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Romain Gicquaud - One of the best experts on this subject based on the ideXlab platform.
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Limit Equation for vacuum einstein constraints with a translational killing vector field in the compact hyperbolic case
Journal of Geometry and Physics, 2016Co-Authors: Romain Gicquaud, Cecile HuneauAbstract:Abstract We construct solutions to the constraint Equations in general relativity using the Limit Equation criterion introduced in Dahl et al. (2012). We focus on solutions over compact 3-manifolds admitting a S 1 -symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.
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Limit Equation for vacuum einstein constraints with a translational killing vector field in the compact hyperbolic case
arXiv: General Relativity and Quantum Cosmology, 2014Co-Authors: Romain Gicquaud, Cecile HuneauAbstract:We construct solutions to the constraint Equations in general relativity using the Limit Equation criterion introduced by Dahl, Humbert and the first author. We focus on solutions over compact 3-manifolds admitting a $\bS^1$-symmetry group. When the quotient manifold has genus greater than 2, we obtain strong far from CMC results.
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a Limit Equation associated to the solvability of the vacuum einstein constraint Equations by using the conformal method
Duke Mathematical Journal, 2012Co-Authors: Mattias Dahl, Romain Gicquaud, Emmanuel HumbertAbstract:Let (M, g) be a compact Riemannian manifold on which a trace-free and divergence-free sigma is an element of W-1,W-p and a positive function tau is an element of W-1,W-p, p > n are fixed. In thi ...
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A large class of non constant mean curvature solutions of the Einstein constraint Equations on an asymptotically hyperbolic manifold
Communications in Mathematical Physics, 2012Co-Authors: Romain Gicquaud, Anna SakovichAbstract:We construct solutions of the constraint Equation with non constant mean curvature on an asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain exponent appearing in the Equations, constructing solutions of these sub-critical Equations and then in letting the exponent tend to its true value. We prove that the solutions of the sub-critical Equations remain bounded which yields solutions of the constraint Equation unless a certain Limit Equation admits a non-trivial solution. Finally, we give conditions which ensure that the Limit Equation admits no non-trivial solution.
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a Limit Equation associated to the solvability of the vacuum einstein constraint Equations using the conformal method
arXiv: General Relativity and Quantum Cosmology, 2010Co-Authors: Mattias Dahl, Romain Gicquaud, Emmanuel HumbertAbstract:Let $(M,g)$ be a compact Riemannian manifold on which a trace-free and divergence-free $\sigma \in W^{1,p}$ and a positive function $\tau \in W^{1,p}$, $p > n$, are fixed. In this paper, we study the vacuum Einstein constraint Equations using the well known conformal method with data $\sigma$ and $\tau$. We show that if no solution exists then there is a non-trivial solution of another non-linear Limit Equation on $1$-forms. This last Equation can be shown to be without solutions no solution in many situations. As a corollary, we get existence of solutions of the vacuum Einstein constraint Equation under explicit assumptions which in particular hold on a dense set of metrics $g$ for the $C^0$-topology.
M Lambert - One of the best experts on this subject based on the ideXlab platform.
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ballistic Limit Equation for equipment placed behind satellite structure walls
International Journal of Impact Engineering, 2008Co-Authors: Frank K Schafer, S. Ryan, M Lambert, Robin PutzarAbstract:Abstract A new ballistic Limit Equation has been developed for the case of a Whipple shield configuration or a sandwich panel with honeycomb core placed in front of a backwall. This “triple plate” ballistic Limit Equation considers explicitly the thicknesses, materials and spacings of each of the three plates. The third plate, i.e., the backwall, represents the cover plate or external wall of the equipment that is placed behind the satellite structure wall. The ballistic Limit Equation has been calibrated with experimental results obtained from hypervelocity impact tests on satellite equipment that was placed behind typical satellite structure walls. The equipment considered were fuel and heat pipes, pressure vessels, electronic boxes, harness, and batteries, all representative of real satellite equipment. The new Equation was applied to prove that if the inherent protection capability of satellite equipment against hypervelocity impacts is explicitly considered in a ballistic Limit Equation, the critical projectile diameters for failure of such equipment are raised considerably compared to the case where equipment is assumed to fail as soon as the structure wall that protects it is perforated.
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a ballistic Limit Equation for hypervelocity impacts on composite honeycomb sandwich panel satellite structures
Advances in Space Research, 2008Co-Authors: S. Ryan, F Schaefer, R Destefanis, M LambertAbstract:During a recent experimental test campaign performed in the framework of ESA Contract 16721, the ballistic performance of multiple satellite-representative Carbon Fibre Reinforced Plastic (CFRP)/Aluminium honeycomb sandwich panel structural configurations (GOCE, Radarsat-2, Herschel/Planck, BeppoSax) was investigated using the two-stage light-gas guns at EMI. The experimental results were used to develop and validate a new empirical Ballistic Limit Equation (BLE), which was derived from an existing Whipple-shield BLE. This new BLE provided a good level of accuracy in predicting the ballistic performance of stand-alone sandwich panel structures. Additionally, the Equation is capable of predicting the ballistic Limit of a thin Al plate located at a standoff behind the sandwich panel structure. This thin plate is the representative of internal satellite systems, e.g. an Al electronic box cover, a wall of a metallic vessel, etc. Good agreement was achieved with both the experimental test campaign results and additional test data from the literature for the vast majority of set-ups investigated. For some experiments, the ballistic Limit was conservatively predicted, a result attributed to shortcomings in correctly accounting for the presence of high surface density multi-layer insulation on the outer facesheet. Four existing BLEs commonly applied for application with stand-alone sandwich panels were reviewed using the new impact test data. It was found that a number of these common approaches provided non-conservative predictions for sandwich panels with CFRP facesheets.
