Extra dimensions as a source of the electroweak model

The Higgs boson of the Standard model is described by a set of off-diagonal components of the multidimensional metric tensor, as well as the gauge fields. In the low-energy limit, the basic properties of the Higgs boson are reproduced, including the shape of the potential and interactions with the gauge fields of the electroweak part of the Standard model.Comment: 11 pages, revtex4. Some wording changed, misprints corrected, 1 reference adde

Navier-Stokes calculations with a coupled strongly implicit method. Part 2: Spline solutions

A coupled strongly implicit method is combined with a deferred-corrector spline solver for the vorticity-stream function form of the Navier-Stokes equation. Solutions for cavity, channel and cylinder flows are obtained with the fourth-order spline 4 procedure. The strongly coupled spline corrector method converges as rapidly as the finite difference calculations and also allows for arbitrary large time increments for the Reynolds numbers considered. In some cases fourth-order smoothing or filtering is required in order to suppress high frequency oscillations

High-order numerical solutions using cubic splines

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes

A pressure flux-split technique for computation of inlet flow behavior

A method for calculating the flow field in aircraft engine inlets is presented. The phenomena of inlet unstart and restart are investigated. Solutions of the reduced Navier-Stokes (RNS) equations are obtained with a time consistent direct sparse matrix solver that computes the transient flow field both internal and external to the inlet. Time varying shocks and time varying recirculation regions can be efficiently analyzed. The code is quite general and is suitable for the computation of flow for a wide variety of geometries and over a wide range of Mach and Reynolds numbers

Solution of three-dimensional afterbody flow using reduced Navier-Stokes equations

The flow over afterbody geometries was investigated using the reduced Navier-Stokes (RNS) approximation. Both pressure velocity flux-split and composites velocity primitive variable formulations were considered. Pressure or pseudopotential relaxation procedures are combined with sparse matrix or coupled strongly implicit algorithms to form a three-dimensional solver for general non-orthogonal coordinates. Three-dimensional subsonic and transonic viscous/inviscid interacting flows were evaluated. Solutions with and without regions of recirculation were obtained

Self-stabilization of extra dimensions

We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can work with rather a general form of the gravitational action. As examples, we consider pure gravity with Lagrangians quadratic and cubic in the scalar curvature and some more complex ones in a simple Kaluza-Klein framework. After a transition to the 4D Einstein conformal frame, this results in effective scalar field theories with certain effective potentials, which in many cases possess positive minima providing stable small-size extra dimensions. Estimates made in the original (Jordan) conformal frame show that the problem of a small value of the cosmological constant in the present Universe is softened in this framework but is not solved completely.}Comment: 10 pages, 4 figures, revtex4. Version with additions and corrections, accepted at Phys. Rev.

Stationary Points of Scalar Fields Coupled to Gravity

We investigate the dynamics of gravity coupled to a scalar field using a non-canonical form of the kinetic term. It is shown that its singular point represents an attractor for classical solutions and the stationary value of the field may occur distant from the minimum of the potential. In this paper properties of universes with such stationary states are considered. We reveal that such state can be responsible for modern dark energy density.Comment: H. Kroger, invited talk, FFP6, Udine (2004), revised version with corrected author lis

ALLY: An operator's associate for satellite ground control systems

The key characteristics of an intelligent advisory system is explored. A central feature is that human-machine cooperation should be based on a metaphor of human-to-human cooperation. ALLY, a computer-based operator's associate which is based on a preliminary theory of human-to-human cooperation, is discussed. ALLY assists the operator in carrying out the supervisory control functions for a simulated NASA ground control system. Experimental evaluation of ALLY indicates that operators using ALLY performed at least as well as they did when using a human associate and in some cases even better