Uniqueness for a seismic inverse source problem modeling a subsonic rupture

We consider an inverse problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. We assume that the sources occur along a path with subsonic velocity, and that data are collected over time on some detection surface. We explore the question of uniqueness for these problems, show how to recover the times and locations of sources microlocally, and then reconstruct the smooth part of the source assuming that it is the same at each source location

Enantioselective Total Synthesis of (+)-Cassiol

An enantioselective total synthesis of (+)-cassiol is reported. The complex derived from Pd-2(pmdba)(3) and enantiopure t-BuPHOX ligand catalyzes enantioconvergent decarboxylative alkylation to generate the quaternary carbon stereocenter at an early stage. The overall synthetic strategy involves a convergent late-stage coupling of two fragments. The synthesis features a longest linear sequence of eight steps

Critical exponents of the O(N) model in the infrared limit from functional renormalization

We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.Comment: final version, 7 pages 7 figures, to appear in Phys. Rev.

Prediction of VO\u3csub\u3e2\u3c/sub\u3e Peak Using Sub-Maximum Bench Step Test in Children

The purpose of this study was to develop a valid prediction of maximal oxygen uptake from data collected during a submaximum bench stepping test among children ages 8-12 years. Twentyseven active subjects (16 male and 11 female), weight 36.1 kg, height 144.4 cm and VO2 47.4 ± 7.9 ml/kg/min participated. Subjects completed a maximal oxygen consumption test with analysis of expired air and a submaximal bench stepping test. A formula to predict VO2max was developed from height, resting heart rate and heart rate response during the submaximum bench stepping test. This formula accounted for 71% of the variability in maximal oxygen consumption and is the first step in verifying the validity of the submaximum bench stepping test to predict VO2max. VO2max = -2.354 + (Height in cm * 0.065) + (Resting Heart Rate * 0.008) + (Step Test Average Heart Rate as a Percentage of Resting Heart Rate * -0.870

Using stiffness to assess injury risk:comparison of methods for quantifying stiffness and their reliability in triathletes

Background: A review of the literature has indicated that lower body stiffness, defined as the extent to which the lower extremity joints resists deformation upon contact with the ground, may be a useful measure for assessing Achilles injury risk in triathletes. The nature of overuse injuries suggests that a variety of different movement patterns could conceivably contribute to the final injury outcome, any number and combination of which might be observed in a single individual. Measurements which incorporate both kinetics and kinematics (such as stiffness) of a movement may be better able to shed light on individuals at risk of injury, with further analysis then providing the exact mechanism of injury for the individual. Stiffness can be measured as vertical, leg or joint stiffness to model how the individual interacts with the environment upon landing. However, several issues with stiffness assessments limit the effectiveness of these measures to monitor athletes’ performance and/or injury risk. This may reflect the variety of common biomechanical stiffness calculations (dynamic, time, true leg and joint) that have been used to examine these three stiffness levels (vertical, leg and joint) across a variety of human movements (i.e. running or hopping) as well as potential issues with the reliability of these measures, especially joint stiffness. Therefore, the aims of this study were to provide a comparison of the various methods for measuring stiffness during two forms of human bouncing locomotion (running and hopping) along with the measurement reliability to determine the best methods to assess links with injury risk in triathletes. Methods: Vertical, leg and joint stiffness were estimated in 12 healthy male competitive triathletes on two occasions, 7 days apart, using both running at 5.0 ms−1 and hopping (2.2 Hz) tasks. Results: Inter-day reliability was good for vertical (ICC = 0.85) and leg (ICC = 0.98) stiffness using the time method. Joint stiffness reliability was poor when assessed individually. Reliability was improved when taken as the sum of the hip, knee and ankle (ICC = 0.86). The knee and ankle combination provided the best correlation with leg stiffness during running (Pearson’s Correlation = 0.82). Discussion: The dynamic and time methods of calculating leg stiffness had better reliability than the “true” method. The time and dynamic methods had the best correlation with the different combinations of joint stiffness, which suggests that they should be considered for biomechanical screening of triathletes. The knee and ankle combination had the best correlation with leg stiffness and is therefore proposed to provide the most information regarding lower limb mechanics during gait in triathletes

Vison gap in the Rokhsar-Kivelson dimer model on the triangular lattice

With the classical Monte Carlo method, I find the energy gap in the Rokhsar-Kivelson dimer model on the triangular lattice. I identify the lowest excitations as visons, and compute their energy as a function of the momentum.Comment: 5 page