On random walks arising in queueing systems: ergodicity and transience via quadratic forms as lyapounov functions — Part I

A simple and quite general approach is proposed to derive criteria for transience and ergodicity of a certain class of irreducibleN-dimensional Markov chains in ₊ ^N assuming a boundedness condition on the second moment of the jumps. The method consists in constructing convenient smooth supermartingales outside some compact set. The Lyapounov functions introduced belong to the set of quadratic forms in ₊ ^N and do not always have a definite sign. Existence and construction of these forms is shown to be basically equivalent to finding vectors satisfying a system of linear inequalities.Part I is restricted toN=2, in which case a complete characterization is obtained for the type of random walks analyzed by Malyshev and Mensikov, thus relaxing their condition of boundedness of the jumps. The motivation for this work is partly from a large class of queueing systems that give rise to random walks in ₊ ^N      

Review: Auto-oxidation of aliphatic polyamides

The literature on oxidation kinetics of polyamides and model compounds has been reviewed in order to try to extract suitable information for non-empirical kinetic modeling. Polyamide characteristics are systematically compared to polyolefin ones, these latter being more extensively studied. From kinetic analysis point of view, it is shown that oxidation attacks predominantly α amino methylenes of which C–H bond is considerably weaker than the other methylenes. As a result, propagation by H abstraction is considerably faster in polyamides than in polyethylene for instance. Termination by radical combination is also very fast. Another cause of PA oxidizability is the instability of α amino hydroperoxides linked to the inductive effect of nitrogen. This instability is responsible for many key features of oxidation kinetics especially the absence of induction period.     

Comparison of PIV parameters effects on displacement identification and cross correlation

An algorithm is presented to determine displacements thanks to the identification method. Its main properties are described: no link with the particle size, measurement of the velocity distribution. Determination of effects of PIV parameters on displacement identification is made. Parameters used are noise, bias, velocity distribution. Therefore, we can define a validity domain of PIV parameters for identification and compare it with the domain of cross correlation. The identification validity range is based on 70% of isolated particles, on a displacement norm and on displacement gradients corresponding to less than half the size of the interrogation cell and to 10% of the average velocity. The comparison with cross correlation domains indicates that the cross correlation is more robust. However, the identification method is interesting because of the possibility of displacement distribution measurement. We use it to measure the decreasing of the turbulence intensity for a grid-generated turbulence.     

Induction period in the low‐temperature thermal oxidation of saturated hydrocarbons: Example of polyethylene

Thermal oxidation of hydrocarbon substrates at low‐to‐moderate temperature, typically T ≤ 150^°C, results from a radical chain process initiated by hydroperoxide decomposition and displays an induction period. A reliable model exists to simulate oxidation kinetics, but an incertitude remains on initial steps because they are out of reach of all available analytical methods. This work is aimed to have a kinetic approach of the problem, by comparing various mechanisms, i.e., (A) bimolecular decomposition of initially present hydroperoxides; (B) combined uni‐ and bimolecular decomposition of hydroperoxides; (C) the presence of radicals at the beginning of the exposure; and (D) radicals generation at (low) constant rate from irradiation, for instance by ionizing radiation linked to natural radioactivity or from a direct oxygen–substrate reaction. Scheme A is not realistic at low initial hydroperoxide concentrations. All the other mechanisms generate similar behaviors: the induction time tends toward a constant value almost independent of the nature of initial steps, when the concentration of precursors (initially present hydroperoxides or radicals) or the rate of their initial production (from species other than hydroperoxides) tends toward zero. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 769–777, 2008     

Relationships between molar mass and fracture properties of segmented urethane and amide copolymers modified by chemical degradation

This publication highlights the structure–property relationships in several thermoplastic elastomers (TPEs): one poly(ether-block-amide) and two thermoplastic polyurethane elastomers with ester and ether soft blocks. Structural changes are induced by chemical degradation from virgin samples through hydrolysis and oxidation. Molar mass measurements show an exclusive chain scission mechanism for all TPEs, regardless of the chemical modification condition. Mechanical behavior was nevertheless obtained from uniaxial tensile testing and fracture testing while considering the essential work of fracture (EWF) concept. During the macromolecular scission process, elongation at break shows a plateau followed by a drop, while stress at break decreases steadily. Once again, the trend is identical for all TPEs in all conditions considered. The βw_p parameter determined using the EWF concept exhibits an interesting sensitivity to scissions (i.e., molar mas decrease). Plotting elongation at break as a function of molar mass reveals a strong correlation between these two parameters. This master curve is particularly remarkable considering the range of TPEs and chemical breakdown pathways considered (hydrolysis and oxidation at several temperatures). Relevant structure–property relationships are proposed, highlighting that molar mass is a predominant parameter for determining the mechanical properties of thermoplastic elastomers.     

Oxidation induced embrittlement in polypropylene — a tensile testing study

The thermal oxidation of polypropylene films (100 μm) in air at 90°C was studied by IR spectroscopy, rheometry at 210°C and tensile testing. Tensile testing reveals a sudden embrittlement before the end of the induction period determined from carbonyl build-up curves. Embrittlement occurs at a very low conversion of the chain scission process (only 1 chain scission per 3 initial chains) and it can be demonstrated that it results from a decrease in polymer toughness rather than from the build-up of defects linked to a presumed heterogeneity of the oxidation process. Tensile testing is not necessarily a good tool to characterize embrittlement given that phenomena such as necking and crack initiation at geometric defects are not taken into account with the usual measuring methods. The sudden drop of ultimate elongation could be, at least partly, an artifact.     

On Variational and PDE-Based Methods for Accurate Distance Function Estimation

Computational Mathematics and Mathematical Physics - A new variational problem for accurate approximation of the distance from the boundary of a domain is proposed and studied. It is shown that the...     

Stochastic Dynamics of Discrete Curves and Multi-Type Exclusion Processes

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a reaction-diffusion nature. In the non-reversible case, the invariant measure has in general a non Gibbs form. The corresponding steady-state regime is analyzed in detail, by using a tagged particle together with a state-graph cycle expansion of the probability currents. As a consequence, the constants appearing in Lotka–Volterra equations—which describe the fluid limits of stationary states—can be traced back directly at the discrete level to tagged particle cycles coefficients. Current fluctuations are also studied and the Lagrangian is obtained via an iterative scheme. The related Hamilton–Jacobi equation, which leads to the large deviation functional, is investigated and solved in the reversible case, just for the sake of checking.     

Models for transporation networks

Various stochastic models are proposed for transportation networks, by increasing order of complexity. The mathematical tools rely on queueing theory and asymptotic analysis. These models are mainly applied to service vehicle systems, like PRAXITELE, but the methods used are more far-reaching. In particular, the asymptotic independence of nodes is proved in the thermodynamical limit, i.e., when the volume of the system increases. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russian, 1995. Part III.