Cosmological Equations for a Thick Brane

Generalized Friedmann equations governing the cosmological evolution inside a thick brane embedded in a five-dimensional Anti-de Sitter spacetime are derived. These equations are written in terms of four-dimensional effective brane quantities obtained by integrating, along the fifth dimension, over the brane thickness. In the case of a Randall-Sundrum type cosmology, different limits of these effective quantities are considered yielding cosmological equations which interpolate between the thin brane limit (governed by unconventional brane cosmology), and the opposite limit of an ``infinite'' brane thickness corresponding to the familiar Kaluza-Klein approach. In the more restrictive case of a Minkowski bulk, it is shown that no effective four-dimensional reduction is possible in the regimes where the brane thickness is not small enough.Comment: 23 pages, Latex, 2 figure

Contact Pressure Measurement System in Cross Wedge Rolling

In the cross wedge rolling process (CWR), plastic deformation is geared by a driving torque transmitted by friction on die surface. Friction plays a role which has to be further identified in this metal forming process. The local contact pressure between a cylindrical billet and flat dies seems to be a relevant parameter to characterize the severe contact conditions during the rolling. This paper deals with an experimental measurement technology, which has been designed and implemented on a semi-industrial CWR test bench with plate configuration. This measurement system using pin and piezoelectric sensor is presented, with an analysis of the system operation and design detail. Characterization of systematic error and calibration tests are then explained. Additional tests performed on hot steel preforms allow to check the ability of the contact pressure measurement system to resist under severe operating conditions. Realistic results for varying temperatures are then discussed

Role of Surface Texture on Workpiece Angular Deformation in Cross Wedge Rolling

The cross wedge rolling process is commonly used for the manufacturing of shaft or for preforms, being used for preliminary operation of forming cycle. The presence of angular deformation produced during the rolling process is analyzed in this paper. This work shows some experimental results obtained on parts made of steel in semi-industrial condition. Visioplasticity technique is used to measure the angular displacement occurring in some sections with reference to the adjacent ones. Thus the test samples are prepared to include surface grooves filled up with quite similar steel grade. After rolling process, angular deformations are highlighted by observations and external deformation profile. Influence of surface texture of the forming area is experimentally demonstrated. Moreover, the numerical simulation with the software FORGE is used to verify the adequacy between the observed phenomena and forecasts which can be obtained today.Conclusions about the relative influence of friction factors on the internal stresses creation are finally presented to better identify potential occurrence of these phenomena. Strain diagrams are used to bring out the magnitude of angular variations depending on local plastic strain on parts. Possible consequences for process optimization are raised

Stochastic Localization of Instability and Deterministic Enhancement of Accuracy for Iterative Algorithms

Finite precision computations may affect the stability of iterative algorithms and the accuracy of computed solutions. Automatic approaches are proposed to control these effects as for example, the CESTAC and the CENA methods. We focus here on a complementary use of these two methods to localize unstable behavior of the algorithm, improve its stability and the accuracy of the solutions. We present computational experiments on ill-conditioned polynomial roots approximated with Newton's iteration

A Revised Presentation of the CENA Method

The CENA method is a new automatic method to correct the first-order effect of floating point rounding errors on the result of a numerical algorithm. A first presentation of this method is proposed in the previous report RR-3828 (december 1999). The current report completes and replaces the previous one. We hark back to the presentation of the CENA method exhibiting new important aspects. We illustrate the pros-and-cons of the method solving triangular linear systems. These systems are designed to generate a significantly inaccurate computed solution. We propose a new analysis of the analogy and discrepancy between the linear correction and computing with extented precision

An Automatic Correcting Method

Correcting methods intend to improve the accuracy of results computed in finite precision. The CENA method processes an automatic correction of the first-order effect of the rounding errors the computation generates. The method provides a corrected result and a bound of the residual error for a class of algorithms we identify. We present the main features of the CENA method and illustrate its interests and limitations with examples

From Rounding Error Estimation to Automatic Correction with Automatic Differentiation

Using automatic differentiation (AD) to estimate the propagation of rounding errors in numerical algorithms is classic. We propose a new application of AD to roundoff analysis providing an automatic correction of the first order effect of the elementary rounding errors. We present the main characteri- stics of this method and significant examples of its application to improve the accuracy of computed results and/or the stability of the algorithm

Compensated Horner algorithm in K times the working precision

We introduce an algorithm to evaluate a polynomial with floating point coefficients as accurately as the Horner scheme performed in K times the working precision, for K an arbitrary integer. The principle is to iterate the error-free transformation of the compensated Horner algorithm and to accurately sum the final decomposition. We prove this accuracy property with an apriori error analysis. We illustrate its practical efficiency with numerical experiments on significant environments and IEEE-754 arithmetic. Comparing to existing alternatives we conclude that this K-times compensated algorithm is competitive for K up to 4, i.e. up to 212 mantissa bits