1,334 research outputs found

    Monodromy dependence and connection formulae for isomonodromic tau functions

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    We discuss an extension of the Jimbo-Miwa-Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational coefficients. This extension is based on the results of M. Bertola generalizing a previous construction by B. Malgrange. We show how this 1-form can be used to solve a long-standing problem of evaluation of the connection formulae for the isomonodromic tau functions which would include an explicit computation of the relevant constant factors. We explain how this scheme works for Fuchsian systems and, in particular, calculate the connection constant for generic Painlev\'e VI tau function. The result proves the conjectural formula for this constant proposed in \cite{ILT13}. We also apply the method to non-Fuchsian systems and evaluate constant factors in the asymptotics of Painlev\'e II tau function.Comment: 54 pages, 6 figures; v4: rewritten Introduction and Subsection 3.3, added few refs to match published articl

    Beam halo collimation in heavy ion synchrotrons

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    This paper presents a systematic study of the halo collimation of ion beams from proton up to uranium in synchrotrons. The projected Facility for Antiproton and Ion Research synchrotron SIS100 is used as a reference case. The concepts are separated into fully stripped (e.g., ^{238}U^{92+}) and partially stripped (e.g., ^{238}U^{28+}) ion collimation. An application of the two-stage betatron collimation system, well established for proton accelerators, is intended also for fully stripped ions. The two-stage system consists of a primary collimator (a scattering foil) and secondary collimators (bulky absorbers). Interaction of the particles with the primary collimator (scattering, momentum losses, and nuclear interactions) was simulated by using fluka. Particle-tracking simulations were performed by using mad-x. Finally, the dependence of the collimation efficiency on the primary ion species was determined. The influence of the collimation system adjustment, lattice imperfections, and beam parameters was estimated. The concept for the collimation of partially stripped ions employs a thin stripping foil in order to change their charge state. These ions are subsequently deflected towards a dump location using a beam optical element. The charge state distribution after the stripping foil was obtained from global. The ions were tracked by using mad–x

    Halo collimation of fully-stripped light and heavy ions in the SIS100

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    Theoretical Approach for Developing the Thermographic Method in Ultrasonic Fatigue

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    AbstractIn the last years, several approaches were developed in literature for predicting the fatigue strength of different kinds of materials. One approach is the Thermographic Method, based on the thermographic technique. This study is devoted to the development of a theoretical approach for modeling of surface and undersurface fatigue crack initiation and temperature evolution during ultrasonic fatigue test. The proposed model is based on the statistical description of mesodefect ensemble and describes an energy balance in materials (including power of energy dissipation) under cyclic loading. The model allows us to simulate the damage to fracture transition and corresponding temperature evolution in critical cross section of a sample tested in very high cyclic fatigue regime
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