Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons

Due to their explicit construction, Aloff-Wallach spaces are prominent in flux compactifications. They carry G_2-structures and admit the G_2-instanton equations, which are natural BPS equations for Yang-Mills instantons on seven-manifolds and extremize a Chern-Simons-type functional. We consider the Chern-Simons flow between different G_2-instantons on Aloff-Wallach spaces, which is equivalent to Spin(7)-instantons on a cylinder over them. For a general SU(3)-equivariant gauge connection, the generalized instanton equations turn into gradient-flow equations on C^3 x R^2, with a particular cubic superpotential. For the simplest member of the Aloff-Wallach family (with 3-Sasakian structure) we present an explicit instanton solution of tanh-like shape.Comment: 1+17 pages, 1 figur

Self-dual Yang-Mills fields in pseudoeuclidean spaces

The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations are constructed from these solutions.Comment: 9 pages, LaTeX, no figure

Supernova Ia: a Converging Delayed Detonation Wave

A model of a carbon-oxygen (C--O) presupernova core with an initial mass 1.33 M_\odot, an initial carbon mass fraction 0.27, and with an average mass growth-rate 5 x 10^{-7} M_\odot/yr due to accretion in a binary system was evolved from initial central density 10^9 g/cm^3, and temperature 2.05 x 10^8 K through convective core formation and its subsequent expansion to the carbon runaway at the center. The only thermonuclear reaction contained in the equations of evolution and runaway was the carbon burning reaction 12C + 12C with an energy release corresponding to the full transition of carbon and oxygen (with the same rate as carbon) into 56Ni. As a parameter we take \alpha_c - a ratio of a mixing length to the size of the convective zone. In spite of the crude assumptions, we obtained a pattern of the runaway acceptable for the supernova theory with the strong dependence of its duration on \alpha_c. In the variants with large enough values of \alpha_c=4.0 x 10^{-3} and 3.0 x 10^{-3} the fuel combustion occurred from the very beginning as a prompt detonation. In the range of 2.0 x 10^{-3} >= \alpha_c >= 3.0 x 10^{-4} the burning started as a deflagration with excitation of stellar pulsations with growing amplitude. Eventually, the detonation set in, which was activated near the surface layers of the presupernova (with m about 1.33 M_\odot) and penetrated into the star down to the deflagration front. Excitation of model pulsations and formation of a detonation front are described in detail for the variant with \alpha_c=1.0 x 10^{-3}.Comment: 13 pages, 11 figures, to appear in Astronomy Letter

Patterns of mercury accumulation in the organs of bank vole Myodes glareolus (Rodentia, Cricetidae)

Mercury (Hg) and its compounds are among the most hazardous environmental pollutants with a high cumulative potential and they can have toxic effects on human and animal health even in low concentrations. Due to the increasing rate of human economic activity and the increase in the amount of Hg in the total cycling of matter, the study of its distribution, transformation, redistribution and accumulation in the abiotic and biotic components of various ecosystems remains important up to the present time. We assessed the content of metal in organs and tissues of the bank vole Myodes (Clethrionomys) glareolus Schreber, 1780 (Rodentia, Cricetidae), a widespread small rodent, caught in different biotopes of forest-steppe and steppe zones of Voronezh region. Measurements of Hg in samples were carried out with a mercury analyzer RA-915+ with the accessory PYRO (Lumex) using the atomic absorption method of cold steam without preliminary sample preparation (the lower limit of mercury detection in samples was 0.001 mg/kg). The sample size was 344 specimens. Mean Hg concentrations ranged from values below the analytical determination threshold to 0.887 mg/kg dry weight in the kidneys, 0.411 in the liver, 0.031 in the muscle tissue, and 0.040 in the brain. A positive correlation was found between the metal content in all possible pairs of organs (except for the “muscle – brain” pair) and a weak negative correlation was found between the Hg level and the mass of the animals. Hg concentrations in the studied organs did not differ between males and females. The metal content in the liver and kidneys of voles from the forest-steppe zone was significantly higher than in those from the steppe zone. Among all studied biotopes (meadow, pine and mixed forest, shrub thickets), the lowest concentrations were observed in animals living in pine forests, while the highest one – in more humidified bush thickets. During the vegetation season, there was a decrease in the average values of animal body mass in the samples and an increase in the content of Hg in the liver and kidneys. The results of the study are relevant in the assessment of atmospheric mercury pollution of terrestrial ecosystems using small mammals, such as Myodes glareolus, as a model object

Cardiovascular response to postural perturbations of different intensities in healthy young adults

The ability to regain control of balance is vital in limiting falls and injuries. Little is known regarding how the autonomic nervous system responds during recovery from balance perturbations of different intensities. The purpose of this study was to examine the cardiovascular response following a standing balance perturbation of varying intensities, quantify cardiac baroreflex sensitivity (cBRS) during standing perturbations, and to establish the stability of the cardiac baroreflex during quiet standing before and after balance disturbances. Twenty healthy participants experienced three different perturbation intensity conditions that each included 25 brief posteriorly-directed perturbations, 8–10 s apart. Three perturbation intensity conditions (low, medium, high) were given in random order. Physiological data were collected in quiet stance for 5 min before testing (Baseline) and again after the perturbation conditions (Recovery) to examine baroreflex stability. Beat-to-beat heart rate (HR) and systolic blood pressure (SBP) analysis post-perturbation indicated an immediate acceleration of the HR for 1–2 s, with elevated SBP 4–5 s post-perturbation. Heart rate changes were greatest in the medium (p = 0.035) and high (p = 0.012) intensities compared to low, while there were no intensity-dependent changes in SBP. The cBRS was not intensity-dependent (p = 0.402) but when perturbation conditions were combined, cBRS was elevated compared to Baseline (p = 0.046). The stability of baseline cBRS was excellent (ICC = 0.896) between quiet standing conditions. In summary, HR, but not SBP or cBRS were intensity-specific during postural perturbations. This was the first study to examine cardiovascular response and cBRS to postural perturbations

Hierarchy of Conservation Laws of Diffusion--Convection Equations

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation laws, we develop and apply the most direct method which is effective to use in the case of two independent variables. Admitting possibility of dependence of conserved vectors on a number of potentials, we generalize the iteration procedure proposed by Bluman and Doran-Wu for finding nonlocal (potential) conservation laws. As an example, we completely classify potential conservation laws (including arbitrary order local ones) of diffusion--convection equations with respect to the equivalence group and construct an exhaustive list of locally inequivalent potential systems corresponding to these equations.Comment: 24 page