Velocity-curvature Relationship Research Articles

The effect of the preferred hand on drawing movement

The observation that different effectors can execute the same movement suggests functional equivalences driven by limb independent representation of action in the central nervous system. A common invariant motor behavior is the speed and curvature coupling (the 1/3 power law), a low dimensional (abstract) descriptor of movement which is resilient to different sensorimotor contexts. Our purpose is to verify the consistency of such motor equivalence during a drawing task, by testing the effect of manual dominance and movement speed on motor performance. We hypothesize that abstract kinematic variables are not the most resistant to speed or limb effector changes. The results show specific effects of speed and hand side on the drawing task. Movement duration, speed-curvature covariation, and maximum velocity were not significantly affected by hand side, while geometrical features were strongly speed and limb dependent. However, intra-trial analysis performed over the successive drawing movements reveals a significant hand side effect on the variability of movement vigor and velocity-curvature relationship (the 1/3 PL). The identified effects of speed and hand dominance on the kinematic parameters suggest different neural strategies, in a pattern that does not go from the most abstract to the least abstract component, as proposed by the traditional hierarchical organization of the motor plan.

Ray-tracking methods for characterizing the dynamics of curved detonation

Current analyses of curved detonations are mostly limited to the dynamics along the wall or the symmetry axis due to the lack of efficient approaches for reliably tracking stream tubes with curved shock fronts. To address this lack, the present work proposes a novel curved ray-tracking algorithm with two implementation methods. The curved ray is characterized by a specific arc of constant curvature perpendicularly intersecting both successive fronts. The methods were validated against Whitham's exact geometrical shock dynamics solutions of the self-similar shock diffraction problem. As compared to the typical forward straight-ray method, which is of the first order, the proposed methods demonstrate convergence rates greater by more than one order of magnitude and tend to be of the second order. The convergence analysis enabled to determine the range of time resolution required for the proposed methods to provide reliable results. This range is comparable to the acquisition rate of a modern high-speed camera that is commonly used in detonation visualization experiments. Differences between the proposed curved ray-tracking methods and the typical forward straight-ray method have been further examined by analyzing the ray dynamics during the weakly unstable hydrogen–oxygen–argon detonation diffraction. The ray-tube-based velocity-curvature relationship showed satisfactory agreement with those already well-established in quasi-steady experiments and predicted by the generalized Zeldovich–von Neumann–Doering model. This suggests the limited role of unsteadiness and cellular structure in the macro-scale dynamics of weakly unstable detonations.

Effect of Temporal Organization of the Visuo-Locomotor Coupling on the Predictive Steering

Studies on the direction of a driver’s gaze while taking a bend show that the individual looks toward the tangent-point of the inside curve. Mathematically, the direction of this point in relation to the car enables the driver to predict the curvature of the road. In the same way, when a person walking in the street turns a corner, his/her gaze anticipates the rotation of the body. A current explanation for the visuo-motor anticipation over the locomotion would be that the brain, involved in a steering behavior, executes an internal model of the trajectory that anticipates the completion of the path, and not the contrary. This paper proposes to test this hypothesis by studying the effect of an artificial manipulation of the visuo-locomotor coupling on the trajectory prediction. In this experiment, subjects remotely control a mobile robot with a pan-tilt camera. This experimental paradigm is chosen to manipulate in an easy and precise way the temporal organization of the visuo-locomotor coupling. The results show that only the visuo-locomotor coupling organized from the visual sensor to the locomotor organs enables (i) a significant smoothness of the trajectory and (ii) a velocity-curvature relationship that follows the “2/3 Power Law.” These findings are consistent with the theory of an anticipatory construction of an internal model of the trajectory. This mental representation used by the brain as a forward prediction of the formation of the path seems conditioned by the motor program. The overall results are discussed in terms of the sensorimotor scheme bases of the predictive coding.

