42,528 research outputs found
Range of the Fractional Weak Discrepancy Function
In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy wdF (P) of a poset P=(V,≺) to be the minimum nonnegative k for which there exists a function f:V→R satisfying (1) if a≺b then f(a)+1≤f(b) and (2) if a∥b then |f(a)−f(b)|≤k. This notion builds on previous work on weak discrepancy in [3, 7, 8]. We prove here that the range of values of the function wdF is the set of rational numbers that are either at least one or equal to r [over] r+1 for some nonnegative integer r. Moreover, P is a semiorder if and only if wdF (P) \u3c 1, and the range taken over all semiorders is the set of such fractions r [over] r+1
Impact of disorder on the 5/2 fractional quantum Hall state
We compare the energy gap of the \nu=5/2 fractional quantum Hall effect state
obtained in conventional high mobility modulation doped quantum well samples
with those obtained in high quality GaAs transistors (heterojunction insulated
gate field-effect transistors). We are able to identify the different roles
that long range and short range disorders play in the 5/2 state and observe
that the long range potential fluctuations are more detrimental to the strength
of the 5/2 state than short-range potential disorder.Comment: PRL 106, 206806 (2011
The Scattered Disk as the source of the Jupiter Family comets
The short period Jupiter family comets (JFCs) are thought to originate in the
Kuiper Belt; specifically, a dynamical subclass of the Kuiper Belt known as the
`scattered disk' is argued to be the dominant source of JFCs. However, the best
estimates from observational surveys indicate that this source may fall short
by more than two orders of magnitude the estimates obtained from theoretical
models of the dynamical evolution of Kuiper belt objects into JFCs. We
re-examine the scattered disk as a source of the JFCs and make a rigorous
estimate of the discrepancy. We find that the uncertainties in the dynamical
models combined with a change in the size distribution function of the
scattered disk at faint magnitudes (small sizes) beyond the current
observational limit offer a possible but problematic resolution to the
discrepancy. We discuss several other possibilities: that the present
population of JFCs is a large fluctuation above their long term average, that
larger scattered disk objects tidally break-up into multiple fragments during
close planetary encounters as their orbits evolve from the trans-Neptune zone
to near Jupiter, or that there are alternative source populations that
contribute significantly to the JFCs. Well-characterized observational
investigations of the Centaurs, objects that are transitioning between the
trans-Neptune Kuiper belt region and the inner solar system, can test the
predictions of the non-steady state and the tidal break-up hypotheses. The
classical and resonant classes of the Kuiper belt are worth re-consideration as
significant additional or alternate sources of the JFCs.Comment: 33 pages, 6 figures. Revised Content. To be published in The
Astrophysical Journa
A Model for Persistent Levy Motion
We propose the model, which allows us to approximate fractional Levy noise
and fractional Levy motion. Our model is based (i) on the Gnedenko limit
theorem for an attraction basin of stable probability law, and (ii) on
regarding fractional noise as the result of fractional
integration/differentiation of a white Levy noise. We investigate self - affine
properties of the approximation and conclude that it is suitable for modeling
persistent Levy motion with the Levy index between 1 and 2.Comment: 14 pages, REVTeX, 5 figures PostScrip
Seismic tests for solar models with tachocline mixing
We have computed accurate 1-D solar models including both a macroscopic
mixing process in the solar tachocline as well as up-to-date microscopic
physical ingredients. Using sound speed and density profiles inferred through
primary inversion of the solar oscillation frequencies coupled with the
equation of thermal equilibrium, we have extracted the temperature and hydrogen
abundance profiles. These inferred quantities place strong constraints on our
theoretical models in terms of the extent and strength of our macroscopic
mixing, on the photospheric heavy elements abundance, on the nuclear reaction
rates such as and and on the efficiency of the microscopic
diffusion. We find a good overall agreement between the seismic Sun and our
models if we introduce a macroscopic mixing in the tachocline and allow for
variation within their uncertainties of the main physical ingredients. From our
study we deduce that the solar hydrogen abundance at the solar age is and that based on the Be photospheric depletion, the
maximum extent of mixing in the tachocline is 5% of the solar radius. The
nuclear reaction rate for the fundamental reaction is found to be
MeV barns, i.e., 1.5% higher than the
present theoretical determination. The predicted solar neutrino fluxes are
discussed in the light of the new SNO/SuperKamiokande results.Comment: 16 pages, 12 figures, A&A in press (1) JILA, University of Colorado,
Boulder, CO 80309-0440, USA, (2) LUTH, Observatoire de Paris-Meudon, 92195
Meudon, France, (3) Tata Institute of Fundamental Research, Homi Bhabha road,
Mumbai 400005, India, (4) Department of Physics, University of Mumbai, Mumbai
400098, Indi
- …