On the Penrose inequality for dust null shells in the Minkowski spacetime of arbitrary dimension

A particular, yet relevant, particular case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper we rewrite this inequality in terms of the geometry of the surface obtained by intersecting the past null cone of the original surface S with a constant time hyperplane and the "time height" function of S over this hyperplane. We also specialize to the case when S lies in the past null cone of a point and show the validity of the corresponding inequality in any dimension (in four dimensions this inequality was proved by Tod). Exploiting properties of convex hypersurfaces in Euclidean space we write down the Penrose inequality in the Minkowski spacetime of arbitrary dimension n+2 as an inequality for two smooth functions on the sphere. We finally obtain a sufficient condition for the validity of the Penrose inequality in the four dimensional Minkowski spacetime and show that this condition is satisfied by a large class of surfaces.Comment: 25 pages, 2 figures, Late

Geometry of normal graphs in Euclidean space and applications to the Penrose inequality in Minkowski

The Penrose inequality in Minkowski is a geometric inequality relating the total outer null expansion and the area of closed, connected and spacelike codimension-two surfaces S in the Minkowski spacetime, subject to an additional convexity assumption. In a recent paper, Brendle and Wang find a sufficient condition for the validity of this Penrose inequality in terms of the geometry of the orthogonal projection of S onto a constant time hyperplane. In this work, we study the geometry of hypersurfaces in n-dimensional euclidean space which are normal graphs over other surfaces and relate the intrinsic and extrinsic geometry of the graph with that of the base hypersurface. These results are used to rewrite Brendle and Wang's condition explicitly in terms of the time height function of S over a hyperplane and the geometry of the projection of S along its past null cone onto this hyperplane. We also include, in an Appendix, a self-contained summary of known and new results on the geometry of projections along the Killing direction of codimension two-spacelike surfaces in a strictly static spacetime.Comment: 15 pages, 1 figure, Late

Changes in school structure according to external stimuli : description and influence on acoustic assessment

The study of the internal school structure and behaviour of pelagic fish provides interesting information in relation to acoustic surveys, especially when comparing the undisturbed structure with the structure observed beneath a vessel passing over a school. The methodological approach involves in situ observations and combines acoustic and visual (aerial and underwater) techniques. The internal school structure is heterogeneous, including vacuoles, and this structure changes when the school is overpassed by a vessel during the day. In this case compression of the upper layer of the school is observed. The influence of this school structure on the variability of the density estimation has been studied. For the subsurface schools, the usual rate of sampling may be too low for some heterogenous schools. Other consequences of the school structure on acoustics are discussed. (Résumé d'auteur

Analysis of vessel influence on spatial behaviour of fish schools using a multi-beam sonar and consequences for biomass estimates by echo-sounder

Biases in the measurements of spatial distribution of fish schools and their consequences for school biomass estimates during conventional acoustic surveys are mainly due to vertical and lateral avoidance of the vessel. In this paper, we quantify school avoidance during an acoustic survey carried out from 10 to 29 May 1994 in the Catalan Sea. From a lateral multi-beam sonar the geometric characteristics (depth, length, width, height, surface, and volume) of 1268 schools were obtained. The 60 beams (1.5° X 15°) of the sonar scanned a vertical plane from 0° to 90°, perpendicular to the vessel path within a range of 100 m. Within this plane, the projected area ensonified by the echo-sounder used aboard for acoustic evaluation was evaluated to simulate a comparison between the sonar and the echo-sounder. The results have enabled us to improve our knowledge on the vertical and lateral avoidance patterns of schools in relation to their size, external structure, and their position in the water column, and to quantify the vessel influence on biomass estimated by echo-sounder. (Résumé d'auteur

Diel variability of school structure with special reference to transition periods

Pelagic fishes generally dispers at dusk and aggregate in schools at dawn. The dynamics (duration, variation in school number, and characteristics) of these two behavioural processes have been studied during a 26 h survey in a small area of high fish abundance in the Catalan Sea (Spain). The dynamics of aggregation and dispersion were investigated using a dual-beam vertical echo-sounder (BioSonics) connected to a special school integrator software package (INES-MOVIES-B) which estimates school parameters in terms of size, geometry, and density. This study shows that, during the night, fish dispersion is limited and schools can still be observed. They are characterized by a highly skewed distribution of the cross-sectional area (many small schools plus a few medium and large schools), low values of packing density and biomass, and irregular shape, while during the day there are only a few schools which have a lower variability of the area, high values of packing density, and a more regular shape. The dynamics of schooling are different between dawn (fast aggregation) and dusk (slower dispersion). (Résumé d'auteur

Structure et stabilité des bancs et agrégations de poissons pélagiques côtiers tropicaux : application halieutique

Afin de cerner le rôle du comportement animal dans les problèmes rencontrés lors de l'estimation des stocks de poissons pélagiques en halieutique par les méthodes d'évaluation directes (acoustique) et indirectes, nous avons entrepris l'étude, en milieu naturel, de la structure et de la stabilité des bancs de petits poissons pélagiques côtiers tropicaux (Clupéidés, Engraulidés). Cette étude est basée sur des observations acoustiques et visuelles (aériennes et sous-marines) simultanées... Nous comparons ces résultats avec ceux obtenus à partir de l'analyse d'une banque de données acoustiques constituée de 18 campagnes effectuées en milieu tropical d'une part, et d'autre part, de l'analyse acoustique de la variabilité d'une concentration de #Sardinella aurita$ suivie pendant 24 heures par un navire de recherche. A partir de ces observations nous proposons un schéma d'occupation spatiale des poissons grégaires. Ce schéma permet de rendre compte de la variabilité spatiale et temporelle de la structure des populations. L'influence des facteurs externes de contrôle et de régulation du comportement (facteur trophique, de prédation et de reproduction) sur la distribution spatiale des poissons pélagiques est discutée. (D'après résumé d'auteur

Distortion correction of two-component - two-dimensional PIV using a large imaging sensor with application to measurements of a turbulent boundary layer flow at Reτ=2386Re_{\tau} = 2386

In the past decade, advances in electronics technology have made larger imaging sensors available to the experimental fluid mechanics community. These advancements have enabled the measurement of 2-component 2-dimensional (2C-2D) velocity fields using particle image velocimetry (PIV) with much higher spatial resolution than previously possible. However, due to the large size of the sensor, the lens distortion needs to be taken into account as it will now have a more significant effect on the measurement quality that must be corrected to ensure accurate high-fidelity 2C-2D velocity field measurements. In this paper, two dewarping models, a second-order rational function (R2) and a bicubic polynomial (P3) are investigated with regards to 2C-2D PIV measurements of a turbulent boundary layer (TBL) using a large imaging sensor. Two approaches are considered and compared: (i) dewarping the images prior to the PIV cross-correlation analysis and (ii) undertaking the PIV cross-correlation analysis using the original recorded distorted images then followed by using the mapping functions derived for image dewarping to provide the correct spatial location of the velocity measurement point. The results demonstrate that the use of P3 dewarping model to correct lens distortion yields better results than the R2 dewarping model. Furthermore, both approaches for the P3 dewarping model yield results which are statistically indistinguishable