Structure and spacing of cellulose microfibrils in woody cell walls of dicots

The structure of cellulose microfibrils in situ in wood from the dicotyledonous (hardwood) species cherry and birch, and the vascular tissue from sunflower stems, was examined by wide-angle X-ray and neutron scattering (WAXS and WANS) and small-angle neutron scattering (SANS). Deuteration of accessible cellulose chains followed by WANS showed that these chains were packed at similar spacings to crystalline cellulose, consistent with their inclusion in the microfibril dimensions and with a location at the surface of the microfibrils. Using the Scherrer equation and correcting for considerable lateral disorder, the microfibril dimensions of cherry, birch and sunflower microfibrils perpendicular to the [200] crystal plane were estimated as 3.0, 3.4 and 3.3 nm respectively. The lateral dimensions in other directions were more difficult to correct for disorder but appeared to be 3 nm or less. However for cherry and sunflower, the microfibril spacing estimated by SANS was about 4 nm and was insensitive to the presence of moisture. If the microfibril width was 3 nm as estimated by WAXS, the SANS spacing suggests that a non-cellulosic polymer segment might in places separate the aggregated cellulose microfibrils

Hemicellulose binding and the spacing of cellulose microfibrils in spruce wood

Cellulose microfibrils in conifers, as in other woody materials, are aggregated into loose bundles called macrofibrils. The centre-to-centre spacing of the microfibrils within these macrofibrils can be estimated from the position of a broad diffraction peak in small-angle neutron scattering (SANS) after deuteration. A known spacing of 3.0 nm, increasing with moisture content, is consistent with direct microfibril to microfibril contact. However recent evidence indicates that conifer microfibrils are partially coated with bound xylan chains, and possibly with lignin and galactoglucomannan, implying a wider centre-to-centre spacing as found in angiosperm wood. Delignification of spruce wood allowed a weak SANS peak to be observed without measurable change in spacing. By deuterating spruce wood in mildly alkaline D2O and then re-equilibrating with ambient H2O, deuterium atoms were trapped in a position that gave a 3.8 nm microfibril spacing under dry conditions as in angiosperm wood, instead of the 3.0 nm spacing normally observed in conifers. After conventional vapour deuteration of spruce wood a minor peak at 3.8 nm could be fitted in addition to the 3.0 nm peak. These observations are consistent with some microfibril segments being separated by bound xylan chains as in angiosperms, in addition to the microfibril segments that are in direct contact

The final fate of spherical inhomogeneous dust collapse II: Initial data and causal structure of singularity

Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of the apparent horizon. We also bring out several related features which throw some useful light towards understanding the nature of this singularity, including the behaviour of geodesic families coming out and some aspects related to the stability of singularity.Comment: Latex file, uses epsf.sty, 15 pages and 3 eps figures. Paragraph on role of smooth functions rewritten. Four references added. To appear in Classical & Quantum Gravit

On the accuracy of time-delay cosmography in the Frontier Fields Cluster MACS J1149.5+2223 with supernova Refsdal

We study possible systematic effects on the values of the cosmological parameters measured through strong lensing analyses of the HFF galaxy cluster MACS J1149.5+2223. We use the observed positions of a large set of spectroscopically selected multiple images, including those of supernova "Refsdal" with their estimated time delays. Starting from our reference model in a flat $\Lambda$CDM cosmology, published in Grillo et al. (2018), we confirm the relevance of the longest measurable time delay, between SX and S1, and an approximately linear relation between its value and that of $H_{0}$. We perform true blind tests by considering a range of time delays around its original estimate of $345 \pm 10$ days, as an accurate measurement of this time delay was not known at the time of analysis and writing. We investigate separately the impact of a constant sheet of mass at the cluster redshift, of a power-law profile for the mass density of the cluster main halo and of some scatter in the cluster member scaling relations. Remarkably, we find that these systematic effects do not introduce a significant bias on the inferred values of $H_{0}$ and $\Omega_{\rm m}$ and that the statistical uncertainties dominate the total error budget: a 3% uncertainty on the time delay of image SX translates into approximately 6% and 40% (including both statistical and systematic $1\sigma$) uncertainties for $H_{0}$ and $\Omega_{\rm m}$, respectively. Furthermore, our model accurately reproduces the extended surface brightness distribution of the supernova host, covering more than $3 \times 10^{4}$ $HST$ pixels. We also present the interesting possibility of measuring the value of the equation-of-state parameter $w$ of the dark energy density, currently with a 30% uncertainty. We conclude that time-delay cluster lenses have the potential to become soon an alternative and competitive cosmological probe.Comment: 10 pages, 8 figures, 1 table; ApJ in press (all main results and figures unchanged, only minor changes during revision

