Polyhedral Finsler spaces with locally unique geodesics

We study Finsler PL spaces, that is simplicial complexes glued out of simplices cut off from some normed spaces. We are interested in the class of Finsler PL spaces featuring local uniqueness of geodesics (for complexes made of Euclidean simplices, this property is equivalent to local CAT(0)). Though non-Euclidean normed spaces never satisfy CAT(0), it turns out that they share many common features. In particular, a globalization theorem holds: in a simply-connected Finsler PL space local uniqueness of geodesics implies the global one. However the situation is more delicate here: some basic convexity properties do not extend to the PL Finsler case.     

The Composition Structure of Alternative and Malcev Algebras

We construct a polynomial of degree 5 from the associative nucleus (kernel) of the free alternative algebra. We show that this polynomial is of minimal degree. Using this polynomial, we obtain decompositions of the varieties of alternative and Malcev algebras.     

Influence of an intense pulsed electromagnetic field on nonresonant scattering of a photon by an electron for the nonrelativistic energy

The theory of nonresonant scattering of a photon by an electron in the field of an intense pulsed light wave is developed. The approximation when a pulse width is considerably greater than the characteristic time of wave oscillation is considered. The nonresonant kinematic region is determined. The general relativistic expression for the nonresonant cross-section is derived for the range of the external field intensities if η ₀ ? 1, η₀ ² ? 1 (see Eq. (12)) is valid. The obtained differential cross-section of the process has form of a sum over partial differential cross-sections. Each of them corresponds to the process with emission (absorption) of a certain number of wave photons. It is shown, that for nonrelativistic energy the cross-section summed over all possible partial processes differs considerably from the cross-section of Compton scattering if the external field is absent and may exceed the latter over than 200%.     

Radiogenic argon distribution within a mineral grain: implications for dating of hydrothermal mineral-forming event in Sludyanka complex,Siberia, Russia

Usually, in age-determination procedures, the experimenter is interested in the mean concentrations of parent and daughter substances. However, the structure of a solution of the Fick’s diffusion equation enables one to specify a procedure, allowing, through macroscopic experiments, one to determine the distribution of radiogenic argon (as well as any of other isotopes) within a mineral grain. Argon, influenced in the geological past by a metamorphic event, has a half-sinusoidal distribution, whereas argon preserved in geological time has a rectangular distribution. The ratio of the quantity of argon of the first type to the total argon is called an α-factor. It is believed that this coefficient can be of great interest for geochronological studies, being a symptom of virtual Ar losses and the time instant, at which they happened. A laboratory procedure and a mathematical algorithm to determine the α-factor are developed. As an example, a determination of the α-factor on a vein-phlogopite from the well-studied Sludyanka deposit, Southern Baikal, Siberia, Russia, is described. Rb–Sr isochron age on phlogopite–calcite–apatite paragenetic assemblage yielded 460±7 Ma and is constrained by U–Pb zircon ages of 471±1 and 447±2 Ma, respectively, on an emplacement of early syenites and monzonites and later ‘post-phlogopitic’ pegmatites [E.B. Salnikova, S.A. Sergeev, A.B. Kotov, S.Z. Yakovleva, R.H. Steiger, L.Z. Reznitskiy, E.P. Vasil’ev. U–Pb zircon dating of granulite metamorphism in the Sludyanskiy complex, Eastern Siberia. Gondwana Res., 1, 195–205 (1998). L.Z. Reznitskii, G.P. Sandimirova, Y.A. Pakhol’chenko, S.V. Kuznetsova. The Rb–Sr age of phlogopite deposits in Sludyanka, southern Baikal region. Dokl. Earth Sci., 367, 711–713 (1999). L.Z. Reznitskii, A.B. Kotov, E.B. Salnikova, E.P. Vasil’ev, S.Z. Yakovleva, V.P. Kovach, A.M. Fedoseenko. The age and time span of the origin of phlogopite and lazurite deposits in the Southwestern Baikal area: U–Pb geochronology. Petrology, 8, 66–76 (2000).]. In this study, the phlogopite gave an apparent K–Ar age of 365.6±10.4 Ma which has no geological meaning. The α-factor of 0.27 was derived from a laboratory kinetic experiment. The age determined by the rectangularly distributed argon corresponded to α×0.129 nmm³/g (total radiogenic argon in the sample)=94.17 nmm³/g, and an age of ～274 Ma (e.g. a period without any argon losses). Here, at the first sight, we deal with common argon losses not conjugated with any geological event, because after 447 Ma only lower temperature (in a range of 50–300 ^°C) hydrothermal processes were recorded. A paragenetic phlogopite-bearing vein mineral, hyalophane, having a disturbed Rb–Sr isotopic system, however, yielded ⁴⁰Ar/³⁹Ar subplateau age of 271±2 Ma [V.V. Ivanenko, M.I. Karpenko, M.A. Litsarev. Age of the Sludyanka phlogopite deposits (in Russian; data of the ³⁹Ar–⁴⁰Ar method). In Geological Series 5, pp. 92–98, Izvestiya Akademii Nauk SSSR, Moskva (1990).], marking similar timing of the K–Ar isotopic system closure. This indicates that K–Ar isotopic system in the phlogopite was not closed (or was partially reset) long after its crystallisation and closing of the Rb–Sr system, in spite of the fact that the crystal was not affected by processes having temperatures above the accepted closure temperatures for micas. There seems to have acted an exchange mechanism of OH-groups between surrounding fluid and hydrocrystal structure. Thus the argon loss did not occur, spontaneously, but argon particles seem to have been captured and carried to the mineral surface by vacancies formed during displacements of OH-groups.     