Hysteresis phenomenon in the dynamics of spiral waves rotating around a hole

Hysteresis in the pinning–depinning transitions of spiral waves rotating around a hole in a circular shaped two-dimensional excitable medium is studied both by use of the continuation software AUTO and by direct numerical integration of the reaction–diffusion equations for the FitzHugh–Nagumo model. In order to clarify the role of different factors in this phenomenon, a kinematical description is applied. It is found that the hysteresis phenomenon computed for the reaction–diffusion model can be reproduced qualitatively only when a nonlinear eikonal equation (i.e. velocity–curvature relationship) is assumed. However, to obtain quantitative agreement, the dispersion relation has to be taken into account.

Is the velocity-curvature relationship disrupted in apraxic patients?

Velocity and curvature of human movements are linked by a proportionality relationship (power-law) whose origin has been attributed either to functional properties of cortical areas or to peripheral constraints. 3D movements made by apraxic patients show a time-shift between velocity and curvature which has been considered as a disruption of the power-law, supporting the central hypothesis. We analysed the power-law in 2D drawing-like movements in healthy subjects and apraxic patients (correlation and cross-correlation analyses). The power-law remained preserved in apraxic patients, suggesting that the velocity-curvature relationship is not globally disrupted and thus that the power-law cannot be only attributed to central planning mechanisms in those associative brain areas injured in apraxic patients.

Propagation laws for steady curved detonations with chain-branching kinetics

An extension to the theory of detonation shock dynamics is made and new propagation laws are derived for steady, near-CJ (Chapman-Jouguet), weakly curved detonations for a chain-branching reaction model having two components. The first is a thermally neutral induction stage governed by an Arrhenius reaction with a large activation energy, which terminates at a location called the transition interface, where instantaneous conversion of fuel into an intermediate species (chain radical) occurs. The second is an exothermic main reaction layer (or chain-recombination zone) having a temperature-independent reaction rate. We make an ansatz that the shock curvature is sufficiently large to have a leading-order influence on the induction zone structure, whereupon it is shown that multi-dimensional effects must necessarily be accounted for in the main reaction layer. Only for exactly cylindrical or spherical waves can such multi-dimensional effects be omitted. A requirement that the main reaction layer structure pass smoothly through a sonic plane leads to a propagation law for the detonation front: a relationship between the detonation velocity, the shock curvature and various shock arclength derivatives of the position of the transition interface. For exactly cylindrically or spherically expanding waves, a multi-valued detonation velocity-curvature relationship is found, similar to that found previously for a state-sensitive one-step reaction. The change in this relationship is investigated as the ratio of the length of the main reaction layer to the induction layer is changed. We also discuss the implications of chain-branching reaction kinetics for the prediction of critical detonation initiation energy based on detonation-velocity curvature laws. Finally several calculations that illustrate the important effect that arclength and transverse flow variations may have on the steady propagation of non-planar detonation fronts are presented. Such variations may be important for the propagation of cellular gaseous detonation fronts and for the axial propagation of detonations in a cylindrical stick of condensed-phase explosive. We also show that the arclength variations provide a formal mechanism for the existence of steady non-planar detonation fronts having converging sections, a possibility ruled out for simple irreversible one-step reaction mechanisms where only diverging steady waves are admissible.

Calcium Waves in Agarose Gel with Cell Organelles: Implications of the Velocity Curvature Relationship

Calcium oscillations and waves have been observed not only in several types of living cells but also in less complex systems of isolated cell organelles. Here we report the determination of apparent Ca 2+ diffusion coefficients in a novel excitable medium of agarose gel with homogeneously distributed vesicles of skeletal sarcoplasmic reticulum. Spatiotemporal calcium patterns were visualized by confocal laser scanning fluorescence microscopy. To obtain characteristic parameters of the velocity curvature relationship, namely, apparent diffusion coefficient, velocity of plane calcium waves, and critical radius, positively and negatively curved wave fronts were analyzed. It is demonstrated that gel-immobilized cell organelles reveal features of an excitable medium. Apparent Ca 2+ diffusion coefficients of the in vitro system, both in the absence or in the presence of mitochondria, were found to be higher than in cardiac myocytes and lower than in unbuffered agarose gel. Plane calcium waves propagated markedly slower in the in vitro system than in rat cardiac myocytes. Whereas mitochondria significantly reduced the apparent Ca 2+ diffusion coefficient of the in vitro system, propagation velocity and critical size of calcium waves were found to be nearly unchanged. These results suggest that calcium wave propagation depends on the kinetics of calcium release rather than on diffusion.

