Velocity-dependent Force Research Articles

Feedforward compensation for novel dynamics depends on force field orientation but is similar for the left and right arms

There are well-documented differences in the way that people typically perform identical motor tasks with their dominant and the nondominant arms. According to Yadav and Sainburg's (Neuroscience 196: 153-167, 2011) hybrid-control model, this is because the two arms rely to different degrees on impedance control versus predictive control processes. Here, we assessed whether differences in limb control mechanisms influence the rate of feedforward compensation to a novel dynamic environment. Seventy-five healthy, right-handed participants, divided into four subsamples depending on the arm (left, right) and direction of the force field (ipsilateral, contralateral), reached to central targets in velocity-dependent curl force fields. We assessed the rate at which participants developed predictive compensation for the force field using intermittent error-clamp trials and assessed both kinematic errors and initial aiming angles in the field trials. Participants who were exposed to fields that pushed the limb toward ipsilateral space reduced kinematic errors more slowly, built up less predictive field compensation, and relied more on strategic reaiming than those exposed to contralateral fields. However, there were no significant differences in predictive field compensation or kinematic errors between limbs, suggesting that participants using either the left or the right arm could adapt equally well to novel dynamics. It therefore appears that the distinct preferences in control mechanisms typically observed for the dominant and nondominant arms reflect a default mode that is based on habitual functional requirements rather than an absolute limit in capacity to access the controller specialized for the opposite limb.

Effect of velocity-dependent friction on multiple-vehicle collisions in traffic flow

Abstract We present the dynamic model for the multiple-vehicle collisions to take into account the velocity-dependent friction force. We study the effect of the velocity-dependent friction on the chain-reaction crash on a road. In the traffic situation, drivers brake according to taillights of the forward vehicle and the friction force depends highly on the vehicular speed. The first crash may induce more collisions. We investigate whether or not the first collision induces the multiple-vehicle collisions, numerically and analytically. The dynamic transitions occur from no collisions, through a single collision and double collisions, to multiple collisions with decreasing the headway. We explore the effect of the velocity-dependent friction on the dynamic transitions and the region maps in the multiple-vehicle collisions.

Local membrane length conservation in two-dimensional vesicle simulation using a multicomponent lattice Boltzmann equation method.

We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.

EP 72. Cerebellar tDCS effects on the adaptation of arm reaching movements to force-field perturbations

Introduction Transcranial direct current stimulation (tDCS) is a non-invasive brain-stimulation technique that can alter cortical excitability and plasticity. Previous studies 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 et al., 2014 ). The first aim of the present study was to replicate these findings in a force field reaching adaptation task. The second aim was to investigate whether tDCS effects differ depending on onset of stimulation. Methods 60 healthy and right-handed subjects (30 females, aged 20–31 years, mean 24.1 ± 2.3) were tested. Subjects held a two-joined manipulandum with their right hand. They moved a cursor from a central origin to one of eight targets presented on a vertical screen. Three baseline blocks were followed by one adaptation block and three post-adaptation blocks. During adaptation a velocity-dependent clockwise perpendicular force (23 N·m−1·s−1) was applied. tDCS electrodes (5 × 5 cm2) were centered 3 cm lateral to the inion on the right and on the ipsilateral buccinator muscle. An equal number of subjects received anodal, cathodal or sham stimulation during adaptation using a Neuroconn® DC stimulator. tDCS started either in the third baseline block or at the beginning of the adaptation block. The maximum error, the final error and the perpendicular velocity shortly after movement onset (after 55 ms) were assessed. Results During adaptation all subjects showed significant effects of learning. They reduced the maximum error as well as the final error and changed the sign of the perpendicular velocity shortly after movement onset (p 0.05). During post-adaptation, there were significant after- and washout effects. Again, there were no significant effects of stimulation, no significant effects of onset of stimulation and no significant interactions (all p-values > 0.05). Conclusions We were unable to replicate previous findings of modulatory cerebellar tDCS effects in a force field reaching adaptation task in healthy subjects. Furthermore, no differential effects of the onset of stimulation were observed. Prior possible application in patients with cerebellar disease, future experiments are needed to determine which tDCS and task parameters lead to robust tDCS effects. Funded by ELAN (Essener Ausbildungsprogramm “Labor und Wissenschaft” fur den aerztlichen Nachwuchs) and DFG TI 239/16-1

Optimal feedback control for a thermoviscoelastic model of Voigt fluid motion

A system of equations describing the motion of viscous fluids with polymer additives is considered. The system involves a temperature-dependent viscosity and a velocity-dependent external force, which is used as a control. The existence of an optimal feedback control for the system is proved.

