Velocity-dependent Force Research Articles

Microscopic theory for the time irreversibility and the entropy production

In stochastic thermodynamics, the entropy production of a thermodynamic system is defined by the irreversibility measured by the logarithm of the ratio of the path probabilities in the forward and reverse processes. We derive the relation between the irreversibility and the entropy production starting from the deterministic equations of motion of the whole system consisting of a physical system and a surrounding thermal environment. The derivation assumes the Markov approximation that the environmental degrees of freedom equilibrate instantaneously. Our approach provides a guideline for the choice of the proper reverse process to a given forward process, especially when there exists a velocity-dependent force. We demonstrate our idea with an example of a charged particle in the presence of a time-varying magnetic field.

Design and Experimental Validation of a Re-centring Viscous Dissipater

The design and experimental validation of a passive, hybrid self-centring supplemental damper for low-damage structures is presented. The device combines rate-dependent dissipation of a viscous damper with the rate-independent dissipation and re-centring restoring force of a ring-spring in a parallel fashion. Experimental proof-of-concept validation tests use sinusoidal displacement inputs consisting of [25, 30]mm amplitudes and [0.25–1.75]Hz frequencies, for two levels of ring-spring pre-load equal to 21% and 34% of the design force. Each component is tested individually to characterise and delineate their specific contributions to the overall device. The ring-spring has a design force capacity of 26kN and a return stiffness ratio of 34% that remain independent of the velocity input. The viscous device input velocities of [50–330]mm/s provide velocity dependent dissipative forces with a maximum of 22kN at the maximum input velocity. Individual results in summation match the hybrid device results for the same input, indicating no loss of efficiency in the hybrid device load transfer. Overall, these results offer a range of new, easily implemented options for energy dissipation in developing low-damage structures, which can also provide necessary re-centring capability within the same package. The overall method is readily generalised for a wide range of hybrid device force capacities and design requirements.

Applying explicit symplectic-like methods to nonconservative nonseparable systems

Extended phase-space explicit symplectic-like integrators were recently developed for nonseparable Hamiltonian systems. Following this idea, we establish numerical integration codes about the explicit symplectic-like algorithms for nonconservative nonseparable problems with velocity-dependent interaction forces, such as a damped harmonic oscillator and the orbital motion of a dust particle experiencing Poynting-Robertson drag. We use integral invariant relations of these nonconservative energies as accuracy checks in numerical integrations. It is found that these explicit symplectic-like methods still make the energy errors remain bounded in the nonconservative case. It is shown that the explicit symplectic-like integrators with the midpoint permutations are superior to those with the sequence two permutations of momenta and coordinates in the numerical accuracy although the latter algorithm is efficiently applicable to these dissipative systems.

Solitary waves in the excitable Burridge–Knopoff model

The Burridge–Knopoff model is a lattice differential equation describing a chain of blocks connected by springs and pulled over a surface. This model was originally introduced to investigate nonlinear effects arising in the dynamics of earthquake faults. One of the main ingredients of the model is a nonlinear velocity-dependent friction force between the blocks and the fixed surface. For some classes of non-monotonic friction forces, the system displays a large response to perturbations above a threshold, which is characteristic of excitable dynamics. Using extensive numerical simulations, we show that this response corresponds to the propagation of a solitary wave for a broad range of friction laws (smooth or nonsmooth) and parameter values. These solitary waves develop shock-like profiles at large coupling (a phenomenon connected with the existence of weak solutions in a formal continuum limit) and propagation failure occurs at low coupling. We introduce a simplified piecewise linear friction law (reminiscent of the McKean nonlinearity for excitable cells) which allows us to obtain an analytical expression of solitary waves and study some of their qualitative properties, such as wave speed and propagation failure. We propose a possible physical realization of this system as a chain of impulsively forced mechanical oscillators. In certain parameter regimes, non-monotonic friction forces can also give rise to bistability between the ground state and limit-cycle oscillations and allow for the propagation of fronts connecting these two stable states.

Nonequilibrium steady states in Langevin thermal systems.

