A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders

We present an algorithm for the numerical solution of nonlinear parabolic partial differential equations. This algorithm extends the classical Feynman-Kac formula to fully nonlinear partial differential equations, by using random trees that carry information on nonlinearities on their branches. It applies to functional, non-polynomial nonlinearities that are not treated by standard branching arguments, and deals with derivative terms of arbitrary orders. A Monte Carlo numerical implementation is provided

Numerical solution of the incompressible Navier-Stokes equation by a deep branching algorithm

We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching trees. This approach covers functional nonlinearities involving gradient terms of arbitrary orders, and it requires only a boundary condition over space at a given terminal time $T$ instead of Dirichlet or Neumann boundary conditions at all times as in standard solvers. Its implementation relies on Monte Carlo estimation, and uses neural networks that perform a meshfree functional estimation on a space-time domain. The algorithm is applied to the numerical solution of the Navier-Stokes equation and is benchmarked to other implementations in the cases of the Taylor-Green vortex and Arnold-Beltrami-Childress flow

Multielectron spectroscopy: Auger decays of the argon 2p hole

All the different Auger decay paths of Argon 2p holes have been characterized using a time of flight spectrometer of the magnetic bottle type. All electrons (the photoelectron and up to three Auger electrons) are detected in coincidence and resolved in energy. Double Auger decay is shown to proceed either through a direct process or by intense cascade paths, implying highly excited autoionizing Ar2+ states, which are identified as Ar2+ 3s−2 correlation satellites. Triple Auger decay is also observed and estimated to account for 0.2% only of all Auger decay

Dynamics of electron emission in double photoionization processes near the Krypton 3d threshold

Two electron emission following photoabsorption near the Kr 3d threshold is investigated both experimentally and theoretically. On the experimental side, electron/electron coincidences using a magnetic bottle time of flight spectrometer allow us to observe the complete Double Photo Ionisation (DPI) continua of selected Kr2+ final states, and to see how these continua are affected by resonant processes in the vicinity of the Kr 3d threshold. The analysis is based on a quantum mechanical approach that takes into account the contribution of three different processes: A) Auger decay of the inner 3d vacancy with the associated post collision interaction (PCI) effects, B) capture of slow photoelectrons into discrete states followed by valence multiplet decay (VMD) of the excited ionic states and C) valence shell DPI. The dominant process for each Kr2+(4p-2) final state is the photoionization of the inner shell followed by Auger decay of the 3d vacancies. Moreover, for the 4p2(3P) and 4p-2(1D) final ionic states an important contribution comes from the processes of slow photoelectron capture followed by VMD as well as from double ionization of the outer shell involving also VMD

4d-inner-shell ionization of Xe+ ions and subsequent Auger decay

We have studied Xe+4d inner-shell photoionization in a direct experiment on Xe+ ions, merging an ion and a photon beam and detecting the ejected electrons with a cylindrical mirror analyzer. The measured 4d photoelectron spectrum is compared to the 4d core valence double ionization spectrum of the neutral Xe atom, obtained with a magnetic bottle spectrometer. This multicoincidence experiment gives access to the spectroscopy of the individual Xe2+4d−15p−1 states and to their respective Auger decays, which are found to present a strong selectivity. The experimental results are interpreted with the help of ab initio calculations.1\. Auflag

A von Hamos spectrometer based on highly annealed pyrolytic graphite crystal in tender x-ray domain

We have built an x-ray spectrometer in a von Hamos configuration based on a highly annealed pyrolytic graphite crystal. The spectrometer is designed to measure x-ray emission in the range of 2–5 keV. A spectral resolution E/ΔE of 4000 was achieved by recording the elastic peak of photons issued from the GALAXIES beamline at the SOLEIL synchrotron radiation facility

Intermanifold similarities in partial photoionization cross sections of helium

Using the eigenchannel R-matrix method we calculate partial photoionization cross sections from the ground state of the helium atom for incident photon energies up to the N=9 manifold. The wide energy range covered by our calculations permits a thorough investigation of general patterns in the cross sections which were first discussed by Menzel and co-workers [Phys. Rev. A {\bf 54}, 2080 (1996)]. The existence of these patterns can easily be understood in terms of propensity rules for autoionization. As the photon energy is increased the regular patterns are locally interrupted by perturber states until they fade out indicating the progressive break-down of the propensity rules and the underlying approximate quantum numbers. We demonstrate that the destructive influence of isolated perturbers can be compensated with an energy-dependent quantum defect.Comment: 10 pages, 10 figures, replacement with some typos correcte