EVALUATION OF A RUNNER’S PHYSIOLOGICAL PARAMETERS USING DIFFERENT SPRINT MODELS

INTRODUCTION: Hill’s model of sprinting, based on Newton’s second law of motion, uses two physiological parameters to characterize the sprinter, the maximum propulsive force per unit mass and the resistance-to-motion parameter related to the runner’s internal energy losses. Furusawa et al. (1927) suggested a resistive force law linear in the running speed. Later Keller (1973) and many others based their studies on Hill’s model. Senator (1982) added the effects of air resistance by a term quadratic in speed. Vaughan (1983) used a modification of these approaches by introducing a 0.7-power law. Recently, utilizing the rotational equation of motion for the leg and experimental data for stride frequency, we have shown that the internal and external resistive forces may well be approximated by a combination of linear and quadratic terms in running speed. We have also derived an expression for the internal resistive force in terms of physiological quantities. METHODS: The different models may be classified according to the resistive force law as linear (L), Vaughan (Va), quadratic (Q) and linearquadratic (LQ) models. We give analytical solutions for the distance-time relationships, except for the Va-model. We have used a numerical gradient method to fit the models with measured 100m data at ten equally spaced time stations of the 1988 Olympic Games in Seoul. Wind velocity and reaction times are also taken into account. RESULTS: By considering the residual errors we found that the best fit was given by the Va-model, followed by the LQ-, L-, and Q-models. The average residual error per time station for the Va- and LQ-models was about 0.01 s, which means a good fit throughout the run. We compared the values of the calculated physiological parameters with those in the existing literature. For the L-model the propulsive and resistive forces found by Vaughan and Matravers (1977) are in close agreement with ours, whereas those found by Woodside (1991) and Keller (1973) are too high, as can also be inferred from recent starting block data. For the parameters of the Va-model Vaughan (1983) obtained values somewhat lower than ours, using Ben Johnson, Carl Lewis and Linford Christie. This is to be expected, however, since Vaughan obtained his data for national university sprinters. As far as we know, the LQ-model has not been previously used. CONCLUSIONS: Our results show that the Va- and LQ-models best fit the Olympic 100 m data. There is a noteworthy difference between the interpretation of the linear resistive term in Hill’s theory and in the LQmodel presented in this paper: Hill and his colleagues invoked the concept of the viscosity of the muscles, while we arrived at the linear term by writing the rotational equation of the leg. It must be noted that already Fenn (1930) criticized the viscosity concept and attributed the resistive force to antagonistic muscles and other kinesiological factors. In view of our derivation of the LQ-model, the resistive force stems mainly from the rotational inertia of the leg, whereas the energy losses occur in the antagonistic muscles during the decelerating phases of the back and forth motion of the legs

Langevin Simulations of Two Dimensional Vortex Fluctuations: Anomalous Dynamics and a New IVIV-exponent

The dynamics of two dimensional (2D) vortex fluctuations are investigated through simulations of the 2D Coulomb gas model in which vortices are represented by soft disks with logarithmic interactions. The simulations trongly support a recent suggestion that 2D vortex fluctuations obey an intrinsic anomalous dynamics manifested in a long range 1/t-tail in the vortex correlations. A new non-linear IV-exponent a, which is different from the commonly used AHNS exponent, a_AHNS and is given by a = 2a_AHNS - 3, is confirmed by the simulations. The results are discussed in the context of earlier simulations, experiments and a phenomenological description.Comment: Submitted to PRB, RevTeX format, 28 pages and 13 figures, figures in postscript format are available at http://www.tp.umu.se/~holmlund/papers.htm

Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films

The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio

Current-voltage characteristics of the two-dimensional XY model with Monte Carlo dynamics

Current-voltage characteristics and the linear resistance of the two-dimensional XY model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent $z$ at various temperatures. From the comparison with the resistively-shunted junction dynamics, it is concluded that $z$ is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.Comment: 5 pages in two columns including 5 figures, to appear in PR

Vortex dynamics for two-dimensional XY models

Two-dimensional XY models with resistively shunted junction (RSJ) dynamics and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is verified that the vortex response is well described by the Minnhagen phenomenology for both types of dynamics. Evidence is presented supporting that the dynamical critical exponent $z$ in the low-temperature phase is given by the scaling prediction (expressed in terms of the Coulomb gas temperature $T^{CG}$ and the vortex renormalization given by the dielectric constant $\tilde\epsilon$) $z=1/\tilde{\epsilon}T^{CG}-2\geq 2$ both for RSJ and TDGL and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature phase. The results are discussed and compared with the results of other recent papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio

Charge Transport in the Dense Two-Dimensional Coulomb Gas

The dynamics of a globally neutral system of diffusing Coulomb charges in two dimensions, driven by an applied electric field, is studied in a wide temperature range around the Berezinskii-Kosterlitz-Thouless transition. I argue that the commonly accepted ``free particle drift'' mechanism of charge transport in this system is limited to relatively low particle densities. For higher densities, I propose a modified picture involving collective ``partner transfer'' between bound pairs. The new picture provides a natural explanation for recent experimental and numerical findings which deviate from standard theory. It also clarifies the origin of dynamical scaling in this context.Comment: 4 pages, RevTeX, 2 eps figures included; some typos corrected, final version to be published in Phys. Rev. Let

Sutureless prepuceplasty with wound healing by second intention: An alternative surgical approach in children's phimosis treatment

Abstract Background A new technique for the treatment of children's phimosis is presented that minimizes the repairing time, the postoperative complications and maintains the physical foreskin appearance intact. Methods Eightyseven children with phimosis were treated with this new developed technique, between 2003 and 2005. Sutureless prepuceplasty creates a permanent surgical extension of the close prepuce. Stretching and retraction of phimotic foreskin reveals a tight prepuce ring that is cutting in its dorsal surface longitudinally. Rarely triple symmetric incisions in the preputial outlet are necessary. The foreskin is loose and moves absolutely free in bilateral courses. The wounds are healing by second intention. Antisepsis, steroids and Elicina cream, (which contains allantoin, collagen, elastin, glycolic acid and vitamins A, D, and E) should apply daily, for twenty to thirty days. Results The foreskin is moving in centripetal or efferent courses absolutely loosely, painlessly and bloodlessly. The mean time of follow-up was 27 months (one to four years). No complications were observed. Conclusion Sutureless prepuceplasty may present an acceptable alternative in children's phimosis reconstruction.</p

The effect of lifelong learning on men's wages

This paper develops a model of earnings and applies this to an examination of the effect of lifelong learning on men’s wages. Using data from the British Household Panel Survey, a variant of the mover–stayer model is developed in which hourly wages are either taken from a stationary distribution (movers) or closely related to the hourly wage one year earlier (stayers). Mover–stayer status is not observed, and we therefore model wages using an endogenous switching regression, estimated by maximum likelihood. Methodologically, the results support the mover–stayer characterisation since the restrictions required for the simpler specifications popular in the literature are rejected. Substantively, simulation of the estimated model shows some statistically significant effects from acquiring qualifications of a higher level than those previously held, but not from acquiring qualifications of the same level