Equilibrium is characterized by its fundamental properties, such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuation-dissipation relation mutually exclude each other, and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocity-dependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.

Representing delayed force feedback as a combination of current and delayed states.

To adapt to deterministic force perturbations that depend on the current state of the hand, internal representations are formed to capture the relationships between forces experienced and motion. However, information from multiple modalities travels at different rates, resulting in intermodal delays that require compensation for these internal representations to develop. To understand how these delays are represented by the brain, we presented participants with delayed velocity-dependent force fields, i.e., forces that depend on hand velocity either 70 or 100 ms beforehand. We probed the internal representation of these delayed forces by examining the forces the participants applied to cope with the perturbations. The findings showed that for both delayed forces, the best model of internal representation consisted of a delayed velocity and current position and velocity. We show that participants relied initially on the current state, but with adaptation, the contribution of the delayed representation to adaptation increased. After adaptation, when the participants were asked to make movements with a higher velocity for which they had not previously experienced with the delayed force field, they applied forces that were consistent with current position and velocity as well as delayed velocity representations. This suggests that the sensorimotor system represents delayed force feedback using current and delayed state information and that it uses this representation when generalizing to faster movements.NEW & NOTEWORTHY The brain compensates for forces in the body and the environment to control movements, but it is unclear how it does so given the inherent delays in information transmission and processing. We examined how participants cope with delayed forces that depend on their arm velocity 70 or 100 ms beforehand. After adaptation, participants applied opposing forces that revealed a partially correct representation of the perturbation using the current and the delayed information.

Multi-body dynamic coupling mechanism for generating throwing arm velocity during baseball pitching

The purpose of this study was to identify the detailed mechanism how the maximum throwing arm endpoint velocity is determined by the muscular torques and non-muscular interactive torques from the perspective of the dynamic coupling among the trunk, thorax and throwing and non-throwing arm segments. The pitching movements of ten male collegiate baseball pitchers were measured by a three-dimensional motion capture system. Using the induced-segmental velocity analysis (IVA) developed in this study, the maximum fingertip velocity of the throwing arm (MFV) was decomposed into each contribution of the muscular torques, passive motion-dependent torques due to gyroscopic moment, Coriolis force and centrifugal force, and other interactive torque components. The results showed that MFV (31.6±1.7m/s) was mainly attributed to two different mechanisms. The first is the passive motion-dependent effect on increasing the angular velocities of three joints (thorax rotation, elbow extension and wrist flexion). The second is the muscular torque effect of the shoulder internal rotation (IR) torque on generating IR angular velocity. In particular, the centrifugal force-induced elbow extension motion, which was the greatest contributor among individual joint contributions, was caused primarily by the angular velocity-dependent forces associated with the humerus, thorax, and trunk rotations. Our study also found that a compensatory mechanism was achieved by the negative and positive contributions of the muscular torque components. The current IVA is helpful to understand how the rapid throwing arm movement is determined by the dynamic coupling mechanism.

Optimal trajectories, nonlinear models and constraints in wave energy device control

The optimal control problem for a generic, one-degree of freedom Wave Energy Converter (WEC) with dynamical nonlinearities is formulated in the frequency-domain. Previous research, concerning more specifically a heaving point-absorber with nonlinear restoring force, shows that the unconstrained optimal velocity trajectory is influenced neither by the linear inertial terms, nor by the linear or nonlinear static forces. Further to this result, in this paper, we examine the influence of velocity-dependent nonlinear forces on the optimal trajectory, as well as the effect of physical system constraints. In particular, we show that, under state constraints (e.g. position and velocity limitations), the optimal velocity trajectory remains uninfluenced by static forces; but this is no longer true for constraints involving the control force, such as force limitation and passivity constraints. In addition, unlike static terms and linear inertial terms, the velocity-dependent forces, such as viscous drag, significantly influence the optimal velocity trajectory, regardless of constraints, and must be carefully modelled at the control design stage. In any case, even when the optimal velocity trajectory is not affected by some of the forces considered, the optimal control force required to achieve it depends on all the model dynamics (inertial terms, velocity-dependent and static forces). Numerical simulations, in the specific case of a heaving point absorber, are used to validate and illustrate the theoretical results.

Nanotribological Properties of Hexadecanethiol Self-Assembled Monolayers on Au(111): Structure, Temperature, and Velocity.

Self-assembled monolayers (SAM) are promising building blocks for the optimization of a large variety of systems both on the nano- and on the microscale. Among other applications, SAM are often used as protective coating or friction modifiers. In this work, we have used hexadecanethiol SAM on Au(111) as a model system and studied the different mechanisms of energy dissipation during temperature and velocity dependent friction force microscopy (FFM). In a number of cases, the SAM remained stable during atomic force microscopy experiments and friction-velocity isotherms related dissipation to an activation energy. In other cases, friction experiments lead to an irreversible deterioration of the SAM. This can rather be associated with the general SAM structure that was analyzed by scanning tunneling microscopy and showed a large variety of potential breakdown points like, for example, grain boundaries, step edges, or substrate-related holes in the SAM.

Time in dissipative tunneling: Subtleties and applications

Characteristic features of tunneling times for dissipative tunneling of a particle through a rectangular barrier are studied within a semiclassical model involving dissipation in the form of a velocity dependent frictional force. The average dwell time and traversal time with dissipation are found to be less than those without dissipation. This counter-intuitive behavior is reversed if one evaluates the physically relevant transmission dwell time. Apart from these observations, we find that the percentage of energy lost by the tunneling particle is higher for smaller energies. The above observations are tested and confirmed in a realistic case by applying the dissipation model to study the current–voltage data in a Al/Al2O3/Al solid state junction at various temperatures. The friction coefficient for Al2O3 as a function of temperature is presented. It is found to decrease with increasing temperature.

Searching for new spin-dependent interactions withSmCo5spin sources and a spin-exchange-relaxation-free comagnetometer

We propose a novel method to search for possible new macro-scale spin- and/or velocity-dependent forces (SVDFs) based on specially designed SmCo$_5$ spin sources and a spin exchange relaxation-free (SERF) comagnetometer. A simulation shows that, by covering a SmCo$_5$ permanent magnet with a layer of pure iron, a high net spin density source of about $1\times 10^{22}$/cm$^3$ could be obtained. Taking advantages of the high spin density of this iron-shielded SmCo$_5$ and the high sensitivity of the SERF, the proposed method could set up new limits of greater than 10 orders of magnitude more sensitive than those from previous experiments or proposals in exploring SVDFs in force ranges larger than 1 cm.

Transfer of dynamic motor skills acquired during isometric training to free motion.

Recent studies have explored the prospects of learning to move without moving, by displaying virtual arm movement related to exerted force. However, it has yet to be tested whether learning the dynamics of moving can transfer to the corresponding movement. Here we present a series of experiments that investigate this isometric training paradigm. Subjects were asked to hold a handle and generate forces as their arms were constrained to a static position. A precise simulation of reaching was used to make a graphic rendering of an arm moving realistically in response to the measured interaction forces and simulated environmental forces. Such graphic rendering was displayed on a horizontal display that blocked their view to their actual (statically constrained) arm and encouraged them to believe they were moving. We studied adaptation of horizontal, planar, goal-directed arm movements in a velocity-dependent force field. Our results show that individuals can learn to compensate for such a force field in a virtual environment and transfer their new skills to the actual free motion condition, with performance comparable to practice while moving. Such nonmoving techniques should impact various training conditions when moving may not be possible.NEW & NOTEWORTHY This study provided early evidence supporting that training movement skills without moving is possible. In contrast to previous studies, our study involves 1) exploiting cross-modal sensory interactions between vision and proprioception in a motionless setting to teach motor skills that could be transferable to a corresponding physical task, and 2) evaluates the movement skill of controlling muscle-generated forces to execute arm movements in the presence of external forces that were only virtually present during training.

Auditory Hopf Amplification Revealed by an Energy Method**Supported by the National Natural Science Foundation of China under Grant Nos 11374118 and 90820001, and the Science Foundation of Hubei Province under Grant No 2013CFB289.

We report on the auditory Hopf amplification contributed by the electrical energy of the hair cell during its bundle deflecting. An energy method to calculate the active force is adopted according to the electrical energy consumption of the hair cell. After some experimental data was analyzed and simulated, we find that the electrical energy determines the value of the active force and enlarges the mechanical response of the hair bundle. This amplification is controlled by the cell voltage and makes the sensor a Hopf vibrator with hearing nonlinear characteristics. A velocity-dependent active force derived previously from the force-gating channel operation strongly reinforces our conclusion.

P242 Cerebellar tDCS effects on the adaptation of arm reaching movements to force-field and visuomotor perturbations

Introduction Studies with transcranial direct current stimulation (tDCS) have shown that anodal tDCS of the cerebellar hemispheres leads to faster adaptation of arm reaching movements to visuomotor rotation and force field perturbations in healthy subjects ( Galea et al., 2011 , Herzfeld, 2014 ). Objectives The first aim of the present study was to replicate the findings mentioned above. The second aim was to investigate whether tDCS effects differ depending on the onset of stimulation, that is during or after an initial baseline phase. Patients and Methods A total of 120 healthy and right-handed subjects (60 females, aged 18–31 years, mean 23.2 ± 2.7) were tested. Subjects moved a cursor with a two-joined manipulandum to one of eight targets presented on a screen. There were three baseline blocks, one adaptation block and three washout blocks. 60 subjects performed a force field (FF) task, 60 subjects a visuomotor adaptation task (VM). During the adaptation block, a velocity-dependent clockwise perpendicular force (23 N ·m−1·s−1 was applied in FF and a 30° clockwise rotation in VM. Equal numbers of subjects received anodal, cathodal or sham stimulation over the right cerebellum beginning either in the third baseline or in the adaptation block. The maximum error (ME), final error (FE) and perpendicular velocity 55 ms after movement onset (PV) were assessed. Results During FF and VM adaptation subjects significantly improved regarding ME, FE and PV (p 0.05). The same was true for the washout blocks. Conclusion Our results show that prior possible clinical application, future experiments are needed to determine which cerebellar tDCS and task parameters lead to robust tDCS effects. Funded by ELAN and DFG TI 239/16-1.

Noetherian symmetries of noncentral forces with drag term

We consider the Noetherian symmetries of second-order ODEs subjected to forces with nonzero curl. Both position and velocity dependent forces are considered. In the former case, the first integrals are shown to follow from the symmetries of the celebrated Emden–Fowler equation.

High-Frequency Intermuscular Coherence between Arm Muscles during Robot-Mediated Motor Adaptation.

Adaptation of arm reaching in a novel force field involves co-contraction of upper limb muscles, but it is not known how the co-ordination of multiple muscle activation is orchestrated. We have used intermuscular coherence (IMC) to test whether a coherent intermuscular coupling between muscle pairs is responsible for novel patterns of activation during adaptation of reaching in a force field. Subjects (N = 16) performed reaching trials during a null force field, then during a velocity-dependent force field and then again during a null force field. Reaching trajectory error increased during early adaptation to the force-field and subsequently decreased during later adaptation. Co-contraction in the majority of all possible muscle pairs also increased during early adaptation and decreased during later adaptation. In contrast, IMC increased during later adaptation and only in a subset of muscle pairs. IMC consistently occurred in frequencies between ~40–100 Hz and during the period of arm movement, suggesting that a coherent intermuscular coupling between those muscles contributing to adaptation enable a reduction in wasteful co-contraction and energetic cost during reaching.

Hopf Amplification Originated from the Force-Gating Channels of Auditory Hair Cells**Supported by the National Natural Science Foundation of China under Grant No 11374118, and the Science Foundation of Hubei Province under Grant No 2013CFB289.

