Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.Comment: 13 pages total, including 5 figure

Blow-up of the hyperbolic Burgers equation

The memory effects on microscopic kinetic systems have been sometimes modelled by means of the introduction of second order time derivatives in the macroscopic hydrodynamic equations. One prototypical example is the hyperbolic modification of the Burgers equation, that has been introduced to clarify the interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous studies suggested the finite time blow-up of this equation, and here we present a rigorous proof of this fact

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

Total score of athleticism: Profiling strength and power characteristics in professional soccer players following anterior cruciate ligament reconstruction to assess return to sport readiness

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

Production of Enhanced Beam Halos via Collective Modes and Colored Noise

We investigate how collective modes and colored noise conspire to produce a beam halo with much larger amplitude than could be generated by either phenomenon separately. The collective modes are lowest-order radial eigenmodes calculated self-consistently for a configuration corresponding to a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium. The colored noise arises from unavoidable machine errors and influences the internal space-charge force. Its presence quickly launches statistically rare particles to ever-growing amplitudes by continually kicking them back into phase with the collective-mode oscillations. The halo amplitude is essentially the same for purely radial orbits as for orbits that are initially purely azimuthal; orbital angular momentum has no statistically significant impact. Factors that do have an impact include the amplitudes of the collective modes and the strength and autocorrelation time of the colored noise. The underlying dynamics ensues because the noise breaks the Kolmogorov-Arnol'd-Moser tori that otherwise would confine the beam. These tori are fragile; even very weak noise will eventually break them, though the time scale for their disintegration depends on the noise strength. Both collective modes and noise are therefore centrally important to the dynamics of halo formation in real beams.Comment: For full resolution pictures please go to http://www.nicadd.niu.edu/research/beams

A comparison of strength and power characteristics prior to anterior cruciate ligament rupture and at the end of rehabilitation in professional soccer players

Background: Strength and power is often reduced on the involved vs. contralateral limb and healthy controls following anterior cruciate ligament (ACL) reconstruction but no study has compared to pre-injury values at the time of return to sport (RTS). Hypothesis: Divergent recovery patterns in strength and power characteristics will be present at RTS relative to pre-injury baseline data and healthy matched controls. Study design: Cohort study Level of evidence: Level 3 Methods: Isokinetic strength tests, bilateral and single leg countermovement jumps (CMJ; SLCMJ) were measured prior to ACL rupture in 20 professional soccer players. These then had surgical reconstruction (ACL group) and completed follow up testing prior to RTS. Healthy controls (uninjured group) were tested at the same time as the ACL group pre-injury. Values recorded at RTS of the ACL group were compared to pre-injury. We also compared the uninjured and ACL groups at baseline and RTS. Results: Compared to pre-injury, ACL normalised quadriceps peak torque of the involved limb (% difference = -7%), SLCMJ height (% difference = -12.08%) and Reactive Strength Index modified (RSImod) (% difference = -5.04%) were reduced following ACL reconstruction. No significant reductions in CMJ height, RSImod and relative peak power were indicated at RTS in the ACL group when compared to pre-injury values but deficits were present relative to controls. The uninvolved limb significantly improved quadriceps (% difference = 9.34%) and hamstring strength (% difference = 7.36%) from pre-injury to RTS. No significant differences from baseline were shown in SLCMJ height, power and reactive strength of the uninvolved limb following ACL reconstruction. Conclusion: Strength and power in professional soccer players at RTS following ACL reconstruction were often reduced compared to preinjury values and matched healthy controls. Clinical relevance: Deficits were more apparent in the SLCMJ suggesting dynamic and multijoint unilateral force production is an important component of rehabilitation. Use of the uninvolved limb and normative data to determine recovery may not always be appropriate