Complete classification of stationary flows with constant total pressure of ideal incompressible infinitely conducting fluid

The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of the flow the system of magnetohydrodynamics (MHD) equations is reduced to a nonlinear vector wave equation extended by the incompressibility condition in a form of a generalized Cauchy integral. For flows with constant total pressure the wave equation is explicitly integrated, whereas the incompressibility condition is reduced to a scalar equation for functions, depending on different sets of variables. The central difficulty of the investigation is the separation of variables in the scalar equation, and integration of the resulting overdetermined systems of nonlinear partially differential equations. The canonical representatives of all possible types of solutions together with equivalence transformations, that extend the canonical set to the whole amount of solutions are represented

Multidimensional fluid motions with planar waves

In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture of motion is relatively simple: trajectory of one fluid particle from plane x=const completely determines motion of the whole plane. Basing on the symmetry analysis of differential equations we propose generalization of this solution allowing movements in different directions of fluid particles belonging to plane x=const. At that, all functions but an angle determining the direction of particle's motion depend on t and x only, whereas the angle depends on all coordinates. In this solution the whole picture of motion superposes from identical trajectories placed under different angles in 3D space. Orientations of the trajectories are restricted by a finite relation possessing functional arbitrariness. The solution describes three-dimensional nonlinear processes and singularities in infinitely conducting plasma, gas or incompressible liquid.Comment: 21 pages, 13 figure

Uniformity Studies of Scintillator Tiles directly coupled to SiPMs for Imaging Calorimetry

We present a novel geometry of scintillator tiles developed for fiberless coupling to silicon photomultipliers (SiPMs) for applications in highly granular calorimeters. A high degree of uniformity of the tile response over the full active area was achieved by a drilled slit at the coupling position of the photon sensor with 2 mm, 4 mm and 5.5 mm in height, width and depth. Detailed measurements of the response to penetrating electrons were performed for tiles with a lateral size of 3 x 3 cm^2 and thicknesses of 5 mm and 3 mm.Comment: 6 pages, 8 figures, accepted by NIM