Dynamics of a vortex pair in radial flow

The problem of vortex pair motion in two-dimensional radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of a corotating vortex pair in a quiescent environment transforms into motion along a logarithmic spiral in radial flow. The problem may have applications in astrophysics and geophysics.     

Symmetry group of the kinetic equation and stationary distributions in a weakly turbulent plasma

A class of essentially non-equilibrium distributions characterized by the constant flux of one of the “integral of motion” (e.g. energy, number of particles or momentum) both for waves and particles is shown to exist in plasmas due to the symmetry of collision integrals (particle-wave interactions or Boltzmann's integral resp.). As a result, the non-equilibrium distributions can be obtained from a functional equation inferring that the projection of the stoss-integrand on the irreducible group representation should be equal to zero.     

The Dirichlet series for the exterior square <Emphasis Type="Italic">L</Emphasis>-function on GL(<Emphasis Type="Italic">n</Emphasis>)

We present an elementary derivation of the Jacquet–Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients A(m ₁,…,m _n−1).     

Behavior of Viscoplastic Rocks near Fractures: Mathematical Modeling

Doklady Physics - On the basis of the laws of conservation and the principles of thermodynamics, a mathematical model of the flow of a two-phase granular fluid is proposed. One of the phases is the...     

From 1,4-diketones to N-vinyl derivatives of 3,3′-bipyrroles and 4,8-dihydropyrrolo[2,3-f]indole in just two preparative steps

Dioximes of hexane-2,5-dione and cyclohexane-1,4-dione react with acetylene in an autoclave (KOH/DMSO, 100 °C, 1 h, initial pressure 14 atm) to give 2,2′-dimethyl-1,1′-divinyl-[3,3′]bipyrrole and 1,5-divinyl-4,8-dihydropyrrolo[2,3-f]indole in 12% and 6% yields, respectively, thus exemplifying a very simple, straightforward route to inaccessible or unknown pyrrolic assemblies.