Three-points interfacial quadrature for geometrical source terms on nonuniform grids

International audienceThis paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which $L^p$-error estimates, $1\le p < +\infty$, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics)

Spatially homogeneous ground state of the two-dimensional Hubbard model

We investigate the stability with respect to phase separation or charge density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit ($U=4t$) where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to $U=10t$.Comment: 7 pages and 5 figures. Phys. Rev. B, to appear 200

Burgers' Flows as Markovian Diffusion Processes

We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schr\"{o}dinger boundary data problem for the random matter transport. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation $\partial_t\rho =-\nabla (\vec{v}\rho)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $\rho$ is the density of transported matter, is at variance with the explicit diffusion scenario. Under these circumstances, we give a complete characterisation of the diffusive transport that is governed by Burgers velocity fields. The result extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium. Also, in conjunction with the Born statistical postulate in quantum theory, it pertains to the probabilistic (diffusive) counterpart of the Schr\"{o}dinger picture quantum dynamics.Comment: Latex fil

The Theory of Brown Dwarfs and Extrasolar Giant Planets

Straddling the traditional realms of the planets and the stars, objects below the edge of the main sequence have such unique properties, and are being discovered in such quantities, that one can rightly claim that a new field at the interface of planetary science and and astronomy is being born. In this review, we explore the essential elements of the theory of brown dwarfs and giant planets, as well as of the new spectroscopic classes L and T. To this end, we describe their evolution, spectra, atmospheric compositions, chemistry, physics, and nuclear phases and explain the basic systematics of substellar-mass objects across three orders of magnitude in both mass and age and a factor of 30 in effective temperature. Moreover, we discuss the distinctive features of those extrasolar giant planets that are irradiated by a central primary, in particular their reflection spectra, albedos, and transits. Aspects of the latest theory of Jupiter and Saturn are also presented. Throughout, we highlight the effects of condensates, clouds, molecular abundances, and molecular/atomic opacities in brown dwarf and giant planet atmospheres and summarize the resulting spectral diagnostics. Where possible, the theory is put in its current observational context.Comment: 67 pages (including 36 figures), RMP RevTeX LaTeX, accepted for publication in the Reviews of Modern Physics. 30 figures are color. Most of the figures are in GIF format to reduce the overall size. The full version with figures can also be found at: http://jupiter.as.arizona.edu/~burrows/papers/rm

Non-local heat transport, rotation reversals and up/down impurity density asymmetries in Alcator C-Mod ohmic L-mode plasmas

Several seemingly unrelated effects in Alcator C-Mod ohmic L-mode plasmas are shown to be closely connected: non-local heat transport, core toroidal rotation reversals, energy confinement saturation and up/down impurity density asymmetries. These phenomena all abruptly transform at a critical value of the collisionality. At low densities in the linear ohmic confinement regime, with collisionality ν[subscript *] ≤ 0.35 (evaluated inside of the q = 3/2 surface), heat transport exhibits non-local behaviour, core toroidal rotation is directed co-current, edge impurity density profiles are up/down symmetric and a turbulent feature in core density fluctuations with k[subscript θ] up to 15 cm[superscript −1] (k[subscript θ]ρ[subscript s] ~ 1) is present. At high density/collisionality with saturated ohmic confinement, electron thermal transport is diffusive, core rotation is in the counter-current direction, edge impurity density profiles are up/down asymmetric and the high k[subscript θ] turbulent feature is absent. The rotation reversal stagnation point (just inside of the q = 3/2 surface) coincides with the non-local electron temperature profile inversion radius. All of these observations suggest a possible unification in a model with trapped electron mode prevalence at low collisionality and ion temperature gradient mode domination at high collisionality.United States. Dept. of Energy (Contract DE-FC02-99ER54512)United States. Dept. of Energy. Office of Fusion Energy Sciences (Postdoctoral Research Program

Marketing the city of smells

This article explores how smell might contribute to urban identity, building on the strong links between smell, limbic processing and emotion. It critically examines existing scent marketing, psychology, and urban olfaction literatures, exploring the potential for the marketing of urban places through smell and capitalizing in particular on ambient smells that already exist within a locale. The article makes an initial threefold contribution to theory and practice: (i) demonstrating the current use of smell in city marketing, and the inherent challenges arising; (ii) identifying ways in which smell might be used in future urban place marketing activities, and in particular to more explicitly communicate the experiential attributes of being in a particular city; and (iii) proposing that olfaction may, in certain circumstances, be an effective way of incorporating a more participatory modus operandi within urban place marketing effort. The article concludes with a further overarching theoretical contribution, involving a consideration of place marketing that incorporates non-representational perspectives

First results of the Instrumentation Line for the deep-sea ANTARES neutrino telescope

In 2005, the ANTARES Collaboration deployed and operated at a depth of 2500 m a so-called Mini Instrumentation Line equipped with Optical Modules (MILOM) at the ANTARES site. The various data acquired during the continuous operation from April to December 2005 of the MILOM confirm the satisfactory performance of the Optical Modules, their front-end electronics and readout system. as well as the calibration devices of the detector. The in situ measurement of the Optical Module time response yields a resolution better than 0.5 ns. The performance of the acoustic positioning system, which enables the spatial reconstruction of the ANTARES detector with a precision of about 10 cm, is verified. These results demonstrate that with the full ANTARES neutrino telescope the design angular resolution of better than 0.3 degrees can be realistically achieved

Study of large hemispherical photomultiplier tubes for the ANTARES neutrino telescope

The ANTARES neutrino telescope, to be immersed depth in the Mediterranean Sea, will consist of a 3 dimensional matrix of 900 large area photomultiplier tubes housed in pressure resistant glass spheres. The selection of the optimal photomultiplier was a critical step for the project and required an intensive phase of tests and developments carried out in close collaboration with the main manufacturers worldwide. This paper provides an overview of the tests performed by the collaboration and describes in detail the features of the PMT chosen for ANTARES