21,045 research outputs found
Operator splitting for the Benjamin-Ono equation
In this paper we analyze operator splitting for the Benjamin-Ono equation,
u_t = uu_x + Hu_xx, where H denotes the Hilbert transform. If the initial data
are sufficiently regular, we show the convergence of both Godunov and Strang
splitting.Comment: 18 Page
Bertrand competition with intertemporal demand
In the text-book model of dynamic Bertrand competition,
competing firms meet the same demand function every period. This is not a
satisfactory model of the demand side if consumers can make intertemporal
substitution between periods. Each period then leaves some residual demand
to future periods, and consumers who observe price under-cutting may correctly
anticipate an ensuing price war and therefore postpone their purchases.
Accordingly, the interaction between the firms no longer constitutes a repeated
game, and hence falls outside the domain of the usual Folk theorems.
We analyze collusive pricing in such situations, and study cases when consumers
have perfect and imperfect foresight and varying degrees of patience.
It turns out that collusion against patient and forward-looking consumers is
easier to sustain than collusion in the text-book model
The Generalized Counting Rule and Oscillatory Scaling
We have studied the energy dependence of the elastic scattering data and
the pion-photoproduction data at 90 c.m. angle in light of the new
generalized counting rule derived for exclusive processes. We show that by
including the helicity flipping amplitudes (with energy dependence given by the
generalized counting rule) and their interference with the Landshoff amplitude,
we are able to reproduce the energy dependence of all cross-section and
spin-correlation (A) data available above the resonance region. The
pion-photoproduction data can also be described by this approach, but in this
case data with much finer energy spacing is needed to confirm the oscillations
about the scaling behavior.Comment: 5 pages, 4 figs, submitted to PRC rapid com
Tau contamination in the platinum channel at neutrino factories
The platinum channel (\nu_e or anti-\nu_e appearance) has been proposed at
neutrino factories as an additional channel that could help in lifting
degeneracies and improving sensitivities to neutrino oscillation parameters,
viz., \theta_{13}, \delta_{CP}, mass hierarchy, deviation of \theta_{23} from
maximality and its octant. This channel corresponds to \nu_\mu -> \nu_e (or the
corresponding anti-particle) oscillations of the initial neutrino flux, with
the subsequent detection of (positrons) electrons from charged current
interactions of the (anti-) \nu_e in the detector. For small values of
\theta_{13}, the dominant \nu_\mu \to \nu_\tau (or corresponding anti-particle)
oscillation results in this signal being swamped by electrons arising from the
leptonic decay of taus produced in charge-current interactions of \nu_\tau
(anti-\nu_\tau) with the detector. We examine for the first time the role of
this tau contamination to the electron events sample and find that it plays a
significant role in the platinum channel compared to other channels, not only
at high energy neutrino factories but surprisingly even at low energy neutrino
factories. Even when the platinum channel is considered in combination with
other channels such as the golden (muon appearance) or muon disappearance
channel, the tau contamination results in a loss in precision of the measured
parameters.Comment: 13 pages latex file with 10 eps figure file
Signature of strong atom-cavity interaction on critical coupling
We study a critically coupled cavity doped with resonant atoms with
metamaterial slabs as mirrors. We show how resonant atom-cavity interaction can
lead to a splitting of the critical coupling dip. The results are explained in
terms of the frequency and lifetime splitting of the coupled system.Comment: 8 pages, 5 figure
Fibers on a graph with local load sharing
We study a random fiber bundle model with tips of the fibers placed on a
graph having co-ordination number 3. These fibers follow local load sharing
with uniformly distributed threshold strengths of the fibers. We have studied
the critical behaviour of the model numerically using a finite size scaling
method and the mean field critical behaviour is established. The avalanche size
distribution is also found to exhibit a mean field nature in the asymptotic
limit.Comment: 9 pages, 6 figures, To appear in International Journal of Modern
Physics
Understanding the Fano Resonance : through Toy Models
The Fano Resonance, involving the mixing between a quasi-bound `discrete'
state of an inelastic channel lying in the continuum of scattering states
belonging to the elastic channel, has several subtle features. The underlying
ideas have recently attracted attention in connection with interference effects
in quantum wires and mesoscopic transport phenomena. Simple toy models are
provided in the present study to illustrate the basics of the Fano resonance in
a simple and tractable setting.Comment: 17 pages, 1 figur
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