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Breaking of balanced and unbalanced equatorial waves.

A clear-cut signature of a wave-breaking event is irreversible modification of the mean flow. In this paper, we provide examples of different breaking mechanisms and show that breaking scenario of equatorial waves in the beta-plane shallow water model is determined by the degree of balance between the zonal component of the Coriolis force and the pressure gradient. Our analysis is based on a specially designed numerical method which guarantees two essential conditions to simulate nonlinear equatorial waves: (i) the scheme converges toward weak solutions including shocks and (ii) preserves the steadiness of balanced stationary solutions. This allows for accurate diagnostics of Lagrangian invariants of motion such as passive tracer density or potential vorticity. For unbalanced waves, the lack of balance leads to shock formation in finite time. In shock fronts, the variation of the dissipation rate induces a nonadvective potential vorticity flux and violates the local potential vorticity conservation valid for smooth solutions. This dissipative breaking mechanism is generic for unbalanced waves and is associated with enhanced mixing. For long, balanced (Rossby) waves, breaking consists in appearance of recirculation regions. It results in the formation of propagating patterns, the equatorial modons, which trap fluid particles. Such breaking occurs during the propagation of Rossby wave packets with positive geopotential anomaly and is strengthened by decreasing fluid depth. The modons are robust and collide quasielastically with Kelvin waves.

Climate↗

Influence of interaction force levels on degree of motor adaptation in a stable dynamic force field.

Studies have shown that the point-to-point reaching movements of subjects seated in a dark, rotating room demonstrate errors in movement trajectories and endpoints, consistent with the direction of the Coriolis force perturbations created by room rotation. Adaptation of successive reaches and the presence of postrotation aftereffects have indicated that subjects form internal models of the Coriolis field dynamics in order to make appropriate movement corrections. It has been argued that these findings are inconsistent with predictions of peripheral stabilization assumed in equilibrium-point models of motor control. A possibility that has been raised, however, is that the Coriolis field findings may in fact stem from changes in control commands elicited due to the magnitude and destabilizing nature of the Coriolis perturbations. That is, it has been suggested that a perturbation threshold exists, below which central reactions are not necessary in order to maintain movement stability. We tested the existence of a perturbation threshold in normal-speed reaching movements. Twelve normal human subjects performed non-visually guided reaching movements while grasping a robotic manipulandum. The endpoints and trajectory deviations of their movements were measured before, during, and after a position-dependent force field (similar to a Coriolis field in terms of the time history of applied forces) was applied to their movements. We examined the responses to a range of perturbation field strengths from small to considerable. Our experimental results demonstrated a substantial adaptation response over the entire range of perturbation field magnitudes examined. Neither the amount of adaptation after 5 trials nor after 25 trials was found to change as disturbance magnitudes decreased. These findings indicate that there is an adaptive response even for small perturbations; i.e., threshold behavior was not found. This result contradicts the assertion that peripheral stabilization mechanisms enable the central controller to ignore small details of peripheral or environmental dynamics. Our findings instead point to a central dynamic modeler that is both highly sensitive and continually active. The results of our study also showed that subjects were able to maintain baseline pointing accuracies despite exposure to perturbation forces of sizeable magnitude (more than 7 N).

Adaptation, Physiological↗

Dynamic interactions between limb segments during planar arm movement.

Movement of multiple segment limbs requires generation of appropriate joint torques which include terms arising from dynamic interactions among the moving segments as well as from such external forces as gravity. The interaction torques, arising from inertial, centripetal, and Coriolis forces, are not present for single joint movements. The significance of the individual interaction forces during reaching movements in a horizontal plane involving only the shoulder and elbow joints has been assessed for different movement paths and movement speeds. Trajectory formation strategies which simplify the dynamics computation are presented.

Arm↗

Multiple-input, multiple-output system identification for characterization of limb stiffness dynamics.

