Search results for "FLATNESS"
showing 10 items of 23 documents
The Joining of LiNbO3, Quartz, TlBr-TlI and Other Optical Materials by the Use of Thin Metal Films as Bonding Agents
2000
A method of joining ferroelectric, optical and other non-metallic materials, such as lithium niobate, quartz, TlBr-TlI, glass, etc., at room temperature under a pressure of 0.1÷0.5 MPa is described. The surfaces to be joined are prepared to optical flatness, and indium or lead coatings as bonding agents are used. To obtain clean surfaces, procedures of the coating deposition and sample joining are performed in situ in a vacuum of l0-4 Pa. The strength of the obtained joints is about 20MPa for indium coatings and about 30MPa for lead coatings. It is supposed that attractive surface forces play a decisive role in the contact formation and bonding of the wafers. The method has been applied for…
Local Gauge Conditions for Ellipticity in Conformal Geometry
2013
In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an $n$-harmonic coordinate system and normalizing the determinant of the metric. We also give corresponding elliptic regularity results and characterizations of local conformal flatness in low regularity settings.
The Calderón problem with partial data on manifolds and applications
2013
We consider Calderon's inverse problem with partial data in dimensions $n \geq 3$. If the inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction, we show that this problem reduces to the invertibility of a broken geodesic ray transform. In Euclidean space, sets satisfying the flatness condition include parts of cylindrical sets, conical sets, and surfaces of revolution. We prove local uniqueness in the Calderon problem with partial data in admissible geometries, and global uniqueness under an additional concavity assumption. This work unifies two earlier approaches to this problem (\cite{KSU} and \cite{I}) and extends both. The proofs are based on impr…
Closure relations during the plateau emission of Swift GRBs and the fundamental plane
2021
The Neil Gehrels Swift observatory observe Gamma-Ray bursts (GRBs) plateaus in X-rays. We test the reliability of the closure relations through the fireball model when dealing with the GRB plateau emission. We analyze 455 X-ray lightcurves (LCs) collected by \emph{Swift} from 2005 (January) until 2019 (August) for which the redshift is both known and unknown using the phenomenological Willingale 2007 model. Using these fits, we analyze the emission mechanisms and astrophysical environments of these GRBs through the closure relations within the time interval of the plateau emission. Finally, we test the 3D fundamental plane relation (Dainotti relation) which connects the prompt peak luminosi…
Super Heavy Dark Matter Anisotropies from D-particles in the Early Universe
2004
We discuss a way of producing anisotropies in the spectrum of superheavy Dark matter, which are due to the distortion of the inflationary space time induced by the recoil of D-particles upon their scattering with ordinary string matter in the Early Universe. We calculate such distortions by world-sheet Liouville string theory (perturbative) methods. The resulting anisotropies are found to be proportional to the average recoil velocity and density of the D-particles. In our analysis we employ a regulated version of de Sitter space, allowing for graceful exit from inflation. This guarantees the asymptotic flatness of the space time, as required for a consistent interpretation, within an effec…
Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation
2005
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an exten…
Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
2001
Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations w…
Improved constrained scheme for the Einstein equations: An approach to the uniqueness issue
2008
Uniqueness problems in the elliptic sector of constrained formulations of Einstein equations have a dramatic effect on the physical validity of some numerical solutions, for instance when calculating the spacetime of very compact stars or nascent black holes. The fully constrained formulation (FCF) proposed by Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak is one of these formulations. It contains, as a particular case, the approximation of the conformal flatness condition (CFC) which, in the last ten years, has been used in many astrophysical applications. The elliptic part of the FCF basically shares the same differential operators as the elliptic equations in CFC scheme. We present he…
SU-E-T-343: Valencia Applicator Commissioning Using a Micro-Chamber Array
2014
Purpose: In the commissioning and QA of surface isotope-based applicators, source-indexer distance (SID) has a great influence in the flatness, symmetry and output. To these purposes, methods described in the literature are the use of a special insert at the entrance of dwell chamber or radiochromic films. Here we present the experience with a micro-chamber array to perform the commissioning and QA of Valencia applicators. Methods: Valencia applicators have been used, the classic and the new extra-shielded version. A micro-chamber array has been employed, 1000 SRS (PTW), with 977 liquid filled, 2.3×2.3×0.5 mm3 sized ion chambers covering 11×11 cm2, which spacing is 2.5 mm in the central 5.5…
Effect of a Steady Magnetic Field and Imposed Rotation of Vessel on Heat and Mass Transfer in Swirling Recirculating Flows
1999
A simplified theoretical model for the solidification interface shape prediction is introduced and tested. We linearised a coupled hydrodynamic-solidification problem about the state with a flat interface. In such a way we split the problem into a hydrodynamic part with a flat solid-liquid front and a solidification part with a calculated heat flux from the liquid phase. The method allows obvious conclusions on optimum heat conditions near the solidification interface providing its flatness and maximum pulling velocity at the same time. Comparison to the results by FLUENT package showed that the method provides a reasonable accuracy even for a noticeably deformed interface shape. Another pa…