Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.     

Incoherent light transport in anisotropic media: Form factor influence for oriented prolate ellipsoids

In turbid media, the partial or global orientation of anisotropic particles induces anisotropic light transport. In this study, we discuss the anisotropic incoherent transport of light in media where prolate ellipsoids are oriented in the same direction. In these anisotropic media, incoherent light transport is investigated using Monte Carlo simulations where the influence of particle anisotropy, size and optical properties are explored in a systematic way, from the local scattering event up to the diffusion limit. The database allows inverting the anisotropy of the backscattered image to yield the form factor of the particles. We then illustrate the relevance of such an analysis to assess the deformability of human erythrocytes in blood samples under normal physiological conditions.     

An Infinite Genus Mapping Class Group and Stable Cohomology

We exhibit a finitely generated group whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus g with n boundary components, for any g ≥ 0 and n > 0. We construct a representation of into the restricted symplectic group of the real Hilbert space generated by the homology classes of non-separating circles on , which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in is the pull-back of the Pressley-Segal class on the restricted linear group via the inclusion . L. F. was partially supported by the ANR Repsurf:ANR-06-BLAN-0311.     

Advances in the measurements of the mass attenuation coefficients

The knowledge of atomic fundamental parameters, such as mass attenuation coefficients or fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. Several databases providing the mass attenuation coefficients are accessible and frequently used within a large community of users. These compilations are most often in good agreement for photon energies in the hard X-ray ranges. However, they significantly differ for low photon energies and around the absorption edges of the elements. Mass attenuation coefficients of several elements were determined experimentally in the photon energy range from 100 eV to 35 keV by using monochromatized radiation at the SOLEIL synchrotron (France). The application of high-accuracy experimental techniques resulted in low uncertainty mass attenuation coefficients. The results are compared with tabulated data.     

Characterization of a sCMOS‐based high‐resolution imaging system

The detection system is a key part of any imaging station. Here the performance of the novel sCMOS‐based detection system installed at the ID17 biomedical beamline of the European Synchrotron Radiation Facility and dedicated to high‐resolution computed‐tomography imaging is analysed. The system consists of an X‐ray–visible‐light converter, a visible‐light optics and a PCO.Edge5.5 sCMOS detector. Measurements of the optical characteristics, the linearity of the system, the detection lag, the modulation transfer function, the normalized power spectrum, the detective quantum efficiency and the photon transfer curve are presented and discussed. The study was carried out at two different X‐ray energies (35 and 50 keV) using both 2× and 1× optical magnification systems. The final pixel size resulted in 3.1 and 6.2 µm, respectively. The measured characteristic parameters of the PCO.Edge5.5 are in good agreement with the manufacturer specifications. Fast imaging can be achieved using this detection system, but at the price of unavoidable losses in terms of image quality. The way in which the X‐ray beam inhomogeneity limited some of the performances of the system is also discussed.     

Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary

The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed.     

Plastic folding of buckling structures

Atomic force microscopy observations of the free surface of gold thin films deposited on silicon substrates have evidenced the buckling of the films and the formation of blister patterns undergoing plastic folding. The classical elastic buckling and plastic deformation of the films are analyzed in the framework of the F?ppl-Von Kármán theory of thin plates introducing the notion of low-angle tilt boundaries and dislocation distributions to describe this folding effect. It is demonstrated that, in agreement with elementary plasticity of bent crystals, the presence of such tilt-boundaries results in the formation of buckling patterns of lower energy than "classical" elastic blisters.     

Variational wave functions and their overlap with the ground state

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The overlap is simply related to the area under the E(tau) curve, i.e., the energy as a function of imaginary time. This has important applications to, for example, quantum Monte Carlo simulations where the overlap becomes as a simple by-product of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte Carlo simulations, i.e., fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.     

Characterization of a Liquid Fuel Injector under Continuous and Modulated Flow Conditions

The purpose of this work was to characterize the spray delivered by a modulated liquid fuel injector designed for active combustion control applications. A novel actuator is used to create a time-varying liquid fuel flow rate upstream of a commercially available injector. In order to be useful in existing burners, the actuator must not degrade the spray, by changing either the size or velocity distributions of the droplets produced by the injector. The amplitude of the induced modulations in flow rate must be strong enough to induce the required periodicity in heat release rate. This paper reports the results obtained from particle imaging velocimetry and phase Doppler anemometry used to characterize the spray, plus hot-film anemometry and pressure transducer measurements used to characterize the response of the fuel line to the induced flow rate fluctuations and to measure the excitation amplitude. It is found that the actuator response time is sufficiently rapid to modulate the liquid flow rate without changing the spray characteristics. Strong modulation of the flow rate is possible at low forcing frequencies, but the time-averaged flow rate is reduced. At higher forcing frequencies, the actuator response time cuts off, leading to a smaller amplitude flow rate modulation, and a relatively unchanged time-averaged fuel flow rate. For these reasons, this actuator is well suited to the control applications envisaged.