Belabored: the work of style

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Static loads on the lower back for two modalities of the isometric smith squat

Introduction: The squat is one of the most effective exercises in athletic training. However, there is a scarcity of research that reports the muscular and joint loads in the lumbar region incurred when performing the high bar and the low bar isometric squat modalities in a Smith machine. Therefore, this study aims to determine the muscle force of the lower back extensors, and the compressive (Rc) and shear (Rs) forces at the lumbosacral joint for the one repetition maximum (1RM) high bar and low bar isometric parallel-depth Smith squats. Methods: Eight healthy male well-trained 400-m sprinters participated in the study. The athletes performed the two modalities of the isometric squat on a 7° backward-inclined Smith machine using a mean ± SD 1RM external resistance of 100.3 ± 7.2 kg. During the squat, the participants paused for 2-3 s at the bottom of the squat, corresponding to a position in which the thighs are parallel to the ground. This was, therefore, considered a static position for the calculation of isometric muscle forces and joint loads using static mechanical analysis. Moment arms, and joint and segmental angles were calculated from video images of the squatting performance. Internal forces were computed using a geometrical model of the trunk and lower limb. Results: Spinal extensor muscular forces and lumbo-sacral joint forces were higher when using the low bar technique; with the exception of Rs which was approximately equal. The mean Rc were 10.2 body weights (BW) or 8,014 N (high bar) and 11.1 BW or 8,729 N (low bar). Discussion: The low bar technique yields higher Rc and may therefore be avoided in the rehabilitation of spinal injuries. Increased bone mineral density and well-developed trunk musculature due to long term squat training can provide protection against passive spinal tissue failure. Therefore, the Rc found for the 1RM isometric parallel-depth Smith squat do not appear excessive for healthy well-trained athletes. The presence of Rs at the lumbo-sacral joint in both squat modalities suggests potential for damage to the intervertebral disc. The findings provide an in-depth understanding of the two squat modalities in isometric conditions for the prevention of lower back injury and the design of rehabilitation programs

A Lumbering Soul

Ope

Renormalizability of Liouville Quantum Gravity at the Seiberg bound

Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d Riemannian metrics $e^{\phi(z)}dz^2$, conjecturally describing scaling limits of discrete $2d$-random surfaces. The law of the random field $\phi$ in LQFT depends on weights $\alpha\in \mathbb{R}$ that in classical Riemannian geometry parametrize power law singularities in the metric. A rigorous construction of LQFT has been carried out in \cite{DKRV} in the case when the weights are below the so called Seiberg bound: $\alpha<Q$ where $Q$ parametrizes the random surface model in question. These correspond to conical singularities in the classical setup. In this paper, we construct LQFT in the case when the Seiberg bound is saturated which can be seen as the probabilistic version of Riemann surfaces with cusp singularities. Their construction involves methods from Gaussian Multiplicative Chaos theory at criticality

Liouville Quantum Gravity on the Riemann sphere

In this paper, we rigorously construct $2d$ Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov "Quantum Geometry of bosonic strings". We also establish some of its fundamental properties like conformal covariance under PSL$_2(\mathbb{C})$-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quantum Gravity.Comment: Added conjectures relating Liouville quantum field theory to random planar map and optimal conditions in order to ensure existence of the unit volume Liouville measur

Static loads on the knee and ankle for two modalities of the isometric smith squat

Introduction: The back squat is a popular strength training exercise that recruits approximately 75% of the muscular system. However, knowledge of muscular and joint loads incurred when performing two variations of the back squat, namely the high bar and the low bar isometric parallel-depth Smith squat, is limited. Therefore this study aims to determine the lower limb muscle forces and the compressive and shear joint forces at the knee and ankle incurred in these two subtle variations of the one repetition maximum (1RM) isometric Smith squat. Method: Eight healthy male 400-m sprinters participated in the study. The participants performed the two modalities of the squat using a 7° backward-inclined Smith machine. The bottom of the squat corresponded to a position in which the thighs are parallel to the ground. The mean ± SD 1RM external load for the eight participants was 100.3 ± 7.2 kg. During the squat, the participants paused for 2-3 s at the bottom of the squat. This was, therefore, considered a static position for the calculation of isometric muscle forces and joint loads using static mechanical analysis. Moment arms, and joint and segmental angles were calculated from video images of the squat obtained at 25 Hz. Internal forces were computed using a geometrical model of the lower limb. Results: Quadriceps muscle and knee joint forces were higher in the high bar squat; where, the mean patellofemoral joint reaction force was 3.7 body weights (BW). The ankle extensor muscle and ankle joint forces were larger in the low bar squat; whereby, the mean compressive force at the ankle joint was 3.0 BW. Discussion: The high bar squatting modality may be avoided in the rehabilitation of ACL injury. Conversely, the low bar technique may be discouraged in conditions of ankle joint instability, strained Achilles tendon, and damaged gastrocnemius and soleus muscles. The findings of the static biomechanical evaluation provide an in-depth understanding of the musculoskeletal loads associated with the two squat modalities in isometric conditions and offer a foundation for the dynamic modelling of the high bar and low bar Smith squat. Further, the knowledge gained can be used for the prevention of injury in strength training and in the design of rehabilitation programs that control muscle recruitment and joint loads

Cold-Formed Steel Sections with Web Openings Subjected to Web Crippling under Two-Flange Loading Conditions — Part I : Tests and Finite Element Analysis

The results of 82 web crippling tests are presented, with 20 tests conducted on channel sections without web openings and 62 tests conducted on channel sections with web openings. The tests consider both end-two-flange and interior-two-flange loading conditions. In the case of the tests with web openings, the hole was located directly under the concentrated load. The concentrated load was applied through bearing plates; the effect of different bearing lengths is investigated. In addition, the cases of both flanges fastened and unfastened to the support were considered. A non-linear elasto-plastic finite element model is described, and the results compared against the laboratory test results; a good agreement was obtained in terms of both strength and failure modes