S. Ryan - One of the best experts on this subject based on the ideXlab platform.
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ballistic Limit Equation for equipment placed behind satellite structure walls
International Journal of Impact Engineering, 2008Co-Authors: Frank K Schafer, S. Ryan, M Lambert, Robin PutzarAbstract:Abstract A new ballistic Limit Equation has been developed for the case of a Whipple shield configuration or a sandwich panel with honeycomb core placed in front of a backwall. This “triple plate” ballistic Limit Equation considers explicitly the thicknesses, materials and spacings of each of the three plates. The third plate, i.e., the backwall, represents the cover plate or external wall of the equipment that is placed behind the satellite structure wall. The ballistic Limit Equation has been calibrated with experimental results obtained from hypervelocity impact tests on satellite equipment that was placed behind typical satellite structure walls. The equipment considered were fuel and heat pipes, pressure vessels, electronic boxes, harness, and batteries, all representative of real satellite equipment. The new Equation was applied to prove that if the inherent protection capability of satellite equipment against hypervelocity impacts is explicitly considered in a ballistic Limit Equation, the critical projectile diameters for failure of such equipment are raised considerably compared to the case where equipment is assumed to fail as soon as the structure wall that protects it is perforated.
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a ballistic Limit Equation for hypervelocity impacts on composite honeycomb sandwich panel satellite structures
Advances in Space Research, 2008Co-Authors: S. Ryan, F Schaefer, R Destefanis, M LambertAbstract:During a recent experimental test campaign performed in the framework of ESA Contract 16721, the ballistic performance of multiple satellite-representative Carbon Fibre Reinforced Plastic (CFRP)/Aluminium honeycomb sandwich panel structural configurations (GOCE, Radarsat-2, Herschel/Planck, BeppoSax) was investigated using the two-stage light-gas guns at EMI. The experimental results were used to develop and validate a new empirical Ballistic Limit Equation (BLE), which was derived from an existing Whipple-shield BLE. This new BLE provided a good level of accuracy in predicting the ballistic performance of stand-alone sandwich panel structures. Additionally, the Equation is capable of predicting the ballistic Limit of a thin Al plate located at a standoff behind the sandwich panel structure. This thin plate is the representative of internal satellite systems, e.g. an Al electronic box cover, a wall of a metallic vessel, etc. Good agreement was achieved with both the experimental test campaign results and additional test data from the literature for the vast majority of set-ups investigated. For some experiments, the ballistic Limit was conservatively predicted, a result attributed to shortcomings in correctly accounting for the presence of high surface density multi-layer insulation on the outer facesheet. Four existing BLEs commonly applied for application with stand-alone sandwich panels were reviewed using the new impact test data. It was found that a number of these common approaches provided non-conservative predictions for sandwich panels with CFRP facesheets.
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A ballistic Limit Equation for hypervelocity impacts on CFRP Al H/C satellite structures
2006Co-Authors: S. RyanAbstract:Composite sandwich panels consisting of Carbon Fiber Reinforced Plastic facesheets bonded to Aluminum honeycomb cores (CFRP Al H/C SP) are amongst the most commonly used structures for satellites due to their relative low mass and high thermal and mechanical stability. To assess the threat of micrometeoroid/orbital debris (M/OD) on a satellite mission, Equations which define the Limits of structural perforation in terms of impactor mass, velocity and angle are required. This type of Equation is referred to as a Ballistic Limit Equation (BLE). There is presently no validated BLE existing for application in the risk assessment of CFRP Al H/C SP structures.
Juan Soler - One of the best experts on this subject based on the ideXlab platform.
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High-Field Limit for the Vlasov-Poisson-Fokker-Planck System
Archive for Rational Mechanics and Analysis, 2001Co-Authors: Juan Nieto, Frédéric Poupaud, Juan SolerAbstract:This paper is concerned with the analysis of the stability of the Vlasov-PoissonFokker-Planck system with respect to the physical constants. If the scaled thermal mean free path converges to zero and the scaled thermal velocity remains constant, then a hyperbolic Limit or equivalently a high-field Limit Equation is obtained for the mass density. The passage to the Limit as well as the existence and uniqueness of solutions of the Limit Equation in L 1 , global or local in time, are analyzed according to the electrostatic or gravitational character of the field and to the space dimension. In the one-dimensional case a new concept of global solution is introduced. For the gravitational field this concept is shown to be equivalent to the concept of entropy solutions of hyperbolic systems of conservation laws.
Zhitao Zhang - One of the best experts on this subject based on the ideXlab platform.
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the Limit Equation for the gross pitaevskii Equations and s terraciniʼs conjecture
Journal of Functional Analysis, 2012Co-Authors: E. N. Dancer, Kelei Wang, Zhitao ZhangAbstract:Abstract We establish the Limit system for the Gross–Pitaevskii Equations when the segregation phenomenon appears, and shows this Limit is the one arising from the competing systems in population dynamics. This covers and verifies a conjecture of S. Terracini et al., both in the parabolic case and the elliptic case.
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The Limit Equation for the Gross–Pitaevskii Equations and S. Terraciniʼs conjecture
Journal of Functional Analysis, 2012Co-Authors: E. N. Dancer, Kelei Wang, Zhitao ZhangAbstract:Abstract We establish the Limit system for the Gross–Pitaevskii Equations when the segregation phenomenon appears, and shows this Limit is the one arising from the competing systems in population dynamics. This covers and verifies a conjecture of S. Terracini et al., both in the parabolic case and the elliptic case.