Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics

Observations of distorted discs have highlighted the ubiquity of warps in a variety of astrophysical contexts. This has been complemented by theoretical efforts to understand the dynamics of warp evolution. Despite significant efforts to understand the dynamics of warped discs, previous work fails to address arguably the most prevalent regime – nonlinear warps in Keplerian discs for which there is a resonance between the orbital, epicyclic and vertical oscillation frequencies. In this work, we implement a novel nonlinear ring model, developed recently by Fairbairn and Ogilvie, as a framework for understanding such resonant warp dynamics. Here we uncover two distinct nonlinear regimes as the warp amplitude is increased. Initially we find a smooth modulation theory which describes warp evolution in terms of the averaged Lagrangian of the oscillatory vertical motions of the disc. This hints towards the possibility of connecting previous warp theory under a generalised secular framework. Upon the warp amplitude exceeding a critical value, which scales as the square root of the aspect-ratio of our ring, the disc enters into a bouncing regime with extreme vertical compressions twice per orbit. We develop an impulsive theory which predicts special retrograde and prograde precessing warped solutions, which are identified numerically using our full equation set. Such solutions emphasise the essential activation of nonlinear vertical oscillations within the disc and may have important implications for energy and warp dissipation. Future work should search for this behaviour in detailed numerical studies of the internal flow structure of warped discs.

Mechanics, energetics and implementation of grounded running technique: a narrative review

Grounded running predominantly differs from traditional aerial running by having alternating single and double stance with no flight phase. Approximately, 16% of runners in an open marathon and 33% of recreational runners in a 5 km running event adopted a grounded running technique. Grounded running typically occurs at a speed range of 2–3 m·s−1, is characterised by a larger duty factor, reduced vertical leg stiffness, lower vertical oscillation of the centre of mass (COM) and greater impact attenuation than aerial running. Grounded running typically induces an acute increase in metabolic cost, likely due to the larger duty factor. The increased duty factor may translate to a more stable locomotion. The reduced vertical oscillation of COM, attenuated impact shock, and potential for improved postural stability may make grounded running a preferred form of physical exercise in people new to running or with low loading capacities (eg, novice overweight/obese, elderly runners, rehabilitating athletes). Grounded running as a less impactful, but metabolically more challenging form, could benefit these runners to optimise their cardio-metabolic health, while at the same time minimise running-related injury risk. This review discusses the mechanical demands and energetics of grounded running along with recommendations and suggestions to implement this technique in practice.

Validation of Garmin Fenix 3 HR Fitness Tracker Biomechanics and Metabolics (VO2max)

The purpose of this study was to determine the validity of the Garmin fēnix® 3 HR fitness tracker. Methods: A total of 34 healthy recreational runners participated in biomechanical or metabolic testing. Biomechanics participants completed three running conditions (flat, incline, and decline) at a self-selected running pace, on an instrumented treadmill while running biomechanics were tracked using a motion capture system. Variables extracted were compared with data collected by the Garmin fēnix 3 HR (worn on the wrist) that was paired with a chest heart rate monitor and a Garmin Foot Pod (worn on the shoe). Metabolic testing involved two separate tests; a graded exercise test to exhaustion utilizing a metabolic cart and treadmill, and a 15-min submaximal outdoor track session while wearing the Garmin. 2 × 3 analysis of variances with post hoc t tests, mean absolute percentage errors, Pearson’s correlation (R), and a t test were used to determine validity. Results: The fēnix kinematics had a mean absolute percentage errors of 9.44%, 0.21%, 26.38%, and 5.77% for stride length, run cadence, vertical oscillation, and ground contact time, respectively. The fēnix overestimated (p < .05) VO2max with a mean absolute percentage error of 8.05% and an R value of .917. Conclusion: The Garmin fēnix 3 HR appears to produce a valid measure of run cadence and ground contact time during running, while it overestimated vertical oscillation in every condition (p < .05) and should be used with caution when determining stride length. The fēnix appears to produce a valid VO2max estimate and may be used when more accurate methods are not available.

The Effects of Chronic Branched-Chain Amino Acid Supplementation on Running Kinematics: Single Case Research

