28,037 research outputs found
Space-time correlations in urban sprawl
Understanding demographic and migrational patterns constitutes a great
challenge. Millions of individual decisions, motivated by economic, political,
demographic, rational, and/or emotional reasons underlie the high complexity of
demographic dynamics. Significant advances in quantitatively understanding such
complexity have been registered in recent years, as those involving the growth
of cities [Bettencourt LMA, Lobo J, Helbing D, Kuehnert C, West GB (2007)
Growth,. Innovation, Scaling, and the Pace of Life in Cities, Proc Natl Acad
Sci USA 104 (17) 7301-7306] but many fundamental issues still defy
comprehension. We present here compelling empirical evidence of a high level of
regularity regarding time and spatial correlations in urban sprawl, unraveling
patterns about the inertia in the growth of cities and their interaction with
each other. By using one of the world's most exhaustive extant demographic data
basis ---that of the Spanish Government's Institute INE, with records covering
111 years and (in 2011) 45 million people, distributed amongst more than 8000
population nuclei--- we show that the inertia of city growth has a
characteristic time of 15 years, and its interaction with the growth of other
cities has a characteristic distance of 70 km. Distance is shown to be the main
factor that entangles two cities (a 60% of total correlations). We present a
mathematical model for population flows that i) reproduces all these
regularities and ii) can be used to predict the population-evolution of cities.
The power of our current social theories is thereby enhanced
Multipole structure of compact objects
We analyze the applications of general relativity in relativistic
astrophysics in order to solve the problem of describing the geometric and
physical properties of the interior and exterior gravitational and
electromagnetic fields of compact objects. We focus on the interpretation of
exact solutions of Einstein's equations in terms of their multipole moments
structure. In view of the lack of physical interior solutions, we propose an
alternative approach in which higher multipoles should be taken into account
Matching conditions in relativistic astrophysics
We present an exact electrovacuum solution of Einstein-Maxwell equations with
infinite sets of multipole moments which can be used to describe the exterior
gravitational field of a rotating charged mass distribution. We show that in
the special case of a slowly rotating and slightly deformed body, the exterior
solution can be matched to an interior solution belonging to the Hartle-Thorne
family of approximate solutions. To search for exact interior solutions, we
propose to use the derivatives of the curvature eigenvalues to formulate a
matching condition from which the minimum radius can be derived at which
the matching of interior and exterior spacetimes can be carried out. We prove
the validity of the matching in the particular case of a static mass with
a quadrupole moment. The corresponding interior solution is obtained
numerically and the matching with the exterior solution gives as a result the
minimum radius of the mass configuration
Pioneer's Anomaly and the Solar Quadrupole Moment
The trajectories of test particles moving in the gravitational field of a
non-spherically symmetric mass distribution become affected by the presence of
multipole moments. In the case of hyperbolic trajectories, the quadrupole
moment of an oblate mass induces a displacement of the trajectory towards the
mass source, an effect that can be interpreted as an additional acceleration
directed towards the source. Although this additional acceleration is not
constant, we perform a general relativistic analysis in order to evaluate the
possibility of explaining Pioneer's anomalous acceleration by means of the
observed Solar quadrupole moment, within the range of accuracy of the observed
anomalous acceleration. We conclude that the Solar quadrupole moment generates
an acceleration which is of the same order of magnitude of Pioneer's constant
acceleration only at distances of a few astronomical units.Comment: Typos corrected, references adde
Density functional theory in the canonical ensemble I General formalism
Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM)
theorem in the grand canonical ensemble (GCE). However, as recent work shows,
although its extension to the canonical ensemble (CE) is not straightforward,
work in nanopore systems could certainly benefit from a mesoscopic DFT in the
CE. The stumbling block is the fixed constraint which is responsible for
the failure in proving the interchangeability of density profiles and external
potentials as independent variables. Here we prove that, if in the CE the
correlation functions are stripped off of their asymptotic behaviour (which is
not in the form of a properly irreducible -body function), the HKSM theorem
can be extended to the CE. In proving that, we generate a new {\it hierarchy}
of -modified distribution and correlation functions which have the same
formal structure that the more conventional ones have (but with the proper
irreducible -body behaviour) and show that, if they are employed, either a
modified external field or the density profiles can indistinctly be used as
independent variables. We also write down the -modified free energy
functional and prove that the thermodynamic potential is minimized by the
equilibrium values of the new hierarchy.Comment: 17 pages, IOP style, submitted to J. Phys. Condens. Matte
Competition among auctioneers
In this paper, we analyse a multistage game of competition among auctioneers. In a first stage, auctioneers commit to some publicly announced reserve prices, and in a second stage, bidders choose to participate in one of the auctions. We prove existence of Nash equilibria in mixed strategies for the whole game. We also show that one property of the equilibrium set is that when the numbers of auctioneers and bidders tend to infinity, almost all auctioneers with production cost low enough to trade announce a reserve price equal to their production costs. Our paper confirms previous results for some "limit" versions of the model by McAfee [9], Peters [13], and Peters and Severinov [18]
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