Single leg drop jump is affected by physical capacities in male soccer players following ACL reconstruction

Single leg drop jump (SLDJ) assessment is commonly used during the later stages of rehabilitation to identify residual deficits in reactive strength but the effects of physical capacity on kinetic and kinematic variables in male soccer players following ACL reconstruction remains unknown. Isokinetic knee extension strength, kinematics from an inertial measurement unit 3D system and SLDJ performance variables and mechanics derived from a force plate were measured in 64 professional soccer players (24.7 ± 3.4 years) prior to return to sport (RTS). SLDJ between-limb differences were measured (part 1) and players were divided into tertiles based on isokinetic knee extension strength (weak, moderate and strong) and reactive strength index (RSI) (low, medium and high) (part 2). Moderate to large significant differences between the ACL reconstructed and uninjured limb in SLDJ performance (d = 0.92 – 1.05), kinetic (d = 0.62 – 0.71) and kinematic variables (d = 0.56) were evident. Stronger athletes jumped higher (p = 0.002; d = 0.85), produced greater concentric (p = 0.001; d = 0.85) and eccentric power (p = 0.002; d = 0.84). Similar findings were present for RSI, but the effects were larger (d = 1.52 – 3.84). Weaker players, and in particular those who had lower RSI, displayed landing mechanics indicative of a “stiff” knee movement strategy. SLDJ performance, kinetic and kinematic differences were identified between-limbs in soccer players at the end of their rehabilitation following ACL reconstruction. Players with lower knee extension strength and RSI displayed reduced performance and kinetic strategies associated with increased injury risk

Dispersion and collapse of wave maps

We study numerically the Cauchy problem for equivariant wave maps from 3+1 Minkowski spacetime into the 3-sphere. On the basis of numerical evidence combined with stability analysis of self-similar solutions we formulate two conjectures. The first conjecture states that singularities which are produced in the evolution of sufficiently large initial data are approached in a universal manner given by the profile of a stable self-similar solution. The second conjecture states that the codimension-one stable manifold of a self-similar solution with exactly one instability determines the threshold of singularity formation for a large class of initial data. Our results can be considered as a toy-model for some aspects of the critical behavior in formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte

Global exponential stability of classical solutions to the hydrodynamic model for semiconductors

In this paper, the global well-posedness and stability of classical solutions to the multidimensional hydrodynamic model for semiconductors on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve some known results in Sobolev space. The local existence of classical solutions to the Cauchy problem is obtained by the regularized means and compactness argument. Using the high- and low- frequency decomposition method, we prove the global exponential stability of classical solutions (close to equilibrium). Furthermore, it is also shown that the vorticity decays to zero exponentially in the 2D and 3D space. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.Comment: 18 page

Global Solutions for Incompressible Viscoelastic Fluids

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data. The results hold in both two and three dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial dat

The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models

The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data for an expanding cosmological model of this type is subjected to a small perturbation then the corresponding solution exists globally in the future and the perturbation decays in a way which can be described precisely. It is emphasized that no linearization of the equations or special symmetry assumptions are needed. The result can also be interpreted as a proof of the nonlinear stability of the homogeneous models. In order to prove the theorem we write the general solution as the sum of a homogeneous background and a perturbation. As a by-product of the analysis it is found that there is an invariant sense in which an inhomogeneous model can be regarded as a perturbation of a unique homogeneous model. A method is given for associating uniquely to each Newtonian cosmological model with compact spatial sections a spatially homogeneous model which incorporates its large-scale dynamics. This procedure appears very natural in the Newton-Cartan theory which we take as the starting point for Newtonian cosmology.Comment: 16 pages, MPA-AR-94-

Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

Chaotic mixing in noisy Hamiltonian systems

This paper summarises an investigation of the effects of low amplitude noise and periodic driving on phase space transport in 3-D Hamiltonian systems, a problem directly applicable to systems like galaxies, where such perturbations reflect internal irregularities and.or a surrounding environment. A new diagnsotic tool is exploited to quantify how, over long times, different segments of the same chaotic orbit can exhibit very different amounts of chaos. First passage time experiments are used to study how small perturbations of an individual orbit can dramatically accelerate phase space transport, allowing `sticky' chaotic orbits trapped near regular islands to become unstuck on suprisingly short time scales. Small perturbations are also studied in the context of orbit ensembles with the aim of understanding how such irregularities can increase the efficacy of chaotic mixing. For both noise and periodic driving, the effect of the perturbation scales roughly in amplitude. For white noise, the details are unimportant: additive and multiplicative noise tend to have similar effects and the presence or absence of a friction related to the noise by a Fluctuation- Dissipation Theorem is largely irrelevant. Allowing for coloured noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time, which vanishes for white noise, becomes so large that t here is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. Potential implications for galaxies are discussed.Comment: 15 pages including 18 figures, uses MNRAS LaTeX macro

Art as a Means to Disrupt Routine Use of Space

This paper examines the publicly visible aspects of counter-terrorism activity in pedestrian spaces as mechanisms of disruption. We discuss the objectives of counter-terrorism in terms of disruption of routine for both hostile actors and general users of public spaces, categorising the desired effects as 1) triangulation of attention; 2) creation of unexpected performance; and 3) choreographing of crowd flow. We review the potential effects of these existing forms of disruption used in counter-terrorism. We then present a palette of art, advertising, architecture, and entertainment projects that offer examples of the same disruption effects of triangulation, performance and flow. We conclude by reviewing the existing support for public art in counter-terrorism policy, and build on the argument for art as an important alternative to authority. We suggest that while advocates of authority-based disruption might regard the playfulness of some art as a weakness, the unexpectedness it offers is perhaps a key strengt