This study presents time-domain and frequency-domain, multiple-input, multiple-output (MIMO) linear system identification techniques that can be used to estimate the dynamic endpoint stiffness of a multijoint limb. The stiffness of a joint or limb arises from a number of physiological mechanisms and is thought to play a fundamental role in the control of posture and movement. Estimates of endpoint stiffness can therefore be used to characterize its modulation during physiological tasks and may provide insight into how the nervous system normally controls motor behavior. Previous MIMO stiffness estimates have focused upon the static stiffness components only or assumed simple parametric models with elastic, viscous, and inertial components. The method presented here captures the full stiffness dynamics during a relatively short experimental trial while assuming only that the system is linear for small perturbations. Simulation studies were performed to investigate the performance of this approach under typical experimental conditions. It was found that a linear MIMO description of endpoint stiffness dynamics was sufficient to describe the displacement responses to small stochastic force perturbations. Distortion of these linear estimates by nonlinear centripetal and Coriolis forces was virtually undetectable for these perturbations. The system identification techniques were also found to be robust in the presence of significant output measurement noise and input coupling. These results indicate that the approach described here will allow the estimation of endpoint stiffness dynamics in an experimentally efficient manner with minimal assumptions about the specific form of these properties.

Algorithms↗

Vision of the hand prior to movement onset allows full motor adaptation to a multi-force environment.

In everyday life, because of unexpected mechanical perturbation applied to the hand or to the whole body, hand movements may become suddenly inaccurate. With prolonged exposure to the perturbation, trajectories slowly recover their normal accuracy, which is the mark of motor adaptation. However, full development of this adaptive process in complete darkness has been recently challenged in a multi-force environment. Here, we report on the effectiveness of static hand position information as specified through vision prior to movement onset on the adaptative changes, over trials, of pointing movements performed in a gravitoinertial force field. For this, subjects seated off-center on a platform rotating at constant velocity, were either confined to complete darkness (No Vision Session, NV) or provided with vision of the hand resting on the starting position prior to movement onset (Hand Vision Prior to Movement Session, HVPM). Overall, our results showed that adaptation to the centrifugal force was very rapid, and allowed subjects to demonstrate appropriate motor control as early as of the very first trials performed during the rotation period, even in the NV condition. They also showed that the integration by the Central Nervous System (CNS) of visual and proprioceptive information prior to the execution of a reaching movement allows subjects to reach full motor adaptation in a multi-force environment. Furthermore, our data confirm the existence of differentiated motor adaptive mechanisms for centrifugal and Coriolis forces. Adaptation to the former may fully develop on the basis of an a priori coding of the characteristics of the background force level even without visual information, while the latter needs visual cues about hand position prior to movement onset to take place.

Adaptation, Physiological↗

Protein simulations using techniques suitable for very large systems: the cell multipole method for nonbond interactions and the Newton-Euler inverse mass operator method for internal coordinate dynamics.

Two new methods developed for molecular dynamics simulations of very large proteins are applied to a series of proteins ranging up to the protein capsid of tomato bushy stunt virus (TBSV). For molecular dynamics of very large proteins and polymers, it is useful to carry out the dynamics using internal coordinates (say, torsions only) rather than Cartesian coordinates. This allows larger time steps, eliminates problems with the classical description of high energy modes, and focuses on the important degrees of freedom. The resulting equation of motion has the form. [formula: see text] where for T is the vector of generalized forces, M(theta) is the moments of inertia tensor, theta is the vector of torsions, and C is a vector containing Coriolis forces and nonbond forces. The problem is that to calculate the acceleration vector theta from M, C, and T requires inverting M(theta), an order N3 calculation. Since the number of degrees of freedom might be 300,000 for a million atom system, solving these equations every time step is impractical, restricting internal coordinate methods to small systems. The new method, Newton-Euler Inverse Mass Operator (NEIMO) dynamics, constructs the torsional accelerations vector theta = M-1 (T-C) directly by an order N process, allowing internal-coordinate dynamics to be solved for super larger (million atom) systems. The first use of the NEIMO method for molecular dynamics of proteins is presented here. A second serious difficulty for large proteins is calculation of the nonbond forces. We report here the first application to proteins of the new Cell Multipole Method (CMM) to evaluate the Coulomb and van der Waals interactions. The costs of CMM scales linearly with the number of particles while retaining an accuracy significantly better than standard nonbond methods (involving cutoffs). Results for NEIMO and CMM are given for simulations of a wide range of peptide and protein systems, including the protein capsid of TBSV with 488,000 atoms. The computational times for NEIMO and CMM are demonstrated to scale linearly with size. With NEIMO the dynamics time steps can be as large as 20 fs (for small peptides), much larger than possible with standard Cartesian coordinate dynamics. For TBSV we considered both the normal form and the high pH form, in which the Ca2+ ions are removed. These calculations lead to a contraction of the protein for both forms (probably because of ignoring the RNA core not observed in the X-ray).

Algorithms↗

Significance of vestibular organs in problems of weightlessness.

Two important questions concerning the organs of equilibrium are posed by orbital and space flights. The first is whether exposure to weightlessness may evoke symptoms of vestibular origin, and the second is how to prevent symptoms of vestibular origin should it be decided to abolish weightlessness by causing the spacecraft to spin. It is important to determine whether vestibular symptoms are to be ascribed to the otolith apparatus or to the semicircular canals, or to both. During exposure to weightlessness the usual gravitational stimulus to the otolith apparatus is lost, and this reduction in afferent input might be expected to disturb the integrative patterns in the central nervous system. All such disturbances are special instances of a common cause for the appearance of functional syndromes such as seasickness. If orbiting vehicles are caused to rotate in order to abolish weightlessness, the angular velocity will be determined by the effective radius of rotation and the rate of spin, i.e., how nearly it is desired to simulate 1 g. At very short radii the complicating effects of exposure of the body to variations in centripetal force must be considered. With longer radii the principal stress will arise as a result of constant rotation, which, in combination with head movements, generates Coriolis forces. These forces cause bizarre patterns of stimulation of the semicircular canals which in turn may result in illusions and "canal sickness". This type of motion sickness has its origin in the semicircular canals and deserves the term "canal sickness". The angular velocities which represent a negligible stress or a tolerable stress are defined. A brief description is given of illusory phenomena and other manifestations together with the time-course of the adaptive process.

Acceleration↗

Effect of the centrifugal force on domain chaos in Rayleigh-Bénard convection.

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary nearly radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency f approximately epsilon(mu) with mu approximately equal to 1 as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, mu and the domain size were consistent with experiment.

Journal Article↗

The use of sample rotation for minimizing convection effects in self-diffusion NMR measurements.

Undesirable temperature gradients in a NMR sample tube are usually generated by an inappropriate temperature regulation system. We have shown that such convection effects can greatly distort the measurement of translational self-diffusion coefficients. The use of sample spinning helps to minimize such undesirable effects by disruption of convection fluxes due to resulting Coriolis forces that have a strongly stabilizing effect on the conducting state of the system (J. Lounila et al., J. Magn. Reson. A 118, 50 (1996)). This simple trick allows the accurate measurement of diffusion coefficients for a wide range of temperatures and solvents without the need for a convection-compensated NMR pulse sequences or more sophisticated temperature control units. Experimental data obtained for some target compounds dissolved in several common deuterated solvents at different temperatures are reported and discussed.

Journal Article↗

Balance in a rotating artificial gravity environment.

