Swimming in curved space or The Baron and the cat

We study the swimming of non-relativistic deformable bodies in (empty) static curved spaces. We focus on the case where the ambient geometry allows for rigid body motions. In this case the swimming equations turn out to be geometric. For a small swimmer, the swimming distance in one stroke is determined by the Riemann curvature times certain moments of the swimmer.Comment: 19 pages 6 figure

Speckle-visibility spectroscopy: A tool to study time-varying dynamics

We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern formed by the scattered light as detected by a single exposure of a digital camera. Whereas previous multispeckle methods rely on correlations between images, here the connection with scattering site dynamics is made more simply in terms of the variance of intensity among the pixels of the camera for the specified exposure duration. The essence is that the speckle pattern is more visible, i.e. the variance of detected intensity levels is greater, when the dynamics of the scattering site motion is slow compared to the exposure time of the camera. The theory for analyzing the moments of the spatial intensity distribution in terms of the electric field autocorrelation is presented. It is demonstrated for two well-understood samples, a colloidal suspension of Brownian particles and a coarsening foam, where the dynamics can be treated as stationary. However, the method is particularly appropriate for samples in which the dynamics vary with time, either slowly or rapidly, limited only by the exposure time fidelity of the camera. Potential applications range from soft-glassy materials, to granular avalanches, to flowmetry of living tissue.Comment: review - theory and experimen

Innermost Stable Circular Orbit of a Spinning Particle in Kerr Spacetime

We study stability of a circular orbit of a spinning test particle in a Kerr spacetime. We find that some of the circular orbits become unstable in the direction perpendicular to the equatorial plane, although the orbits are still stable in the radial direction. Then for the large spin case ($S < \sim O(1)), the innermost stable circular orbit (ISCO) appears before the minimum of the effective potential in the equatorial plane disappears. This changes the radius of ISCO and then the frequency of the last circular orbit.Comment: 25 pages including 8 figure

The importance of visual control and biomechanics in the regulation of gesture-speech synchrony for an individual deprived of proprioceptive feedback of body position.

Do communicative actions such as gestures fundamentally differ in their control mechanisms from other actions? Evidence for such fundamental differences comes from a classic gesture-speech coordination experiment performed with a person (IW) with deafferentation (McNeill, 2005). Although IW has lost both his primary source of information about body position (i.e., proprioception) and discriminative touch from the neck down, his gesture-speech coordination has been reported to be largely unaffected, even if his vision is blocked. This is surprising because, without vision, his object-directed actions almost completely break down. We examine the hypothesis that IW’s gesture-speech coordination is supported by the biomechanical effects of gesturing on head posture and speech. We find that when vision is blocked, there are micro-scale increases in gesture-speech timing variability, consistent with IW’s reported experience that gesturing is difficult without vision. Supporting the hypothesis that IW exploits biomechanical consequences of the act of gesturing, we find that: (1) gestures with larger physical impulses co-occur with greater head movement, (2) gesture-speech synchrony relates to larger gesture-concurrent head movements (i.e. for bimanual gestures), (3) when vision is blocked, gestures generate more physical impulse, and (4) moments of acoustic prominence couple more with peaks of physical impulse when vision is blocked. It can be concluded that IW’s gesturing ability is not based on a specialized language-based feedforward control as originally concluded from previous research, but is still dependent on a varied means of recurrent feedback from the body

Post-Newtonian corrections to the motion of spinning bodies in NRGR

In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning bodies is developed and spin-orbit, spin-spin and quadrupole-spin Hamiltonians are found at leading order. The existence of tidal, as well as self induced finite size effects is shown, and the contribution to the Hamiltonian is calculated in the latter. It is shown that tidal deformations start formally at O(v^6) and O(v^10) for maximally rotating general and compact objects respectively, whereas self induced effects can show up at leading order. Agreement is found for the cases where the results are known.Comment: 18 pages, 9 figures. Typos corrected, to appear in Physical Review

On the motion of spinning test particles in plane gravitational waves

The Mathisson-Papapetrou-Dixon equations for a massive spinning test particle in plane gravitational waves are analysed and explicit solutions constructed in terms of solutions of certain linear ordinary differential equations. For harmonic waves this system reduces to a single equation of Mathieu-Hill type. In this case spinning particles may exhibit parametric excitation by gravitational fields. For a spinning test particle scattered by a gravitational wave pulse, the final energy-momentum of the particle may be related to the width, height, polarisation of the wave and spin orientation of the particle.Comment: 11 page

Signature of chaos in gravitational waves from a spinning particle

A spinning test particle around a Schwarzschild black hole shows a chaotic behavior, if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion is not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find out a chaotic behavior of the system. Such a peculiar behavior, if it will be found, may also provide us some additional informations to determine parameters of a system such as a spin.Comment: 14 pages, LaTeX, to appear in Phys. Rev.