Algebraic construction and numerical behaviour of a new s-consistent difference scheme for the 2D Navier-Stokes equations

In this paper we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier-Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier-Stokes equations. Then, we compute the canonical Gröbner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier-Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behaviour of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and also with the scheme which is not strongly consistent

On the General Analytical Solution of the Kinematic Cosserat Equations

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure

Therapeutic physical training for arthrosis of the shoulder joints of athletes

This article examines the statistics of the occurrence of arthrosis of the shoulder joints in athletes and its connection with the popularization of various sports, as well as compares the methods of treatment of this diseaseВ данной статье рассматривается статистика возникновения артроза плечевых суставов у спортсменов и связь её с популяризацией различных видов спорта, а также сравниваются методы лечения данного заболевания. Артроз часто является следствием травмы, поэтому в статье будет рассмотрена статистика травм плечевого сустав

Comparative Analysis of the Subventricular Zone in Rat, Ferret and Macaque: Evidence for an Outer Subventricular Zone in Rodents

The mammalian cerebral cortex arises from precursor cells that reside in a proliferative region surrounding the lateral ventricles of the developing brain. Recent work has shown that precursor cells in the subventricular zone (SVZ) provide a major contribution to prenatal cortical neurogenesis, and that the SVZ is significantly thicker in gyrencephalic mammals such as primates than it is in lissencephalic mammals including rodents. Identifying characteristics that are shared by or that distinguish cortical precursor cells across mammalian species will shed light on factors that regulate cortical neurogenesis and may point toward mechanisms that underlie the evolutionary expansion of the neocortex in gyrencephalic mammals. We immunostained sections of the developing cerebral cortex from lissencephalic rats, and from gyrencephalic ferrets and macaques to compare the distribution of precursor cell types in each species. We also performed time-lapse imaging of precursor cells in the developing rat neocortex. We show that the distribution of Pax6+ and Tbr2+ precursor cells is similar in lissencephalic rat and gyrencephalic ferret, and different in the gyrencephalic cortex of macaque. We show that mitotic Pax6+ translocating radial glial cells (tRG) are present in the cerebral cortex of each species during and after neurogenesis, demonstrating that the function of Pax6+ tRG cells is not restricted to neurogenesis. Furthermore, we show that Olig2 expression distinguishes two distinct subtypes of Pax6+ tRG cells. Finally we present a novel method for discriminating the inner and outer SVZ across mammalian species and show that the key cytoarchitectural features and cell types that define the outer SVZ in developing primates are present in the developing rat neocortex. Our data demonstrate that the developing rat cerebral cortex possesses an outer subventricular zone during late stages of cortical neurogenesis and that the developing rodent cortex shares important features with that of primates

Measuring 129Xe transfer across the blood‐brain barrier using MR spectroscopy

Purpose This study develops a tracer kinetic model of xenon uptake in the human brain to determine the transfer rate of inhaled hyperpolarized 129Xe from cerebral blood to gray matter that accounts for the effects of cerebral physiology, perfusion and magnetization dynamics. The 129Xe transfer rate is expressed using a tracer transfer coefficient, which estimates the quantity of hyperpolarized 129Xe dissolved in cerebral blood under exchange with depolarized 129Xe dissolved in gray matter under equilibrium of concentration. Theory and Methods Time‐resolved MR spectra of hyperpolarized 129Xe dissolved in the human brain were acquired from three healthy volunteers. Acquired spectra were numerically fitted with five Lorentzian peaks in accordance with known 129Xe brain spectral peaks. The signal dynamics of spectral peaks for gray matter and red blood cells were quantified, and correction for the 129Xe T1 dependence upon blood oxygenation was applied. 129Xe transfer dynamics determined from the ratio of the peaks for gray matter and red blood cells was numerically fitted with the developed tracer kinetic model. Results For all the acquired NMR spectra, the developed tracer kinetic model fitted the data with tracer transfer coefficients between 0.1 and 0.14. Conclusion In this study, a tracer kinetic model was developed and validated that estimates the transfer rate of HP 129Xe from cerebral blood to gray matter in the human brain

Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier–Stokes equations

In this paper, we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier–Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier–Stokes equations. Then, we compute the canonical Gröbner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier–Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behavior of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and with the scheme which is not strongly consistent. © 2017 Elsevier Inc

Algebraic construction and numerical behavior of a new s-consistent difference scheme for the 2D Navier–Stokes equations

In this paper, we consider a regular grid with equal spatial spacings and construct a new finite difference approximation (difference scheme) for the system of two-dimensional Navier–Stokes equations describing the unsteady motion of an incompressible viscous liquid of constant viscosity. In so doing, we use earlier constructed discretization of the system of three equations: the continuity equation and the proper Navier–Stokes equations. Then, we compute the canonical Gröbner basis form for the obtained discrete system. It gives one more difference equation which is equivalent to the pressure Poisson equation modulo difference ideal generated by the Navier–Stokes equations, and thereby comprises a new finite difference approximation (scheme). We show that the new scheme is strongly consistent. Besides, our computational experiments demonstrate much better numerical behavior of the new scheme in comparison with the other strongly consistent schemes we constructed earlier and with the scheme which is not strongly consistent. © 2017 Elsevier Inc

Insights and Highlights from Embedded Topical Meeting International Meeting on Best Estimate Methods in Nuclear Installation Safety Analysis

The first (later on called) Best Estimate Plus Uncertainty (BEPU) Conference, was held in the US in the year 2000. The authors of this paper were invited to submit a summary paper to the American Nuclear Society (ANS) Milwaukee Conference in 2001. The paper was discussed in a specific Panel attended by F. D’Auria