The sense of mammalian hearing exhibits nonlinear phenomena which are most significant to hearing function, such as nonlinear dynamic compression, nonlinear tuning and combination tones. These nonlinear phenomena are suggested to originate from the Hopf amplification within the cochlea, while the mechanism underlying the Hopf amplification remains elusive. According to the experimental results of force-gating channel operation in hair cells, through a theoretic model, this work reveals a velocity-dependent open probability of force-gating channels in auditory hair cells, and a velocity-dependent active force produced by the force-gating channel operating, which makes sensors hear typical Hopf vibrators with nonlinear hearing phenomena.

Effect of Position- and Velocity-Dependent Forces on Reaching Movements at Different Speeds.

The speed of voluntary movements is determined by the conflicting needs of maximizing accuracy and minimizing mechanical effort. Dynamic perturbations, e.g., force fields, may be used to manipulate movements in order to investigate these mechanisms. Here, we focus on how the presence of position- and velocity-dependent force fields affects the relation between speed and accuracy during hand reaching movements. Participants were instructed to perform reaching movements under visual control in two directions, corresponding to either low or high arm inertia. The subjects were required to maintain four different movement durations (very slow, slow, fast, very fast). The experimental protocol included three phases: (i) familiarization—the robot generated no force; (ii) force field—the robot generated a force; and (iii) after-effect—again, no force. Participants were randomly assigned to four groups, depending on the type of force that was applied during the “force field” phase. The robot was programmed to generate position-dependent forces—with positive (K+) or negative stiffness (K−)—or velocity-dependent forces, with either positive (B+) or negative viscosity (B−). We focused on path curvature, smoothness, and endpoint error; in the latter we distinguished between bias and variability components. Movements in the high-inertia direction are smoother and less curved; smoothness also increases with movement speed. Endpoint bias and variability are greater in, respectively, the high and low inertia directions. A robust dependence on movement speed was only observed in the longitudinal components of both bias and variability. The strongest and more consistent effects of perturbation were observed with negative viscosity (B−), which resulted in increased variability during force field adaptation and in a reduction of the endpoint bias, which was retained in the subsequent after-effect phase. These findings confirm that training with negative viscosity produces lasting effects in movement accuracy at all speeds.

Impact of online visual feedback on motor acquisition and retention when learning to reach in a force field

When subjects learn a novel motor task, several sources of feedback (proprioceptive, visual or auditory) contribute to the performance. Over the past few years, several studies have investigated the role of visual feedback in motor learning, yet evidence remains conflicting. The aim of this study was therefore to investigate the role of online visual feedback (VFb) on the acquisition and retention stages of motor learning associated with training in a reaching task. Thirty healthy subjects made ballistic reaching movements with their dominant arm toward two targets, on 2 consecutive days using a robotized exoskeleton (KINARM). They were randomly assigned to a group with (VFb) or without (NoVFb) VFb of index position during movement. On day 1, the task was performed before (baseline) and during the application of a velocity-dependent resistive force field (adaptation). To assess retention, participants repeated the task with the force field on day 2. Motor learning was characterized by: (1) the final endpoint error (movement accuracy) and (2) the initial angle (iANG) of deviation (motor planning). Even though both groups showed motor adaptation, the NoVFb-group exhibited slower learning and higher final endpoint error than the VFb-group. In some condition, subjects trained without visual feedback used more curved initial trajectories to anticipate for the perturbation. This observation suggests that learning to reach targets in a velocity-dependent resistive force field is possible even when feedback is limited. However, the absence of VFb leads to different strategies that were only apparent when reaching toward the most challenging target.

Entropy production by active particles: Coupling of odd and even functions of velocity.

Nonequilibrium stochastic dynamics of several active Brownian systems are modeled in terms of nonlinear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for total entropy production in such systems using the Fokker-Planck equation. The result is consistent with the expression for stochastic entropy production in the reservoir that we obtain from probabilities of time-forward and time-reversed trajectories, leading to fluctuation theorems. Numerical simulation is used to find probability distribution of entropy production, which shows good agreement with the detailed fluctuation theorem.