Rotating strings

Analytical expressions are provided for the configurations of an inextensible, flexible, twistable inertial string rotating rigidly about a fixed axis. Solutions with trivial radial dependence are helices of arbitrary radius and pitch. Non-helical solutions are governed by a cubic equation whose roots delimit permissible values of the squared radial coordinate. Only curves coplanar with the axis of rotation make contact with it.Comment: added to discussion and made small revisions to tex

Dynamical Renormalization Group Study for a Class of Non-local Interface Equations

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and the less studied case in which pattern formation occurs, for which flat surfaces are linearly unstable to periodic perturbations. We show that the latter leads to non-trivial scaling behavior in an appropriate parameter range when combined with the Kardar-Parisi-Zhang (KPZ) non-linearity, that nevertheless does not correspond to the KPZ universality class. This novel asymptotic behavior is characterized by two scaling laws that fix the critical exponents to dimension-independent values, that agree with previous reports from numerical simulations and experimental systems. We show that the precise form of the linear stabilizing terms does not modify the hydrodynamic behavior of these equations. One of the scaling laws, usually associated with Galilean invariance, is shown to derive from a vertex cancellation that occurs (at least to one loop order) for any choice of linear terms in the equation of motion and is independent on the morphological stability of the surface, hence generalizing this well-known property of the KPZ equation. Moreover, the argument carries over to other systems like the Lai-Das Sarma-Villain equation, in which vertex cancellation is known {\em not to} imply an associated symmetry of the equation.Comment: 34 pages, 9 figures. Journal of Statistical Mechanics: Theory and Experiments (in press

UK Large-scale Wind Power Programme from 1970 to 1990: the Carmarthen Bay experiments and the Musgrove Vertical-Axis Turbines

This article describes the development of the Musgrove Vertical Axis Wind Turbine (VAWT) concept, the UK ‘Carmarthen Bay’ wind turbine test programme, and UK government’s wind power programme to 1990. One of the most significant developments in the story of British wind power occurred during the 1970s, 1980s, and 1990s, with the development of the Musgrove vertical axis wind turbine and its inclusion within the UK Government’s wind turbine test programme. Evolving from a supervisor’s idea for an undergraduate project at Reading University, the Musgrove VAWT was once seen as an able competitor to the horizontal axis wind systems that were also being encouraged at the time by both the UK government and the Central Electricity Generating Board, the then nationalised electricity utility for England and Wales. During the 1980s and 1990s the most developed Musgrove VAWT system, along with three other commercial turbine designs was tested at Carmarthen Bay, South Wales as part of a national wind power test programme. From these developmental tests, operational data was collected and lessons learnt, which were incorporated into subsequent wind power operations.http://dx.doi.org/10.1260/03095240677860621

Type Ia Supernova Explosion Models

Because calibrated light curves of Type Ia supernovae have become a major tool to determine the local expansion rate of the Universe and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most Type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, M_ch ~ 1.39 M_sun, and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling Type Ia supernovae as well as several of the still open questions are addressed in this review. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics of turbulent nuclear combustion in degenerate stars, we also discuss observational constraints.Comment: 38 pages, 4 figures, Annual Review of Astronomy and Astrophysics, in pres

Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation

Using pole decompositions as starting points, the one parameter (-1 =< c < 1) nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of premixed gaseous flames is studied in the large-wrinkle limit. The singular integral equations for pole densities are closely related to those satisfied by the spectral density in the O(n) matrix model, with n = -2(1 + c)/(1 - c). They can be solved via the introduction of complex resolvents and the use of complex analysis. We retrieve results obtained recently for -1 =< c =< 0, and we explain and cure their pathologies when they are continued naively to 0 < c < 1. Moreover, for any -1 =< c < 1, we derive closed-form expressions for the shapes of steady isolated flame crests, and then bicoalesced periodic fronts. These theoretical results fully agree with numerical resolutions. Open problems are evoked.Comment: v2: 29 pages, 6 figures, some typos correcte

Sur une forme remarquable des équations de Maxwell-Lorentz dans l'univers à 5 dimensions

En admettant, suivant une suggestion de M. L. de Broglie, que l'équation dite complémentaire de Lorentz [FORMULE] doive être abandonnée, ajoutons au 1er membre un nouveau terme ∂b/∂x° où x° représente la 5e dimension de l'univers de Kaluza et Klein, et b, une 5e composante du potentiel d'univers, dont les 4 autres composantes sont le potentiel scalaire ψ et le potentiel vecteur a. L'hypothèse [FORMULE] où U représente le courant d'univers généralisé par l'adjonction, aux 4 composantes que donnent la densité d'électricité p et le vecteur courant C'c, d'une 5e composante β = -Δb + 1/c² . ∂²b/∂t² réduit les 5 équations de propagation telles que : Ψ = ΔΨ - 1/c² . ∂²Ψ/∂t² à l'unique équation [FORMULE]

Le mouvement des lignes d'induction et les travaux du Pr S. R. Milner

A la notion des lignes d'induction de Faraday, qui peuvent être, soit magnétiques, soit électriques, la considération des lois de transformation des grandeurs du champ électromagnétique qu'exprime le groupe de Lorentz, amène à substituer celle d'un système unique orthogonal de directions privilégiées dans l'univers quadridimensionnel. L'association au polyaxe de référence ainsi défini de manière absolue en chaque point, de deux invariants R et α tels que R² e^(2iα) = e² - h² + i.2(eh)(où e et h désignent les vecteurs électrique et magnétique) permet de traduire les lois du champ (équations de Maxwell) en simples relations de géométrie différentielle qui régissent la convergence et la torsion des directions caractéristiques du champ, et remplacent les anciennes relations de conservation. La notion de tube élémentaire d'induction, en tant qu'entité physique persistant au cours du temps, ne peut être maintenue en général, mais doit être remplacée par celle d'éléments quadridimensionnels présentant, avec la densité R², un contenu d'action égal au quantum h de Planck, et aux deux sections orthogonales duquel (xt et yz) se trouvent respectivement associés les deux facteurs e, quantum d'électricité, et ϕ quantum de flux magnétique, du produit h = eϕ. Ces éléments d'action donnent une expression concrète au principe d'indétermination d'Heisenberg pour le champ électromagnétique, et suggèrent maints rapprochements, tant avec d'autres travaux récents (théorie de la charge électrique d'Eddington, lignes singulières d'indétermination de la phase de la fonction d'onde de Dirac, théories unitaires... etc), qu'avec ceux plus anciens de Cunningham, Bateman, F. Klein, soulignant le domaine d'invariance, plus étendu que le groupe de Lorentz, des équations de Maxwell, et laissant entrevoir les ressources d'une représentation conforme généralisée

Note sur la réforme de l’enseignement.

Avis membre de l'académie des science