Instabilités de frottement : Approches temporelle et fréquentielle

International audienceThe vibrations generated at the interface between the two bodies in friction are responsible for various noises such as squealing, juddering, hammering, hooting, etc... In order to model and understand friction-induced vibration phenomenon, two approaches are compared in this article: temporal approach and modal approach. This analysis has been made on a simplified system composed of two beams in contact. The two different approaches have been programmed using Finite Element method. Assumptions on the contact calculation are different for the two approaches. Modal approach consists in calculating eigenvalues of the friction coupled system. Instabilities appear when a pair of modes merges. Eigenvalues with positive real parts are identified as potentially unstable modes. Temporal approach calculates the evolution of displacements, velocities, accelerations, forces ... One speaks about instabilities when stick or separation zones appear in the contact surfaces. With this approach frequencies which are excited during instability are obtained. Results have been compared and both methods give coherent and complementary results

Infinite index extensions of local nets and defects

Subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [LR95] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi, Longo, Popa [ILP98] and Fidaleo, Isola [FI99], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [Lon94] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [BKLR16].Comment: 50 page

Apports des méthodes fréquentielle et temporelle dans l'étude des instabilités de frottement responsables du crissement

International audienceIn order to model and understand friction-induced vibration phenomenon, two approaches are compared in this article: temporal approach and modal approach. This analysis has been made on a simplified system composed of two beams in contact. Modal approach consists in calculating eigenvalues of the friction coupled system. Instabilities appear when a pair of modes merges. Eigenvalues with positive real parts are identified as potentially unstable modes. Temporal approach calculates the evolution of displacements, velocities, accelerations, forces ... One speaks about instabilities when stick or separation zones appear in the contact surfaces. With this approach frequencies which are excited during instability are obtained. Results have been compared and both methods give coherent and complementary results

Friction-induced instabilities: modal, transient analysis and experimental validation

International audienceThe vibrations generated at the interface between the two bodies in friction are responsible for various noises such as squealing, juddering, hammering, hooting, etc. In order to model and understand friction-induced vibration phenomenon, two types of analysis, modal analysis and transient analysis, are compared in this article. This study has been made on a simplified system composed of two beams in contact. In modal analysis, instabilities appear when a pair of modes merges. Eigenvalues with positive real parts are identified as potentially unstable modes. In transient analysis, one speaks about instabilities when stick or separation zones appear in the contact surfaces. Results have been compared and both analysis give coherent and complementary results. An experimental validation has been made and shows a good correlation between experimental and numerical results

Numerical and experimental analysis of nonlinear vibrational response due to pressure-dependent interface stiffness

Modelling interface interaction with wave propagation in a medium is a fundamental requirement for several types of application, such as structural diagnostic and quality control. In order to study the influence of a pressure-dependent interface stiffness on the nonlinear response of contact interfaces, two nonlinear contact laws are investigated. The study consists of a complementary numerical and experimental analysis of nonlinear vibrational responses due to the contact interface. The laws investigated here are based on an interface stiffness model, where the stiffness property is described as a nonlinear function of the nominal contact pressure. The results obtained by the proposed laws are compared with experimental results. The nonlinearity introduced by the interface is highlighted by analysing the second harmonic contribution and the vibrational time response. The analysis emphasizes the dependence of the system response, i.e., fundamental and second harmonic amplitudes and frequencies, on the contact parameters and in particular on contact stiffness. The study shows that the stiffness-pressure trend at lower pressures has a major effect on the nonlinear response of systems with contact interfaces

Inference algorithms for gene networks: a statistical mechanics analysis

The inference of gene regulatory networks from high throughput gene expression data is one of the major challenges in systems biology. This paper aims at analysing and comparing two different algorithmic approaches. The first approach uses pairwise correlations between regulated and regulating genes; the second one uses message-passing techniques for inferring activating and inhibiting regulatory interactions. The performance of these two algorithms can be analysed theoretically on well-defined test sets, using tools from the statistical physics of disordered systems like the replica method. We find that the second algorithm outperforms the first one since it takes into account collective effects of multiple regulators

Quantized reduction as a tensor product

Symplectic reduction is reinterpreted as the composition of arrows in the category of integrable Poisson manifolds, whose arrows are isomorphism classes of dual pairs, with symplectic groupoids as units. Morita equivalence of Poisson manifolds amounts to isomorphism of objects in this category. This description paves the way for the quantization of the classical reduction procedure, which is based on the formal analogy between dual pairs of Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with correspondences between von Neumann algebras. Further analogies are drawn with categories of groupoids (of algebraic, measured, Lie, and symplectic type). In all cases, the arrows are isomorphism classes of appropriate bimodules, and their composition may be seen as a tensor product. Hence in suitable categories reduction is simply composition of arrows, and Morita equivalence is isomorphism of objects.Comment: 44 pages, categorical interpretation adde

Progress in noncommutative function theory

In this expository paper we describe the study of certain non-self-adjoint operator algebras, the Hardy algebras, and their representation theory. We view these algebras as algebras of (operator valued) functions on their spaces of representations. We will show that these spaces of representations can be parameterized as unit balls of certain $W^{*}$-correspondences and the functions can be viewed as Schur class operator functions on these balls. We will provide evidence to show that the elements in these (non commutative) Hardy algebras behave very much like bounded analytic functions and the study of these algebras should be viewed as noncommutative function theory