When subjects stand at the center of a fully enclosed room that is rotating at constant velocity, their natural postural sway generates Coriolis forces that destabilize their center of mass and head. We quantitatively assessed how exposure to constant velocity rotation at 10 rpm affected postural control. Twelve subjects stood in a heel-to-toe stance in the rotating room. Each test session involved three phases: (1) pre-rotation, (2) per-rotation, and (3) post-rotation. In each phase, subjects were tested in both eyes open and eyes closed conditions. Four measures were used to characterize center of mass movement and head movement: mean sway amplitude, total power, mean power frequency, and frequency of maximum power. Each measure was computed for anterior-posterior and medial-lateral sway. Both anterior-posterior and medial-lateral head and center of mass sway during rotation had significantly greater mean sway amplitude and total power compared with pre- and post-rotation values. Mean power frequency and frequency of maximum power were little affected. Eyes open conditions were significantly more stable in all test phases than eyes-closed, but vision did not completely suppress the effects of rotation. The greatest effect of rotation was in the eyes-closed condition with mean sway amplitude and total power increasing more than twofold. Inverted pendulum sway was maintained in all phases of both test conditions. No aftereffects of rotation were present after the four 25-s exposures each subject received. We expect that with longer exposure periods and with active generation of body sway subjects would both adapt to rotation and exhibit post-rotary aftereffects.

Adult↗

Learning to throw on a rotating carousel: recalibration based on limb dynamics and projectile kinematics.

Skilled actions exhibit adjustment in calibration to bring about their goals. The sought-after calibrations change as a function of the environmental situation that stages the actions. In these experiments participants sat on one side of a rotating carousel and threw beanbags underhanded at a target fixed on the opposite side. Logically, aimed throwing in this situation involves adjustment to fit changes in limb dynamics (originating from Coriolis forces) and changes in perceived projectile kinematics (originating from the tangential velocity of thrower and target). We studied whether such adjustment involved one or multiple components of recalibration. An initial experiment showed that exposure to rotation while throwing beanbags produced a robust recalibration in the direction of underhanded throws as manifest in throwing at stationary targets from a stationary position. Following some initial decay this recalibration persisted and approached an asymptote. Subsequent experiments suggested two independent components of recalibration. One is based on limb dynamics and accounts for the initial decay. The other is based on the perceived projectile kinematics and accounts for the stable change in throwing direction. These results raised the question of how multiple components of recalibration of an action are related. We propose that movement components are independent and calibrated separately at different levels in the organization of an action.

Adult↗

Pointing movement in an artificial perturbing inertial field: a prospective paradigm for motor control study.

The present experiment focused on spatial accuracy and kinematics of fast pointing movements submitted to a multi-directional inertial perturbation. Pointing movements were performed without direct visual control, on a rotating armchair adding centrifugal and Coriolis forces to the natural displacement of the arm. The simultaneous action of these two forces induced a perturbation of the arm displacement both in amplitude and direction. Results showed that these two parameters were adjusted differently according to their own temporal constraint. Movement amplitude was adjusted on-line from the very first trial through the amendment of the whole acceleration pattern. Conversely, adjustment to directional perturbation was progressively achieved through several movement rehearsals. This correction appeared to be primarily due to a modification of the initial orientation of the arm trajectory, based seemingly on kinaesthetic knowledge from previous performances. The amendment of spatial parameters during motor response in the perturbing environment was discussed with an emphasis on the involvement of the cerebellum in reaching movement and the learning process.

Adult↗

Fos expression in the vestibular brainstem: what one marker can tell us about the network.

Fos inducible transcription factor expression in rodent brains (rats and gerbils) during manipulations of vestibular input is reviewed. Stimuli included centripetal hypergravity, unilateral labyrinth lesion or semicircular canal plugging, rotational axis cross-coupling (Coriolis forces), high and low rotational vestibulo-ocular reflex gain adaptation, translabyrinth galvanic stimulation, pharmacological manipulation, and combinations thereof. Each type of stimulation elicited unique but partially redundant response patterns in the vestibulo-olivo-cerebellar (VOC) network that reflect the origin and interaction of the labyrinth inputs. On the basis of these patterns, a trained observer can predict what the animal experienced during testing; the patterns of VOC Fos expression reveal a trace of recent genomic activity. Based on principal component analysis, VOC network modules associated with lesion recovery, spatial representation and the calibration of gravity, and optokinetic influences are proposed. Probable and possible gene targets of the Fos protein are also reviewed.

