An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited

A photonic basis for deriving nonlinear optical response

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as coefficients in a power series - nonlinear optical susceptibilities signifying a propensity to generate optical harmonics, for example. Taking the subject to a deeper level requires a more detailed knowledge of the structure and properties of each nonlinear susceptibility tensor, the latter differing in form according to the process under investigation. Typically, the derivations involve intricate development based on time-dependent perturbation theory, assisted by recourse to a set of Feynman diagrams. This paper presents a more direct route to the required results, based on photonic rather than semiclassical principles, and offers a significantly clearer perspective on the photophysics underlying nonlinear optical response. The method, here illustrated by specific application to harmonic generation and down-conversion processes, is simple, intuitive and readily amenable for processes of arbitrary photonic order. © 2009 IOP Publishing Ltd

Multi-Phase Sedment-Discharge Dynamics of Subglacial Drainage Recorded by a Glacier-Linked Esker in NW Tempe Terra, Mars

International audienceIntroduction: Our recent discoveries of eskers associated with 110-150 Myr old debris-covered glaciers in Phlegra Montes [1] and NW Tempe Terra [2], Mars, indicate that localised wet-based glaciation has occurred in at least two locations during the late Amazonian , despite cold climate conditions. Eskers are sedi-mentary ridges deposited by meltwater flowing through drainage tunnels within or beneath glaciers. In this study, we use new 3D measurements of the NW Tempe Terra esker (46.17 °N, 83.06 °W) to develop a conceptual model for the sediment-discharge dynamics of the esker-forming drainage episode(s). Methods: Following [3], we used a 2 m/pixel digital elevation model derived from High Resolution Imaging Science Experiment (HiRISE) images to measure ridge height (H) and width (W) every ~20 m along the esker. We exclude ridge portions obscured by the parent glacier (Fig 1), as well as transitions between morphological zones. Results: A scatterplot of the raw height and width measurements (Fig 2A) has multiple limbs which correspond to subzones of the esker with common morphological characteristics (Fig 1)

3D Morphometries of Eskers on Mars, and Comparisons to Eskers in Finland

International audienceIntroduction: We present new, high-resolution measurements of the 3D morphometries of eskers associated with debris-covered glaciers in the Phlegra Mon-tes [1] and NW Tempe Terra [2] regions of Mars' northern mid-latitudes. We compare them with the ancient south polar 'Dorsa Argentea' eskers on Mars [3], and first large database (n > 20,000) of 3D morphome-tries of terrestrial eskers, from SW Finland [4]. Eskers are ridges of glaciofluvial sediment deposited by meltwater flowing through tunnels within or beneath glaciers. They are vital tools for reconstructing the dynamics, extent, and environmental drivers of wet-based glaciation on Earth and Mars. For example, reconstructions of Mars' climate conditions at the Noa-chian-Hesperian transition [e.g., 5] have relied heavily upon insights from the Dorsa Argentea eskers [e.g., 3], which record basal melting of a large south polar ice sheet ~3.5 Ga. Morphometric studies of candidate eskers on Mars are vital both for testing hypotheses of their origins as eskers [e.g., 3], and for informing insights into the magnitude and dynamics of meltwater flows that formed them [e.g., 5-6]. Previously, such work has been limited by a lack of large-scale surveys of the 3D morphometries of eskers on Earth, to which the martian landforms can be compared. A new database comprising >20 000 measurements of 3D esker morphometries from SW Finland provides new opportunities for such-comparisons, which we exploit in this study [4]. Methods: We used 1-2 m/pixel digital elevation models generated from High Resolution Imaging Science Experiment (HiRISE) images to measure esker heights (H) and widths (W) from cross-sectional tran-sects spaced at 10 and 20 m intervals along the Phlegra Montes and NW Tempe Terra eskers, respectively (fol-lowing [3]). We calculated average slopes across cross-sectional transects (θ) as: tan −1 (H/0.5W). We classified transects into sharp-, multi-, and round-crested morphologies according to the scheme of [6]. The NW Tempe Terra esker comprises two 'stacked' esker ridges (see [7], this conference) which we treat separately in the present study. Storrar and Jones [4] obtained similar H, W, and θ measurements at 10 m intervals along ~70 km of Qua-ternary-aged eskers in SW Finland, using 2 m/pixel elevation data from airborne LiDAR

Anomalous Thermal Transport in Quantum Wires

We study thermal transport in a one-dimensional quantum wire, connected to reservoirs. Despite of the absence of electron backscattering, interactions in the wire strongly influence thermal transport. Electrons propagate with unitary transmission through the wire and electric conductance is not affected. Energy, however, is carried by bosonic excitations (plasmons) which suffer from scattering even on scales much larger than the Fermi wavelength. If the electron density varies randomly, plasmons are localized and {\em charge-energy separation} occurs. We also discuss the effect of plasmon-plasmon interaction using Levinson's theory of nonlocal heat transport.Comment: replaced with published versio

Secular Evolution of Galaxy Morphologies

Today we have numerous evidences that spirals evolve dynamically through various secular or episodic processes, such as bar formation and destruction, bulge growth and mergers, sometimes over much shorter periods than the standard galaxy age of 10-15 Gyr. This, coupled to the known properties of the Hubble sequence, leads to a unique sense of evolution: from Sm to Sa. Linking this to the known mass components provides new indications on the nature of dark matter in galaxies. The existence of large amounts of yet undetected dark gas appears as the most natural option. Bounds on the amount of dark stars can be given since their formation is mostly irreversible and requires obviously a same amount of gas.Comment: 8 pages, Latex2e, crckapb.sty macros, 1 Postscript figure, replaced with TeX source; To be published in the proceeedings of the "Dust-Morphology" conference, Johannesburg, 22-26 January, 1996, D. Block (ed.), (Kluwer Dordrecht

Analytical solutions to the third-harmonic generation in trans-polyacetylene: Application of dipole-dipole correlation on the single electron models

The analytical solutions for the third-harmonic generation (THG) on infinite chains in both Su-Shrieffer-Heeger (SSH) and Takayama-Lin-Liu-Maki (TLM) models of trans-polyacetylene are obtained through the scheme of dipole-dipole ($DD$) correlation. They are not equivalent to the results obtained through static current-current ($J_0J_0$) correlation or under polarization operator $\hat{P}$. The van Hove singularity disappears exactly in the analytical forms, showing that the experimentally observed two-photon absorption peak (TPA) in THG may not be directly explained by the single electron models.Comment: 10 pages, 4 figures, submitted to Phys. Rev.

Variable X-ray Absorption in the Seyfert 2 Galaxy Mrk 348

We present RXTE monitoring observations of the Seyfert 2 galaxy Mrk 348 spanning a 6 month period. The time-averaged spectrum in the 3-20 keV band shows many features characteristic of a Compton-thin Seyfert 2 galaxy, namely a hard underlying power-law continuum (photon index = 1.8) with heavy soft X-ray absorption (N_h ~ 10^23 cm^-2) plus measureable iron line emission (equivalent width ~ 100 eV) and, at high energy, evidence for a reflection component (R < 1). During the first half of the monitoring period the X-ray continuum flux from Mrk 348 remained relatively steady. However this was followed by a significant brightening of the source (by roughly a factor of 4) with the fastest change corresponding to a doubling of its X-ray flux on a timescale of about 20 days. The flux increase was accompanied by a marked softening of X-ray spectrum most likely attributable to a factor 3 decline in the intrinsic line-of-sight column density. In contrast the iron line and the reflection components showed no evidence of variability. These observations suggest a scenario in which the central X-ray source is surrounded by a patchy distribution of absorbing material located within about a light-week of the nucleus of Mrk 348. The random movement of individual clouds within the absorbing screen, across our line of sight, produces substantial temporal variations in the measured column density on timescales of weeks to months and gives rise to the observed X-ray spectral variability. However, as viewed from the nucleus the global coverage and typical thickness of the cloud layer remains relatively constant.Comment: 19 pages, 3 figures Accepted for publication in the Astrophysical Journa