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Ginoux J.,University of Toulon | Letellier C.,CNRS Complex Interprofessional Research in Aerothermochemistry
Chaos | Year: 2012

Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit. Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed: (i) the series dynamo machine conducted by Gérard-Lescuyer (1880), (ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905), (iii) the triode invented by de Forest (1907), and (iv) the multivibrator elaborated by Abraham and Bloch (1917). The differential equation describing such a self-oscillating system was proposed by Poincaré for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol's contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller's help, he popularized the "relaxation oscillations" using the previous experiments as examples and, turned them into a concept. © 2012 American Institute of Physics.

Aguirre L.A.,University Federeal Of Minas Gerais | Letellier C.,CNRS Complex Interprofessional Research in Aerothermochemistry
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

Investigation of observability properties of nonlinear dynamical systems aims at giving a hint on how much dynamical information can be retrieved from a system using a certain measuring function. Such an investigation usually requires knowledge of the system equations. This paper addresses the challenging problem of investigating observability properties of a system only from recorded data. From previous studies it is known that phase spaces reconstructed from poor observables are characterized by local sharp pleatings, local strong squeezing of trajectories, and global inhomogeneity. A statistic is then proposed to quantify such properties of poor observability. Such a statistic was computed for a number of bench models for which observability studies had been previously performed. It was found that the statistic proposed in this paper, estimated exclusively from data, correlates generally well with observability results obtained using the system equations. It is possible to arrive at the same order of observability among the state variables using the proposed statistic even in the presence of noise with a standard deviation as high as 10% of the data. The paper includes the application of the proposed statistic to sunspot time series. © 2011 American Physical Society.

Gouesbet G.,CNRS Complex Interprofessional Research in Aerothermochemistry | Gouesbet G.,INSA Rouen
Optics Communications | Year: 2010

There has been recently a growing interest in the development of what is usually known as the T-matrix method (better to be named: T-matrix formulation), in connection with studies concerning light scattering by nonspherical particles. Another line of research has been devoted to the development of generalized Lorenz-Mie theories dealing with the interaction between arbitrary electromagnetic shaped beams and some regular particles, allowing one to solve Maxwell's equations by using a method of separation of variables. Both lines of research are conjointly considered in this paper. Results of generalized Lorenz-Mie theories in spherical coordinates (for homogeneous spheres, multilayered spheres, spheres with an eccentrically located spherical inclusion, assemblies of spheres and aggregates) are modified from scalar results in the framework of the Bromwich method to vectorial expressions using vector spherical wave functions (VSWFs) in order to match the T-matrix formulation, and to express the T-matrix. The results obtained are used as a basis to clarify statements, some of them erroneous, concerning the T-matrix formulation and to provide recommendations for better terminologies. © 2009 Elsevier B.V. All rights reserved.

Gouesbet G.,CNRS Complex Interprofessional Research in Aerothermochemistry | Lock J.A.,Cleveland State University
Applied Optics | Year: 2013

The expression "generalized Lorenz-Mie theories" generically denotes a class of light-scattering theories describing the interaction between an illuminating electromagnetic arbitrary-shaped beam and a particle possessing a high degree of symmetry. This allows one to use the method of separation of variables in which the illuminating beam is expressed as an expansion over a set of basis functions. Such theories have been derived and applied over the past 35 years. Although, as a whole, these theories are now well developed, there remains a list of problems to be solved, some of which are described in this paper. © 2013 Optical Society of America.

Letellier C.,CNRS Complex Interprofessional Research in Aerothermochemistry | Aguirre L.A.,Federal University of Minas Gerais
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

After suggesting criteria to recognize a new system and a new attractor-and to make a distinction between them-the paper details the topological analysis of the "cord" attractor. This attractor, which resembles a cord between two leaves, is produced by a three-dimensional system that is obtained after a modification of the Lorenz-84 model for the global atmospheric circulation. The nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe, that is, to a spiral Rössler attractor with negative and positive global π twists. Due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable, this attractor qualifies as a challenging benchmark in nonlinear dynamics. © 2012 American Physical Society.

Bultel A.,CNRS Complex Interprofessional Research in Aerothermochemistry | Annaloro J.,CNRS Complex Interprofessional Research in Aerothermochemistry
Plasma Sources Science and Technology | Year: 2013

The most relevant way to predict the excited state number density in a nonequilibrium plasma is to elaborate a collisional-radiative (CR) model taking into account most of the collisional and radiative elementary processes. Three examples of such an elaboration are given in this paper in the case of various plasma flows related to planetary atmospheric entries. The case of theoretical determination of nitrogen atom ionization or recombination global rate coefficients under electron impact is addressed first. The global rate coefficient can be implemented in multidimensional computational fluid dynamics calculations. The case of relaxation after a shock front crossing a gas of N2 molecules treated in the framework of the Rankine-Hugoniot assumptions is also studied. The vibrational and electronic specific CR model elaborated in this case allows one to understand how the plasma reaches equilibrium and to estimate the role of the radiative losses. These radiative losses play a significant role at low pressure in the third case studied. This case concerns CO2 plasma jets inductively generated in high enthalpy wind tunnels used as ground test facilities. We focus our attention on the behaviour of CO and C2 electronic excited states, the radiative signature of which can be particularly significant in this type of plasma. These three cases illustrate the elaboration of CR models and their coupling with balance equations. © 2013 IOP Publishing Ltd.

