Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Musculoskeletal effects and injury risk in collegiate Indian classical and ballet dancers

Dancers of all forms often engage in aesthetic yet challenging movements. Their training, choreography, and performances require strength, stamina, flexibility, grace, passion, and emotion. Ballet and Bharatanatyam (an Indian classical dance form) dancers utilize two movements in each of their dance forms that are similar—a half-sitting pose and a full-sitting pose, both requiring external rotation of the legs and bending at the knee joints. The purpose of this study was to examine and compare the biomechanics of joint reaction forces and knee angles in both styles of dance for these particular poses. The study included nine female ballet dancers and seven female Bharatanatyam dancers. Hamstring and gastrocnemius flexibility were measured for each dancer. Knee angles, vertical peak forces, and moments were determined for dancers at the lowest point of their bending positions. Mann-Whitney U tests found significant differences in hamstring flexibility, right gastrocnemius flexibility, and knee angles for the full-sitting poses between ballet and Bharatanatyam dancers. No significant difference was found in the vertical peak forces as a ratio to total body weight and moments between the two styles of dance. Further research can be done to more directly assess a difference in injury risk between the ballet and Bharatanatyam dancers.