The story of supernova 'Refsdal' told by MUSE

We present MUSE observations in the core of the HFF galaxy cluster MACS J1149.5+2223, where the first magnified and spatially-resolved multiple images of SN 'Refsdal' at redshift 1.489 were detected. Thanks to a DDT program with the VLT and the extraordinary efficiency of MUSE, we measure 117 secure redshifts with just 4.8 hours of total integration time on a single target pointing. We spectroscopically confirm 68 galaxy cluster members, with redshift values ranging from 0.5272 to 0.5660, and 18 multiple images belonging to 7 background, lensed sources distributed in redshifts between 1.240 and 3.703. Starting from the combination of our catalog with those obtained from extensive spectroscopic and photometric campaigns using the HST, we select a sample of 300 (164 spectroscopic and 136 photometric) cluster members, within approximately 500 kpc from the BCG, and a set of 88 reliable multiple images associated to 10 different background source galaxies and 18 distinct knots in the spiral galaxy hosting SN 'Refsdal'. We exploit this valuable information to build 6 detailed strong lensing models, the best of which reproduces the observed positions of the multiple images with a rms offset of only 0.26". We use these models to quantify the statistical and systematic errors on the predicted values of magnification and time delay of the next emerging image of SN 'Refsdal'. We find that its peak luminosity should should occur between March and June 2016, and should be approximately 20% fainter than the dimmest (S4) of the previously detected images but above the detection limit of the planned HST/WFC3 follow-up. We present our two-dimensional reconstruction of the cluster mass density distribution and of the SN 'Refsdal' host galaxy surface brightness distribution. We outline the roadmap towards even better strong lensing models with a synergetic MUSE and HST effort.Comment: 21 pages, 9 figures, 6 tables; accepted for publication in the Astrophysical Journal - extra information on data analysis added, all model predictions and results unchange

Critical Behavior of the Schwinger Model with Wilson Fermions

We present a detailed analysis, in the framework of the MFA approach, of the critical behaviour of the lattice Schwinger model with Wilson fermions on lattices up to $24^2$, through the study of the Lee-Yang zeros and the specific heat. We find compelling evidence for a critical line ending at $\kappa = 0.25$ at large $\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2, 20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation is verified in the explored $\beta$ region.Comment: 12 pages LaTeX file, 10 figures in one uuencoded compressed postscript file. Report LNF-95/049(P

Constraining the multi-scale dark-matter distribution in CASSOWARY 31 with strong gravitational lensing and stellar dynamics

We study the inner structure of the group-scale lens CASSOWARY 31 (CSWA 31) by adopting both strong lensing and dynamical modeling. CSWA 31 is a peculiar lens system. The brightest group galaxy (BGG) is an ultra-massive elliptical galaxy at z = 0.683 with a weighted mean velocity dispersion of $\sigma = 432 \pm 31$ km s$^{-1}$. It is surrounded by group members and several lensed arcs probing up to ~150 kpc in projection. Our results significantly improve previous analyses of CSWA 31 thanks to the new HST imaging and MUSE integral-field spectroscopy. From the secure identification of five sets of multiple images and measurements of the spatially-resolved stellar kinematics of the BGG, we conduct a detailed analysis of the multi-scale mass distribution using various modeling approaches, both in the single and multiple lens-plane scenarios. Our best-fit mass models reproduce the positions of multiple images and provide robust reconstructions for two background galaxies at z = 1.4869 and z = 2.763. The relative contributions from the BGG and group-scale halo are remarkably consistent in our three reference models, demonstrating the self-consistency between strong lensing analyses based on image position and extended image modeling. We find that the ultra-massive BGG dominates the projected total mass profiles within 20 kpc, while the group-scale halo dominates at larger radii. The total projected mass enclosed within $R_{eff}$ = 27.2 kpc is $1.10_{-0.04}^{+0.02} \times 10^{13}$ M$_\odot$. We find that CSWA 31 is a peculiar fossil group, strongly dark-matter dominated towards the central region, and with a projected total mass profile similar to higher-mass cluster-scale halos. The total mass-density slope within the effective radius is shallower than isothermal, consistent with previous analyses of early-type galaxies in overdense environments.Comment: 22 pages, 12 figures, 5 tables, submitted to Astronomy & Astrophysics. We welcome the comments from reader

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

Joint Elastic Side-Scattering Lidar and Raman Lidar Measurements of Aerosol Optical Properties in South East Colorado

We describe an experiment, located in south-east Colorado, USA, that measured aerosol optical depth profiles using two Lidar techniques. Two independent detectors measured scattered light from a vertical UV laser beam. One detector, located at the laser site, measured light via the inelastic Raman backscattering process. This is a common method used in atmospheric science for measuring aerosol optical depth profiles. The other detector, located approximately 40km distant, viewed the laser beam from the side. This detector featured a 3.5m2 mirror and measured elastically scattered light in a bistatic Lidar configuration following the method used at the Pierre Auger cosmic ray observatory. The goal of this experiment was to assess and improve methods to measure atmospheric clarity, specifically aerosol optical depth profiles, for cosmic ray UV fluorescence detectors that use the atmosphere as a giant calorimeter. The experiment collected data from September 2010 to July 2011 under varying conditions of aerosol loading. We describe the instruments and techniques and compare the aerosol optical depth profiles measured by the Raman and bistatic Lidar detectors.Comment: 34 pages, 16 figure

