3,365 research outputs found
Statistics of conductance and shot-noise power for chaotic cavities
We report on an analytical study of the statistics of conductance, , and
shot-noise power, , for a chaotic cavity with arbitrary numbers of
channels in two leads and symmetry parameter . With the theory
of Selberg's integral the first four cumulants of and first two cumulants
of are calculated explicitly. We give analytical expressions for the
conductance and shot-noise distributions and determine their exact asymptotics
near the edges up to linear order in distances from the edges. For a
power law for the conductance distribution is exact. All results are also
consistent with numerical simulations.Comment: 7 pages, 3 figures. Proc. of the 3rd Workshop on Quantum Chaos and
Localisation Phenomena, Warsaw, Poland, May 25-27, 200
Isostatic equilibrium in spherical coordinates and implications for crustal thickness on the Moon, Mars, Enceladus, and elsewhere
Isostatic equilibrium is commonly defined as the state achieved when there
are no lateral gradients in hydrostatic pressure, and thus no lateral flow, at
depth within the lower viscosity mantle that underlies a planetary body's outer
crust. In a constant-gravity Cartesian framework, this definition is equivalent
to the requirement that columns of equal width contain equal masses. Here we
show, however, that this equivalence breaks down when the spherical geometry of
the problem is taken into account. Imposing the "equal masses" requirement in a
spherical geometry, as is commonly done in the literature, leads to significant
lateral pressure gradients along internal equipotential surfaces, and thus
corresponds to a state of disequilibrium. Compared with the "equal pressures"
model we present here, the "equal masses" model always overestimates the
compensation depth--by ~27% in the case of the lunar highlands and by nearly a
factor of two in the case of Enceladus.Comment: 23 pages of text; 3 figures; accepted for publication in GR
Spatiospectral concentration on a sphere
We pose and solve the analogue of Slepian's time-frequency concentration
problem on the surface of the unit sphere to determine an orthogonal family of
strictly bandlimited functions that are optimally concentrated within a closed
region of the sphere, or, alternatively, of strictly spacelimited functions
that are optimally concentrated within the spherical harmonic domain. Such a
basis of simultaneously spatially and spectrally concentrated functions should
be a useful data analysis and representation tool in a variety of geophysical
and planetary applications, as well as in medical imaging, computer science,
cosmology and numerical analysis. The spherical Slepian functions can be found
either by solving an algebraic eigenvalue problem in the spectral domain or by
solving a Fredholm integral equation in the spatial domain. The associated
eigenvalues are a measure of the spatiospectral concentration. When the
concentration region is an axisymmetric polar cap the spatiospectral projection
operator commutes with a Sturm-Liouville operator; this enables the
eigenfunctions to be computed extremely accurately and efficiently, even when
their area-bandwidth product, or Shannon number, is large. In the asymptotic
limit of a small concentration region and a large spherical harmonic bandwidth
the spherical concentration problem approaches its planar equivalent, which
exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200
Contemporary Innovation Policy and Instruments: Challenges and Implications
In this paper we review major theoretical (neoclassical economics, evolutionary, systemic and knowledge-based) insights about innovation and we analyse their implications for the characteristics of contemporary innovation policy and instruments. We show that the perspectives complement each other but altogether reveal the need to redefine the current general philosophy as well as the modes of operationalisation of contemporary innovation policy. We argue that systemic instruments ensuring proper organisation of innovation systems give a promise of increased rates and desired (more sustainable) direction of innovation.systemic instruments, innovation policy, innovation theory, policy mix, innovation system, sustainability
Family studies of somatic and functional characteristics in the polish rural population
In the present investigation we were trying to determine the genetic and environmental conditioning of the chosen somatic and functional traits in Polish rural population during ontogenesis. In order to find out interactions between environmental and genetic conditions of the studied traits, classical methods of quantitative features were applied: correlation coefficients corrected by assortative mating in the chosen types of heritability were evaluated on their base, heritability coefficients of analyzed features were assessed. The biggest stability of the correlation coefficients was observed for the length-parameters. We did not noticed stronger genetic control of functional features in men. Mean-strong genetic control among analyzed traits was observed in: reaction time, space orientation and static strength expressed as relative and absolute strength
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