Gouesbet G.,CNRS Complex Interprofessional Research in Aerothermochemistry
Annalen der Physik | Year: 2014

Generalized Lorenz-Mie theories form a set of analytical approaches dealing with the interaction between electromagnetic arbitrary shaped beams and a class of particles possessing enough symmetries to allow one to use the method of separation of variables. This paper provides a commented reference database concerning generalized Lorenz-Mie theories for the period 2009-2013. © 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Chaudhuri A.,CNRS Complex Interprofessional Research in Aerothermochemistry | Hadjadj A.,CNRS Complex Interprofessional Research in Aerothermochemistry | Chinnayya A.,CNRS Complex Interprofessional Research in Aerothermochemistry
Journal of Computational Physics | Year: 2011

This paper describes the implementation of immersed boundary method using the direct-forcing concept to investigate complex shock-obstacle interactions. An interpolation algorithm is developed for more stable boundary conditions with easier implementation procedure. The values of the fluid variables at the embedded ghost-cells are obtained using a local quadratic scheme which involves the neighboring fluid nodes. Detailed discussions of the method are presented on the interpolation of flow variables, direct-forcing of ghost cells, resolution of immersed-boundary points and internal treatment. The method is then applied to a high-order WENO scheme to simulate the complex fluid-solid interactions. The developed solver is first validated against the theoretical solutions of supersonic flow past triangular prism and circular cylinder. Simulated results for test cases with moving shocks are further compared with the previous experimental results of literature in terms of triple-point trajectory and vortex evolution. Excellent agreement is obtained showing the accuracy and the capability of the proposed method for solving complex strong-shock/obstacle interactions for both stationary and moving shock waves. © 2010 Elsevier Inc.

Albin E.,CNRS Complex Interprofessional Research in Aerothermochemistry | D'Angelo Y.,CNRS Complex Interprofessional Research in Aerothermochemistry
Combustion and Flame | Year: 2012

Direct Numerical Simulations (DNS), Evolution Equation Modelling (EEM) and Experimental results from the literature (EXP) are presented and analyzed for an expanding propane/air flame. DNS results are obtained thanks to the in-house finite-difference code HAllegro. Computed (DNS/EEM) and measured (EXP) equivalent radii R P and R S, mean stretch k and consumption velocity S C, as well as sample front shapes, are compared using the same post-processing procedure. Small perturbations in the EEM input parameters induce comparatively small shifts in the compared results, showing the robustness of the approach. When slightly adapting only one O(1) parameter for the EEM strategy (the effective turbulent forcing amplitude felt by the flame), DNS, EEM and EXP show quite fair agreement one another, except for one of the experiments at early times. In the context of expanding flames, this validated EEM methodology can constitute a reliable tool to compute realistically large sized flames. © 2012 The Combustion Institute.

Yon S.,CNRS Complex Interprofessional Research in Aerothermochemistry | Sautet J.-C.,CNRS Complex Interprofessional Research in Aerothermochemistry
Applied Thermal Engineering | Year: 2012

The development of oxy-fuel burner with highly separated jets of fuel and oxidizer presents attractive perspectives because reactives separation generates a better thermal efficiency and a reduction of pollutant emissions by dilution effect. The aim of this work is to study the effects of the addition of hydrogen and the decrease of the equivalence ratio (φ < 1) on the flame lift-off height and the mixing between the jets of hythane and oxygen. The oxy-fuel burner is made up of two nozzles, the first is hythane flow (mixing between natural gas and hydrogen) and the second is pure oxygen. Owing to the high diffusivity and reactivity of hydrogen in combustion, the use of hythane solves instability problems of flame linked to lean combustion. The OH radical emission results show that addition of hydrogen and reduction of equivalence ratio permit to decrease the flame lift-off height and to reduce its fluctuations. Thanks to the Particle Image Velocimetry of non-reacting and reacting flows, the comparison of 2-D mean velocity fields shows that the various parameters favour jets combination, a better mixing quality and a decrease of the size of the recirculation zone. In its kind of oxy-fuel burner, hydrogen and a lean equivalence ratio allow therefore an early combustion, a better flame stability and a decrease of amount of fuel used. © 2011 Elsevier Ltd. All rights reserved.

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