Wigner-Lindblad Equations for Quantum Friction.

Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena.

A Solvable N-body Problem of Goldfish Type Featuring N2 Arbitrary Coupling Constants

A N-body problem “of goldfish type” is introduced, the Newtonian (“acceleration equal force”) equations of motion of which describe the motion of N pointlike unit-mass particles moving in the complex z-plane. The model—for arbitrary N—is solvable, namely its configuration (positions and velocities of the N “particles”) at any later time t can be obtained from its configuration at the initial time by algebraic operations. It features specific nonlinear velocity-dependent many-body forces depending on N2 arbitrary (complex) coupling constants. Sufficient conditions on these constants are identified which cause the model to be isochronous—so that all its solutions are then periodic with a fixed period independent of the initial data. A variant with twice as many arbitrary coupling constants, or even more, is also identified.

Velocity-dependent dipole forces on an excited atom

We present a time-dependent calculation of the velocity-dependent forces which act on an excited atomic dipole in relative motion with respect to ground state atoms of a different kind. Both, its interaction with a single atom and with a dilute atomic plate are evaluated. In either case, the total force consists of a conservative van der Waals component and a non-conservative Rontgen component. On physical grounds, the former corresponds to the velocity-dependent recoil experienced by the excited atom in the processes of absorption and emission of the photons that it exchanges with the ground state atoms on a periodic basis. The latter corresponds to the time-variation of the Rontgen momentum, which is also mediated by the periodic exchange of quasi-resonant photons. We find that, at leading order, all these interactions are linear in the velocity. In the non-retarded regime the van der Waals force dominates, being antiparallel to the velocity. On the contrary, in the retarded regime the velocity-dependent forces oscillate in space, van der Waals and Rontgen forces are of the same order in the atom-atom interaction, and the Rontgen component dominates in the atom-surface interaction.

Dynamically adjustable foot-ground contact model to estimate ground reaction force during walking and running

Human dynamic models have been used to estimate joint kinetics during various activities. Kinetics estimation is in demand in sports and clinical applications where data on external forces, such as the ground reaction force (GRF), are not available. The purpose of this study was to estimate the GRF during gait by utilizing distance- and velocity-dependent force models between the foot and ground in an inverse-dynamics-based optimization. Ten males were tested as they walked at four different speeds on a force plate-embedded treadmill system. The full-GRF model whose foot-ground reaction elements were dynamically adjusted according to vertical displacement and anterior-posterior speed between the foot and ground was implemented in a full-body skeletal model. The model estimated the vertical and shear forces of the GRF from body kinematics. The shear-GRF model with dynamically adjustable shear reaction elements according to the input vertical force was also implemented in the foot of a full-body skeletal model. Shear forces of the GRF were estimated from body kinematics, vertical GRF, and center of pressure. The estimated full GRF had the lowest root mean square (RMS) errors at the slow walking speed (1.0m/s) with 4.2, 1.3, and 5.7% BW for anterior–posterior, medial–lateral, and vertical forces, respectively. The estimated shear forces were not significantly different between the full-GRF and shear-GRF models, but the RMS errors of the estimated knee joint kinetics were significantly lower for the shear-GRF model. Providing COP and vertical GRF with sensors, such as an insole-type pressure mat, can help estimate shear forces of the GRF and increase accuracy for estimation of joint kinetics.

Integrable 2D Time-Irreversible Systems with a Cubic Second Integral

We construct a very rare integrable 2D mechanical system which admits a complementary integral of motion cubic in the velocities in the presence of conservative potential and velocity-dependent (gyroscopic) forces. Special cases are given interpretation as a motion of a particle on a sphere endowed with a Riemannian metric, a particle in the Euclidean plane, and new generalizations of two cases of motion of a rigid body with a cubic integral, known by names of Goriachev-Chaplygin and Goriachev.

