The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method

The periodic standing wave (PSW) method for the binary inspiral of black holes and neutron stars computes exact numerical solutions for periodic standing wave spacetimes and then extracts approximate solutions of the physical problem, with outgoing waves. The method requires solution of a boundary value problem with a mixed (hyperbolic and elliptic) character. We present here a new numerical method for such problems, based on three innovations: (i) a coordinate system adapted to the geometry of the problem, (ii) an expansion in multipole moments of these coordinates and a filtering out of higher moments, and (iii) the replacement of the continuum multipole moments with their analogs for a discrete grid. We illustrate the efficiency and accuracy of this method with nonlinear scalar model problems. Finally, we take advantage of the ability of this method to handle highly nonlinear models to demonstrate that the outgoing approximations extracted from the standing wave solutions are highly accurate even in the presence of strong nonlinearities.Comment: RevTex, 32 pages, 13 figures, 6 table

The periodic standing-wave approximation: eigenspectral computations for linear gravity and nonlinear toy models

The periodic standing wave approach to binary inspiral assumes rigid rotation of gravitational fields and hence helically symmetric solutions. To exploit the symmetry, numerical computations must solve for ``helical scalars,'' fields that are functions only of corotating coordinates, the labels on the helical Killing trajectories. Here we present the formalism for describing linearized general relativity in terms of helical scalars and we present solutions to the mixed partial differential equations of the linearized gravity problem (and to a toy nonlinear problem) using the adapted coordinates and numerical techniques previously developed for scalar periodic standing wave computations. We argue that the formalism developed may suffice for periodic standing wave computations for post-Minkowskian computations and for full general relativity.Comment: 21 pages, 10 figures, RevTe

Trace fossil Artichnus pholeoides igen. nov. isp. nov. in Eocene turbidites, Polish Carpathians : possible ascription to holothurians

A hitherto unknown trace fossil was found in some abundance in turbidites of the Polish Outer Carpathians. The occurrence is within the Hieroglyphic Beds of the Silesian Nappe, within the Szczyrzyc Synclinorium, of Middle Eocene age. The trace fossil is a wide, J-shaped structure having a narrow, upward tapering shaft as a connection to the seafloor. The distal end also tapers, to a blind termination. The burrow lumen is surrounded by an irregular spreite structure. The trace fossil is compared with the work of burrowing holothurians, which show some comparative features that suggest a tracemaker belonging to the Apodida

The periodic standing-wave approximation: post-Minkowski computation

The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling motion of black holes and binary stars. Previous work on this model has dealt with nonlinear scalar models, and with linearized general relativity. Here we present the results of the method for the post-Minkowski (PM) approximation to general relativity, the first step beyond linearized gravity. We compute the PM approximation in two ways: first, via the standard approach of computing linearized gravitational fields and constructing from them quadratic driving sources for second-order fields, and second, by solving the second-order equations as an ``exact'' nonlinear system. The results of these computations have two distinct applications: (i) The computational infrastructure for the ``exact'' PM solution will be directly applicable to full general relativity. (ii) The results will allow us to begin supplying initial data to collaborators running general relativistic evolution codes.Comment: 19 pages, 3 figures, 1 table, RevTe

S’Estret des Temps: registro cuaternario, eolianitas y estructuras asociadas

Abstract not availabl

Problems in Interpreting Unusually Large Burrows

Although marine burrows of unusually large dimensions have long been known in certain areas, they are probably much more widespread in the rock record than is generally recognized. Such burrows constitute a heterogeneous group, having little in common other than exceptional size. Yet their size alone unites them in difficulty of interpretation: e.g., densely spaced-dwelling burrows of combined dwelling-escape burrows as much as 12 cm in diameter and 5 m long; vertical dwelling burrows only 0.5 cm in diameter but up to 9 m long; possible escape structures as much as 24 cm in diameter and 3 m long, subsequently penetrated in some cases by secondary burrow-like structures. Numerous special problems are encountered in the study and interpretation of burrows of these extreme dimensions: (1) field exposure and accessibility, so that the full extent, or a large part, of the structures can be studied; (2) preservation of the burrows in continuity, not merely in places where they pass through certain beds or within concretion horizons; (3) the fossilization barrier ; our knowledge of comparable modern structures of similar dimensions or of the animals responsible for them is negligible; and (4) the possibility that certain of these unusual structures were formed by physical rather than organic processes; again, our criteria for comparisons are limited. The examples selected by us—from the Permian of Montana, Idaho, and Wyoming, the Cretaceous and Paleocene of northwestern Europe, and the Pleistocene of North Carolina—are intended primarily (1) to call additional attention to such intriguing structures, and (2) to illustrate some of the problems involved in interpreting their origin and function. Hopefully, future work will solve many of these problems

A single and rapid calcium wave at egg activation in Drosophila.

Activation is an essential process that accompanies fertilisation in all animals and heralds major cellular changes, most notably, resumption of the cell cycle. While activation involves wave-like oscillations in intracellular Ca(2+) concentration in mammals, ascidians and polychaete worms and a single Ca(2+) peak in fish and frogs, in insects, such as Drosophila, to date, it has not been shown what changes in intracellular Ca(2+) levels occur. Here, we utilise ratiometric imaging of Ca(2+) indicator dyes and genetically encoded Ca(2+) indicator proteins to identify and characterise a single, rapid, transient wave of Ca(2+) in the Drosophila egg at activation. Using genetic tools, physical manipulation and pharmacological treatments we demonstrate that the propagation of the Ca(2+) wave requires an intact actin cytoskeleton and an increase in intracellular Ca(2+) can be uncoupled from egg swelling, but not from progression of the cell cycle. We further show that mechanical pressure alone is not sufficient to initiate a Ca(2+) wave. We also find that processing bodies, sites of mRNA decay and translational regulation, become dispersed following the Ca(2+) transient. Based on this data we propose the following model for egg activation in Drosophila: exposure to lateral oviduct fluid initiates an increase in intracellular Ca(2+) at the egg posterior via osmotic swelling, possibly through mechano-sensitive Ca(2+) channels; a single Ca(2+) wave then propagates in an actin dependent manner; this Ca(2+) wave co-ordinates key developmental events including resumption of the cell cycle and initiation of translation of mRNAs such as bicoid.This work was supported by the University of Cambridge, ISSF to T.T.W. [grant number 097814]; and Wellcome Trust Senior Research Fellowship to I.D. [grant number 096144].This is the final version of the article. It first appeared from the Company of Biologists via http://dx.doi.org/10.1242/bio.20141129