Carbon clustering kinetics in detonation wave propagation

Much of the nonideality of insensitive carbon rich explosives such as TATB is thought to be caused by a late-time slow release of energy associated with diffusion limited growth of carbon clusters. We have adapted Shaw and Johnson’s approximate analytic solution of the Smoluchowski rate equations for the evolution of the cluster size distribution function for use in hydrodynamic calculations and in Wood and Kirkwood approximate theory for the detonation velocity-curvature relationship. Solutions for the effect of carbon cluster growth on the structure of the reaction zone are obtained, and the results are compared with available experimental data.

The Normal Detonation Shock Velocity–Curvature Relationship for Materials with Nonideal Equation of State and Multiple Turning Points

We present a model and a simple-to-implement numerical procedure that obtains the normal detonation shock velocity (Dn)–curvature (κ) relationships for an explosive material with nonideal equation of state and an arbitrary reaction rate law. In addition we illustrate numerically (for a nonideal equation of state) and analytically (for an ideal equation of state with a large activation energy rate law) that for sufficient rate-state–sensitive explosives, the corresponding Dn, κ-response curve can have two turning points, at Dn, κ,-pairs [(Dn)1, κ1], [(Dn)2, κ2], such that κ1 > κ2 > 0 for DCJ ≥ (Dn)1 ≥ (Dn)2, and such that the curve has a Z-shape. The top branch of the Z response curve has been previously associated with detonation extinction at a critical curvature. The bottom branch can be possibly associated with low-velocity detonation and rapid change from low-order detonation to high-order.

Velocity-curvature relationship of colliding spherical calcium waves in rat cardiac myocytes

Colliding spherical calcium waves in enzymatically isolated rat cardiac myocytes develop new wavefronts propagating perpendicular to the original direction. When investigated by confocal laser scanning microscopy (CLSM), using the fluorescent Ca2+ indicator fluo-3 AM, "cusp"-like structures become visible that are favorably approximated by double parabolae. The time-dependent position of the vertices is used to determine propagation velocity and negative curvature of the wavefront in the region of collision. It is evident that negatively curved waves propagate faster than positively curved, single waves. Considering two perfectly equal expanding circular waves, we demonstrated that the collision of calcium waves is due to an autocatalytic process (calcium-induced calcium release), and not to a simple phenomenon of interference. Following the spatiotemporal organization in simpler chemical systems maintained under conditions far from the thermodynamic equilibrium (Belousov-Zhabotinskii reaction), the dependence of the normal velocity on the curvature of the spreading wavefront is given by a linear relation. The so-called velocity-curvature relationship makes clear that the velocity is enhanced by curvature toward the direction of forward propagation and decreased by curvature away from the direction of forward propagation (with an influence of the diffusion coefficient). Experimentally obtained velocity data of both negatively and positively curved calcium waves were approximated by orthogonal weighted regression. The negative slope of the straight line resulted in an effective diffusion coefficient of 1.2 x 10(-4) mm2/s. From the so-called critical radius, which must be exceeded to initiate a traveling calcium wave, a critical volume (with enhanced [Ca2+]i) of approximately 12 microm3 was calculated. This is almost identical to the volume that is occupied by a single calcium spark.

95/04327 On the normal detonation shock velocity-curvature relationship for materials with large activation energy

95/04327 On the normal detonation shock velocity-curvature relationship for materials with large activation energy

On the normal detonation shock velocity-curvature relationship for materials with large activation energy

We derive the normal detonation shock velocity-curvature relation for a near-Chapman-Jouguet detonation, for an explosive material with Arrhenius kinetics and a large activation energy. Large activation energy asymptotics are used to develop an explicit exponential formula relating the shock curvature κ to the normal detonation shock speed, D n. In this case, the D n- κ relation is multivalued and has a turning point with a critical curvature κ cr such that for κ > κ cr, the possibility of detonation extinction arises. The asymptotic formula is in excellent agreement with the exact solution found by a numerical shooting procedure.