Velocity-dependent Force Research Articles

Mathematical analysis of left ventricular elastance with respect to afterload change during ejection phase.

Since the left ventricle (LV) has pressure (Plv) and volume (Vlv), we can define LV elastance from the ratio between Plv and Vlv, termed as "instantaneous elastance." On the other hand, end-systolic elastance (Emax) is known to be a good index of LV contractility, which is measured by the slope of several end-systolic Plv-Vlv points obtained by using different loads. The word Emax originates from the assumption that LV elastance increases during the ejection phase and attains its maximum at the end-systole. From this concept, we can define another elastance determined by the slope of isochronous Plv-Vlv points, that is Plv-Vlv points at a certain time after the ejection onset time by using different loads. We refer to this elastance as "load-dependent elastance." To reveal the relation between these two elastances, we used a hemodynamic model that included a detailed ventricular myocyte contraction model. From the simulation results, we found that the isochronous Plv-Vlv points lay in one line and that the line slope corresponding to the load-dependent elastance slightly decreased during the ejection phase, which is quite different from the instantaneous elastance. Subsequently, we analyzed the mechanism determining these elastances from the model equations. We found that instantaneous elastance is directly related to contraction force generated by the ventricular myocyte, but the load-dependent elastance is determined by two factors: one is the transient characteristics of the cardiac cell, i.e., the velocity-dependent force drops characteristics in instantaneous shortening. The other is the force-velocity relation of the cardiac cell. We also found that the linear isochronous pressure-volume relation is based on the approximately linear relation between the time derivative of the cellular contraction force and the cellular shortening velocity that results from the combined characteristics of LV and aortic compliances.

Reexamination of Damping in Sliding Friction.

Friction is responsible for about one-third of the primary energy consumption in the world. So far, a thorough atomistic understanding of the frictional energy dissipation mechanisms is still lacking. The Amontons' law states that kinetic friction is independent of the sliding velocity while the Prandtl-Tomlinson model suggests that damping is proportional to the relative sliding velocity between two contacting objects. Through careful analysis of the energy dissipation process in atomic force microscopy measurements, here we propose that damping force is proportional to the tip oscillation speed induced by friction. It is shown that a physically well-founded damping term can better reproduce the multiple peaks in the velocity-dependent friction force observed in both experiments and molecular dynamics simulations. Importantly, the analysis gives a clear physical picture of the dynamics of energy dissipation in different friction phases, which provides insight into long-standing puzzles in sliding friction, such as velocity weakening and spring-stiffness-dependent friction.

The hydrodynamic analysis of the fully appended DARPA SUBOFF model in the SPMM tests integrating the LES model with the dynamic mesh method

Abstract To investigate the hydrodynamic coefficients of the fully appended DARPA SUBOFF model under various motion modes, this study develops user-defined functions within a computational fluid dynamics (CFD) model to simulate sting-supported planar motion mechanism tests. A dimensionless yawing velocity (r′) is proposed to evaluate the influence of motion periods and amplitudes on the hydrodynamic coefficients. Taking advantage of high-resolution turbulence simulation, reduced model dependency and applicability to complex geometries, this study integrates large eddy simulation and the dynamic mesh method to simulate each motion mode. Discrepancies between simulation results and experimental data for some velocity-dependent force derivatives in oblique towing tests may be linked to the rotational centers of the planar motion mechanism (PMM) supports. Variations in PMM devices affect some acceleration-dependent moment derivatives in pure sway and heave tests. Finally, turning circle maneuvers were conducted to verify the effectiveness of the simulated hydrodynamic coefficients.

