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Modeling scalar flux and the energy and dissipation equations
Closure models derived from the Two-Scale Direct-Interaction Approximation were compared with data from direct simulations of turbulence. Attention was restricted to anisotropic scalar diffusion models, models for the energy dissipation equation, and models for energy diffusion
Mean electromotive force proportional to mean flow in mhd turbulence
In mean-field magnetohydrodynamics the mean electromotive force due to
velocity and magnetic field fluctuations plays a crucial role. In general it
consists of two parts, one independent of and another one proportional to the
mean magnetic field. The first part may be nonzero only in the presence of mhd
turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a
battery, which lets a mean magnetic field grow from zero to a finite value. The
second part, which covers, e.g., the alpha effect, is important for large-scale
dynamos. Only a few examples of the aforementioned first part of mean
electromotive force have been discussed so far. It is shown that a mean
electromotive force proportional to the mean fluid velocity, but independent of
the mean magnetic field, may occur in an originally homogeneous isotropic mhd
turbulence if there are nonzero correlations of velocity and electric current
fluctuations or, what is equivalent, of vorticity and magnetic field
fluctuations. This goes beyond the Yoshizawa effect, which consists in the
occurrence of mean electromotive forces proportional to the mean vorticity or
to the angular velocity defining the Coriolis force in a rotating frame and
depends on the cross-helicity defined by the velocity and magnetic field
fluctuations. Contributions to the mean electromotive force due to
inhomogeneity of the turbulence are also considered. Possible consequences of
the above and related findings for the generation of magnetic fields in cosmic
bodies are discussed.Comment: 7 pages, 1 figure, Astron. Nachr. (submitted
Abstract local cohomology functors
We propose to define the notion of abstract local cohomology functors. The
derived functors of the ordinary local cohomology functor with support in the
closed subset defined by an ideal and the generalized local cohomology functor
associated with a given pair of ideals are characterized as elements of the set
of all the abstract local cohomology functors.Comment: To appear in Mathematical Journal of Okayama Universit
High Distance Bridge Surfaces
Given integers b, c, g, and n, we construct a manifold M containing a
c-component link L so that there is a bridge surface Sigma for (M,L) of genus g
that intersects L in 2b points and has distance at least n. More generally,
given two possibly disconnected surfaces S and S', each with some even number
(possibly zero) of marked points, and integers b, c, g, and n, we construct a
compact, orientable manifold M with boundary S \cup S' such that M contains a
c-component tangle T with a bridge surface Sigma of genus g that separates the
boundary of M into S and S', |T \cap Sigma|=2b and T intersects S and S'
exactly in their marked points, and Sigma has distance at least n.Comment: 17 pages, 13 figures; v2 clarifying revisions made based on referee's
comment
Local cohomology based on a nonclosed support defined by a pair of ideals
We introduce an idea for generalization of a local cohomology module, which
we call a local cohomology module with respect to a pair of ideals (I,J), and
study their various properties. Some vanishing and nonvanishing theorems are
given for this generalized version of local cohomology. We also discuss its
connection with the ordinary local cohomology.Comment: 28 pages, minor corrections, to appear in J. Pure Appl. Algebr
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