Trace formulas for stochastic evolution operators: Smooth conjugation method

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth conjugacy, a locally analytic nonlinear change of field variables. The perturbative corrections are transfered to the corresponding Jacobian, which we expand in terms of the conjugating function, rather than the action used in defining the path integral. The new perturbative expansion which follows by a recursive evaluation of derivatives appears more compact than the standard Feynman diagram perturbation theory. The result is a stochastic analog of the Gutzwiller trace formula with the ``hbar'' corrections computed an order higher than what has so far been attainable in stochastic and quantum-mechanical applications.Comment: 16 pages, 1 figure, New techniques and results for a problem we considered in chao-dyn/980703

Zutphen-Ooijerhoek-site M

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On the O-rich domain of the U-Am-O phase diagram

International audienceUranium–Americium oxides U$_{1−y}$Am$_y$O$_{2±x}$ are promising candidates as possible transmutation targets for next generation nuclear reactors. In the context of a comprehensive investigation of their thermodynamic and thermal properties, the behaviour in oxidizing conditions is here studied. In a recent work, the behaviour in air of stoichiometric and sub-stoichiometric U$_{1−y}$Am$_y$O$_{2±x}$ compounds, with various Am content, was investigated by high-temperature X-ray Diffraction. Herein, the hyper-stoichiometric oxides obtained from that study are investigated by X-ray Absorption Spectroscopy. The new data, together with the previous XRD results, allow determining the exact compositions of the samples and hence obtaining phase diagram points in the O-rich domain of the U-Am-O system. Indeed, five phase diagram points at 1473 K are obtained: two tie-lines in the M$_4$O${9-}$M$_3$O$_8$ domain, for Am/(Am + U) = 0.10 and 0.15, one tie line in the MO$_{2+x-}$M$_3$O$_8$ domain, for Am/(Am + U) = 0.28, and two points in the single phase MO$_{2±x}$ domain, for higher americium concentration. From these data, it is also concluded that trivalent americium has a small solubility in the M$_4$O$_9$ and M$_3$O$_8$ phases