Animals↗

On the application of computational fluid dynamics codes for liquefied natural gas dispersion.

Computational fluid dynamics (CFD) codes are increasingly being used in the liquefied natural gas (LNG) industry to predict natural gas dispersion distances. This paper addresses several issues regarding the use of CFD for LNG dispersion such as specification of the domain, grid, boundary and initial conditions. A description of the k-epsilon model is presented, along with modifications required for atmospheric flows. Validation issues pertaining to the experimental data from the Burro, Coyote, and Falcon series of LNG dispersion experiments are also discussed. A description of the atmosphere is provided as well as discussion on the inclusion of the Coriolis force to model very large LNG spills.

Accidents↗

Influence of flow patterns on chromatographic efficiency in centrifugal partition chromatography.

Visualization of flow patterns in centrifugal partition chromatography (CPC) was performed with an asynchronous camera and a stroboscope triggered by the CPC rotor, allowing a channel to be selected and observed regardless of rotational speed. Three main types of flow states were noted as a function of rotational speed and flow-rate: jets stuck along channel walls, broken jets and atomization. Our observations emphasize the importance of Coriolis force on flow shape. Chromatographic efficiency was related to the dispersion of the mobile phase in the stationary phase.

Centrifugation↗

Jets.

This is a discussion of concentrated large-scale flows in planetary atmospheres and oceans, argued from the viewpoint of basic geophysical fluid dynamics. We give several elementary examples in which these flows form jets on rotating spheres. Jet formation occurs under a variety of circumstances: when flows driven by external stress have a rigid boundary which can balance the Coriolis force, and at which further concentration can be caused by the beta effect; when there are singular lines like the line of vanishing windstress or windstress-curl, or the Equator; when compact sources of momentum, heat or mass radiate jet-like beta plumes along latitude circles; when random external stirring of the fluid becomes organized by the beta effect into jets; when internal instability of the mass field generates zonal flow which then is concentrated into jets; when bottom topographic obstacles radiate jets, and when frontogenesis leads to shallow jet formation. Essential to the process of jet formation in stratified fluids is the baroclinic life cycle described in geostrophic turbulence studies; there, conversion from potential to kinetic energy generates eddy motions, and these convert to quasibarotropic motions which then radiate and induce jet-like large-scale circulation. Ideas of potential vorticity stirring by eddies generalize the notion of Rossby-wave radiation, showing how jets embedded in an ambient potential vorticity gradient (typically due to the spherical geometry of the rotating planet) gain eastward momentum while promoting broader, weaker westward circulation. Homogenization of potential vorticity is an important limit point, which many geophysical circulations achieve. This well-mixed state is found in subdomains of the terrestrial midlatitude oceans, the high-latitude circumpolar ocean, and episodically in the middle atmosphere. Homogenization expels potential vorticity gradients vertically to the top and bottom of the fluid, and sideways to the edges of flow domains or gyres; in both these ways is jet formation enhanced.

Journal Article↗

Motion of defects in rotating fluids.

We study defect motion in a rotating convection cell. We present numerical results of a generalized Swift-Hohenberg equation, which provides a model description of the vertically averaged three-dimensional (3-D) hydrodynamic equations. Our model includes non-Boussinesq effects. It also accounts for the effects of the Coriolis force induced by a rotation of the fluid layer around its vertical symmetry axis. We show that even a slow rotation well below the Kuppers-Lortz instability causes defect motion perpendicular to the convective rolls. We derive an analytic estimation of that motion.

Journal Article↗

New patterns of centrifugally driven thermal convection.

An experimental study is described of convection driven by thermal buoyancy in the annular gap between two corotating coaxial cylinders, heated from the outside and cooled from the inside. Steady convection patterns of the hexaroll and of the knot type are observed in the case of high Prandtl number fluids, for which the Coriolis force is sufficiently small. Oblique rolls and phase turbulence in the form of irregular patterns of convection can also be observed in wide regions of the parameter space.

Journal Article↗