Dynamics of Special Points on Intermediate Jacobians

We prove some general density statements about the subgroup of invertible points on intermediate jacobians; namely those points in the Abel-Jacobi image of nullhomologous algebraic cycles on projective algebraic manifolds.Comment: 10 page

Modeling water waves beyond perturbations

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein-Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.Comment: 15 pages, 1 figure, 39 references. This document is a contributed chapter to an upcoming volume to be published by Springer in Lecture Notes in Physics Series. Other author's papers can be downloaded at http://www.denys-dutykh.com

The magnetic field topology associated to two M flares

On 27 October, 2003, two GOES M-class flares occurred in the lapse of three hours in active region NOAA 10486. The two flares were confined and their associated brightenings appeared at the same location, displaying a very similar shape both at the chromospheric and coronal levels. We focus on the analysis of magnetic field (SOHO/MDI), chromospheric (HASTA, Kanzelhoehe Solar Observatory, TRACE) and coronal (TRACE) observations. By combining our data analysis with a model of the coronal magnetic field, we compute the magnetic field topology associated to the two M flares. We find that both events can be explained in terms of a localized magnetic reconnection process occurring at a coronal magnetic null point. This null point is also present at the same location one day later, on 28 October, 2003. Magnetic energy release at this null point was proposed as the origin of a localized event that occurred independently with a large X17 flare on 28 October, 2003, at 11:01 UT. The three events, those on 27 October and the one on 28 October, are homologous. Our results show that coronal null points can be stable topological structures where energy release via magnetic reconnection can happen, as proposed by classical magnetic reconnection models.Comment: 14 pages, 7 figure

Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat

Identification of host odour attractants for tsetse flies. Final report 1986-1990

Tsetse flies, Glossina spp., are blood-feeding insects and vectors of trypanosomes, microorganisms which cause sleeping sickness in man and a similar disease, "nagana" in domestic animals. The economic importance of trypanosomiasis is the constraint it imposes on orderly rural development in Africa, leading to under-exploitation of infested land and over-exploitation and degradation of trypanosomiasis-free areas. Traps and targets which attract tsetse flies and kill them could provide environmentally-acceptable, appropriate technology for monitoring and control of tsetse in Africa. Unbaited devices providing only visual attraction have proved effective in monitoring and control of riverine species of tsetse, but not the savannah species found in the fly belt of Malawi, Mozambique, Zambia and Zimbabwe covered by the EDF Regional Tsetse and Trypanosomiasis Control Project (RTTCP). Previously, collaborative was begun between glossinologists of the Zimbabwe Department of Veterinary Services (DVS) and UK Tsetse Research Laboratory (TRL) and chemists at NRI. This brought together the experience of the DVS in the field, the experience of TRL in laboratory bioassay work, and the experience of NRI in using gas chromatography linked to electroantennography (GC-EAG) and chemical techniques to detect and identify insect behaviour-modifying chemicals. Tsetse attractants produced by host animals were identified and synthesised, and dispensing systems for these compounds devised. Traps and targets impregnated with insecticide, baited with these lures were shown to provide effective control of the savannah tsetse species, G. pallidipes and G. m. morsitans

General Relativity as an Attractor in Scalar-Tensor Stochastic Inflation

Quantum fluctuations of scalar fields during inflation could determine the very large-scale structure of the universe. In the case of general scalar-tensor gravity theories these fluctuations lead to the diffusion of fundamental constants like the Planck mass and the effective Brans--Dicke parameter, $\omega$. In the particular case of Brans--Dicke gravity, where $\omega$ is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a theory with variable $\omega$ we find stationary probability distributions with a finite value of the Planck mass peaked at exponentially large values of $\omega$ after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.Comment: LaTeX (with RevTex) 11 pages, 2 uuencoded figures appended, also available on WWW via http://star.maps.susx.ac.uk/index.htm

Marginal deformation of N=4 SYM and Penrose limits with continuum spectrum

We study the Penrose limit about a null geodesic with 3 equal angular momenta in the recently obtained type IIB solution dual to an exactly marginal $\gamma$-deformation of N=4 SYM. The resulting background has non-trivial NS 3-form flux as well as RR 5- and 3-form fluxes. We quantise the light-cone Green-Schwarz action and show that it exhibits a continuum spectrum. We show that this is related to the dynamics of a charged particle moving in a Landau plane with an extra interaction induced by the deformation. We interpret the results in the dual N=1 SCFT.Comment: 26 pages, 2 figures; v2: typos corrected, field theory interpretation extende

Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model

We investigate here the ability of a Green-Naghdi model to reproduce strongly nonlinear and dispersive wave propagation. We test in particular the behavior of the new hybrid finite-volume and finite-difference splitting approach recently developed by the authors and collaborators on the challenging benchmark of waves propagating over a submerged bar. Such a configuration requires a model with very good dispersive properties, because of the high-order harmonics generated by topography-induced nonlinear interactions. We thus depart from the aforementioned work and choose to use a new Green-Naghdi system with improved frequency dispersion characteristics. The absence of dry areas also allows us to improve the treatment of the hyperbolic part of the equations. This leads to very satisfying results for the demanding benchmarks under consideration

Illusions of general relativity in Brans-Dicke gravity

Contrary to common belief, the standard tenet of Brans-Dicke theory reducing to general relativity when omega tends to infinity is false if the trace of the matter energy-momentum tensor vanishes. The issue is clarified in a new approach using conformal transformations. The otherwise unaccountable limiting behavior of Brans-Dicke gravity is easily understood in terms of the conformal invariance of the theory when the sources of gravity have radiation-like properties. The rigorous computation of the asymptotic behavior of the Brans-Dicke scalar field is straightforward in this new approach.Comment: 16 pages, LaTeX, to appear in Physical Review