Numerical study on diverging probability density function of flat-top solitons in an extended Korteweg-de Vries equation

We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV equation in the presence of weak dissipative disorder in the linear growth/damping term. With the weak disorder in the system, the amplitude of solitary wave randomly fluctuates during evolution. We demonstrate numerically that the probability density function of a solitary wave parameter $\kappa$ which characterizes the soliton amplitude exhibits loglognormal divergence near the maximum possible $\kappa$ value.Comment: 8 pages, 4 figure

TRUNK KINEMATICS DURING THE TEE-SHOT OF MALE AND FEMALE GOLFERS

While females comprise 20% of the golfing population in some Western countries (e.g. Australian Bureau of Statistics, 2007), previous research has typically assessed populations that are exclusively comprised of male golfers (e.g. Cheetham et al., 2008). However, the overall prevalence of golf-related injuries is reported to be similar for males and females (McHardy et al., 2006) and thus, it is of interest to assess whether the kinematics of the female golf swing are similar to those demonstrated by male players. This is important, as this knowledge will ensure that any changes that are made by coaches to improve performance and/or reduce the risk of injury in these golfers are appropriate

LOW BACK PAIN IN GOLF: DOES THE CRUNCH FACTOR CONTRIBUTE TO LOW BACK INJURIES IN GOLFERS?

INTRODUCTION: Nearly 41% of low back injuries in golf occur around impact or during early follow-through (McHardy et al., 2007). In view of these recent statistics, it is important consider the significance of the crunch factor as a possible contributor to golf-related back injuries. The crunch factor was described by Sugaya et al. (1997) as the instantaneous product of lateral trunk flexion (LFA) and axial trunk rotational velocity (ARV) and was based on the knowledge that both of these measures reach their peak close to impact. The authors reported that these factors would contribute to spinal degeneration and stated that the crunch factor could be useful to compare trunk mechanics in injured and healthy golfers. However, as only one earlier study (Lindsay & Horton, 2002) has examined the crunch factor in injured golfers, this work further considered the importance of this measure in low back pain golfers. METHODS: Fifteen healthy golfers (NLBP) and twelve golfers with a mild or greater level low back pain (LBP) were recruited. Each golfer performed 20 drives, whilst being filmed three genlocked video cameras (50 Hz). Three-dimensional kinematics were derived for best three swings using Peak Motus. The crunch factor was calculated as the instantaneous product of LFA and ARV, where LFA was the angle between the segments joining the mid-hip and mid-shoulder markers and the right and left hip markers minus ninety degrees ARV was the first derivative of the hip to mid-trunk differential angle with respect to time. ANCOVA controlling for age was used to assess for inter-group differences. RESULTS: The crunch factor for both groups increased rapidly from the mid-point of downswing through impact and into the follow-through, but the statistical results showed significant difference between the groups with respect to the peak value. Similarly, peak lateral flexion and axial trunk rotational velocity did not differ between the golfers (Table 1). Table 1: Peak crunch factor, lateral flexion and axial trunk rotational velocities. LBP NLBP Mean SD Mean SD p Cohen’s Peak Crunch (deg2/s) 4879.7 2194.9 4920.2 2273.4 0.44 0.24 Peak Lateral Flexion (deg) -19.1 5.6 -19.1 5.7 0.36 0.28 Peak Axial Trunk Rotational Velocity (deg/s) -271.0 76.8 -260.4 50.3 0.36 0.33 DISCUSSION: This research showed no significant difference between the LBP and NLBP groups for peak LFA, ARV or the resulting crunch factor. These data were comparable to peak crunch factors reported previously for six injured and uninjured golfers (Lindsay Horton, 2002), but were greater than those presented for healthy golfers (Morgan al.,1999). The non-significant findings together with small effect sizes suggest that the crunch factor is not a contributory factor in the development of low back pain in golfers. REFERENCES: Lindsay, D. M., & Horton, J. F. (2002). Journal of Sports Sciences, 20(8), 599-605. McHardy, A., et al. (2007). Journal of Chiropractic Medicine, 6(1), 20-26. Morgan, D. et al. (1999). Science and Golf III, pp.120-126. Champaign, IL: Human Kinetics. Sugaya, H., et al. (1997). 22nd Annual Meeting of the AOSSM, Sun Valley, ID

Soliton formation from a pulse passing the zero-dispersion point in a nonlinear Schr\"odinger equation

We consider in detail the self-trapping of a soliton from a wave pulse that passes from a defocussing region into a focussing one in a spatially inhomogeneous nonlinear waveguide, described by a nonlinear Schrodinger equation in which the dispersion coefficient changes its sign from normal to anomalous. The model has direct applications to dispersion-decreasing nonlinear optical fibers, and to natural waveguides for internal waves in the ocean. It is found that, depending on the (conserved) energy and (nonconserved) mass of the initial pulse, four qualitatively different outcomes of the pulse transformation are possible: decay into radiation; self-trapping into a single soliton; formation of a breather; and formation of a pair of counterpropagating solitons. A corresponding chart is drawn on a parametric plane, which demonstrates some unexpected features. In particular, it is found that any kind of soliton(s) (including the breather and counterpropagating pair) eventually decays into pure radiation with the increase of the energy, the initial mass being kept constant. It is also noteworthy that a virtually direct transition from a single soliton into a pair of symmetric counterpropagating ones seems possible. An explanation for these features is proposed. In two cases when analytical approximations apply, viz., a simple perturbation theory for broad initial pulses, or the variational approximation for narrow ones, comparison with the direct simulations shows reasonable agreement.Comment: 18 pages, 10 figures, 1 table. Phys. Rev. E, in pres

THE USE OF MOTION ANALYSIS AS A COACHING AID TO IMPROVE THE INDIVIDUAL TECHNIQUE IN SPRINT HURDLES

Biomechanical data are oflen presented as a group average, which may not always help individual athletes to improve their own performance. The purpose of this study was to analyse techniques in sprint hurdles within the athlete and find critical individual aspects, which influence performance. The hurdle clearance of three athletes (eight trials each) were videotaped with four video camera recorders and analysed three-dimensionally. There were several statistically significant correlations between the critical overall horizontal velocity and other variables, especially for one athlete. Such trends in individual performance presented ideas to coaches, athletes and also to researchers, regarding what happened in less successful runs and which technical points were worth individual attention in training

Steady multipolar planar vortices with nonlinear critical layers

This article considers a family of steady multipolar planar vortices which are the superposition of an axisymmetric mean flow, and an azimuthal disturbance in the context of inviscid, incompressible flow. This configuration leads to strongly nonlinear critical layers when the angular velocities of the mean flow and the disturbance are comparable. The poles located on the same critical radius possess the same uniform vorticity, whose weak amplitude is of the same order as the azimuthal disturbance. This problem is examined through a perturbation expansion in which relevant nonlinear terms are retained in the critical layer equations, while viscosity is neglected. In particular, the associated singularity at the meeting point of the separatrices is treated by employing appropriate re-scaled variables. Matched asymptotic expansions are then used to obtain a complete analytical description of these vortices

Using the theory of planned behaviour as a process evaluation tool in randomised trials of knowledge translation strategies : A case study from UK primary care

Peer reviewedPublisher PD

VARIATION IN MOTION ANALYSIS OF SPRINT HURDLES: PART 1CO-ORDINATE DEVIATION IN 3-DIMENSIONAL RECONSTRUCTION

INTRODUCTION. An understanding of the different variation sources in experimental sport research is fundamental to technical analysis (Yeadon, 1994). Individual variable level variation in the event of sprint hurdles was presented by Salo el al. (1995). The aim of this study was to investigate the variation al the digitised co-ordinate level. METHODS Hurdle c1earances were videotaped with two genlocked cameras (50 Hz, at a 90 degree angle from the hurdle symmetrically on both sides of the lane). Two randomly selected trials (female and male) were digitised eight times by the same operator using APAS. The separate raw co-ordinates (u, v) of both camera views and the raw 30 co-ordinates (after OLT) 01 all digitised trials were transformed to Excel software. Standard deviation (SO) for the all 18 body landmarks were calculated separately for every single analysed field. The lowest SO of each condition and each co-ordinate direction (including diagonal combination) was selected as a base unit. All other SOs were standardised to these base units. RESULTS The mean SO of each landmark over all digitised fjelds in u-and v-directions ranged fram 2.3 to 8.7 (female) and from 2.6 to 7.1 (male) relative SO units. This variation resulted in SO of 0.017, 0.009, 0.016 and 0.025 m in X-, y-, z-and diagonal directions, respectively, for the female athlete as a maxirna mean of an individual landmark in the 30 re-construction. The respective SO values for the male trial were 0.017, 0.012, 0.018 and 0.027m. The maximum variation of an individual landmark in a single field of one view was 22.5 SO-units (female) and 30.0 SO-units (male). However, most of the landmarks had less than 4 SO-units variation in most of the analysed fields. DISCUSSION The lowest SO was selected for the base unit, as this presented the most accurate situation which an operator was able to reach in repeated digitising. Generally at an average level, the variation of raw 3D coordinates can be considered acceptable. However, there were c1early problematic situations, when landmarks gained up to 30 times more variation in a single field than the best situation. The influence of this huge variation on variables depends upon whether it appears at a critical moment. In this study, the largest variation occurred in an air phase around the highest point of the flight path. For the male athlete, the trailleg and the ipsilateral arm were obstructed by the trunk for the other camera view. This had only a slight eHect on the maximum height of the centre of mass (GM) (SO= 0.01 m). However, the distance of the GM peak to the hurdle varied significantly (SO= 0.11 m). Oue to lower trail leg path Ihe same problem did not occur for the female athlete (SO= 0.00 and 0.01 m, respectively). Based on this study, it is elear that large variation occurs in manual digitising at the co-ordinate level and this variation can have critica! and important effects for variable values. REFERENCES Salo, A., Grimshaw, P.N. & Viitasalo, J.T. (1995). The repeatabIlity of motion analysis and the reproducibility of athletes in sprint hurdles. In: XlIIISBS Symposium. Abstracts. Thunder Bay, Ontario, Canada. Yeadon, M.A., & Ghallis, J.H. (1994). The future of pertormance-related sports biomechanics research. Journal 01 Sports Sciences, 12, 3-32

Stable embedded solitons

Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.Comment: 2 figures. To appear in Phys. Rev. Let