Also, an experimental signature confirms a causal relation between scattering of marginally trapped particles and damping.     

Brownian motion of massive skyrmions in magnetic thin films

We report on the thermal effects on the motion of current-driven massive magnetic skyrmions. The reduced equation for the motion of skyrmion has the form of a stochastic generalized Thiele’s equation. We propose an ansatz for the magnetization texture of a non-rigid single skyrmion that depends linearly with the velocity. By using this ansatz it is found that the skyrmion mass tensor is closely related to intrinsic skyrmion parameters, such as Gilbert damping, skyrmion-charge and dissipative force. We have found an exact expression for the average drift velocity as well as the mean-square velocity of the skyrmion. The longitudinal and transverse mobility of skyrmions for small spin-velocity of electrons is also determined and found to be independent of the skyrmion mass.     

Dynamic instability of supercritical driveshafts mounted on dissipative supports—Effects of viscous and hysteretic internal damping

The case of a rotating shaft with internal damping mounted either on elastic dissipative bearings or on infinitely rigid bearings with viscoelastic suspensions is investigated in order to obtain the stability region. A Euler-Bernoulli shaft model is adopted, in which the transverse shear effects are neglected and the effects of translational and rotatory inertia, gyroscopic moments, and internal viscous or hysteretic damping are taken into account. The hysteretic damping is incorporated with an equivalent viscous damping coefficient. Free motion analysis yields critical speeds and threshold speeds for each damping model in analytical form. In the case of elastic dissipative bearings, the present results are compared with the results of previous studies on finite element models. In the case of infinitely rigid bearings with viscoelastic suspensions, it is established that viscoelastic supports increase the stability of long shafts, thus compensating for the loss of efficiency which occurs with classical bearings. The instability criteria also show that the effect of the coupling which occured between rigid modes introducing external damping and shaft modes are almost more important than damping factor. Lastly, comparisons between viscous and hysteretic damping conditions lead to the conclusion that an appropriate material damping model is essential to be able to assess these instabilities.     

A model for dissipative magnetotransport in the quantum Hall regime

Summary A model which describes the dissipative quantum magnetotransport in a noninteracting two-dimensional electron gas under the quantum Hall conditions is presented. The resulting dissipative conductivity is proportional to a damping factor γ. The assumption of an exponential dependence of γ on the Hall electric field gives a good fit to the available experimental data.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and singlesided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

Influence of Composite Effect from Quantum Channels on Entanglement

The dynamics of entanglement between two qubits in the local damping two-sided channel and single-sided channel are compared through non-Markovian process and Markovian process. The entanglement between two qubits is found to be longer in the single-sided channel case due to the weakening of the dissipative effects. In the two-sided channel, influenced by the entanglement between qubits, the previous independent dissipative channels incline to the composite effect of the Markovian process. This composite effect results in the dissipative effect of one channel affecting the qubits in the other channel, especially inhibiting the backflow effect in the non-Markovian channel, which is disadvantageous to the entanglement maintenance between qubits. In the Markovian channel, the composite effect of the damping two-sided channels is more obvious since there is no backflow effect, thus more disadvantageous to the entanglement maintenance.     

波驱动等离子体电流的特征

本文指出,只当u=ω/(k_xv_e)≤2—2.5时,波驱动的电流以共振电子电流为主,波的耗散机制也主要是共振阻尼效应;而当u≥3时,非共振电子电流一般将超过共振电子电流,碰撞耗散也将大于共振耗散。波驱动电流所需功率较高,比相应欧姆功率大得多。这对反应器的设计带来困难,一般说来反应器中选取u≤2.5的共振电子电流较为合适。波驱动电流时将出现等离子体旋转,除环向旋转外,还将引起较大的角向旋转,后者伴有较大的径向电场。 关键词：     

The dynamical feature of transition of a Hamiltonian system to a dissipative system

The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formation of attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.     

Fluctuational dissipative electromagnetic interaction between a nanoprobe and a surface

In the framework of fluctuational electromagnetic theory, analytical expressions are obtained for the dynamic dissipative damping forces acting on the probe of an atomic-force microscope (AFM), as well as between two plane surfaces at their contact. The contacts between materials typical of AFM, quartz-microbalance, and surface-force apparatus experiments are considered. The conditions for nondissipative slide are discussed. A comparison between the calculated oscillator quality factor associated with fluctuational dissipative forces and its values obtained in AFM experiments with a silicon probe and a mica sample shows that they are of the same order of magnitude; therefore, an experimental investigation of such forces is feasible.     

S-matrix spin and parity decoherence and damping of coherent nuclear rotation: quantum chaos in dissipative heavy-ion collisions?

We extend the statistical reaction with memory approach to study off-diagonal spin and parity S-matrix energy autocorrelation in dissipative heavy-ion collisions. It is suggested that S-matrix spin and parity decoherence results in (i) damping of the coherent nuclear rotation and (ii) is a manifestation of quantum chaos in dissipative heavy-ion collisions.     

Dynamics of topological defects in a spiral: a scenario for the spin-glass phase of cuprates

We propose that the dissipative dynamics of topological defects in a spiral state is responsible for the transport properties in the spin-glass phase of cuprates. Using the collective-coordinate method, we show that topological defects are coupled to a bath of magnetic excitations. By integrating out the bath degrees of freedom, we find that the dynamical properties of the topological defects are dissipative. The calculated damping matrix is related to the in-plane resistivity, which exhibits an anisotropy and linear temperature dependence in agreement with experimental data.