Why, when, and how fast innovations are adopted

When the full stock of a new product is quickly sold in a few days or weeks, one has the impression that new technologies develop and conquer the market in a very easy way. This may be true for some new technologies, for example the cell phone, but not for others, like the blue-ray. Novelty, usefulness, advertising, price, and fashion are the driving forces behind the adoption of a new product. But, what are the key factors that lead to adopt a new technology? In this paper we propose and investigate a simple model for the adoption of an innovation which depends mainly on three elements: the appeal of the novelty, the inertia or resistance to adopt it, and the interaction with other agents. Social interactions are taken into account in two ways: by imitation and by differentiation, i.e., some agents will be inclined to adopt an innovation if many people do the same, but other will act in the opposite direction, trying to differentiate from the "herd". We determine the conditions for a successful implantation of the new technology, by considering the strength of advertising and the effect of social interactions. We find a balance between the advertising and the number of anti-herding agents that may block the adoption of a new product. We also compare the effect of social interactions, when agents take into account the behavior of the whole society or just a part of it. In a nutshell, the present model reproduces qualitatively the available data on adoption of innovation.Comment: 11 pages, 13 figures (with subfigures), full paper (EPJB 2012) on innovation adoption mode

Moving black holes via singularity excision

We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations of single, non-moving black holes. The excision procedure also shares elements used in recent work to study the dynamics of a scalarfield in the background of a single, boosted black hole. The robustness of our excision method is tested with single black-hole evolutions using a coordinate system in which the coordinate location of the black hole, and thus the excision boundary, moves throughout the computational domain.Comment: 9 pages and 11 figure

Defect formation and local gauge invariance

We propose a new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry. This mechanism leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global theories. We confirm these predictions in numerical simulations, and they can also be tested in superconductor experiments. We believe that the mechanism generalizes to more complicated theories.Comment: REVTeX, 4 pages, 2 figures. The explicit form of the Hamiltonian and the equations of motion added. To appear in PRL (http://prl.aps.org/

Electroweak String Configurations with Baryon Number

In the context of electroweak strings, the baryon number anomaly equation may be reinterpreted as a conservation law for baryon number minus helicity. Since the helicity is a sum of the link and twist numbers, linked or twisted loops of electroweak string carry baryon number. We evaluate the change in the baryon number obtained by delinking loops of electroweak $Z-$string and show that twisted electroweak string segments may be regarded as extended sphalerons. We also suggest an alternative scenario for electroweak baryogenesis.Comment: 11 pages, figure available on request. Added discussion of string-sphaleron connection for non-vanishing Weinberg angle and shortened discussion on formation of linked configuration

Properties of Accretion Flows Around Coalescing Supermassive Black Holes

What are the properties of accretion flows in the vicinity of coalescing supermassive black holes (SBHs)? The answer to this question has direct implications for the feasibility of coincident detections of electromagnetic (EM) and gravitational wave (GW) signals from coalescences. Such detections are considered to be the next observational grand challenge that will enable testing general relativity in the strong, nonlinear regime and improve our understanding of evolution and growth of these massive compact objects. In this paper we review the properties of the environment of coalescing binaries in the context of the circumbinary disk and hot, radiatively inefficient accretion flow models and use them to mark the extent of the parameter space spanned by this problem. We report the results from an ongoing, general relativistic, hydrodynamical study of the inspiral and merger of black holes, motivated by the latter scenario. We find that correlated EM+GW oscillations can arise during the inspiral phase followed by the gradual rise and subsequent drop-off in the light curve at the time of coalescence. While there are indications that the latter EM signature is a more robust one, a detection of either signal coincidentally with GWs would be a convincing evidence for an impending SBH binary coalescence. The observability of an EM counterpart in the hot accretion flow scenario depends on the details of a model. In the case of the most massive binaries observable by the Laser Interferometer Space Antenna, upper limits on luminosity imply that they may be identified by EM searches out to z~0.1-1. However, given the radiatively inefficient nature of the gas flow, we speculate that a majority of massive binaries may appear as low luminosity AGN in the local universe.Comment: Revised version accepted to Class. Quantum Grav. for proceedings of 8th LISA Symposium. 15 pages, 3 figures, includes changes suggested in referee report

Evolution systems for non-linear perturbations of background geometries

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.Comment: 12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review

Winding up by a quench: vortices in the wake of rapid Bose-Einstein condensation

A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their equilibrium expectation values. We use quantum kinetic theory to show that this mechanism, originally postulated in the cosmological context, and analysed so far only on the mean field classical level, should allow spontaneous generation of vortex lines in trapped Bose-Einstein condensates of simple topology, or of winding number in toroidal condensates.Comment: 4 pages, 2 figures; misprint correcte

Hamiltonian Relaxation

Due to the complexity of the required numerical codes, many of the new formulations for the evolution of the gravitational fields in numerical relativity are not tested on binary evolutions. We introduce in this paper a new testing ground for numerical methods based on the simulation of binary neutron stars. This numerical setup is used to develop a new technique, the Hamiltonian relaxation (HR), that is benchmarked against the currently most stable simulations based on the BSSN method. We show that, while the length of the HR run is somewhat shorter than the equivalent BSSN simulation, the HR technique improves the overall quality of the simulation, not only regarding the satisfaction of the Hamiltonian constraint, but also the behavior of the total angular momentum of the binary. The latest quantity agrees well with post-Newtonian estimations for point-mass binaries in circular orbits.Comment: More detailed description of the numerical implementation added and some typos corrected. Version accepted for publication in Class. and Quantum Gravit

Einstein boundary conditions for the 3+1 Einstein equations

In the 3+1 framework of the Einstein equations for the case of vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space-derivatives of the intrinsic metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields.Comment: Revtex 4, 6 pages, text and references added, typos corrected, to appear in Phys. Rev.

Slow 4He^{4}He Quenches Produce Fuzzy, Transient Vortices

We examine the Zurek scenario for the production of vortices in quenches of liquid $^{4}He$ in the light of recent experiments. Extending our previous results to later times, we argue that short wavelength thermal fluctuations make vortices poorly defined until after the transition has occurred. Further, if and when vortices appear, it is plausible that that they will decay faster than anticipated from turbulence experiments, irrespective of quench rates.Comment: 4 pages, Revtex file, no figures Apart from a more appropriate title, this paper differs from its predecessor by including temperature, as well as pressure, quenche