Mechanics of extended masses in general relativity

The "external" or "bulk" motion of extended bodies is studied in general relativity. Compact material objects of essentially arbitrary shape, spin, internal composition, and velocity are allowed as long as there is no direct (non-gravitational) contact with other sources of stress-energy. Physically reasonable linear and angular momenta are proposed for such bodies and exact equations describing their evolution are derived. Changes in the momenta depend on a certain "effective metric" that is closely related to a non-perturbative generalization of the Detweiler-Whiting R-field originally introduced in the self-force literature. If the effective metric inside a self-gravitating body can be adequately approximated by an appropriate power series, the instantaneous gravitational force and torque exerted on it is shown to be identical to the force and torque exerted on an appropriate test body moving in the effective metric. This result holds to all multipole orders. The only instantaneous effect of a body's self-field is to finitely renormalize the "bare" multipole moments of its stress-energy tensor. The MiSaTaQuWa expression for the gravitational self-force is recovered as a simple application. A gravitational self-torque is obtained as well. Lastly, it is shown that the effective metric in which objects appear to move is approximately a solution to the vacuum Einstein equation if the physical metric is an approximate solution to Einstein's equation linearized about a vacuum background.Comment: 39 pages, 2 figures; fixed equation satisfied by the Green function used to construct the effective metri

A conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. However, to date iterative Fourier transform algorithms have been predominantly used. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.Comment: 11 pages, 4 figure

Electromagnetic self-forces and generalized Killing fields

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte

Self-forces from generalized Killing fields

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.Comment: 21 page

On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder

Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of the local order parameter $\rho(r)$ scale with a set $x(q)$ of non-trivial exponents $x(q) \neq q x(1)$. In this paper, we revisit these ideas to incorporate more recent findings: (i) whenever a multifractal measure $w(r)$ normalized over space $\sum_r w(r)=1$ occurs in a random system, it is crucial to distinguish between the typical values and the disorder averaged values of the generalized moments $Y_q =\sum_r w^q(r)$, since they may scale with different generalized dimensions $D(q)$ and $\tilde D(q)$ (ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E {\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces a lack of self-averaging at critical points for thermodynamic observables, in particular for the order parameter. After this general discussion valid for any random critical point, we apply these ideas to random polymer models that can be studied numerically for large sizes and good statistics over the samples. We study the bidimensional wetting or the Poland-Scheraga DNA model with loop exponent $c=1.5$ (marginal disorder) and $c=1.75$ (relevant disorder). Finally, we argue that the presence of finite Griffiths ordered clusters at criticality determines the asymptotic value $x(q \to \infty) =d$ and the minimal value $\alpha_{min}=D(q \to \infty)=d-x(1)$ of the typical multifractal spectrum $f(\alpha)$.Comment: 17 pages, 20 figure

Palaeontological site conservation and the law in Britain

The legal situation regarding palaeontological site conservation in Britain is unclear. There is no modern review of the law. Five main areas of concern are identified. Most exsisting laws do not specifically consider the needs of palaeontological conservation. Legislation empowers the Nature Conservancy Council upon policy decisions. The NCC is primarily concerned with nationally important sites, and responsibility for recording other sites therefore falls upon voluntary National Scheme for Geological Site Documentation. Local authorities have potentially useful powers. Site occupiers are disadvantaged by the damage caused by, and to some extent the liability due to visitiors, but they can forbid access to almost all sites on private land. The ownership of in situ fossils may be presumed to go with the mineral rights in the land, and collecting them without permission may involve criminal damage and theft. Loose fossils may in some cases be legally collected without express permission. If the landowner has not exerted rights of controil of access or ownership. This is potentially important for coastal exposures. The compulsary public ownership of fossils is not likely to be a successful strategy in geological conservation. Resources are on the whole better spent in education and popularization than on compulsion

Linearity and Scaling of a Statistical Model for the Species Abundance Distribution

We derive a linear recursion relation for the species abundance distribution in a statistical model of ecology and demonstrate the existence of a scaling solution