Capillary-lubrication force exerted on a two-dimensional particle moving towards a thin fluid film

A rigid object moving in a viscous fluid and in close proximity to an elastic wall experiences self-generated elastohydrodynamic interactions. This has been the subject of intense research activity, with recent and growing attention given to the particular case of elastomeric and gel-like substrates. Here, we address the situation where the elastic wall is replaced by a capillary surface. Specifically, we analyse the lubrication flow generated by the prescribed normal motion of a rigid infinite cylinder near the deformable interface separating two immiscible and incompressible viscous fluids. Using a combination of analytical and numerical treatments, we compute the emergent capillary-lubrication force at leading order in capillary compliance, and characterize its dependencies with the interfacial tension, viscosities of the fluids, and length scales of the problem. Interestingly, we identify two main contributions: (i) a velocity-dependent adhesive-like force; (ii) an acceleration-dependant inertia-like force. Our results may have implications for the mobility of colloids near complex interfaces and for the motility of confined microbiological entities.

Velocity-dependent forces and non-hydrodynamic initial conditions in quantum and classical fluids

Velocity-dependent forces and non-hydrodynamic initial conditions in quantum and classical fluids

Impairments of saccadic and reaching adaptation in essential tremor are linked to movement execution.

Essential tremor (ET) is a neurological disorder characterized by involuntary oscillations of the limbs. Previous studies have hypothesized that ET is a cerebellar disorder and reported impairments in motor adaptation. However, recent advances have highlighted that motor adaptation involves several components linked to anticipation and control, all dependent on cerebellum. We studied the contribution of both components in adaptation to better understand the adaptation impairments observed in ET from a behavioral perspective. To address this question, we investigated behavioral markers of adaptation in ET patients (n = 20) and age-matched neurologically intact volunteers (n = 20) in saccadic and upper limb adaptation tasks, probing compensation for target jumps and for velocity-dependent force fields, respectively. We found that both groups adapted their movements to the novel contexts; however, ET patients adapted to a lesser extent compared with neurologically intact volunteers. Importantly, components of the movement linked to anticipation were preserved in the ET group, whereas components linked to movement execution appeared responsible for the adaptation deficit in this group. Altogether, our results suggest that execution deficits may be a specific functional consequence of the alteration of neural pathways associated with ET.NEW & NOTEWORTHY We tested essential tremor patients' adaptation abilities in classical tasks including saccadic adaptation to target jumps and reaching adaptation to force field disturbances. Patients' adaptation was present but impaired in both tasks. Interestingly, the deficits were mainly present during movement execution, whereas the anticipatory components of movements were similar to neurologically intact volunteers. These findings reinforce the hypothesis of a cerebellar origin for essential tremor and detail the motor adaptation impairments previously found in this disorder.

Propagators for molecular dynamics in a magnetic field

ABSTRACT Ab initio molecular dynamics in a magnetic field requires solving equations of motion with velocity-dependent forces – namely, the Lorentz force arising from the nuclear charges moving in a magnetic field and the Berry force arising from the shielding of these charges from the magnetic field by the surrounding electrons. In this work, we revisit two existing propagators for these equations of motion, the auxiliary-coordinates-and-momenta (ACM) propagator and the Tajima propagator (TAJ), and compare them with a new exponential (EXP) propagator based on the Magnus expansion. Additionally, we explore limits (for example, the zero-shielding limit), the implementation of higher-order integration schemes, and series truncation to reduce computational cost by carrying out simulations of a HeH + model system for a wide range of field strengths. While being as efficient as the TAJ propagator, the EXP propagator is the only propagator that converges to both the schemes of Spreiter and Walter (derived for systems without shielding of the Lorentz force) and to the exact cyclotronic motion of a charged particle. Since it also performs best in our model simulations, we conclude that the EXP propagator is the recommended propagator for molecules in magnetic fields.

Congruent visual cues speed dynamic motor adaptation

We demonstrate that adaptation to novel dynamics is stronger when additional online visual cues that are congruent with the dynamics are presented during adaptation, compared with either a constant or incongruent visual cue. This effect was found regardless of whether a bidirectional or unidirectional velocity-dependent force field was presented to the participants. We propose that this effect might arise through the inclusion of this additional visual cue information within the state estimation process.

Molecular vibrations in the presence of velocity-dependent forces.

