Diffusion in the presence of cylindrical obstacles arranged in a square lattice analyzed with generalized Fick-Jacobs equation

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period.     

A Single-Gallery Model for the In Situ Production of Polyethylene-Clay Nanocomposites

Polyolefin-clay nanocomposites are finding many new applications because of their improved properties, such as high modulus, elevated scratch resistance and low gas permeability. Currently, these composites are produced by melt blending organically modified clay with polyolefins. The most challenging step in this process is the intercalation and exfoliation of the clay to produce a homogenously dispersed phase at the nanoscale. A promising alternative to melt blending is in-situ polymerization, where the polymer is produced between the clay layers in the polymerization reactor. In-situ polymerization of olefins with metallocene catalysts supported on clay can produce nanocomposites using conventional polymerization reactors, provided that the clay can be used as a support for the olefin polymerization catalyst. In this approach, the clay fulfills the functions of catalyst support and dispersed phase in the final nanocomposite. In this work, a mathematical model describing particle growth during in-situ polymerization of ethylene with a metallocene catalyst supported on clay will be discussed. The model expands the approach of the multi-grain model used in heterogeneous olefin polymerization to account for the layered structure of clays.     

Elastic characterization of orthotropic plates of any shape via static testing

The paper presents an inverse procedure for identifying elastic properties of isotropic or orthotropic materials from the full-field measurement of the surface displacements of plates under flexural loading configurations. The procedure is based on a numerical–experimental optimisation process which minimizes an error function defined by subtracting the experimental data from the outputs of the numerical analysis. In each iteration the optimisation process updates the values of the elastic constants in a finite element model of the specimen used in the experimental tests. The unknown parameters are simultaneously identified by a single test and without damaging the structural integrity of the specimen. The possibility of using the methodology for characterizing any-shaped plates was investigated. The applicability and the robustness of the procedure were carried out on aluminum and unidirectional Graphite/PEEK laminate specimens. Phase-shifting speckle interferometry was employed to detect the out-of-plane displacement field of a portion of the observed surface of the specimen.     

Modeling Transverse Relative Locality

We investigate some aspects of relativistic classical theories with “relative locality”, in which pairs of events established to be coincident by nearby observers may be described as non-coincident by distant observers. While previous studies focused mainly on the case of longitudinal relative locality, where the effect occurs along the direction connecting the distant observer to the events, we here focus on transverse relative locality, in which instead the effect is found in a direction orthogonal to the one connecting the distant observer to the events. Our findings suggest that, at least for theories of free particles, transverse relative locality is as significant as longitudinal relative locality both conceptually and quantitatively. And we observe that “dual gravity lensing” can be viewed as one of two components of transverse relative locality. We also speculate about a type of spacetime noncommutativity for which transverse relative locality could be particularly significant.     

Analysis of Organic Compounds in Antarctic Snow and Their Origin

Abstract

Organic compounds extractable with n-hexane were identified and quantitatively determined in pack, surface and deep snow samples taken at different depths and collected at several altitudes above sea level from Antarctica during the 1993/94 Italian expedition. The comparison between the composition of organic compounds in snow and the ones in pack and sea-water samples pointed out that the three matrices substantially contain the same biogenic and anthropogenic organic compounds. The contribution of marine aerosol to organic content in the snow is confirmed by the enrichment ratios calculated for the more representative classes of identified compounds (n-alkanes, phthalates and low molecular weight alkylbenzenes). The changes in the composition of organic compounds in snow as the altitude increases seem to depend on the dimensional spectrum of the aerosol. Thus, smallest particles, richest in surfactant material, reach the highest altitudes.     

Thermal photon production in a strongly coupled anisotropic plasma

Journal of High Energy Physics - For the homogeneous configuration given by the long string limit of the folded string with a spin in AdS 3 and a spin and a winding number in S 1, we solve the...     

Synthesis of Lewis a and Lewis X Pentasaccharides Based on N-Trichloroethoxycarbonyl Protection 1

Abstract

Thexyldimethylsilyl 4,6-O-benzylidene-2-deoxy-2-trichloroethoxycarbonylamino-β-D- glucopyranoside (4), having the 3-hydroxy group unprotected, is a versatile starting material for the synthesis of glucosamine containing oligosaccharides. Thus, reaction with galactosyl donor 5 or fucosyl donor 6 afforded the desired β(1-3)- and α(1-3)-linked disaccharides 7 and 8, respectively, in high yields. Reductive opening of the benzylidene moieties in 7 and 8 gave access to the 4-hydroxy groups in 9 and 10. Ensuing fucosylation of 9 or galactosylation of 10 led to Lewis A (Le^a) and Lewis X (Le^x) trisaccharide building blocks 13 and 14, respectively. Their transformation into glycosyl donors 19 and 20 and subsequent reaction with 3b-O-unprotected lactose derivative 23 as acceptor furnished the Le^a? and Le^x pentasaccharide precursors 24 and 25. Exchange of the N-trichloroethoxycarbonyl group for an N-acetyl group and removal of the O-benzyl and O-acetyl protective groups afforded the desired Le^a? and Le^x? pentasaccharides 1 and 2.

     

Synthesis of some 2,3-benzo-l-oxaoctems

The synthesis of some 8-hydroxy-2,3-benzo-l-oxaoctems is reported. The imide 7 , a potential β-lactamase inhibitor, was also synthesized.