Modulational instability criteria for two-component Bose-Einstein condensates

The stability of colliding Bose-Einstein condensates is investigated. A set of coupled Gross-Pitaevskii equations is thus considered, and analyzed via a perturbative approach. No assumption is made on the signs (or magnitudes) of the relevant parameters like the scattering lengths and the coupling coefficients. The formalism is therefore valid for asymmetric as well as symmetric coupled condensate wave states. A new set of explicit criteria is derived and analyzed. An extended instability region, in addition to an enhanced instability growth rate is predicted for unstable two component bosons, as compared to the individual (uncoupled) state.Comment: 4 pages, 1 figur

A description of the ratio between electric and magnetic proton form factors by using space-like, time-like data and dispersion relations

We use the available information on the ratio between the electric and magnetic proton form factors coming from recently published space-like data and from the few available time-like data. We apply a dispersive procedure on these data to evaluate the behaviour of this ratio, as a complex function, for all values of q^2.Comment: 12 pages, 7 Encapsulated Postscript figures, uses epsfig, rotating, exscale, amsmath, cite, latexsym, graphics, color packages, added reference

Zemach and magnetic radius of the proton from the hyperfine splitting in hydrogen

The current status of the determination of corrections to the hyperfine splitting of the ground state in hydrogen is considered. Improved calculations are provided taking into account the most recent value for the proton charge radius. Comparing experimental data with predictions for the hyperfine splitting, the Zemach radius of the proton is deduced to be $1.045(16)$ fm. Employing exponential parametrizations for the electromagnetic form factors we determine the magnetic radius of the proton to be $0.778(29)$ fm. Both values are compared with the corresponding ones derived from the data obtained in electron-proton scattering experiments and the data extracted from a rescaled difference between the hyperfine splittings in hydrogen and muonium

Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

Eikonal representation in the momentum-transfer space

By means of empirical fits to the differential cross section data on pp and p(bar)p elastic scattering, above 10 GeV (center-of-mass energy), we determine the eikonal in the momentum - transfer space (q^2- space). We make use of a numerical method and a novel semi-analytical method, through which the uncertainties from the fit parameters can be propagated up to the eikonal in the $q^2$- space. A systematic study of the effect of the experimental information at large values of the momentum transfer is developed and discussed in detail. We present statistical evidence that the imaginary part of the eikonal changes sign in the q^2- space and that the position of the zero decreases as the energy increases; after the position of the zero, the eikonal presents a minimum and then goes to zero through negative values. We discuss the applicability of our results in the phenomenological context, outlining some connections with nonperturbative QCD. A short review and a critical discussion on the main results concerning "model-independent" analyses are also presented.Comment: 18 pages, 17 figures, 4 tables, svjour.cls. Revised discussion on the proton's electromagnetic form factor and references added. To appear in Eur. Phys. J.

Decomposition of semigroup algebras

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.Comment: 12 pages, 2 figures, minor revisions. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/MonomialAlgebras/html

Coherence length of an elongated condensate: a study by matter-wave interferometry

We measure the spatial correlation function of Bose-Einstein condensates in the cross-over region between phase-coherent and strongly phase-fluctuating condensates. We observe the continuous path from a gaussian-like shape to an exponential-like shape characteristic of one-dimensional phase-fluctuations. The width of the spatial correlation function as a function of the temperature shows that the condensate coherence length undergoes no sharp transition between these two regimes.Comment: 8 pages, 6 figure, submitted to EPJ

Observation of the TeV gamma-ray source MGRO J1908+06 with ARGO-YBJ

The extended gamma ray source MGRO J1908+06, discovered by the Milagro air shower detector in 2007, has been observed for about 4 years by the ARGO-YBJ experiment at TeV energies, with a statistical significance of 6.2 standard deviations. The peak of the signal is found at a position consistent with the pulsar PSR J1907+0602. Parametrizing the source shape with a two-dimensional Gauss function we estimate an extension \sigma = 0.49 \pm 0.22 degrees, consistent with a previous measurement by the Cherenkov Array H.E.S.S.. The observed energy spectrum is dN/dE = 6.1 \pm 1.4 \times 10^-13 (E/4 TeV)^{-2.54 \pm 0.36} photons cm^-2 s^-1 TeV^-1, in the energy range 1-20 TeV. The measured gamma ray flux is consistent with the results of the Milagro detector, but is 2-3 times larger than the flux previously derived by H.E.S.S. at energies of a few TeV. The continuity of the Milagro and ARGO-YBJ observations and the stable excess rate observed by ARGO-YBJ along 4 years of data taking support the identification of MGRO J1908+06 as the steady powerful TeV pulsar wind nebula of PSR J1907+0602, with an integrated luminosity above 1 TeV about 1.8 times the Crab Nebula luminosity.Comment: 6 pages, accepted for pubblication by ApJ. Replaced to correct the author lis

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations