Functional Maps Representation on Product Manifolds

We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace--Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.Comment: Accepted to Computer Graphics Foru

Direct perturbation theory on the shift of Electron Spin Resonance

We formulate a direct and systematic perturbation theory on the shift of the main paramagnetic peak in Electron Spin Resonance, and derive a general expression up to second order. It is applied to one-dimensional XXZ and transverse Ising models in the high field limit, to obtain explicit results including the polarization dependence for arbitrary temperature.Comment: 5 pages (no figures) in REVTE

A Hot Gap Around Jupiter's Orbit in the Solar Nebula

The Sun was an order of magnitude more luminous during the first few hundred thousand years of its existence, due in part to the gravitational energy released by material accreting from the Solar nebula. If Jupiter was already near its present mass, the planet's tides opened an optically-thin gap in the nebula. We show using Monte Carlo radiative transfer calculations that sunlight absorbed by the nebula and re-radiated into the gap raised temperatures well above the sublimation threshold for water ice, with potentially drastic consequences for the icy bodies in Jupiter's feeding zone. Bodies up to a meter in size were vaporized within a single orbit if the planet was near its present location during this early epoch. Dust particles lost their ice mantles, and planetesimals were partially to fully devolatilized, depending on their size. Scenarios in which Jupiter formed promptly, such as those involving a gravitational instability of the massive early nebula, must cope with the high temperatures. Enriching Jupiter in the noble gases through delivery trapped in clathrate hydrates will be more difficult, but might be achieved by either forming the planet much further from the star, or capturing planetesimals at later epochs. The hot gap resulting from an early origin for Jupiter also would affect the surface compositions of any primordial Trojan asteroids.Comment: 25 pages, 10 figures. ApJ in press. Discussion of Jupiter's volatile enrichment revised in sec. 4.

Electron Irradiation and Thermal Processing of Mixed-ices of Potential Relevance to Jupiter Trojan Asteroids

In this work we explore the chemistry that occurs during the irradiation of ice mixtures on planetary surfaces, with the goal of linking the presence of specific chemical compounds to their formation locations in the solar system and subsequent processing by later migration inward. We focus on the outer solar system and the chemical differences for ice mixtures inside and outside the stability line for H_2S. We perform a set of experiments to explore the hypothesis advanced by Wong & Brown that links the color bimodality in Jupiter's Trojans to the presence of H_2S in the surface of their precursors. Non-thermal (10 keV electron irradiation) and thermally driven chemistry of CH_3OH–NH_3–H_2O ("without H_2S") and H_2S–CH_3OH–NH_3–H_2O ("with H_2S") ices were examined. Mid-IR analyses of ice and mass spectrometry monitoring of the volatiles released during heating show a rich chemistry in both of the ice mixtures. The "with H_2S" mixture experiment shows a rapid consumption of H_2S molecules and production of OCS molecules after a few hours of irradiation. The heating of the irradiated "with H_2S" mixture to temperatures above 120 K leads to the appearance of new infrared bands that we provisionally assign to SO_2 and CS. We show that radiolysis products are stable under the temperature and irradiation conditions of Jupiter Trojan asteroids. This makes them suitable target molecules for potential future missions as well as telescope observations with a high signal-to-noise ratio. We also suggest the consideration of sulfur chemistry in the theoretical modeling aimed at understanding the chemical composition of Trojans and KOBs

Electron Spin Resonance in S=1/2 antiferromagnetic chains

A systematic field-theory approach to Electron Spin Resonance (ESR) in the $S=1/2$ quantum antiferromagnetic chain at low temperature $T$ (compared to the exchange coupling $J$) is developed. In particular, effects of a transverse staggered field $h$ and an exchange anisotropy (including a dipolar interaction) $\delta$ on the ESR lineshape are discussed. In the lowest order of perturbation theory, the linewidth is given as $\propto Jh^2/T^2$ and $\propto (\delta/J)^2 T$, respectively. In the case of a transverse staggered field, the perturbative expansion diverges at lower temperature; non-perturbative effects at very low temperature are discussed using exact results on the sine-Gordon field theory. We also compare our field-theory results with the predictions of Kubo-Tomita theory for the high-temperature regime, and discuss the crossover between the two regimes. It is argued that a naive application of the standard Kubo-Tomita theory to the Dzyaloshinskii-Moriya interaction gives an incorrect result. A rigorous and exact identity on the polarization dependence is derived for certain class of anisotropy, and compared with the field-theory results.Comment: 53 pages in REVTEX, 7 figures in EPS included; revised version with missing references and correction

Development of an X-ray polarimeter at the SOLEIL Synchrotron

Synchrotron radiation facilities provide highly polarized X-ray beams across a wide energy range. However, the exact type and degree of polarization varies according to the beamline and experimental setup. To accurately determine the angle and degree of linear polarization, a portable X-ray polarimeter has been developed. This setup consists of a Silicon Drift Detector that rotates around a target made of high-density polyethylene. The imprint generated in the angular distribution of scattered photons at a 90-degree angle from the target has been exploited to determine the beam polarization. Measurements were conducted at the GALAXIES beamline of the SOLEIL Synchrotron. The expected angular distribution of the scattered photons for a given beam polarization was obtained through simulations using the Geant4 simulation toolkit. An excellent agreement between simulations and the collected data has been obtained, validating the setup and enabling a precise determination of the beam polarization

Platelet-rich plasma for regeneration of neural feedback pathways around dental implants: a concise review and outlook on future possibilities

published_or_final_versio

What proportion of riverine nutrients reaches the open ocean?

Globally, rivers deliver significant quantities of nitrogen (N) and phosphorus (P) to the coastal ocean each year. Currently, there are no viable estimates of how much of this N and P escapes biogeochemical processing on the shelf to be exported to the open ocean; most models of N and P cycling assume that either all or none of the riverine nutrients reach the open ocean. We address this problem by using a simple mechanistic model of how a low-salinity plume behaves outside an estuary mouth. The model results in a global map of riverine water residence times on the shelf, typically a few weeks at low latitudes and up to a year at higher latitudes, which agrees well with observations. We combine the map of plume residence times on the shelf with empirical relationships that link residence time to the proportions of dissolved inorganic N (DIN) and P (DIP) exported and use a database of riverine nutrient loads to estimate the global distribution of riverine DIN and DIP supplied to the open ocean. We estimate that 75% of DIN and 80% of DIP reaches the open ocean. Ignoring processing within estuaries yields annual totals of 17 Tg DIN and 1.2 Tg DIP reaching the open ocean. For DIN this supply is about 50% of that supplied via atmospheric deposition, with significant east-west contrasts across the main ocean basins. The main sources of uncertainty are exchange rates across the shelf break and the empirical relationships between nutrient processing and plume residence time

Micromechanical Properties of Injection-Molded Starch–Wood Particle Composites

The micromechanical properties of injection molded starch–wood particle composites were investigated as a function of particle content and humidity conditions. The composite materials were characterized by scanning electron microscopy and X-ray diffraction methods. The microhardness of the composites was shown to increase notably with the concentration of the wood particles. In addition,creep behavior under the indenter and temperature dependence were evaluated in terms of the independent contribution of the starch matrix and the wood microparticles to the hardness value. The influence of drying time on the density and weight uptake of the injection-molded composites was highlighted. The results revealed the role of the mechanism of water evaporation, showing that the dependence of water uptake and temperature was greater for the starch–wood composites than for the pure starch sample. Experiments performed during the drying process at 70°C indicated that the wood in the starch composites did not prevent water loss from the samples.Peer reviewe