Laplace operators with eigenfunctions whose nodal set is a knot

We prove that, given any knot $\gamma$ in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set $u^{-1}(0)$ has a connected component given by $\gamma$. Higher dimensional analogs of this result will also be considered.Comment: 16 page

Dislocations of arbitrary topology in Coulomb eigenfunctions

For any finite link $L$ in $\mathbb{R}^3$ we prove the existence of a high-energy complex-valued eigenfunction of the hydrogen atom such that its nodal set contains a union of connected components diffeomorphic to $L$. This problem goes back to Berry, who constructed such eigenfunctions in the case where $L$ is the trefoil knot or the Hopf link and asked the question about the general result.Comment: 10 page

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

Volcanic forcing from two sides : Drainage and plant ecosystem development in the Columbia River Flood Basalt Province, Washington State

Peer reviewedPublisher PD

The Survey Action Center

The Survey Action Center (SAC) is an international organization with its headquarters in Washington, D.C. It is registered in the United States as a non-profit organization. SAC serves as the executing agency for Landmine Impact Surveys (LISs). These surveys will allow for greater prioritization of demining efforts and further integration of the various mine action sectors

HALO Trust in Angola

The HALO Trust, a British charity, is gaining acclaim for both the scope and quality of their demining operations. In Angola, HALO has successfully adapted to an unstable political climate to help clear mines and allow for the return of hundreds of thousands of displaced refugees. In light of Angola’s newfound peace, the Trust plans to expand their operations and finish the job