The Square Root Depth Wave Equations

We introduce a set of coupled equations for multilayer water waves that removes the ill-posedness of the multilayer Green-Naghdi (MGN) equations in the presence of shear. The new well-posed equations are Hamiltonian and in the absence of imposed background shear they retain the same travelling wave solutions as MGN. We call the new model the Square Root Depth equations, from the modified form of their kinetic energy of vertical motion. Our numerical results show how the Square Root Depth equations model the effects of multilayer wave propagation and interaction, with and without shear.Comment: 10 pages, 5 figure

A Constrained Approach to Multiscale Stochastic Simulation of\ud Chemically Reacting Systems

Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper we introduce a multiscale methodology suitable to address this problem. It is based on the Conditional Stochastic Simulation Algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the Constrained Multiscale Algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Stochastic Differential Equation (SDE) approximation, we can in turn approximate average switching times in stochastic chemical systems

The Redshift Distribution of FIRST Radio Sources at 1 mJy

We present spectra for a sample of radio sources from the FIRST survey, and use them to define the form of the redshift distribution of radio sources at mJy levels.We targeted 365 sources and obtained 46 redshifts (13 per cent of the sample). We find that our sample is complete in redshift measurement to R $\sim 18.6$, corresponding to $z\sim 0.2$. Early-type galaxies represent the largest subset (45 per cent) of the sample and have redshifts 0.15\la z \la 0.5 ; late-type galaxies make up 15 per cent of the sample and have redshifts 0.05\la z \la 0.2; starbursting galaxies are a small fraction ($\sim 6$ per cent), and are very nearby (z\la 0.05). Some 9 per cent of the population have Seyfert1/quasar-type spectra, all at z\ga 0.8, and there are 4 per cent are Seyfert2 type galaxies at intermediate redshifts ($z\sim 0.2$). Using our measurements and data from the Phoenix survey, we obtain an estimate for $N(z)$ at $S_{1.4 \rm {GHz}}\ge 1$ mJy and compare this with model predictions. At variance with previous conclusions, we find that the population of starbursting objects makes up \la 5 per cent of the radio population at S $\sim 1$ mJy.Comment: 20 pages, sumbitted to MNRA

Defences against brood parasites from a social immunity perspective

Parasitic interactions are so ubiquitous that all multicellular organisms have evolved a system of defences to reduce their costs, whether the parasites they encounter are the “classic parasites” that feed on the individual, or “brood parasites” that usurp parental care. Many parallels have been drawn between defences deployed against both types of parasite, but typically, whilst defences against classic parasites have been selected to protect survival, those against brood parasites have been selected to protect the parent’s inclusive fitness, suggesting that the selection pressures they impose are fundamentally different. However, there is another class of defences against classic parasites that have specifically been selected to protect an individual’s inclusive fitness, known as “social immunity”. Social immune responses include the anti-parasite defences typically provided for others in kin-structured groups, such as the antifungal secretions produced by termite workers to protect the brood. Defences against brood parasites, therefore, are more closely aligned with social immune responses. Much like social immunity, host defences against brood parasitism are employed by a donor (a parent) for the benefit of one or more recipients (typically kin), and as with social defences against classic parasites, defences have therefore evolved to protect the donor’s inclusive fitness, not the survival or ultimately the fitness of individual recipients This can lead to severe conflicts between the different parties, whose interests are not always aligned. Here we consider defences against brood parasitism in the light of social immunity, at different stages of parasite encounter, addressing where conflicts occur and how they might be resolved. We finish with considering how this approach could help us to address longstanding questions in our understanding of brood parasitism.Peer reviewe

Variational water-wave model with accurate dispersion and vertical vorticity

A new water-wave model has been derived which is based on variational techniques and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite-element profile with a small number of elements (say), leading to a framework for efficient modeling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves

Characteristics of Gamma-Ray Loud Blazars in the VLBA Imaging and Polarimetry Survey

The radio properties of blazars detected by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope have been observed as part of the VLBA Imaging and Polarimetry Survey (VIPS). This large, flux-limited sample of active galactic nuclei (AGN) provides insights into the mechanism that produces strong gamma-ray emission. At lower flux levels, radio flux density does not directly correlate with gamma-ray flux. We find that the LAT-detected BL Lacs tend to be similar to the non-LAT BL Lacs, but that the LAT-detected FSRQs are often significantly different from the non-LAT FSRQs. The differences between the gamma-ray loud and quiet FSRQs can be explained by Doppler boosting; these objects appear to require larger Doppler factors than those of the BL Lacs. It is possible that the gamma-ray loud FSRQs are fundamentally different from the gamma-ray quiet FSRQs. Strong polarization at the base of the jet appears to be a signature for gamma-ray loud AGN.Comment: 32 pages, 9 figures, accepted by Ap

Continuous and discrete Clebsch variational principles

The Clebsch method provides a unifying approach for deriving variational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group \emph{via} a velocity map. This paper proves a reduction theorem which states that the canonical variables on the Lie group can be eliminated, if and only if the velocity map is a Lie algebra action, thereby producing the Euler-Poincar\'e (EP) equation for the vector space variables. In this case, the map from the canonical variables on the Lie group to the vector space is the standard momentum map defined using the diamond operator. We apply the Clebsch method in examples of the rotating rigid body and the incompressible Euler equations. Along the way, we explain how singular solutions of the EP equation for the diffeomorphism group (EPDiff) arise as momentum maps in the Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch variational principle is discretised to produce a variational integrator for the dynamical system. We obtain a discrete map from which the variables on the cotangent bundle of a Lie group may be eliminated to produce a discrete EP equation for elements of the vector space. We give an integrator for the rotating rigid body as an example. We also briefly discuss how to discretise infinite-dimensional Clebsch systems, so as to produce conservative numerical methods for fluid dynamics

ENVIROSAT-2000 report: Federal agency satellite requirements

The requirement of Federal agencies, other than NOAA, for the data and services of civil operational environmental satellites (both polar orbiting and geostationary) are summarized. Agency plans for taking advantage of proposed future Earth sensing space systems, domestic and foreign, are cited also. Current data uses and future requirements are addressed as identified by each agency

Completeness and confusion in the identification of Lyman-break galaxies

We have carried out a study to simulate distant clusters of galaxies in deep ground-based optical images. We find that when model galaxies are added to deep images obtained with the William Herschel Telescope, there is considerable scatter of the recovered galaxy colours away from the model values; this scatter is larger than that expected from photometric errors and is significantly affected by confusion, due to ground-based seeing, between objects in the field. In typical conditions of $\approx$ 1-arcsec seeing, the combination of confusion and incompleteness causes a considerable underestimation of the true surface density of $z \approx 3$ galaxies. We argue that the actual surface density of $z \approx 3$ galaxies may be several times greater than that estimated by previous ground-based studies, consistent with the surface density of such objects found in the HDF

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio