Asymptotic analysis for small long-wave perturbations of a given stationary shear flow of an ideal fluid with free boundary as t → ∞ is performed. It is shown that small disturbances of the flow are attracted to periodic solution in the case where the governing equations are hyperbolic on the main shear flow solution. A class of shear flows for which Landau damping is realizable, is described. Analytical results obtained are validated by numerical calculations.
The long-wave equations describing three-dimensional shear wave motion of a free-surface ideal fluid are rearranged to a special form and used to describe discontinuous solutions. Relations at the discontinuity front are derived, and stability conditions for the discontinuity are formulated. The problem of determining the flow parameters behind the discontinuity front from known parameters before the front and specified velocity of motion of the front are investigated.
Introduction.We consider a mathematical model which describes three-dimensional shear flows of a heavy incompressible ideal fluid with a free surface above an even bottom in the long-wave approximation. This model, which extends the classical shallow water model, reduces to a system of integrodifferential equations. Unlike for the classical model, the propagation of nonlinear wave perturbations for the integrodifferential model has been studied less extensively. New approaches to the solution of these questions were proposed in [1-4] using a new mathematical apparatus. In [1], generalized characteristics were found and hyperbolicity conditions were formulated for the system of integrodifferential shallow-water equations describing three-dimensional stationary shear flows of a free-boundary ideal fluid. The spatial simple waves described by the indicated system of equations were studied in [2]. A definition of discontinuous solutions for a mathematical model of shear plane-parallel incompressible flows was proposed in [3]. In the same paper, the properties of strong-discontinuity relations were analyzed. A similar analysis for a model of plane-parallel flows of barotropic fluids was performed in [4]. New approaches to the description of the interaction of shear flows of an incompressible ideal fluid were used in [5]. Problems of conjugation of various filtration and channel flows of a viscous incompressible fluid and various mathematical models of two-phase fluids were studied in [6,7].In the present paper, we consider the spatial problem of conjugation of non-one-dimensional flows of an ideal incompressible fluid with a free boundary. Relations at the discontinuity front and stability conditions for discontinuous flow are formulated.1. Formulation of the Problem. We consider the system of equations
Reconstruction of vascular net of small laboratory animals from magnetic resonance imaging magnetic resonance imaging (MRI) data is associated with some problems. First of all this is due to the physics of nuclear magnetic resonance nuclear magnetic resonance signal registration. Scanner is sensible to the blood flow propagating through the section and shows real situation about vessel presence only if it is perpendicular to the scanning plane. If the vessel is parallel to the scanning planeThe study was completed thanks to the support of Russian Science Foundation (project #14-35-00020, all MRI experimentation studies using Bruker BioSpec 117/16 USR scanner), Russian Foundation for Basic Research (projects #14-01-00036, #15-01-00745 A, mathematical modelling). Experiments were carried out on unique scientific installation -Centre for Genetic Resources Laboratory Animals (RFMEFI61914X0005 and RFMEFI62114X0010).
& S. V. Maltseva
AppliedMagnetic Resonance scanner does not shows vessel presence. This circumstance causes the fragmentation of reconstructed vascular net. Despite the fact that all vessels in brain must be connected reconstructed vascular net consists of several fragments. We propose new algorithm allowing for reconstruction fragmentation-free vascular net according to the data of MRI scanner. Our approach is based on multiple scanning, object under consideration is probed by several sets of parallel planes. Our method allows for elimination or significant reduction mentioned disadvantage. The algorithm is applied to real MRI data of small laboratory animals and shows good results.
The paper presents a model of a cerebral vascular system including two types of vessel networks (arterial and venous) joined by a porous medium as a substitute to a microcapillary system. The aim of the paper is to reproduce numerically experimental data on endovascular measurements of fluid velocity and pressure in the afferent artery and the efferent vein of the arteriovenous malformation (AVM). The suggested model qualitatively simulates all the main features of the experimental $vp$-diagrams: presence of the time shift between velocity and pressure waves, semicircular shape of the diagram, difference in the direction of circulation in the arterial and venous parts and upper-left drift of the diagram during the embolisation of the AVM. The velocity–pressure time shift is analysed on the modelling example of pulsation flow within a vessel in a cylindrical porous medium. The demonstrated adequacy of the model allows its further use for simulation of various strategies of AVM treatment, haemorrhage risk estimations, etc.
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