On the Two Obstacles Problem in Orlicz-Sobolev Spaces and Applications

We prove the Lewy-Stampacchia inequalities for the two obstacles problem in abstract form for T-monotone operators. As a consequence for a general class of quasi-linear elliptic operators of Ladyzhenskaya-Uraltseva type, including p(x)-Laplacian type operators, we derive new results of $C^{1,\alpha}$ regularity for the solution. We also apply those inequalities to obtain new results to the N-membranes problem and the regularity and monotonicity properties to obtain the existence of a solution to a quasi-variational problem in (generalized) Orlicz-Sobolev spaces

Locally Inertial Reference Frames in Lorentzian and Riemann-Cartan Spacetimes

In this paper we scrutinize the concept of locally inertial reference frames (LIRF) in Lorentzian and Riemann-Cartan spacetime structures. We present rigorous mathematical definitions for those objects, something that needs preliminary a clear mathematical distinction between the concepts of observers, reference frames, naturally adapted coordinate functions to a given reference frame and which properties may characterize an inertial reference frame (if any) in the Lorentzian and Riemann-Cartan structures. We hope to have clarified some eventual obscure issues associated to the concept of LIRF appearing in the literature, in particular the relationship between LIRFs in Lorentzian and Riemann-Cartan spacetimes and Einstein's most happy though, i.e., the equivalence principle.Comment: In this version a new reference has been added, some misprints and typos have been corrected and some few sentences in two remarks and in the conclusions have been changed for better intelligibilit

Lorentz-violating nonminimal coupling contributions in mesonic hydrogen atoms and generation of photon higher-order derivative terms

We have studied the contributions of Lorentz-violating CPT-odd and CPT-even nonminimal couplings to the energy spectrum of the mesonic hydrogen and the higher-order radiative corrections to the effective action of the photon sector of a Lorentz-violating version of the scalar electrodynamics. By considering the complex scalar field describes charged mesons (pion or kaon), the non-relativistic limit of the model allows to attain upper-bounds by analyzing its contribution to the mesonic hydrogen energy. By using the experimental data for the $1S$ strong correction shift and the pure QED transitions $4P \rightarrow 3P$, the best upper-bound for the CPT-odd coupling is $<10^{-12}\text{eV}^{-1}$ and for the CPT-even one is $<10^{-16}\text{eV}^{-2}$. Besides, the CPT-odd radiative correction to the photon action is a dimension-5 operator which looks like a higher-order Carroll-Field-Jackiw term. The CPT-even radiative contribution to the photon effective action is a dimension-6 operator which would be a higher-order derivative version of the minimal CPT-even term of the standard model extension

The runaway black hole GRO J1655-40

We have used the Hubble Space Telescope to measure the motion in the sky and compute the galactocentric orbit of the black hole X-ray binary GRO J1655-40. The system moves with a runaway space velocity of $112\pm 18$ km s$^{-1}$ in a highly eccentric ($e = 0.34\pm 0.05$) orbit. The black hole was formed in the disk at a distance greater than 3 kpc from the Galactic centre and must have been shot to such an eccentric orbit by the explosion of the progenitor star. The runaway linear momentum and kinetic energy of this black hole binary are comparable to those of solitary neutron stars and millisecond pulsars. GRO J1655-40 is the first black hole for which there is evidence for a runaway motion imparted by a natal kick in a supernova explosion.Comment: Published in Astronomy and Astrophysics. 5 pages, 2 color figures. Color figure and animation can be found at http://www.iafe.uba.ar/astronomia/mirabel/mirabel.html or ftp://ftp.cea.fr/incoming/y2k01/mirabe

Using presence-absence data to establish reserve selection procedures that are robust to temporal species turnover

Previous studies suggest that a network of nature reserves with maximum efficiency (obtained by selecting the minimum area such that each species is represented once) is likely to be insufficient to maintain species in the network over time. Here, we test the performance of three selection strategies which require presence-absence data, two of them previously proposed (multiple representations and selecting an increasing percentage of each species' range) and a novel one based on selecting the site where each species has exhibited a higher permanence rate in the past. Multiple representations appear to be a safer strategy than selecting a percentage of range because the former gives priority to rarer species while the latter favours the most widespread. The most effective strategy was the one based on the permanence rate, indicating that the robustness of reserve networks can be improved by adopting reserve selection procedures that integrate information about the relative value of sites. This strategy was also very efficient, suggesting that the investment made in the monitoring schemes may be compensated for by a lower cost in reserve acquisition

Analyzing Trails in Complex Networks

Even more interesting than the intricate organization of complex networks are the dynamical behavior of systems which such structures underly. Among the many types of dynamics, one particularly interesting category involves the evolution of trails left by moving agents progressing through random walks and dilating processes in a complex network. The emergence of trails is present in many dynamical process, such as pedestrian traffic, information flow and metabolic pathways. Important problems related with trails include the reconstruction of the trail and the identification of its source, when complete knowledge of the trail is missing. In addition, the following of trails in multi-agent systems represent a particularly interesting situation related to pedestrian dynamics and swarming intelligence. The present work addresses these three issues while taking into account permanent and transient marks left in the visited nodes. Different topologies are considered for trail reconstruction and trail source identification, including four complex networks models and four real networks, namely the Internet, the US airlines network, an email network and the scientific collaboration network of complex network researchers. Our results show that the topology of the network influence in trail reconstruction, source identification and agent dynamics.Comment: 10 pages, 16 figures. A working manuscript, comments and criticisms welcome

The role of electron-electron interactions in two-dimensional Dirac fermions

The role of electron-electron interactions on two-dimensional Dirac fermions remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. Most interestingly, experimental realizations of Dirac fermions span the crossover between these two regimes providing the physical mechanism that masks this velocity divergence. We explain several long-standing mysteries including why the observed Fermi velocity in graphene is consistently about 20 percent larger than the best values calculated using ab initio and why graphene on different substrates show different behavior.Comment: 11 pages, 4 figure