1,594 research outputs found
A metric property of umbilic points
In the space of cubic forms of surfaces, regarded as a
-space and endowed with a natural invariant metric, the ratio of the volumes
of those representing umbilic points with negative to those with positive
indexes is evaluated in terms of the asymmetry of the metric, defined here. A
connection of this ratio with that reported by Berry and Hannay (1977) in the
domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur
Hopf Bifurcations in a Watt Governor With a Spring
This paper pursues the study carried out by the authors in "Stability and
Hopf bifurcation in a hexagonal governor system", focusing on the codimension
one Hopf bifurcations in the hexagonal Watt governor differential system. Here
are studied the codimension two, three and four Hopf bifurcations and the
pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating
the number, types and positions of bifurcating small amplitude periodic orbits,
are determined. As a consequence it is found an open region in the parameter
space where two attracting periodic orbits coexist with an attracting
equilibrium point.Comment: 30 pages and 7 figure
The Minimal Geometric Deformation Approach: a brief introduction
We review the basic elements of the Minimal Geometric Deformation approach in
details. This method has been successfully used to generate brane-world
configurations from general relativistic perfect fluid solutions.Comment: Brief review; minor corrections; references adde
Anisotropic solutions by gravitational decoupling
We investigate the extension of isotropic interior solutions for static
self-gravitating systems to include the effects of anisotropic spherically
symmetric gravitational sources by means of the gravitational decoupling
realised via the minimal geometric deformation approach. In particular, the
matching conditions at the star surface with the outer Schwarzschild space-time
are studied in great details, and we describe how to generate, from a single
physically acceptable isotropic solution, new families of anisotropic solutions
whose physical acceptability is also inherited from their isotropic parent.Comment: 20 pages, 4 figures; references and typos corrected; final version to
match the EPJC versio
A causal Schwarzschild-de Sitter interior solution by gravitational decoupling
We employ the minimal geometric deformation approach to gravitational
decoupling (MGD- decoupling) in order to build an exact anisotropic version of
the Schwarzschild interior solution in a space-time with cosmological constant.
Contrary to the well-known Schwarzschild interior, the matter density in the
new solution is not uniform and possesses subluminal sound speed. It therefore
satisfies all standard physical requirements for a candidate astrophysical
object.Comment: 15 pages, 6 figure
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