Statistics of conductance and shot-noise power for chaotic cavities

We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$. With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ 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 $0<g<1$ 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