Isabelle Charpentier

Dynamics of electron impact ionization of the outer and inner valence (1t2 and 2a1) molecular orbitals of CH4 at intermediate and large ion recoil momentum

The triply differential cross section has been measured for electron-impact ionization of the outer valence 1t2 and the inner valence 2a1 orbitals of methane using the (e,2e) technique with coplanar asymmetric kinematics. The measurements are performed at scattered electron energy of 500 eV, ejected electron energy of 12, 37 and 74 eV and for scattering angle of the fast outgoing electron of 6?. This kinematics is characterized by a target ion recoil momentum ranging from moderate (0.25 au) to very large (3.2 au) values. The results are compared with theoretical cross sections calculated using the 1CW and the BBK models recently extended to molecules. The experimental cross sections exhibit a very large recoil scattering, especially for the inner 2a1 molecular orbital, which is not predicted by the theory. The differences between experiment and theory are attributed to the very strong scattering from the ion, not properly accounted for by theory. This indicates the need for further theoretical developments as well as experimental investigations in order to correctly model the process of molecular ionization.

Definition and Computation of Tensegrity Mechanism Workspace

Tensegrity mechanisms using linear springs as tensioned elements constitute an interesting class of mechanisms. When considered as manipulators, their workspace remains however to be defined in a generic way. In this article, we introduce a workspace definition and at the same time a computation method, based on the estimation of the workspace boundaries. The method is implemented using a continuation method. As an example, the workspace assessment of a two degrees of freedom (DOF) planar tensegrity mechanism is presented. [DOI: 10.1115/1.4029809]

Fast higher-order derivative tensors with Rapsodia

A number of practical problems in physics can be solved by using accurate higher-order derivatives. Such derivatives can be obtained with automatic differentiation. However, one has to be concerned with the complexity of computing higher-order derivative tensors even for a modest order and number of independents. Initial experiments using univariate Taylor polynomials with interpolation and operator overloading with unrolled loops showed better runtimes than using other automatic differentiation tools. Motivated by these results, we developed the Rapsodia code generator that produces Fortran and C++libraries for the most common intrinsics. Here we explain the algorithmic approach, implementation, and present test results on a select set of applications. Further details on the Rapsodia tool, and an example for user extensions are given in the Appendix.

On higher-order differentiation in nonlinear mechanics

Modelling often involves nonlinear parametric problems and bifurcation analysis. This interdisciplinary paper reviews higher-order numerical methods for the solution of nonlinear problems, and proposes a synthesis of two different conceptual frameworks, namely automatic differentiation and the asymptotic numerical method. Various mechanical problems and references illustrate the presentation.

Efficient adjoint derivatives: application to the meteorological model meso-nh

This paper describes a quite automatic method that allows for optimizing the adjoint codes produced by automatic differentiation tools. The automatic differentiator Odyssee that generates both tangent linear (Forward Automatic Differentiation) and adjoint (Reverse Automatic Differentiation) codes, is chosen to illustrate the discussion. As with many other tools, Odyss6e allows the hand coding construction of the linearized codes to be avoided, but it sometimes generates huge executable codes that cannot be run. We propose an algorithm that removes this drawback by means of modifications of both the tangent linear code and the adjoint code. In particular a study of the nonlinear parts of the code is proposed to determine the parts of the trajectory that must be stored, the other parts are not stored In the second part of the paper, this method is used for the differentiation of Meso-NH with respect to the state variables. When generated in such a way, the resulting codes are efficient

The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method

Based on high-order Taylor expansions, the asymptotic numerical method (ANM) is devoted to the solution of nonlinear partial differential equation (PDE) problems arising, for instance, in mechanics. Up to now, series were mainly handwritten and hand-coded. The note discusses the automation of the specific derivative computations involved in the ANM and presents the automatic differentiation (AD) approach Diamant. As any AD tool, Diamant is generic and may be used to differentiate the code of any differentiable behaviour law. Numerical performances, measured while solving a mechanical PDE problem, prove the efficiency of the Diamant approach.

Double ionization of H2 by electron impact: a second Born treatment

A second Born treatment is applied to study the (e, 3e) and (e, 3 − 1e) reactions for H2 targets. The results of this approximation are compared to the (e, 3 − 1e) experimental data obtained at about 600 eV impact energy. Several single-centre wavefunctions are used to describe the initial state and excited states of the molecule. Even if the second Born approximation is able to explain part of the experimental results the agreement is not good, similar to the case of the double ionization of helium (Gotz et al 2003 J. Phys. B: At. Mol. Opt. Phys. 36 L77).

Second Born approximation for the ionization of H2 by electron impact

The second Born approximation is applied to study the (e, 2e) reaction for H2 targets. The results of this approximation are compared to a new set of experimental data obtained at about 600 eV impact energy, as well as to previous experiments performed at larger (~4 keV) or smaller (250 eV) energy. Several single-centre wavefunctions are used to describe the initial state and excited states of the molecule. A generally good agreement is obtained with the experiments and with recent calculations.

Higher-order automatic differentiation of mathematical functions

Abstract Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faa di Bruno’s formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Particle shape analysis of volcanic clast samples with the Matlab tool MORPHEO

This paper presents a modular Matlab tool, namely MORPHEO, devoted to the study of particle morphology by Fourier analysis. A benchmark made of four sample images with different features (digitized coins, a pebble chart, gears, digitized volcanic clasts) is then proposed to assess the abilities of the software. Attention is brought to the Weibull distribution introduced to enhance fine variations of particle morphology. Finally, as an example, samples pertaining to a lahar deposit located in La Lumbre ravine (Colima Volcano, Mexico) are analysed. MORPHEO and the benchmark are freely available for research purposes.