259 research outputs found
Arrival Time Statistics in Global Disease Spread
Metapopulation models describing cities with different populations coupled by
the travel of individuals are of great importance in the understanding of
disease spread on a large scale. An important example is the Rvachev-Longini
model [{\it Math. Biosci.} {\bf 75}, 3-22 (1985)] which is widely used in
computational epidemiology. Few analytical results are however available and in
particular little is known about paths followed by epidemics and disease
arrival times. We study the arrival time of a disease in a city as a function
of the starting seed of the epidemics. We propose an analytical Ansatz, test it
in the case of a spreading on the world wide air transportation network, and
show that it predicts accurately the arrival order of a disease in world-wide
cities
Singular shell embedded into a cosmological model
We generalize Israel's formalism to cover singular shells embedded in a
non-vacuum Universe. That is, we deduce the relativistic equation of motion for
a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker
spacetime. Also, we review the embedding of a Schwarzschild mass into a
cosmological model using "curvature" coordinates and give solutions with
(Sch/FLRW) and without the embedded mass (FLRW).Comment: 25 pages, 2 figure
Classical Electron Model with Negative Energy Density in Einstein-Cartan Theory of Gravitation
Experimental result regarding the maximum limit of the radius of the electron
\sim 10^{-16} cm and a few of the theoretical works suggest that the
gravitational mass which is a priori a positive quantity in Newtonian mechanics
may become negative in general theory of relativity. It is argued that such a
negative gravitational mass and hence negative energy density also can be
obtained with a better physical interpretation in the framework of
Einstein-Cartan theory.Comment: 12 Latex pages, added refs and conclusion
Axially symmetric Einstein-Straus models
The existence of static and axially symmetric regions in a Friedman-Lemaitre
cosmology is investigated under the only assumption that the cosmic time and
the static time match properly on the boundary hypersurface. It turns out that
the most general form for the static region is a two-sphere with arbitrarily
changing radius which moves along the axis of symmetry in a determined way. The
geometry of the interior region is completely determined in terms of background
objects. When any of the most widely used energy-momentum contents for the
interior region is imposed, both the interior geometry and the shape of the
static region must become exactly spherically symmetric. This shows that the
Einstein-Straus model, which is the generally accepted answer for the null
influence of the cosmic expansion on the local physics, is not a robust model
and it is rather an exceptional and isolated situation. Hence, its suitability
for solving the interplay between cosmic expansion and local physics is
doubtful and more adequate models should be investigated.Comment: Latex, no figure
Comments on photonic shells
We investigate in detail the special case of an infinitely thin static
cylindrical shell composed of counter-rotating photons on circular geodetical
paths separating two distinct parts of Minkowski spacetimes--one inside and the
other outside the shell--and compare it to a static disk shell formed by null
particles counter-rotating on circular geodesics within the shell located
between two sections of flat spacetime. One might ask whether the two cases are
not, in fact, merely one
Trapped imbalanced fermionic superfluids in one dimension: A variational approach
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable
Exact Charged 2-Body Motion and the Static Balance Condition in Lineal Gravity
We find an exact solution to the charged 2-body problem in
dimensional lineal gravity which provides the first example of a relativistic
system that generalizes the Majumdar-Papapetrou condition for static balance.Comment: latex,7 pages, 2 figure
Gravitational Lensing by Wormholes
Gravitational lensing by traversable Lorentzian wormholes is a ew possibility
which is analyzed here in the strong field limit. Wormhole solutions are
considered in the Einstein minimally coupled theory and in the brane world
model. The observables in both the theories show significant differences from
those arising in the Schwarzschild black hole lensing. As a corollary, it
follows that wormholes with zero Keplerian mass exhibit lensing properties
which are qualitatively (though not quantitatively) the same as those of a
Schwarzschild black hole. Some special features of the considered solutions are
pointed out.Comment: 20 pages, no figure
A class of exact solutions of Einstein's field equations in higher dimensional spacetimes, d: Majumdar-Papapetrou solutions
The Newtonian theory of gravitation and electrostatics admit equilibrium
configurations of charged fluids where the charge density can be equal to the
mass density, in appropriate units. The general relativistic analog for charged
dust stars was discovered by Majumdar and by Papapetrou. In the present work we
consider Einstein-Maxwell solutions in d-dimensional spacetimes and show that
there are Majumdar-Papapetrou type solutions for all . It is
verified that the equilibrium is independent of the shape of the distribution
of the charged matter. It is also showed that for perfect fluid solutions
satisfying the Majumdar-Papapetrou condition with a boundary where the pressure
is zero, the pressure vanishes everywhere, and that the -dimensional spatial section of the spacetime is conformal to a
Ricci-flat space. The Weyl d-dimensional axisymmetric solutions are generalized
to include electric field and charged matter.Comment: 26 pages, no figure
Quantum singularity of Levi-Civita spacetimes
Quantum singularities in general relativistic spacetimes are determined by
the behavior of quantum test particles. A static spacetime is quantum
mechanically singular if the spatial portion of the wave operator is not
essentially self-adjoint. Here Weyl's limit point-limit circle criterion is
used to determine whether a wave operator is essentially self-adjoint. This
test is then applied to scalar wave packets in Levi-Civita spacetimes to help
elucidate the physical properties of the spacetimes in terms of their metric
parameters
- …