The Reach-and-Evolve Algorithm for Reachability Analysis of Nonlinear Dynamical Systems

This paper introduces a new algorithm dedicated to the rigorous reachability analysis of nonlinear dynamical systems. The algorithm is initially presented in the context of discrete time dynamical systems, and then extended to continuous time dynamical systems driven by ODEs. In continuous time, this algorithm is called the Reach and Evolve algorithm. The Reach and Evolve algorithm is based on interval analysis and a rigorous discretization of space and time. Promising numerical experiments are presented

Latest Developments on the IEEE 1788 Effort for the Standardization of Interval Arithmetic

(Standardization effort supported by the INRIA D2T.)International audienceInterval arithmetic undergoes a standardization effort started in 2008 by the IEEE P1788 working group. The structure of the proposed standard is presented: the mathematical level is distinguished from both the implementation and representation levels. The main definitions are introduced: interval, mathematical functions, either arithmetic operations or trigonometric functions, comparison relations, set operations. While developing this standard, some topics led to hot debate. Such a hot topic is the handling of exceptions. Eventually, the system of decorations has been adopted. A decoration is a piece of information that is attached to each interval. Rules for the propagation of decorations have also been defined. Another hot topic is the mathematical model used for interval arithmetic. Historically, the model introduced by R. Moore in the 60s covered only non-empty and bounded intervals. The set-based model includes the empty set and unbounded intervals as well. Tenants of Kaucher arithmetic also insisted on offering "reverse" intervals. It has eventually been decided that an implementation must provide at least one of these flavors of interval arithmetic. The standard provides hooks for these different flavors. As the preparation of the draft should end in December 2013, no chapter is missing. However, a reference implementation would be welcome

Inner approximated reachability analysis

International audienceComputing a tight inner approximation of the range of a function over some set is notoriously di cult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves a ne forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems

HySIA: Tool for Simulating and Monitoring Hybrid Automata Based on Interval Analysis

We present HySIA: a reliable runtime verification tool for nonlinear hybrid automata (HA) and signal temporal logic (STL) properties. HySIA simulates an HA with interval analysis techniques so that a trajectory is enclosed sharply within a set of intervals. Then, HySIA computes whether the simulated trajectory satisfies a given STL property; the computation is performed again with interval analysis to achieve reliability. Simulation and verification using HySIA are demonstrated through several example HA and STL formulas.Comment: Appeared in RV'17; the final publication is available at Springe

Two-to-one Auger decay of a double L vacancy in argon

We have observed L223−M3 Auger decay in argon where a double vacancy is filled by two valence electrons and a single electron is ejected from the atom. A well-resolved spectrum of these two-to-one electron transitions is compared to the result of the second-order perturbation theory and its decay branching ratio is determined

A Contractor Based on Convex Interval Taylor

International audienceInterval Taylor has been proposed in the sixties by the interval analysis community for relaxing continuous non-convex constraint systems. However, it generally produces a non-convex relaxation of the solution set. A simple way to build a convex polyhedral relaxation is to select a corner of the studied domain/box as expansion point of the interval Taylor form, instead of the usual midpoint. The idea has been proposed by Neumaier to produce a sharp range of a single function andby Lin and Stadtherr to handle n × n (square) systems of equations. This paper presents an interval Newton-like operator, called X-Newton, that iteratively calls this interval convexification based on an endpoint interval Taylor. This general-purpose contractor uses no preconditioning and can handle any system of equality and inequality constraints. It uses Hansen's variant to compute the interval Taylor form and uses two opposite corners of the domain for every constraint. The X-Newton operator can be rapidly encoded, and produces good speedups in constrained global optimization and constraint satisfaction. First experiments compare X-Newton with affine arithmetic

Subfemtosecond Control of Molecular Fragmentation by Hard X-Ray Photons

Tuning hard x-ray excitation energy along Cl 1s→σ∗ resonance in gaseous HCl allows manipulating molecular fragmentation in the course of the induced multistep ultrafast dissociation. The observations are supported by theoretical modeling, which shows a strong interplay between the topology of the potential energy curves, involved in the Auger cascades, and the so-called core-hole clock, which determines the time spent by the system in the very first step. The asymmetric profile of the fragmentation ratios reflects different dynamics of nuclear wave packets dependent on the photon energy

Auger resonant-Raman decay after Xe L-edge photoexcitation

We have investigated resonant Auger decay of xenon following photoexcitation of each of the three L edges under resonant-Raman conditions, which allowed us to characterize several higher Rydberg transitions. Relative intensities for spectator final states reached after L1−, L2−, and L3-edge excitations are studied in detail. Thanks to state-of-the-art experimental arrangements, our results not only reproduce the previously calculated 3d−25d and nd(n>5) state cross sections after L3 excitation, but also allow extracting the 3d−26d spectator state energy position and revealing its resonant behavior, blurred by the insufficient experimental resolution in previous data sets. The 3d−26p and 3d−27p states reached after L1 excitation as well as the 3d−25d and 3d−26d states reached after L2 excitation are also investigated and their relative intensities are reported and compared to ab initio Dirac-Hartree-Fock configuration-interaction calculations. We found the signature of electronic- state-lifetime interference effects between several coherently excited intermediate states, due to large lifetime broadening. Electron recapture processes are also identified above all three photoionization thresholds

The MPFI Library: Towards IEEE 1788-2015 Compliance

International audienceThe IEEE 1788-2015 has standardized interval arithmetic. However, few libraries for interval arithmetic are compliant with this standard. The main features of the IEEE 1788-2015 standard are detailed, namely the structure into 4 levels, the possibility to accomodate a new mathematical theory of interval arithmetic through the notion of flavor, and the mechanism of decoration for handling exceptions. These features were not present in the libraries developed prior to the elaboration of the standard. MPFI is such a library: it is a C library, based on MPFR, for arbitrary precision interval arithmetic. MPFI is not (yet) compliant with the IEEE 1788-2015 standard for interval arithmetic: the planned modifications are presented. Some considerations about performance and HPC on interval computations based on this standard, or on MPFI, conclude the paper

Detailed assignment of normal and resonant Auger spectra of Xe near the L edges

We present a comprehensive experimental and theoretical investigation on the LMM, LMN, and LNN normal Auger spectra of xenon, which reveal excellent agreement with theory when core-hole lifetimes of the two-hole final states are taken into account. Generally, the spectra turned out to be highly complex due to a strong overlap of the Auger transitions subsequent to 2s−11/2, 2p−11/2, and 2p−13/2 ionization. This overlap is due to the splitting of the three initial L core holes and the different final M and N core holes being on the same order of magnitude of several hundred eV. The Auger transitions are assigned in detail based on the theoretical results. Most of the MM, MN, and NN final states are described well based on jj coupling. In addition, we present a detailed assignment of the resonant LM45M45 Auger transition subsequent to the 2s→6p, 7p and 2p→5d, 6d excitations