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

How geckos stick in nature: ecology and biomechanics of gecko feet

Phenotype and performance play a fundamental role in evolution and ecology. Studies of form and function often use correlations between morphology, performance, and habitat use to examine patterns of ecomorphology and morphological adaptation. Geckos, of the taxonomic group Gekkota, are an understudied yet diverse clade of lizards in which studies of form and function would greatly improve our understanding of their evolution. Geckos have the rather unique trait of adhesive toe pads, enabling them to use arboreal and rocky environments in a way few other creatures can. Gecko toe pad morphology and adhesive abilities are highly variable across species, suggesting ecological adaptations may have driven their evolution, yet few studies has considered gecko adhesive morphology and performance in an ecological context. In this study, we quantified morphology, adhesive performance, and habitat use of 13 gecko species from Queensland, Australia including tropical, arid, arboreal, and rock-dwelling species. We found toe detachment angle to be correlated with residual limb length. We also found residual limb length to be correlated with the use of arboreal and rock microhabitats as well as negatively correlated with perch diameter. This study is one of the first examples investigating gecko adhesive performance and specific microhabitat parameters. We suggest additional comparative studies investigating gecko limb kinematics and setal mechanics to corroborate our observational results

Diffusion in multiscale spacetimes

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples and the most general spectral-dimension profile of multifractional spaces is constructed.Comment: 23 pages, 5 figures. v2: discussion improved, typos corrected, references adde

Universal Magnetic Fluctuations with a Field Induced Length Scale

We calculate the probability density function for the order parameter fluctuations in the low temperature phase of the 2D-XY model of magnetism near the line of critical points. A finite correlation length, \xi, is introduced with a small magnetic field, h, and an accurate expression for \xi(h) is developed by treating non-linear contributions to the field energy using a Hartree approximation. We find analytically a series of universal non-Gaussian distributions with a finite size scaling form and present a Gumbel-like function that gives the PDF to an excellent approximation. We propose the Gumbel exponent, a(h), as an indirect measure of the length scale of correlations in a wide range of complex systems.Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev.

The source of Dalradian detritus in the Buchan Block, NE Scotland: Application of new tools to detrital datasets

Detrital zircons from four samples of upper Dalradian metasedimentary rocks from the Buchan Block in the NE Grampian Highlands of Scotland were analysed by laser ablation inductively coupled plasma mass spectrometry to establish their U–Pb age and trace element composition. The analysed grains (magmatic cores) mainly yield concordant ages ranging from Neoproterozoic to Eoarchaean. Kernel density plots of the data show pronounced peaks in the late Mesoproterozoic, Palaeoproterozoic and Neoarchaean eras. The data are indistinguishable from detrital zircon age spectra from Dalradian rocks elsewhere, an interpretation supported by application of a non-parametric multidimensional scaling algorithm, and are consistent with a Laurentian source. Similar to existing studies from other Dalradian rocks, the age spectra from the Buchan Block reveal an increase in the relative proportion of older detritus with time, suggesting derivation from late Mesoproterozoic (Grenville) then Palaeoproterozoic orogens before widespread exposure and denudation of their Archaean basement rocks. Application of a novel approach to estimate the most likely time of radiogenic-Pb loss indicates that some detrital zircon grains were affected by element mobility around 470–450 Ma as a result of Grampian orogenesis

Self-forces on extended bodies in electrodynamics

In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion. We place essentially no restrictions (other than boundedness) on the shape of the charge, and allow for inhomogeneity, internal currents, elasticity, and spin. Even if the angular momentum remains small, many such systems are found to be affected by large self-interaction effects beyond the standard Lorentz-Dirac force. These are particularly significant if the particle's charge density fails to be much greater than its 3-current density (or vice versa) in the center-of-mass frame. Additional terms also arise in the equations of motion if the dipole moment is too large, and when the `center-of-electromagnetic mass' is far from the `center-of-bare mass' (roughly speaking). These conditions are often quite restrictive. General equations of motion were also derived under the assumption that the particle can only interact with the radiative component of its self-field. These are much simpler than the equations derived using the full retarded self-field; as are the conditions required to recover the Lorentz-Dirac equation.Comment: 30 pages; significantly improved presentation; accepted for publication in Phys. Rev.

Motion in classical field theories and the foundations of the self-force problem

This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally associated with self-interacting point particles arise as straightforward perturbative limits of these (more fundamental) results. Additionally, generic mechanisms are discussed which dynamically shift --- i.e., renormalize --- the apparent multipole moments associated with self-interacting extended bodies. Although this is primarily a synthesis of earlier work, several new results and interpretations are included as well.Comment: 68 pages, 1 figur

A mechanism for the inhibition of DNA-PK-mediated DNA sensing by a virus

The innate immune system is critical in the response to infection by pathogens and it is activated by pattern recognition receptors (PRRs) binding to pathogen associated molecular patterns (PAMPs). During viral infection, the direct recognition of the viral nucleic acids, such as the genomes of DNA viruses, is very important for activation of innate immunity. Recently, DNA-dependent protein kinase (DNA-PK), a heterotrimeric complex consisting of the Ku70/Ku80 heterodimer and the catalytic subunit DNA-PKcs was identified as a cytoplasmic PRR for DNA that is important for the innate immune response to intracellular DNA and DNA virus infection. Here we show that vaccinia virus (VACV) has evolved to inhibit this function of DNA-PK by expression of a highly conserved protein called C16, which was known to contribute to virulence but by an unknown mechanism. Data presented show that C16 binds directly to the Ku heterodimer and thereby inhibits the innate immune response to DNA in fibroblasts, characterised by the decreased production of cytokines and chemokines. Mechanistically, C16 acts by blocking DNA-PK binding to DNA, which correlates with reduced DNA-PK-dependent DNA sensing. The C-terminal region of C16 is sufficient for binding Ku and this activity is conserved in the variola virus (VARV) orthologue of C16. In contrast, deletion of 5 amino acids in this domain is enough to knockout this function from the attenuated vaccine strain modified vaccinia virus Ankara (MVA). In vivo a VACV mutant lacking C16 induced higher levels of cytokines and chemokines early after infection compared to control viruses, confirming the role of this virulence factor in attenuating the innate immune response. Overall this study describes the inhibition of DNA-PK-dependent DNA sensing by a poxvirus protein, adding to the evidence that DNA-PK is a critical component of innate immunity to DNA viruses

Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system

We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent $\eta$. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high resolution molecular dynamics and Monte Carlo simulations. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than four, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behaviour observed in models of interface growth and for dissipative systems driven into a non-equilibrium steady state.Comment: 32 pages, 13 figures, 1 table. Few changes. To appear in Phys. Rev.