890 research outputs found
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 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 Quenches Produce Fuzzy, Transient Vortices
We examine the Zurek scenario for the production of vortices in quenches of
liquid 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
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