A semiclassical theory of small oscillations is developed for nuclei that are subject to velocity-dependent forces in addition to the usual interatomic forces. When the velocity-dependent forces are due to a strong magnetic field, novel effects arise-for example, the coupling of vibrational, rotational, and translational modes. The theory is first developed using Newtonian mechanics and we provide a simple quantification of the coupling between these types of modes. We also discuss the mathematical structure of the problem, which turns out to be a quadratic eigenvalue problem rather than a standard eigenvalue problem. The theory is then re-derived using the Hamiltonian formalism, which brings additional insight, including a close analogy to the quantum-mechanical treatment of the problem. Finally, we provide numerical examples for the H2, HT, and HCN molecules in a strong magnetic field.

Constraints on Spin-Spin Velocity-Dependent Interactions.

The existence of exotic spin-dependent forces may shine light on new physics beyond the standard model. We utilize two iron shielded SmCo_{5} electron-spin sources and two optically pumped magnetometers to search for exotic long-range spin-spin velocity-dependent force. The orientations of spin sources and magnetometers are optimized such that the exotic force is enhanced and common-mode noise is effectively subtracted. We set direct limit on proton-electron interaction in the force range from 1cm to 1km. Our experiment represents more than 10 orders of magnitude improvement than previous works.

The growth of intermediate mass black holes through tidal captures and tidal disruption events

ABSTRACTWe present N-body simulations, including post-Newtonian dynamics, of dense clusters of low-mass stars harbouring central black holes (BHs) with initial masses of 50, 300, and 2000 M⊙. The models are evolved with the N-body code bifrost to investigate the possible formation and growth of massive BHs by the tidal capture of stars and tidal disruption events (TDEs). We model star–BH tidal interactions using a velocity-dependent drag force, which causes orbital energy and angular momentum loss near the BH. About ∼20–30 per cent of the stars within the spheres of influence of the black holes form Bahcall–Wolf cusps and prevent the systems from core collapse. Within the first 40 Myr of evolution, the systems experience 500–1300 TDEs, depending on the initial cluster structure. Most (>95 per cent) of the TDEs originate from stars in the Bahcall–Wolf cusp. We derive an analytical formula for the TDE rate as a function of the central BH mass, density, and velocity dispersion of the clusters ($\dot{N}_{\mathrm{TDE}} \propto M\mathrm{_{BH}}\rho \sigma ^{-3}$). We find that TDEs can lead a 300 M⊙ BH to reach $\sim 7000 \, \mathrm{{M}_{\odot }}$ within a Gyr. This indicates that TDEs can drive the formation and growth of massive BHs in sufficiently dense environments, which might be present in the central regions of nuclear star clusters.

Geodesic and Newtonian Vector Fields and Symmetries of Mechanical Systems

Geodesic vector fields and other distinguished vector fields on a Riemann manifold were used in the study of free motions on such a manifold, and we applied the geometric Hamilton–Jacobi theory for the search of geodesic vector fields from Hamilton–Jacobi vector fields and the same for closed vector fields. These properties were appropriately extended to the framework of Newtonian and generalised Newtonian systems, in particular systems defined by Lagrangians of the mechanical type and velocity-dependent forces. Conserved quantities and a generalised concept of symmetry were developed, particularly for Killing vector fields. Nonholonomic constrained Newtonian systems were also analysed from this perspective, as well as the relation among Newtonian vector fields and Hamilton–Jacobi equations for conformally related metrics.

String Stability Under Actuator Saturation on Straight Level Roads: Sufficient Conditions and Optimal Trajectory Generation

The heterogeneity of vehicles is an important factor when realizing cooperative adaptive cruise control (CACC) in practice. Specifically, it has to be considered that platoons generally consist of vehicles with both different dynamic properties and actuator limits on the engine and braking force, which is expected to have a negative impact on important properties such as string stability. Accordingly, the subject of this paper is the preservation of string stability for CACC in heterogeneous vehicle strings with potential actuator saturation. To this end, the paper formulates a velocity-dependent force bound that enables the derivation of sufficient conditions for preserving string stability during velocity changes of heterogeneous platoons. These conditions are then used for the analytical computation of trajectories for time-optimal velocity changes. The formal results of the paper are supported by an illustrative simulation study.

