Study on Optical Fiber Insertion in Underground Telecommunication Networks Using Hydraulic Similarity

AbstractThe European regulations require a new approach of cities facilities networks, including the communication ones. In this respect, the communication providers generalize the underground networks, following the streets trails. The transmission support consists in a network of tubes, protecting a number of micro-tubes/microducts, which protect the real transmission facilitators made by optical fibers. Presently, the producers of this type of devices promote special norms of information on characteristics and installation of the product, but there are not reliable accepted standardized methods for optical fibers insertion in pre-installed micro-tubes/microducts and for the devices forces computation, necessary for underground communication networks. The micro-tubes are already installed in the protection cables and together are buried in the ground on different routes. It appears the necessity to introduce the fibers in the micro-tubes in this situation. Generally, it is a significant difference between the practical reality and the producers norms and indicators. In order to explain this situation, and considering the optical fibers dimensions, and the necessity to insert the fibers using specific lubricants, the paper propose a similarity model of the optical fibers insertion in the micro-tubes with the hydraulic model of laminar incompressible fluids flow in parallel or concentric micro- layers. In this phase, there are presented the results of experimental measurements and tests on in situ networks, composed by different types of materials and lubricants, as support for the hydraulic similitude

Stochastic Properties of Static Friction

The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the applied force at this particular instant when the frictional interface loses stability. However, experimental studies are known to present important scatter in the measurement of static friction; the origin of which remains unexplained. Here, we study the nucleation of local slip at interfaces with slip-weakening friction of random strength and analyze the resulting variability in the measured global strength. Using numerical simulations that solve the elastodynamic equations, we observe that multiple slip patches nucleate simultaneously, many of which are stable and grow only slowly, but one reaches a critical length and starts propagating dynamically. We show that a theoretical criterion based on a static equilibrium solution predicts quantitatively well the onset of frictional sliding. We develop a Monte-Carlo model by adapting the theoretical criterion and pre-computing modal convolution terms, which enables us to run efficiently a large number of samples and to study variability in global strength distribution caused by the stochastic properties of local frictional strength. The results demonstrate that an increasing spatial correlation length on the interface, representing geometric imperfections and roughness, causes lower global static friction. Conversely, smaller correlation length increases the macroscopic strength while its variability decreases. We further show that randomness in local friction properties is insufficient for the existence of systematic precursory slip events. Random or systematic non-uniformity in the driving force, such as potential energy or stress drop, is required for arrested slip fronts. Our model and observations..

Convergence properties of polynomial chaos approximations for L2 random variables.

Polynomial chaos (PC) representations for non-Gaussian random variables are infinite series of Hermite polynomials of standard Gaussian random variables with deterministic coefficients. For calculations, the PC representations are truncated, creating what are herein referred to as PC approximations. We study some convergence properties of PC approximations for L{sub 2} random variables. The well-known property of mean-square convergence is reviewed. Mathematical proof is then provided to show that higher-order moments (i.e., greater than two) of PC approximations may or may not converge as the number of terms retained in the series, denoted by n, grows large. In particular, it is shown that the third absolute moment of the PC approximation for a lognormal random variable does converge, while moments of order four and higher of PC approximations for uniform random variables do not converge. It has been previously demonstrated through numerical study that this lack of convergence in the higher-order moments can have a profound effect on the rate of convergence of the tails of the distribution of the PC approximation. As a result, reliability estimates based on PC approximations can exhibit large errors, even when n is large. The purpose of this report is not to criticize the use of polynomial chaos for probabilistic analysis but, rather, to motivate the need for further study of the efficacy of the method

Stochastic Systems: Uncertainty Quantification and Propagation

Uncertainty is an inherent feature of both properties of physical systems and the inputs to these systems that needs to be quantified for cost effective and reliable designs. The states of these systems satisfy equations with random entries, referred to as stochastic equations, so that they are random functions of time and/or space. The solution of stochastic equations poses notable technical difficulties that are frequently circumvented by heuristic assumptions at the expense of accuracy and rigor. The main objective of Stochastic Systems is to promoting the development of accurate and efficient methods for solving stochastic equations and to foster interactions between engineers, scientists, and mathematicians. To achieve these objectives Stochastic Systems presents: ·         A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis   ·          Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences   ·          Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions   Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. Numerous examples are used to clarify and illustrate theoretical concepts and methods for solving stochastic equations. The extensive bibliography and index at the end of the book constitute an ideal resource for both theoreticians and practitioners