Integrable boundary interaction in 3D target space: The “pillow-brane” model

We propose a model of boundary interaction, with three-dimensional target space, and the boundary values of the field X∈R³$\mathbf{X}\in {\mathbb{R}}^3$ constrained to lay on a two-dimensional surface of the “pillow” shape. We argue that the model is integrable, and suggest that its exact solution is described in terms of certain linear ordinary differential equation.     

An efficient numerical tool for dose deposition prediction applied to synchrotron medical imaging and radiation therapy

Medical imaging and radiation therapy are widely used synchrotron‐based techniques which have one thing in common: a significant dose delivery to typically biological samples. Among the ways to provide the experimenters with image guidance techniques indicating optimization strategies, Monte Carlo simulation has become the gold standard for accurately predicting radiation dose levels under specific irradiation conditions. A highly important hampering factor of this method is, however, its slow statistical convergence. A track length estimator (TLE) module has been coded and implemented for the first time in the open‐source Monte Carlo code GATE/Geant4. Results obtained with the module and the procedures used to validate them are presented. A database of energy‐absorption coefficients was also generated, which is used by the TLE calculations and is now also included in GATE/Geant4. The validation was carried out by comparing the TLE‐simulated doses with experimental data in a synchrotron radiation computed tomography experiment. The TLE technique shows good agreement versus both experimental measurements and the results of a classical Monte Carlo simulation. Compared with the latter, it is possible to reach a pre‐defined statistical uncertainty in about two to three orders of magnitude less time for complex geometries without loss of accuracy.     

Hyperfine Interaction Tensors of 13C Nuclei for Ring Carbons of Ubisemiquinone-10 Hydrogen Bonded in Alcohol Solvents

The anion radicals of ubiquinones-10 ¹³C chemically labeled at the C₅ or C₆ ring positions in alcohol have been studied by 1D and 2D ESEEM to define the hyperfine interaction tensors with the ¹³C nuclei. Analysis of the cross-peak line shapes and simulations of the spectra allowed us to conclude that the hyperfine tensors are characterized by an anisotropic component T ~6 MHz and an isotropic coupling a ~?3 MHz with support from DFT calculations. However, these values were found to be inconsistent with the shift of the sum combination harmonic in the four-pulse ESEEM spectra. Simulations resolve this apparent discrepancy by showing that the shift of the sum combination to lower frequency and its broadening can be accounted for by a distribution of the hyperfine couplings. A spread of the methoxy group conformations, as supported by previous experimental observations, is suggested as the mechanism influencing the distribution of the hyperfine couplings for the ring carbons.