Separability of Human Motor Memories during reaching adaptation with force cues.

Judging by the breadth of our motor repertoire during daily activities, it is clear that learning different tasks is a hallmark of the human motor system. However, for reaching adaptation to different force fields, the conditions under which this is possible in laboratory settings have remained a challenging question. Previous work has shown that independent movement representations or goals enabled dual adaptation. Considering the importance of force feedback during limb control, here we hypothesised that independent cues delivered by means of background loads could support simultaneous adaptation to various velocity-dependent force fields, for identical kinematic plan and movement goal. We demonstrate in a series of experiments that indeed healthy adults can adapt to opposite force fields, independently of the direction of the background force cue. However, when the cue and force field were in the same direction but differed by heir magnitude, the formation of different motor representations was still observed but the associated mechanism was subject to increased interference. Finally, we highlight that this paradigm allows dissociating trial-by-trial adaptation from online feedback adaptation, as these two mechanisms are associated with different time scales that can be identified reliably and reproduced in a computational model.

Motion state-dependent motor learning based on explicit visual feedback is quickly recalled, but is less stable than adaptation to physical perturbations.

Recent studies have shown that adaptation to visual feedback perturbations during arm reaching movements involves implicit and explicit learning components. Evidence also suggests that explicit, intentional learning mechanisms are largely responsible for savings-a faster recalibration compared with initial training. However, the extent explicit learning mechanisms facilitate learning and early savings (i.e., the rapid recall of previous performance) for motion state-dependent learning is generally unknown. To address this question, we compared the early savings/recall achieved by two groups of human subjects. One experienced physical perturbations (a velocity-dependent force-field, vFF) to promote adaptation that is thought to be a largely implicit process. The second was only given visual feedback of the required force-velocity relationship; subjects moved in force channels and we provided visual feedback of the lateral force exerted during the movement, as well as the required force pattern based on the movement velocity. Thus, subjects were shown explicit information on the extent the applied temporal pattern of force matched the required velocity-dependent force profile if the force-field perturbation had been applied. After training, both groups experienced a decay and washout period, which was followed by a reexposure block to assess early savings/recall. Although decay was faster for the explicit visual feedback group, the single-trial recall was similar to the physical perturbation group. Thus, compared with visual feedback perturbations, conscious modification of motor output based on motion state-dependent feedback demonstrates rapid recall, but this adjustment is less stable than adaptation based on experiencing the multisensory errors that accompany physical perturbations.NEW & NOTEWORTHY The extent explicit feedback facilitates motion state-dependent changes to motor output is largely unknown. Here, we examined motor adaptation for subjects that experienced physical perturbations and another that made adjustments based on explicit visual feedback information of the required force-velocity relationship. Our results suggest that adjustment of motor output can be based on explicit motion state-dependent information and demonstrates rapid recall, but this learning is less stable than adaptation based on physical perturbations to movement.

What is the nature of motor adaptation to dynamic perturbations?

When human participants repeatedly encounter a velocity-dependent force field that distorts their movement trajectories, they adapt their motor behavior to recover straight trajectories. Computational models suggest that adaptation to a force field occurs at the action selection level through changes in the mapping between goals and actions. The quantitative prediction from these models indicates that early perturbed trajectories before adaptation and late unperturbed trajectories after adaptation should have opposite curvature, i.e. one being a mirror image of the other. We tested these predictions in a human adaptation experiment and we found that the expected mirror organization was either absent or much weaker than predicted by the models. These results are incompatible with adaptation occurring at the action selection level but compatible with adaptation occurring at the goal selection level, as if adaptation corresponds to aiming toward spatially remapped targets.