Purpose: To monitor the effects of chronic branched-chain amino acid (BCAA) supplementation on running kinematics in a trained ultra-endurance runner. Methods: One well-trained ultra-endurance runner followed three 10-day cycles of an AB design consuming a BCAA drink (SUP) or placebo (PLA) surrounding daily key workouts leading up to a 50-mile race (dosage = 0.08g/kg/day = 3.52g BCAA/day and 10.32g AA/day). During each 10-day cycle, the athlete completed a 5km run on an outdoor track at 6:30min/mile pace. A 10-meter capture zone was measured and marked with two orange cones for video recording and analysis. Kinovea open-source software (Version 0.8.15) was used to measure running kinematic variables: ground contact time (GCT), flight time (FT), and vertical oscillation (VO). Results: Vertical oscillation (VO) during a constant-pace run was significantly reduced from 88mm to 76mm when athlete was on SUP vs PLA condition (p = 0.00, Tau-U = 0.40). Statistical significance was not achieved for differences in GCT and FT between SUP and PLA (p = 0.06, Tau-U = 0.-17 and p = 0.28, Tau-U = 0.10 for GCT and FT, respectively). Weighted Tau-U results suggest that the BCAA supplement was overall 11% effective in improving combined measures of running kinematics (p = 0.04, Tau-U = 0.11). Discussion: A decrease in VO can indicate less overall muscle support requirements during stance phase and a reduced aerobic demand for a given task. We observed decreased VO during the 5km running tests on SUP indicating a reduction in wasteful vertical motion. Possible explanations for this could relate to improvement in muscle recovery characteristics from increased availability of BCAAs resulting in less chronic fatigue. Less fatigue can allow greater coactivation between two-joint muscles of the leg during stance resulting in more efficient joint rotations that are transferred into desired external forces, promoting more efficient movement and a more economical runner.

Corrugation of an unpaved road surface under vehicle weight

Road corrugation refers to the formation of periodic, transverse ripples on unpaved road surfaces. It forms spontaneously on an initially flat surface under heavy traffic and can be considered to be a type of unstable growth phenomenon, possibly caused by the local volume contraction of the underlying soil due to a moving vehicle’s weight. In the present work, we demonstrate a possible mechanism for road corrugation using experimental data of soil consolidation and numerical simulations. The results indicate that the vertical oscillation of moving vehicles, which is excited by the initial irregularities of the surface, plays a key role in the development of corrugation.

Predictive ability of motion sickness susceptibility questionnaire for seasickness individual difference in Chinese military personnel

Background Motion sickness susceptibility questionnaire (MSSQ) has been widely used for assessing individual differences in motion sickness. The present study tried to investigate its efficacy for predicting seasickness susceptible (SUS) and insusceptible (INSUS) subjects among Chinese military personnel. Methods Two cohorts of young male army volunteers were exposed to real ship motion (n=125) and laboratory vertical oscillation motion (n=77). Predictive ability of the MSSQ and its vomiting (MSV) and nausea (MSN) subscales (including child and adult subitems) was examined via analyzing area under the curve (AUC) of receiver operating characteristic (ROC) with seasickness susceptibility defined by Graybiel score or nausea latency. Results Higher Graybiel scores and lower percentage of INSUS subjects was observed in the ship motion trial than the vertical oscillation trial. MSSQ and its subscales positively correlated with the Graybiel score in both trials. The MSN child showed no predictive ability for the INSUS subjects, leading to lower AUC of the MSN than the MSSQ and the MSV for INSUS prediction in ship motion (0.587 vs. 0.647 and 0.644, P < 0.01) and vertical oscillation trial (0.696 vs. 0.761 and 0.788, P < 0.01 and 0.05) when seasickness susceptibility was defined by Graybiel score. Lower AUC in the MSN than the MSSQ (0.691 vs. 0.758, P < 0.05 and 0.01) was observed due to invalidity of MSN child when susceptibility was defined by nausea latency in the vertical oscillation trial. The prediction ability of SUS did not differ among the MSSQ and its subscales in both trials. Relative to the ship motion trial, the vertical oscillation trial showed higher predictive efficacy of the MSSQ for the Graybiel score-defined SUS subjects (0.840 vs. 0.686, P < 0.05) as a result of higher AUC in both the MSV (0.840 vs. 0.690, P < 0.05) and the MSN (0.806 vs. 0.651, P < 0.01). Conclusions The MSSQ was effective for predicting seasickness susceptibility in young male Chinese military members, but the efficacy varies with motion intensity and complexity and the vomiting scale should be recommended for application.

Reliability of Trail Walking and Running Tasks Using the Stryd Power Meter

Footpod monitors are wearable devices attaching to the shoe with the ability to sense oscillations in leg movement; however, few studies provide reliability. The purpose was to provide reliability data for outdoor tasks as measured by the Stryd Power Meter, which is a footpod monitor. Young healthy individuals (N=20, male n=12, female n=8) completed two 5-min self-paced walks along a trail, and two 5-min trail runs. Reliability of the tasks was determined using Coefficient of Variation (CV), Intraclass Correlation (ICC), and 95% confidence intervals (CI). Measures during trail running that returned a CV less than 10%, met the ICC threshold of 0.70, and displayed good to excellent 95% CI included pace, average elapsed power, average elapsed form power, average elapsed leg spring, and vertical oscillation. The only variable during walking to meet these criteria was maximal power (CV=4.02%, ICC=0.968, CI=0.902, 0.989). Running tasks completed on a trail generally return more consistent measures for variables that can be obtained from the Stryd footpod device than walking tasks.