42 research outputs found
Intra--Galactic thin shell wormhole and its stability
In this paper, we construct an intra-galactic thin shell wormhole joining two
copies of identical galactic space times described by the Mannheim-Kazanas de
Sitter solution in conformal gravity and study its stability under spherical
perturbations. We assume the thin shell material as a Chaplygin gas and discuss
in detail the values of the relevant parameters under which the wormhole is
stable. We study the stability following the method by Eiroa and we also
qualitatively analyze the dynamics through the method of Weierstrass. We find
that the wormhole is generally unstable but there is a small interval in radius
for which the wormhole is stable
Buckling and longterm dynamics of a nonlinear model for the extensible beam
This work is focused on the longtime behavior of a non linear evolution
problem describing the vibrations of an extensible elastic homogeneous beam
resting on a viscoelastic foundation with stiffness k>0 and positive damping
constant. Buckling of solutions occurs as the axial load exceeds the first
critical value, \beta_c, which turns out to increase piecewise-linearly with k.
Under hinged boundary conditions and for a general axial load P, the existence
of a global attractor, along with its characterization, is proved by exploiting
a previous result on the extensible viscoelastic beam. As P<\beta_c, the
stability of the straight position is shown for all values of k. But, unlike
the case with null stiffness, the exponential decay of the related energy is
proved if P<\bar\beta(k), where \bar\beta(k) < \beta_c(k) and the equality
holds only for small values of k.Comment: 14 pages, 2 figure
Longtime behavior for oscillations of an extensible viscoelastic beam with elastic external supply
This work is focused on a nonlinear equation describing the oscillations of
an extensible viscoelastic beam with fixed ends, subject to distributed elastic
external force. For a general axial load , the existence of a
finite/infinite set of stationary solutions and buckling occurrence are
scrutinized. The exponential stability of the straight position is discussed.
Finally, the related dynamical system in the history space framework is shown
to possess a regular global attractor.Comment: 16 pages, 2 figure
Correct light deflection in Weyl conformal gravity
The conformal gravity fit to observed galactic rotation curves requires
{\gamma}>0. On the other hand, conventional method for light deflection by
galaxies gives a negative contribution to Schwarzschild value for {\gamma}>0,
which is contrary to observation. Thus, it is very important that the
contribution to bending should in principle be positive, no matter how small
its magnitude is. Here we show that the Rindler-Ishak method gives a positive
contribution to Schwarzschild deflection for {\gamma}>0, as desired. We also
obtain the exact local coupling term derived earlier by Sereno. These results
indicate that conformal gravity can potentially test well against all
astrophysical observations to date.Comment: 6 page
An Application of Saint Venant's Theory to Volterra's Distortions
This paper deals with the analysis of the sixth elementary Volterra's distortion for a circular hollow, homogeneous, elastic, isotropic cylinder. More precisely, the specific load connected to the sixth distortion is proved to be equivalent (in Saint Venant's theory) to a right combined compressive and bending stress and to a right combined tensile and bending stress. Our results have been applied to a material made up of steel to compare the obtained numerical results with Volterra's predictions: the values calculated through Saint Venant's theory are more strictly related to those calculated by Volterra when the cylinder thickness tends to zero
Long-Term Damped Dynamics of the Extensible Suspension Bridge
This work is focused on the doubly nonlinear equation, whose solutions
represent the bending motion of an extensible, elastic bridge suspended by
continuously distributed cables which are flexible and elastic with stiffness
k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary
values of axial load p and stiffness k^2. For a general external source f, we
prove the existence of bounded absorbing sets.When f is timeindependent, the
related semigroup of solutions is shown to possess the global attractor of
optimal regularity and its characterization is given in terms of the steady
states of the problem.Comment: 19 pages, 1 figur
Simplicial Approach to Fractal Structures
A fractal lattice is defined by iterative maps on a simplex. In particular, Sierpinski gasket and von Koch flake are explicitly obtained by simplex transformations
Generalized potential for apparent forces: the Coriolis effect
It is well known, from Newtonian physics, that apparent forces appear when
the motion of masses is described by using a non-inertial frame of reference.
The generalized potential of such forces is rigorously analyzed focusing on
their mathematical aspects.Comment: 8 pages, accepted for publication in Eur. J. Phy