Generic features of brittle crack propagation engendered by the dynamics of the process zone

We demonstrate that internal dynamics within the transformational process zone at the tip of a propagating crack gives rise to energy dissipation. It manifests itself as a velocity-dependent resistance force exerted on the crack tip. It has the effect of limiting the terminal crack speed to below the Rayleigh velocity as well as giving rise to a discontinuous dependence of the crack velocity upon the driving force.

To transfer or not to transfer? Kinematics and laterality quotient predict interlimb transfer of motor learning.

Humans can remarkably adapt their motor behavior to novel environmental conditions, yet it remains unclear which factors enable us to transfer what we have learned with one limb to the other. Here we tested the hypothesis that interlimb transfer of sensorimotor adaptation is determined by environmental conditions but also by individual characteristics. We specifically examined the adaptation of unconstrained reaching movements to a novel Coriolis, velocity-dependent force field. Right-handed subjects sat at the center of a rotating platform and performed forward reaching movements with the upper limb toward flashed visual targets in prerotation, per-rotation (i.e., adaptation), and postrotation tests. Here only the dominant arm was used during adaptation and interlimb transfer was assessed by comparing performance of the nondominant arm before and after dominant-arm adaptation. Vision and no-vision conditions did not significantly influence interlimb transfer of trajectory adaptation, which on average was significant but limited. We uncovered a substantial heterogeneity of interlimb transfer across subjects and found that interlimb transfer can be qualitatively and quantitatively predicted for each healthy young individual. A classifier showed that in our study, interlimb transfer could be predicted based on the subject's task performance, most notably motor variability during learning, and his or her laterality quotient. Positive correlations suggested that variability of motor performance and lateralization of arm movement control facilitate interlimb transfer. We further show that these individual characteristics can predict the presence and the magnitude of interlimb transfer of left-handers. Overall, this study suggests that individual characteristics shape the way the nervous system can generalize motor learning.

Interferometric Laser Cooling of Atomic Rubidium.

We report the 1D cooling of ^{85}Rb atoms using a velocity-dependent optical force based upon Ramsey matter-wave interferometry. Using stimulated Raman transitions between ground hyperfine states, 12 cycles of the interferometer sequence cool a freely moving atom cloud from 21 to 3 μK. This pulsed analog of continuous-wave Doppler cooling is effective at temperatures down to the recoil limit; with augmentation pulses to increase the interferometer area, it should cool more quickly than conventional methods and be more suitable for species that lack a closed radiative transition.

Entropy production for velocity-dependent macroscopic forces: The problem of dissipation without fluctuations

In macroscopic systems, velocity-dependent phenomenological forces F(v) are used to model friction, feedback devices or self-propulsion. Such forces usually include a dissipative component which conceals the fast energy exchanges with a thermostat at the environment temperature T, ruled by a microscopic Hamiltonian H. The mapping —even if effective for many purposes— may lead to applications of stochastic thermodynamics where an incomplete fluctuating entropy production (FEP) is derived. An enlighting example is offered by recent macroscopic experiments where dissipation is dominated by solid-on-solid friction, typically modelled through a deterministic Coulomb force F(v). Through an adaptation of the microscopic Prandtl-Tomlinson model for friction, we show how the FEP is dominated by the heat released to the T-thermostat, ignored by the macroscopic Coulomb model. This problem, which haunts several studies in the literature, cannot be cured by weighing the time-reversed trajectories with a different auxiliary dynamics: it is only solved by a more accurate stochastic modelling of the thermostat underlying dissipation.

Point particle motion in topologically nontrivial spacetimes

It is well known that compactifying a space can break symmetries that are present in the covering space. In this paper we study the effects of such topological symmetry breaking on point particle motion when the particle is coupled to a massless field on the space. For a torus topology where Lorentz invariance is broken but translation invariance is maintained, particles can move at a constant velocity through the space; however, nonlocal, velocity-dependent forces arise whenever the particle is accelerated. For a topology where translation invariance is broken, such as the Klein bottle, interactions with the massless field generate an effective potential as a function of position. The potential creates special stable points in the space, and prevents constant velocity motion. The latter would appear to be the generic case. This class of effects may be applicable whenever a localized object moves through a compactified bulk, such as in brane-world cosmology, or some condensed matter systems.