Theory of viscoelastic adhesion and friction

We present a novel theory of the adhesive contact of linear viscoelastic materials sliding at constant velocity against rough substrates. Despite the non-conservative behaviour of the system, the closure equation, needed to calculate the unknown size of the contact area, can be rigorously formulated in the form of a local energy balance. The results highlight three main peculiar features of the contact, which are strictly ascribable to the interplay of adhesion and viscoelasticity. First, a velocity dependent pull-off force is predicted, whose maximum value occurs at intermediate sliding velocity. Second, the energy release rates G1 and G2 at the contact trailing and leading edges respectively, present a non-monotonic dependence on the indenter sliding velocity. Third, the velocity dependence of the hysteretic friction μ is significantly altered and presents a friction peak much more pronounced compared to the adhesiveless viscoelastic case. Theoretical predictions are in very good agreement with existing experimental data.

PIMesh: An automatic point cloud and unstructured mesh generation algorithm for meshless methods and finite element analysis-with applications in surgical simulations.

We propose a point cloud and mesh generation algorithm, particle injection mesh generator (PIMesh), that can be used to generate optimized high-quality point clouds and unstructured meshes for domains in any shape with minimum (or even no) user intervention. The domains can be scanned images in OBJ format in 2D and 3D or just a line drawing in 2D. Mesh grading can also be easily controlled. The PIMesh is robust and easy to be implemented and is useful for a variety of applications, ranging from generating point clouds for meshless methods, mesh generation for finite element methods, computer graphics applications and surgical simulators. The core idea of the PIMesh is that a mesh domain is considered as an "airtight container" into which particles are "injected" at one or multiple selected interior points. The motion of the particles is controlled by a pseudo-molecular dynamics (PMD) formulation with a pairwise purely repelling "force" moderated by an absolute velocity dependent drag force. The particles repel each other and occupy the whole domain somewhat like blowing up a balloon. When the container is full of particles and the motion is stopped (the particles can be considered as a point cloud), a Delaunay triangulation algorithm is employed to link the particles together to generate an unstructured mesh. The performance of the PIMesh and the comparison with other unstructured mesh generation approaches are demonstrated through generating node distributions and meshes for several 2D and 3D object domains including a scanned image of bones and others.

Two Lab Activities Demonstrating Some Physics of High Altitude Balloon Launches

We present two lab activities that involve similar physics to that of high altitude balloon flights. One lab involves a descending helium-filled balloon and the other involves a descending parachute. In both of these activities, the descending object is subject to a sum of forces in the vertical direction. Forces involved include the velocity-dependent drag force, which varies with time and thereby makes theoretical predictions of both our lab activities nontrivial. The aim of both lab activities is to measure and model the time of descent for the falling body.

Effects of Driving Style on Energy Consumption and CO2 Emissions

The tractive force developed by energy consumption (EC) in a car engine produces its acceleration and sustains the motion against velocity dependent resistance forces. In internal combustion engines, fuel burning entails pollutant emissions (PE) released into the atmosphere. In vehicular traffic, EC and PE depend on the driving style. This paper assumed that the transition rules in a traffic cellular automata (TCA) represent a driving style, and its effect on EC and PE in TCA is studied. Extending empirical relationships, we proposed models to estimate EC and PE in TCA from the velocity and acceleration distributions, which we obtained by computer simulations for three well-known TCA. The Nagel-Schreckenberg (NS) and Fukui-Ishibashi (FI) models, and a variant (NS+FI) defined by combining the NS and FI rules, were considered. The FI driving style revealed EC and CO2 emission rates dependent on the stochastic delay (p) only for low vehicular densities. We also detected that the larger EC and CO2 emission rates were 45.4 kW and 26.7 g/s with no dependence on p. With NS and NS+FI driving styles, the larger energy consumption and CO2 emission rates occurred for small stochastic delays, 18.4 kW and 6.6 g/s and 61.1kW and 30.2 g/s for p = 0.2. On average, for NS, FI, and NS+FI models (p = 0.2), we obtained energy consumptions of 1.88, 2.60, and 2.76 MJ/km, fuel consumptions of 0.08, 0.12, and 0.13 L/km, and CO2 emissions of 0.158, 0.460, and 0.562 kgCO2/km. Our results agree with those (3.37 MJ/km and 0.235 kgCO2/km) of petrol combustion car engines at 10 km/L. This work may help in designing flow and driving style scenarios to optimize vehicular traffic EC and reduce PE.