Dephasing of Kuramoto oscillators in kinetic regime towards a fixed asymptotically free state

We study the kinetic Kuramoto model for coupled oscillators. We prove that for any regular asymptotically free state, if the interaction is small enough, it exists a solution which is asymptotically close to it. For this class of solution the order parameter vanishes to zero, showing a behavior similar to the phenomenon of Landau damping in plasma physics. We obtain an exponential decay of the order parameter in the case on analytical regularity of the asymptotic state, and a polynomial decay in the case of Sobolev regularity

On the complete phase synchronization for the Kuramoto model in the mean-field limit

We study the Kuramoto model for coupled oscillators. For the case of identical natural frequencies, we give a new proof of the complete frequency synchronization for all initial data; extending this result to the continuous version of the model, we manage to prove the complete phase synchronization for any non-atomic measure-valued initial datum. We also discuss the relation between the boundedness of the entropy and the convergence to an incoherent state, for the case of non identical natural frequencies

Time Calibration of the ANTARES Neutrino Telescope

AbstractThe ANTARES deep-sea neutrino telescope consists of a three dimensional array of photomultipliers to detect the Cherenkov light induced by relativistic charged particles originating from neutrino interactions in the vicinity of the detector. It was completed in 2008 and is taking data smoothly since then. The large scattering length of light in the deep sea allows for an angular resolution of a few tenths of a degree for neutrino energies exceeding 10 TeV. In order to achieve this optimal performance, the time calibration systems should ensure a measurement of the relative time offsets between the photomultipliers at the level of about 1ns. The time calibration is performed through different systems/procedures: the on-shore calibration in a dark room, the echo-based clock system, the internal LEDs, the Optical Beacon systems and the potassium-40 present in the water. In this contribution, the methods developed to attain the needed level of precision and the results obtained with the data taken in situ will be shown

Power-cadence relationship in endurance cycling

In maximal sprint cycling, the power-cadence relationship to assess the maximal power output (P max) and the corresponding optimal cadence (C opt) has been widely investigated in experimental studies. These studies have generally reported a quadratic power-cadence relationship passing through the origin. The aim of the present study was to evaluate an equivalent method to assess P max and C opt for endurance cycling. The two main hypotheses were: (1) in the range of cadences normally used by cyclists, the power-cadence relationship can be well fitted with a quadratic regression constrained to pass through the origin; (2) P max and C opt can be well estimated using this quadratic fit. We tested our hypothesis using a theoretical and an experimental approach. The power-cadence relationship simulated with the theoretical model was well fitted with a quadratic regression and the bias of the estimated P max and C opt was negligible (1.0W and 0.6rpm). In the experimental part, eight cyclists performed an incremental cycling test at 70, 80, 90, 100, and 110rpm to yield power-cadence relationships at fixed blood lactate concentrations of 3, 3.5, and 4mmol L−1. The determined power outputs were well fitted with quadratic regressions (R 2=0.94-0.96, residual standard deviation=1.7%). The 95% confidence interval for assessing individual P max and C opt was ±4.4W and ±2.9rpm. These theoretical and experimental results suggest that P max, C opt, and the power-cadence relationship around C opt could be well estimated with the proposed metho

Influence of road incline and body position on power-cadence relationship in endurance cycling

In race cycling, the external power-cadence relationship at the performance level, that is sustainable for the given race distance, plays a key role. The two variables of interest from this relationship are the maximal external power output (P max) and the corresponding optimal cadence (C opt). Experimental studies and field observations of cyclists have revealed that when cycling uphill is compared to cycling on level ground, the freely chosen cadence is lower and a more upright body position seems to be advantageous. To date, no study has addressed whether P max or C opt is influenced by road incline or body position. Thus, the main aim of this study was to examine the effect of road incline (0 vs. 7%) and racing position (upright posture vs. dropped posture) on P max and C opt. Eighteen experienced cyclists participated in this study. Experiment I tested the hypothesis that road incline influenced P max and C opt at the second ventilatory threshold ( $$P_{ \max }^{{{\text{VT}}_{ 2} }}$$ and $$C_{\text{opt}}^{{{\text{VT}}_{ 2} }}$$ ). Experiment II tested the hypothesis that the racing position influenced $$P_{ \max }^{{{\text{VT}}_{ 2} }}$$ , but not $$C_{\text{opt}}^{{{\text{VT}}_{ 2} }}$$ . The results of experiment I showed that $$C_{\text{opt}}^{{{\text{VT}}_{ 2} }}$$ and $$P_{ \max }^{{{\text{VT}}_{ 2} }}$$ were significantly lower when cycling uphill compared to cycling on level ground (P<0.01). Experiment II revealed that $$P_{ \max }^{{{\text{VT}}_{ 2} }}$$ was significantly greater for the upright posture than for the dropped posture (P<0.01) and that the racing position did not affect $$C_{\text{opt}}^{{{\text{VT}}_{ 2} }}$$ . The main conclusions of this study were that when cycling uphill, it is reasonable to choose (1) a lower cadence and (2) a more upright body positio

Exponential dephasing of oscillators in the Kinetic Kuramoto Model

We study the kinetic Kuramoto model for coupled oscillators with coupling constant below the synchronization threshold. We manage to prove that, for any analytic initial datum, if the interaction is small enough, the order parameter of the model vanishes exponentially fast, and the solution is asymptotically described by a free flow. This behavior is similar to the phenomenon of Landau damping in plasma physics. In the proof we use a combination of techniques from Landau damping and from abstract Cauchy-Kowalewskaya theorem

INFLUENCE OF RACING POSITION ON CYCLING PATTERNS

The aim of this study was to examine the effect of racing position on the pedal forces, the kinematics of the lower limbs, the muscular joint moments and the muscular joint powers. Cycling in an upright position (UP) and in a dropped position (DP) was analyzed in six subjects during cycling at 200 W with a cadence of 80 rpm. The pedal forces showed only slight differences between the two positions. The kinematic analyses revealed that only the mean hip angle was affected by body position. The inverse dynamics showed that body position significantly influenced the joint powers. The main reason for these changed power outputs could be the change in mean sarcomere length and mean moment arm of the hip muscles with different racing positions