49,149 research outputs found
Gaussian superpositions in scalar-tensor quantum cosmological models
A free scalar field minimally coupled to gravity model is quantized and the
Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiting
positive and negative frequency modes. The analysis is performed for positive,
negative and zero values of the curvature of the spatial section. Gaussian
superpositions of the modes are constructed, and the quantum bohmian
trajectories are determined in the framework of the Bohm-de Broglie
interpretation of quantum cosmology. Oscillating universes appear in all cases,
but with a characteristic scale of the order of the Planck scale. Bouncing
regular solutions emerge for the flat curvature case. They contract classically
from infinity until a minimum size, where quantum effects become important
acting as repulsive forces avoiding the singularity and creating an
inflationary phase, expanding afterwards to an infinite size, approaching the
classical expansion as long as the scale factor increases. These are
non-singular solutions which are viable models to describe the early Universe.Comment: 14 pages, LaTeX, 3 Postscript figures, uses graficx.st
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
On the stability of the -rheology for granular flow
This article deals with the Hadamard instability of the so-called
model of dense rapidly-sheared granular flow, as reported recently by Barker et
al. (2015,this journal, , 794-818). The present paper presents a
more comprehensive study of the linear stability of planar simple shearing and
pure shearing flows, with account taken of convective Kelvin wave-vector
stretching by the base flow. We provide a closed form solution for the linear
stability problem and show that wave-vector stretching leads to asymptotic
stabilization of the non-convective instability found by Barker et al. We also
explore the stabilizing effects of higher velocity gradients achieved by an
enhanced-continuum model based on a dissipative analog of the van der
Waals-Cahn-Hilliard equation of equilibrium thermodynamics. This model involves
a dissipative hyper-stress, as the analog of a special Korteweg stress, with
surface viscosity representing the counterpart of elastic surface tension.
Based on the enhanced continuum model, we also present a model of steady shear
bands and their non-linear stability against parallel shearing. Finally, we
propose a theoretical connection between the non-convective instability of
Barker et al. and the loss of generalized ellipticity in the quasi-static field
equations. Apart from the theoretical interest, the present work may suggest
stratagems for the numerical simulation of continuum field equations involving
the rheology and variants thereof.Comment: 30 pages, 13 figure
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