304 research outputs found
Demazure roots and spherical varieties: the example of horizontal SL(2)-actions
Let be a connected reductive group, and let be an affine
-spherical variety. We show that the classification of
-actions on normalized by can be reduced to the
description of quasi-affine homogeneous spaces under the action of a
semi-direct product with the following property. The
induced -action is spherical and the complement of the open orbit is either
empty or a -orbit of codimension one. These homogeneous spaces are
parametrized by a subset of the character lattice
of , which we call the set of Demazure roots of . We give a complete
description of the set when is a semi-direct product of and an algebraic torus; we show particularly that can be
obtained explicitly as the intersection of a finite union of polyhedra in
and a sublattice of
. We conjecture that can be described in a similar
combinatorial way for an arbitrary affine spherical variety .Comment: Added Section 4; modified main result, Theorem 5.18 now; other
change
On automorphism groups of affine surfaces
This is a survey on the automorphism groups in various classes of affine
algebraic surfaces and the algebraic group actions on such surfaces. Being
infinite-dimensional, these automorphism groups share some important features
of algebraic groups. At the same time, they can be studied from the viewpoint
of the combinatorial group theory, so we put a special accent on
group-theoretical aspects (ind-groups, amalgams, etc.). We provide different
approaches to classification, prove certain new results, and attract attention
to several open problems.Comment: Proposition 2.10 from the previous version (published in Algebraic
Varieties and Automorphism Groups, ASPM 75) deleted. There is a mistake in
the proof kindly indicated by J.-P. Furter; the validity of the result
remains open. This does not affect the rest of the pape
Hyperbolic Models of Homogeneous Two-Fluid Mixtures
One derives the governing equations and the Rankine - Hugoniot conditions for
a mixture of two miscible fluids using an extended form of Hamilton's principle
of least action. The Lagrangian is constructed as the difference between the
kinetic energy and a potential depending on the relative velocity of
components. To obtain the governing equations and the jump conditions one uses
two reference frames related with the Lagrangian coordinates of each component.
Under some hypotheses on flow properties one proves the hyperbolicity of the
governing system for small relative velocity of phases.Comment: 14 page
Modeling the multiphase flows in deformable porous media
This work proposes the nonlinear model for the flow of mixture of compressible liquids in a porous medium with consideration of finite deformations and thermal effects. Development of this model is based on the method of thermodynamically consistent systems of conservation laws. Numerical analysis of the model is based on the WENO-Runge-Kutta method of the high accuracy. The model is developed to solve the problems arising when studying the different-scale fluid dynamic processes. Evolution of the wave fields in inhomogeneous saturated porous media is considered
A variational principle for two-fluid models
A variational principle for two-fluid mixtures is proposed. The Lagrangian is
constructed as the difference between the kinetic energy of the mixture and a
thermodynamic potential conjugated to the internal energy with respect to the
relative velocity of phases. The equations of motion and a set of
Rankine-Hugoniot conditions are obtained. It is proved also that the convexity
of the internal energy guarantees the hyperbolicity of the one-dimensional
equations of motion linearized at rest.Comment: 7 page
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