Modelling Pricing Policy Based on Shelf-Life of Non Homogeneous Available-To-Promise in Fruit Supply Chains

[EN] Fruit Supply Chains (SCs) are influenced by uncontrollable natural factors causing heterogeneity in their products, as regards certain attributes that are relevant to customers and vary over time because of the shelf-life. As a consequence customers should be served not only with the required quantity and due date as usual, but also with the quality, freshness and homogeneity specified in their orders. The order promising process (OPP) is based on the uncommitted availability of homogeneous product quantities in planned lots (ATP) that are uncertain. Therefore, there is a risk of not being reliable in the commitments because of discrepancies between the real and planned homogeneous quantities. Furthermore, due to the shelf-life (SL), serving customers with the freshest product introduce the risk of increasing waste because of the aging process. To efficiently manage these risks, this work proposes a mathematical model for handling the heterogeneous ATP in fruit SCs and a pricing policy based on the product SL in the moment of delivery. In order to illustrate the application of the modelling approach, a short numerical example is introduced. The example evidences a conflictive situation when optimizing the assignation of homogeneous ATP between serving orders with fresh and more valuable product, what could lead to increase the risk of having waste because of expiration, and consequently, more costs and less profit.This research has been supported by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the program of innovation and human capital for competitiveness (PINN) (PED-019-2015-1).Grillo-Espinoza, H.; Alemany Díaz, MDM.; Ortiz Bas, Á. (2016). Modelling Pricing Policy Based on Shelf-Life of Non Homogeneous Available-To-Promise in Fruit Supply Chains. IFIP Advances in Information and Communication Technology. 480:608-617. https://doi.org/10.1007/978-3-319-45390-3_52S608617480Alarcon, F., Alemany, M.M.E., Lario, F.C., Oltra, R.F.: The lack of homogeneity in the product (LHP) in the ceramic tile industry and its impact on the reallocation of inventories. Boletin Soc. Espanola Ceram. Vidr. 50, 49–57 (2011). doi: 10.3989/cyv.072011Alemany, M.M.E., Grillo, H., Ortiz, A., Fuertes-Miquel, V.S.: A fuzzy model for shortage planning under uncertainty due to lack of homogeneity in planned production lots. Appl. Math. Model. (2015). doi: 10.1016/j.apm.2014.12.057Alemany, M.M.E., Lario, F.-C., Ortiz, A., Gomez, F.: Available-To-Promise modeling for multi-plant manufacturing characterized by lack of homogeneity in the product: an illustration of a ceramic case. Appl. Math. Model. 37, 3380–3398 (2013). doi: 10.1016/j.apm.2012.07.022Blanco, A.M., Masini, G., Petracci, N., Bandoni, J.A.: Operations management of a packaging plant in the fruit industry. J. Food Eng. 70, 299–307 (2005). doi: 10.1016/j.jfoodeng.2004.05.075Grillo, H., Alemany, M.M.E., Ortiz, A.: A review of mathematical models for supporting the order promising process under Lack of Homogeneity in Product and other sources of uncertainty. Comput. Ind. Eng. 91, 239–261 (2016)Kilic, O.A., van Donk, D.P., Wijngaard, J., Tarim, S.A.: Order acceptance in food processing systems with random raw material requirements. Spectrum 32, 905–925 (2010). doi: 10.1007/s00291-010-0213-4Lin, J.T., Hong, I.H., Wu, C.H., Wang, K.S.: A model for batch available-to-promise in order fulfillment processes for TFT-LCD production chains. Comput. Ind. Eng. 59, 720–729 (2010). doi: 10.1016/j.cie.2010.07.026Maihami, R., Karimi, B.: Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts. Comput. Oper. Res. 51, 302–312 (2014). doi: 10.1016/j.cor.2014.05.022Mundi, M.I., Alemany, M.M.E., Poler, R., Fuertes-Miquel, V.S.: Fuzzy sets to model master production effectively in Make to Stock companies with Lack of Homogeneity in the Product. Fuzzy Sets Syst. 293, 95–112 (2016). http://dx.doi.org/10.1016/j.fss.2015.06.009Tsao, Y.-C., Sheen, G.-J.: Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments. Part Spec. Issue Top. Real-Time Supply Chain Manag. 35, 3562–3580 (2008). doi: 10.1016/j.cor.2007.01.02