14,868 research outputs found
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
-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^(â1)) 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^(â1)) 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^(â1))
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
Solution of Some Integrable One-Dimensional Quantum Systems
In this paper, we investigate a family of one-dimensional multi-component
quantum many-body systems. The interaction is an exchange interaction based on
the familiar family of integrable systems which includes the inverse square
potential. We show these systems to be integrable, and exploit this
integrability to completely determine the spectrum including degeneracy, and
thus the thermodynamics. The periodic inverse square case is worked out
explicitly. Next, we show that in the limit of strong interaction the "spin"
degrees of freedom decouple. Taking this limit for our example, we obtain a
complete solution to a lattice system introduced recently by Shastry, and
Haldane; our solution reproduces the numerical results. Finally, we emphasize
the simple explanation for the high multiplicities found in this model
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 systems
We study the conservation laws of both the classical and the quantum
mechanical continuum 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
Exact Solution of Heisenberg-liquid models with long-range coupling
We present the exact solution of two Heisenberg-liquid models of particles
with arbitrary spin interacting via a hyperbolic long-range potential. In
one model the spin-spin coupling has the simple antiferromagnetic Heisenberg
exchange form, while for the other model the interaction is of the
ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz
equations of these models have a similar structure to that of the
Babujian-Takhatajan spin chain. We also conjecture the integrability of a third
new spin-lattice model with long-range interaction.Comment: 7pages Revte
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