Diffusion approximation for billiards with totally accommodating scatterers

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.     

Improvement of kinetics,yield, and colloidal stability of biogenic gold nanoparticles using living cells of <Emphasis Type="Italic">Euglena gracilis</Emphasis> microalga

Recent years have witnessed a boom in the biosynthesis of a large variety of nanomaterials using different biological resources among which algae-based entities have been gaining much more attention within the community of material scientists worldwide. In our previously published findings, we explored some factors that governed the biofabrication of gold nanoparticles using living cultures of microalgae, such as the utilized microalgal genera, the phylum they belong to, and the impact of tetrachloroauric acid concentrations on the ability of these strains to perform the biosynthesis of gold nanoparticles once in contact with these cations. As a follow-up, we present in this paper an improvement of the features of bioproduced gold colloids using living cells of Euglena gracilis microalga when this species is grown under either mixotrophic or autotrophic conditions, i.e., exposed to light and grown in an organic carbon-enriched culture medium versus under autotrophic conditions. As an outcome to this alteration, the growth rate of this photosynthetic microorganism is multiplied 7–8 times when grown under mixotrophic conditions compared to autotrophic ones. Therefore, the yield, the kinetics, and the colloidal stability of the biosynthesized gold nanoparticles are dramatically enhanced. Moreover, the shape and the size of the as-produced nano-objects via this biological method are affected. In addition to round-shaped gold nanoparticles, particular shapes, such as triangles and hexagons, appear. These findings add up to the amassed knowledge toward the design of photobioreactors for the scalable and sustainable production of interesting nanomaterials.     

Relaxation effects in the quantification of fat using gradient echo imaging

Quantification of fat has been investigated using images acquired from multiple gradient echoes. The evolution of the signal with echo time and flip angle was measured in phantoms of known fat and water composition and in 21 research subjects with fatty liver. Data were compared to different models of the signal equation, in which each model makes different assumptions about the T1 and/or T2* relaxation effects. A range of T1, T2*, fat fraction and number of echoes was investigated to cover situations of relevance to clinical imaging. Results indicate that quantification is most accurate at low flip angles (to minimize T1 effects) with a small number of echoes (to minimize spectral broadening effects). At short echo times, the spectral broadening effects manifest as a short apparent T2 for the fat component.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.     

Lithium solvation in a PMMA membrane plasticized by a lithium‐conducting ionic liquid based on 1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide

The Raman and Infrared (IR) spectra of poly(methyl methacrylate) (PMMA) membranes plasticized by ionic liquids of the (1 − x)[1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide (BMITFSI)],xLiTFSI type, where BMI⁺ is the 1‐butyl‐3‐methylimidazolium cation and TFSI⁻ the bis(trifluoromethanesulfonyl)imide anion, are analyzed for a lithium bis(trifluoromethane sulfone)imide (LiTFSI) mole fraction x = 0.23 and PMMA contents from 0 to 50 wt%. The lithium is found to have an average coordination of about three CO groups and less than one TFSI⁻ anion. It plays the role of a cross‐linker between the ester groups of PMMA and the nonvolatile ionic liquid. Addition of PMMA to the (1 − x)(BMITFSI),xLiTFSI ionic liquid lowers the conductivity but might improve the lithium transference number by transforming the [Li(TFSI)₂]⁻ anionic clusters present in the pure ionic liquid into a mixed coordination by ester groups and TFSI⁻ anions. Copyright © 2008 John Wiley & Sons, Ltd.     

The vibration-rotation spectrum of methinophosphide: The overtone bands 2ν1 and 2ν3, the summation bands ν1 + ν2 and ν2 + ν3, and the difference band ν1 - ν2

The vibration-rotation bands 2ν₁, 2ν₃, ν₁ + ν₂, ν₂ + ν₃, and ν₁ - ν₂ of H¹²CP were recorded and analyzed. These data were combined with previously reported results for this molecule to obtain an improved and extended set of vibrational and rotational constants. All x_ij and γ_ij were calculated except those that require data from a summation band involving ν₁ and ν₃.     

Arbres minimaux d'un graphe preordonne

We study the minimal spanning trees of a connected graph G = (X,U) where U is partially preordered (or quasi-ordered). We characterize several kinds of optimal spanning trees and give conditions for existence of strongly optimal trees. Generalizations to bases of matroids (binary matroïds in part 2) are immediate. Sone of our results are given in terms of Krugdahl's dependence graphs. They imply previous results of Rosenstiehl and Gale in the case of linear orders or preorders.     

Study of the spectrum of CH335C1 between 4250 and 4600 CM?1: thev2+v4 andv4+v5 rovibrational bands

About 2500 lines of CH₃ ³⁵Cl have been assigned. The strong xy Coriolis resonance between thev ₂ andv ₅ modes is quite visible between thev ₄+v ₄ ^±1 perpendicular band, centered around 4383 cm^–1, and thev ₄ ^±1 +v ₅ ^±1 perpendicular component, centered around 4475 cm^–1, with a crossing of upper energy levels allowing the observation of lines which are normally forbidden. Although not yet observed with certainty, because of the great density of lines of the spectrum, thev ₄ ¹ +v ₅ ^±1 parallel component is nevertheless detectable by its effects onv ₂+v ₄ ^±1 which is linked by Coriolis resonance to both components ofv ₄+v ₅. Moreover the spectrum is much complicated by many other resonances with weak bands which occur at level crossings: it is the case ofv ₂+3v ₆ ^±1 , connected tov ₂+v ₄ ^±1 by the well known Darling Dennison resonance which couplesv ₄ ^±1 and 3v ₆ ^±1 , and also ofv ₅ ^±1 +3v ₆ ^±1 connected tov ₄ ^±1 +v ₅ ^±1 by the same resonance; but this last case is complicated by an anharmonic resonance betweenv ₅ ^±1 +3v ₆ ^±1 and 2v ₃+3v ₆ ¹ . Two more perturbations occur on the K=–1 side ofv ₂+v ₄: a weak Coriolis resonance gives rise to one subband ofv ₁+v ₂ at a level crossing withv ₂+v ₄, and thev ₁+v ₅ band (linked of course tov ₁+v ₂ by the Coriolis resonance between thev ₂ andv ₅ modes) is quite visible and perturbs several subbands ofv ₂+v ₄ of high values of K through an anharmonic resonance. Moreover, the complex (3v ₅ ^±1 ,v+2v ₅ ⁰ , 2v ₂+v ₅ ^±1 , 3v ₂,v ₂+2v ₅ ^±2 , 3v ₅ ^±3 ) system of Coriolis-connected bands is linked to the bands studied in the present work by two Fermi resonances: one betweenv ₂+2v ₅ ⁰ andv ₁+v ₂, and the other one betweenv ₁+v ₅ and 3v ₅ ^±1 , whose several subbands have been observed on the low part of the spectrum. The values of all the band centres and of the different coupling constants have been estimated, but all these interactions make the line assignments and the interpretation of the spectrum very difficult.