Covariant hamiltonian spin dynamics in curved space-time

The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.Comment: 14 pages, accepted version for Phys Lett B, added a footnote and two reference

Epicycles and Poincar\'{e} Resonances in General Relativity

The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.Comment: 24 pages, 4 figure

Spinning bodies in curved space-time

We study the motion of neutral and charged spinning bodies in curved space-time in the test-particle limit. We construct equations of motion using a closed covariant Poisson-Dirac bracket formulation which allows for different choices of the hamiltonian. We derive conditions for the existence of constants of motion and apply the formalism to the case of spherically symmetric space-times. We show that the periastron of a spinning body in a stable orbit in a Schwarzschild or Reissner-Nordstr{\o}m background not only precesses, but also varies radially. By analysing the stability conditions for circular motion we find the innermost stable circular orbit (ISCO) as a function of spin. It turns out that there is an absolute lower limit on the ISCOs for increasing prograde spin. Finally we establish that the equations of motion can also be derived from the Einstein equations using an appropriate energy-momentum tensor for spinning particles.Comment: 26 pages, 5 figures; v2: version accepted for publication; small changes in text and references adde

Motions and world-line deviations in Einstein-Maxwell theory

We examine the motion of charged particles in gravitational and electro-magnetic background fields. We study in particular the deviation of world lines, describing the relative acceleration between particles on different space-time trajectories. Two special cases of background fields are considered in detail: (a) pp-waves, a combination of gravitational and electro-magnetic polarized plane waves travelling in the same direction; (b) the Reissner-Nordstr{\o}m solution. We perform a non-trivial check by computing the precession of the periastron for a charged particle in the Reissner-Nordstr{\o}m geometry both directly by solving the geodesic equation, and using the world-line deviation equation. The results agree to the order of approximation considered.Comment: 23 pages, no figure

Control of hierarchical polymer mechanics with bioinspired metal-coordination dynamics.

In conventional polymer materials, mechanical performance is traditionally engineered via material structure, using motifs such as polymer molecular weight, polymer branching, or block copolymer design. Here, by means of a model system of 4-arm poly(ethylene glycol) hydrogels crosslinked with multiple, kinetically distinct dynamic metal-ligand coordinate complexes, we show that polymer materials with decoupled spatial structure and mechanical performance can be designed. By tuning the relative concentration of two types of metal-ligand crosslinks, we demonstrate control over the material's mechanical hierarchy of energy-dissipating modes under dynamic mechanical loading, and therefore the ability to engineer a priori the viscoelastic properties of these materials by controlling the types of crosslinks rather than by modifying the polymer itself. This strategy to decouple material mechanics from structure is general and may inform the design of soft materials for use in complex mechanical environments. Three examples that demonstrate this are provided

Evidence for an eastward flow along the Central and South American Caribbean Coast

11 pages, 8 figures, 2 tables.-- Full-text version available Open Access at: http://www.iim.csic.es/~barton/html/pdfs.htmlHydrographic transects suggest an eastward flow with a subsurface core along the entire southern boundary of the Caribbean Sea. The transport of the coastal limb of the Panama-Colombia Gyre (PCG), known as the Panama-Colombia Countercurrent, decreases toward the east (from ∼6 Sv off Panama), as water is lost into the recirculation of the PCG. Off Panama, the flow is strongest at the surface, but, off Colombia, it is strongest at around 100 m. A portion of the counterflow (∼1 Sv) continues eastward along the Colombian coast as far as the Guajira region (12°N, 72°W), where it submerges to become an undercurrent beneath the coastal upwelling center there. The eastward flow also occurs in the Venezuela Basin, beneath the coastal upwelling region off Cariaco Basin and exits the Caribbean through the Grenada Channel at around 200 m depth. Numerical simulations suggest that this flow, counter to the Caribbean Current, is a semi-continuous feature along the entire southern boundary of the Caribbean, and that it is associated with offshore cyclonic eddies. It probably constitutes part of the Sverdrup circulation of the Tropical North Atlantic cyclonic cell.This work had financial support of the Colombian Institute for the Development of Science and Technology COLCIENCIAS, project 96-044 and the Colombian Navy. Also, the Office of Naval Research provided funding for C. N. K. Mooers and E. D. Barton during manuscript preparation.Peer reviewe

Dynamical supersymmetry of spin particle-magnetic field interaction

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\N=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry without Grassmann variable doubling.Comment: 23 page