Algorithms to solve the Sutherland model

We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.Comment: 15 pages, LaTe

Instabilities in Multi-Planet Circumbinary Systems

The majority of the discovered transiting circumbinary planets are located very near the innermost stable orbits permitted, raising questions about the origins of planets in such perturbed environments. Most favored formation scenarios invoke formation at larger distances and subsequent migration to their current locations. Disk-driven planet migration in multi-planet systems is likely to trap planets in mean motion resonances and drive planets inward into regions of larger dynamical perturbations from the binary. We demonstrate how planet-planet resonances can interact with the binary through secular forcing and mean-motion resonances, driving chaos in the system. We show how this chaos will shape the architecture of circumbinary systems, with specific applications to Kepler 47 and the Pluto-Charon system, limiting maximum possible stable eccentricities and indicating what resonances are likely to exist. We are also able to constrain the minimum migration rates of resonant circumbinary planets.Comment: Accepted for publication in MNRA

Comparative jet wake structure and swimming performance of salps

Salps are barrel-shaped marine invertebrates that swim by jet propulsion. Morphological variations among species and life-cycle stages are accompanied by differences in swimming mode. The goal of this investigation was to compare propulsive jet wakes and swimming performance variables among morphologically distinct salp species (Pegea confoederata, Weelia (Salpa) cylindrica, Cyclosalpa sp.) and relate swimming patterns to ecological function. Using a combination of in situ dye visualization and particle image velocimetry (PIV) measurements, we describe properties of the jet wake and swimming performance variables including thrust, drag and propulsive efficiency. Locomotion by all species investigated was achieved via vortex ring propulsion. The slow-swimming P. confoederata produced the highest weight-specific thrust (T =53 N kg^(–1)) and swam with the highest wholecycle propulsive efficiency (η_wc= 55%). The fast-swimming W. cylindrica had the most streamlined body shape but produced an intermediate weight-specific thrust (T=30 N kg^(–1)) and swam with an intermediate whole-cycle propulsive efficiency (η_wc =52%). Weak swimming performance variables in the slow-swimming C. affinis, including the lowest weight-specific thrust (T=25 N kg^(–1)) and lowest whole-cycle propulsive efficiency (η_wc=47%), may be compensated by low energetic requirements. Swimming performance variables are considered in the context of ecological roles and evolutionary relationships

Interacting Fermion Systems from Two Dimensional QCD

We consider two dimensional U(N) QCD on the cylinder with a timelike Wilson line in an arbitrary representation. We show that the theory is equivalent to N fermions with internal degrees of freedom which interact among themselves with a generalized Sutherland-type interaction. By evaluating the expectation value of the Wilson line in the original theory we explicitly find the spectrum and degeneracies of these particle systems.Comment: 11 pages, UVA-93-11, CERN-TH-6994/9

Integrable Systems for Particles with Internal Degrees of Freedom

We show that a class of models for particles with internal degrees of freedom are integrable. These systems are basically generalizations of the models of Calogero and Sutherland. The proofs of integrability are based on a recently developed exchange operator formalism. We calculate the wave-functions for the Calogero-like models and find the ground-state wave-function for a Calogero-like model in a position dependent magnetic field. This last model might have some relevance for matrix models of open strings.Comment: 10 pages, UVA-92-04, CU-TP-56

Normative EMG activation patterns of school-age children during gait

Gait analysis is widely used in clinics to study walking abnormalities for surgery planning, definition of rehabilitation protocols, and objective evaluation of clinical outcomes. Surface electromyography allows the study of muscle activity non-invasively and the evaluation of the timing of muscle activation during movement. The aim of this study was to present a normative dataset of muscle activation patterns obtained from a large number of strides in a population of 100 healthy children aged 6-11 years. The activity of Tibialis Anterior, Lateral head of Gastrocnemius, Vastus Medialis, Rectus Femoris and Lateral Hamstrings on both lower limbs was analyzed during a 2.5-min walk at free speed. More than 120 consecutive strides were analyzed for each child, resulting in approximately 28,000 strides. Onset and offset instants were reported for each observed muscle. The analysis of a high number of strides for each participant allowed us to obtain the most recurrent patterns of activation during gait, demonstrating that a subject uses a specific muscle with different activation modalities even in the same walk. The knowledge of the various activation patterns and of their statistics will be of help in clinical gait analysis and will serve as reference in the design of future gait studie

Conservation laws in the continuum 1/r21/r^2 systems

We study the conservation laws of both the classical and the quantum mechanical continuum $1/r^2$ type systems. For the classical case, we introduce new integrals of motion along the recent ideas of Shastry and Sutherland (SS), supplementing the usual integrals of motion constructed much earlier by Moser. We show by explicit construction that one set of integrals can be related algebraically to the other. The difference of these two sets of integrals then gives rise to yet another complete set of integrals of motion. For the quantum case, we first need to resum the integrals proposed by Calogero, Marchioro and Ragnisco. We give a diagrammatic construction scheme for these new integrals, which are the quantum analogues of the classical traces. Again we show that there is a relationship between these new integrals and the quantum integrals of SS by explicit construction.Comment: 19 RevTeX 3.0 pages with 2 PS-figures include