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 $(1+1)$ 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≥4{\bm\geq 4}: 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 ${\rm d} \geq 4$. 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 $({\rm d}-1)$-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