A review on the Mullins effect

The Mullins’ effect remains a major challenge in order to provide good mechanical modeling of the complex behavior of industrial rubber materials. It’s been forty years since Mullins [1] wrote his review on the phenomenon and still no general agreement has been found either on the physical source or on the mechanical modeling of this effect. Therefore, we reviewed the literature dedicated to this topic over the past six decades. We present the experimental evidences, which characterize the Mullins’ softening. The phenomenon is observed in filled and crystallizing rubbers. Then, the phenomenological models dedicated to fit the mechanical behavior of rubbers undergoing some Mullins’ softening are studied. To overcome the limit of a descriptive phenomenological modeling, several authors looked for a physical understanding of the phenomenon. Various theories have been exposed, but none of them has been supported unanimously. Nonetheless, these theories favor the emergence of physically based mechanical behavior laws. We tested some of these laws, which show little predictive abilities since the values of their parameters do not compare well with the physical quantities they are linked to.Projet ANR jeunes chercheurs MELAC JC05_43403

Signed Lp-distance fields

We introduce and study a family of generalized double-layer potentials which are used to build smooth and accurate approximants for the signed distance function. Given a surface, the value of an approximant at a given point is a power mean of distances from the point to the surface points parameterized by the angle they are viewed from the given point. We analyze mathematical properties of the potentials and corresponding approximants. In particular, approximation accuracy estimates are derived. Our theoretical results are supported by numerical experiments which reveal high practical potential of our approach

Dynamical Windings of Random Walks and Exclusion Models. Part I: Thermodynamic Limit

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the symmetry between the left and right orientation, the winding distribution of the walk is modified, and the system can be in three different phases: folded, stretched and glassy. An explicit mapping is found, leading to consider the system as a coupling of two exclusion processes. For all closed or periodic initial sample paths, a convenient scaling permits to show a convergence in law (or almost surely on a modified probability space) to a continuous curve, the equation of which is given by a system of two non linear stochastic differential equations. The deterministic part of this system is explicitly analyzed via elliptic functions. In a similar way, by using a formal fluid limit approach, the dynamics of the system is shown to be equivalent to a system of two coupled Burgers' equations.Comment: 31 pages, 13 figures. Pages 5,6,8,9,10,12,23 color printed. INRIA Report 460

Unity and Plurality of the European Cycle

We apply uni- and multivariate unobserved components models to the study of European growth cycles. The multivariate dimension enables to search similar or, more strongly, common components among national GDP series (quarterly data from 1960 to 1999). Three successive ways to exhibit the European cycle satisfactorily converge: the direct decomposition of the aggregate European GDP; the aggregation of the member countries' national cycles; the search for common components between these national cycles. The European aggregate fluctuations reveal two distinct cyclical components, assimilated to the classical Juglar (decennial, related to investment) and Kitchin (triennial, related to inventories) cycles. The European Juglar cycle cannot be reduced to a single common component of the national cycles. It has at least a dimension of "three": it can be understood as the interference of three elementary and independent sequences of stochastic shocks, that correspond to the European geographical division. The euro-zone is not yet an optimal currency area, as the shocks generating the European cycles are not completely symmetrical. Studying the sequences of innovations extracted from the models shows that euro-zone vulnerability to strong shocks and asymmetry of these shocks tend to decrease during the last decades, but this trend is neither regular, nor irreversible.(A)symmetrical shocks, Common factors, European integration, Growth cycles, Stochastic trends, Structural time series model.

Oxidation induced changes in viscoelastic properties of a thermostable epoxy matrix

The thermal ageing of a neat epoxy matrix has been studied at 200°C in air by three complementary analytical techniques: optical microscopy, mechanical spectrometry and nano-indentation. Thermal oxidation is restricted in a superficial layer of about 195 µm of maximal thickness. It consists in a predominant chain scission process involving, in particular, chemical groups whose β motions have the highest degree of cooperativity and thus, are responsible for the high temperature side of β dissipation band. As a result, chain scissions decrease catastrophically the glass transition temperature, but also increase significantly the storage modulus at glassy plateau between Tβ and Tα. This phenomenon is called “internal antiplasticization”. Starting from these observations, the Di Marzio and Gilbert’s theories have been used in order to establish relationships between the glass transition temperature and number of chain scissions, and between the storage modulus and β transition activity respectively. The challenge is now to establish a relationship between the transition activity and the concentration of the corresponding chemical group

Co-oxidation kinetic model for the thermal oxidation of polyethylene-unsaturated substrate systems

The thermal oxidation of polyethylene (PE) impregnated by the methyl esters of unsaturated fatty acids (UFEs) was studied using chemiluminescence, and infra-red spectrophotometry. It was shown that the presence of UFEs accelerates the PE aging process. This can be interpreted as a co-oxidation phenomenon. In this study, the previously established models for PE and UFEs self-oxidation have been coupled in order to develop a co-oxidation model. Using the existing rate constants for the PE and UFEs selfoxidations, this model can simulate the complex shape of the kinetic curves of PE-UFE co-oxidatio

Random Walks in the Quarter-Plane: Advances in Explicit Criterions for the Finiteness of the Associated Group in the Genus 1 Case

In the book [FIM], original methods were proposed to determine the invariant measure of random walks in the quarter plane with small jumps, the general solution being obtained via reduction to boundary value problems. Among other things, an important quantity, the so-called group of the walk, allows to deduce theoretical features about the nature of the solutions. In particular, when the \emph{order} of the group is finite, necessary and sufficient conditions have been given in [FIM] for the solution to be rational or algebraic. In this paper, when the underlying algebraic curve is of genus $1$, we propose a concrete criterion ensuring the finiteness of the group. It turns out that this criterion can be expressed as the cancellation of a determinant of a matrix of order 3 or 4, which depends in a polynomial way on the coefficients of the walk.Comment: 2 figure

A Markovian Analysis of IEEE 802.11 Broadcast Transmission Networks with Buffering

The purpose of this paper is to analyze the so-called back-off technique of the IEEE 802.11 protocol in broadcast mode with waiting queues. In contrast to existing models, packets arriving when a station (or node) is in back-off state are not discarded, but are stored in a buffer of infinite capacity. As in previous studies, the key point of our analysis hinges on the assumption that the time on the channel is viewed as a random succession of transmission slots (whose duration corresponds to the length of a packet) and mini-slots during which the back-o? of the station is decremented. These events occur independently, with given probabilities. The state of a node is represented by a two-dimensional Markov chain in discrete-time, formed by the back-off counter and the number of packets at the station. Two models are proposed both of which are shown to cope reasonably well with the physical principles of the protocol. The stabillity (ergodicity) conditions are obtained and interpreted in terms of maximum throughput. Several approximations related to these models are also discussed