Periodic motions of a perturbed reversible mechanical system

Periodic motions of a reversible mechanical system under perturbations of general form that do not preserve system's reversibility are investigated. The conditions for the existence of periodic motions of a perturbed system that turn at a zero value of a small parameter into symmetrical periodic motions not degenerating into equilibriua are found. Both autonomous and periodic perturbations are considered. Amplitude equations, whose simple roots correspond to periodic solutions of the perturbed system, are derived for the systems investigated. As a result, cycles are found for the autonomous system, and isolated periodic motions are found for the periodic system. Both a separate system and a model containing coupled subsystems are investigated. The characteristic exponents of the cycles are calculated. It is proved that any oscillation of a system that can be described by Lagrange's equations with positional forces is symmetrical and belongs to a family. It is also deduced that for the realization of a cycle or, in the case of non-autonomous forces, an isolated periodic motion, velocity-dependent forces of definite structure are needed. The results obtained are applied to the problem of the oscillations of a satellite under the action of gravitational and aerodynamic torques. The existence of asymmetrical isolated oscillations in a low-eccentricity elliptical orbit is established.

Numerical investigation of the vertical plunging force of a spherical intruder into a prefluidized granular bed.

The plunging of a large intruder sphere into a prefluidized granular bed with various constant velocities and various sphere diameters is investigated using a state-of-the-art hybrid discrete particle and immersed boundary method, in which both the gas-induced drag force and the contact force exerted on the intruder can be investigated separately. We investigate low velocities, where velocity dependent effects first begin to appear. The results show a concave-to-convex dependence of the plunging force as a function of intruder depth. In the concave region the force fits to a power law with an exponent around 1.3, which is in good agreement with existing experimental observations. Our simulation results further show that the force exerted on the frontal hemisphere of the intruder is dominant. At larger intruder velocities, friction with the granular medium causes a velocity-dependent drag force. As long as the granular particles have not yet closed the gap behind the intruder, this drag force is independent of the actual intruder depth. In this regime, the drag force experienced by intruders of different diameter moving at different velocities all fall onto a single master curve if plotted against the Reynolds number, using a single value for the effective viscosity of the granular medium. This master curve corresponds well to the Schiller-Naumann correlation for the drag force between a sphere and a Newtonian fluid. After the gap behind the intruder has closed, the drag force increases not only with velocity but also with depth. We attribute this to the effect of increasing hydrostatic particle pressure in the granular medium, leading to an increase in effective viscosity.

The role of the dissipative and random forces in the calculation of the pressure of simple fluids with dissipative particle dynamics

The role of viscous forces coupled with Brownian forces in momentum-conserving computer simulations is studied here in the context of their contribution to the total average pressure of a simple fluid as derived from the virial theorem, in comparison with the contribution of the conservative force to the total pressure. The specific mesoscopic model used is the one known as dissipative particle dynamics, although our conclusions apply to similar models that obey the fluctuation–dissipation theorem for short range interactions and have velocity-dependent viscous forces. We find that the average contribution of the random and dissipative forces to the pressure is negligible for long simulations, provided these forces are appropriately coupled and when the finite time step used in the integration of the equation of motion is not too small. Finally, we study the properties of the fluid when the random force is made equal to zero and find that the system freezes as a result of the competition of the dissipative and conservative forces.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

Description of the simplest photonuclear reactions within the particle-hole dispersive optical model

A recently developed particle-hole dispersive optical model is applied to describe the cross sections of photoabsorption, $\text{direct}+\text{semidirect}$ photoneutron and inverse reactions accompanied by excitation of the isovector giant dipole and quadrupole resonances in medium--heavy-mass spherical nuclei. The model is an extension of the standard and nonstandard versions of the continuum-random-phase approximation by including the spreading effect in a phenomenological way. It contains the following ingredients: the Landau--Migdal particle-hole interaction and a phenomenological mean field consistent with this interaction, isovector velocity-dependent forces taken in the simplest form and the imaginary part of an effective single-particle optical-model potential determining the corresponding dispersive part. All the model parameters are taken from the other data and from the description of photoabsorption, while the $\text{direct}+\text{semidirect}$ photoneutron and inverse reactions are described without the use of specific adjustable parameters. Calculation results obtained for a few neutron-closed-shell nuclei are compared with the corresponding experimental data.