29,388 research outputs found
Analysis of a diffusive effective mass model for nanowires
We propose in this paper to derive and analyze a self-consistent model
describing the diffusive transport in a nanowire. From a physical point of
view, it describes the electron transport in an ultra-scaled confined
structure, taking in account the interactions of charged particles with
phonons. The transport direction is assumed to be large compared to the wire
section and is described by a drift-diffusion equation including effective
quantities computed from a Bloch problem in the crystal lattice. The
electrostatic potential solves a Poisson equation where the particle density
couples on each energy band a two dimensional confinement density with the
monodimensional transport density given by the Boltzmann statistics. On the one
hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model
from a kinetic level description. On the other hand, we present an existence
result for this model in a bounded domain
What Explains the Stock Market's Reaction to Federal Reserve Policy?
This paper analyzes the impact of changes in monetary policy on equity prices, with the objectives both of measuring the average reaction of the stock market and also of understanding the economic sources of that reaction. We find that, on average, a hypothetical unanticipated 25-basis-point cut in the federal funds rate target is associated with about a one percent increase in broad stock indexes. Adapting a methodology due to Campbell (1991) and Campbell and Ammer (1993), we find that the effects of unanticipated monetary policy actions on expected excess returns account for the largest part of the response of stock prices.
Randomness in Competitions
We study the effects of randomness on competitions based on an elementary
random process in which there is a finite probability that a weaker team upsets
a stronger team. We apply this model to sports leagues and sports tournaments,
and compare the theoretical results with empirical data. Our model shows that
single-elimination tournaments are efficient but unfair: the number of games is
proportional to the number of teams N, but the probability that the weakest
team wins decays only algebraically with N. In contrast, leagues, where every
team plays every other team, are fair but inefficient: the top of
teams remain in contention for the championship, while the probability that the
weakest team becomes champion is exponentially small. We also propose a gradual
elimination schedule that consists of a preliminary round and a championship
round. Initially, teams play a small number of preliminary games, and
subsequently, a few teams qualify for the championship round. This algorithm is
fair and efficient: the best team wins with a high probability and the number
of games scales as , whereas traditional leagues require N^3 games to
fairly determine a champion.Comment: 10 pages, 8 figures, reviews arXiv:physics/0512144,
arXiv:physics/0608007, arXiv:cond-mat/0607694, arXiv:physics/061221
On theories of random variables
We study theories of spaces of random variables: first, we consider random
variables with values in the interval , then with values in an arbitrary
metric structure, generalising Keisler's randomisation of classical structures.
We prove preservation and non-preservation results for model theoretic
properties under this construction: i) The randomisation of a stable structure
is stable. ii) The randomisation of a simple unstable structure is not simple.
We also prove that in the randomised structure, every type is a Lascar type
Circular dichroism induced by Fano resonances in planar chiral oligomers
We present a general theory of circular dichroism in planar chiral
nanostructures with rotational symmetry. It is demonstrated, analytically, that
the handedness of the incident field's polarization can control whether a
nanostructure induces either absorption or scattering losses, even when the
total optical loss (extinction) is polarization-independent. We show that this
effect is a consequence of modal interference so that strong circular dichroism
in absorption and scattering can be engineered by combining Fano resonances
with planar chiral nanoparticle clusters.Comment: 12 pages, 5 figure
Maximum Distance Between the Leader and the Laggard for Three Brownian Walkers
We consider three independent Brownian walkers moving on a line. The process
terminates when the left-most walker (the `Leader') meets either of the other
two walkers. For arbitrary values of the diffusion constants D_1 (the Leader),
D_2 and D_3 of the three walkers, we compute the probability distribution
P(m|y_2,y_3) of the maximum distance m between the Leader and the current
right-most particle (the `Laggard') during the process, where y_2 and y_3 are
the initial distances between the leader and the other two walkers. The result
has, for large m, the form P(m|y_2,y_3) \sim A(y_2,y_3) m^{-\delta}, where
\delta = (2\pi-\theta)/(\pi-\theta) and \theta =
cos^{-1}(D_1/\sqrt{(D_1+D_2)(D_1+D_3)}. The amplitude A(y_2,y_3) is also
determined exactly
Diffusion-Limited One-Species Reactions in the Bethe Lattice
We study the kinetics of diffusion-limited coalescence, A+A-->A, and
annihilation, A+A-->0, in the Bethe lattice of coordination number z.
Correlations build up over time so that the probability to find a particle next
to another varies from \rho^2 (\rho is the particle density), initially, when
the particles are uncorrelated, to [(z-2)/z]\rho^2, in the long-time asymptotic
limit. As a result, the particle density decays inversely proportional to time,
\rho ~ 1/kt, but at a rate k that slowly decreases to an asymptotic constant
value.Comment: To be published in JPCM, special issue on Kinetics of Chemical
Reaction
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