10,268 research outputs found
Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations
In this paper we imitate the traditional method which is used customarily in
the General Relativity and some mathematical literatures to derive the
Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more
distinct concerning geometric meaning than the vielbein method. Especially, if
the lower dimensional metric is independent of reduced dimensions the
counterpart of the symmetric extrinsic curvature is proportional to the
antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal
space, the SO(n) symmetry and SU(n) symmetry are discussed. And the
Kaluza-Klein instanton is also enquired.Comment: 15 page
N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models
We study N=2 nonlinear two dimensional sigma models with boundaries and their
massive generalizations (the Landau-Ginzburg models). These models are defined
over either Kahler or bihermitian target space manifolds. We determine the most
general local N=2 superconformal boundary conditions (D-branes) for these sigma
models. In the Kahler case we reproduce the known results in a systematic
fashion including interesting results concerning the coisotropic A-type branes.
We further analyse the N=2 superconformal boundary conditions for sigma models
defined over a bihermitian manifold with torsion. We interpret the boundary
conditions in terms of different types of submanifolds of the target space. We
point out how the open sigma models correspond to new types of target space
geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitian)
we discuss an important class of supersymmetric boundary conditions which
admits a nice geometrical interpretation.Comment: 48 pages, latex, references and minor comments added, the version to
appear in JHE
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Generalized convective quasi-equilibrium principle
A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection.
The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity
Almost-stationary motions and gauge conditions in General Relativity
An almost-stationary gauge condition is proposed with a view to Numerical
Relativity applications. The time lines are defined as the integral curves of
the timelike solutions of the harmonic almost-Killing equation. This vector
equation is derived by a variational principle, by minimizing the deviations
from isometry. The corresponding almost-stationary gauge condition allows one
to put the field equations in hyperbolic form, both in the free-evolution ADM
and in the Z4 formalisms.Comment: Talk presented at the Spanish Relativity Meeting, September 6-10 2005
Revised versio
Routh's procedure for non-Abelian symmetry groups
We extend Routh's reduction procedure to an arbitrary Lagrangian system (that
is, one whose Lagrangian is not necessarily the difference of kinetic and
potential energies) with a symmetry group which is not necessarily Abelian. To
do so we analyse the restriction of the Euler-Lagrange field to a level set of
momentum in velocity phase space. We present a new method of analysis based on
the use of quasi-velocities. We discuss the reconstruction of solutions of the
full Euler-Lagrange equations from those of the reduced equations.Comment: 30 pages, to appear in J Math Phy
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