Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain

We construct the asymptotics (as ε→0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance ε>0. To cite this article: G. Cardone et al., C. R. Mecanique 335 (2007).     

The effect of side-chain length of cellulose fatty acid esters on their thermal,barrier and mechanical properties

Currently, long-chain cellulose esters are not produced commercially because of high price, and since their preparation typically requires a large quantity of chemicals. To reduce the chemical consumption, cellulose reactivity needs to be increased without losing its quality. One way to increase the reactivity of cellulose is to decrease its molar mass in a controlled manner. In this study, we have synthesized cellulose esters with different side-chain length (C6–C18) in a homogeneous system using ozone molar mass-controlled cellulose. The target was to keep the degree of substitution as low as possible while still ensuring the suitability of cellulose esters for solvent casting. Thermal, barrier and mechanical properties were studied depending on cellulose fatty acid ester side-chain length. All our molar mass-controlled cellulose esters form optically transparent, flexible and heat-sealable films with good water barrier properties and are processable without the addition of an external plasticizer. Furthermore, the films have mechanical properties comparable to some generally used plastics. These good properties suggest that our molar mass-controlled cellulose esters could be potential candidates for various applications such as films and composites.     

Probing surface plasmons by bare V-shaped tips: modeling by geometrical optics and rigorous diffraction theory

Optical Review - We consider probing inhomogeneous waves in the near fields of metallic nanostructures with the aid of a dielectric V-shaped wedge connected to a waveguide. A geometrical model...     

Korn inequality for a thin rod with rounded ends

We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd.     

A note about Volterra operators on weighted Banach spaces of entire functions

We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces.     

Empirical plasticity models applied for paper sheets having different anisotropy and dry solids content levels

The rheological nature of paper or board is usually treated either as elasto-plastic or as viscoelastic depending on the studied paper making process or behavior in converting and end use. In this paper we study several stress–strain curve models and the determination of material parameters from an elasto-plastic point of view. Finally, a suitable approach for all stress–strain curves measured from 180 strips is constructed using a linear function for an elastic region and a nonlinear function for a strain hardening region. This model determines a proportional limit (elastic limit) and gives fairly elegant dependencies between material/fitting parameters and two important factors of mechanical properties of paper: dry solids content and anisotropy. In this paper the dependency of a plastic strain on dry solids content and anisotropy is estimated using the introduced stress–strain curve model. Correspondingly, the model can be used to estimate many other mechanical behaviors, for example, the tension differences arising from non-uniform moisture content of the paper web profile. However, the main target of this study is to produce competent parameters based on modeled stress–strain curves for further construction of a material model. This elasto-plastic material model will be utilized in out-of-plane deformation and fracture models.     

Using a time-delay and integration camera at a non-zero viewing angle under vibration conditions

The use of a TDI camera is restricted to cases of viewing from the direction of the surface normal. Our previous work indicated that a TDI camera can be used with viewing angles up to 30° from the surface normal which extends the usability of TDI for visual inspection applications. The objective of this paper is to examine the use of a TDI camera at a non-zero viewing angle under vibration conditions. The effects caused by vibration of the surface to be viewed become critical when using a TDI camera at non-zero viewing angles. A method of approximating the TDI performance under vibration conditions was determined and evaluated experimentally. The resulting measurements support the approximating method developed here.     

On Extended Polar Decomposition

In this study, we considered the extended polar decomposition using a more general approach than the one provided by Boulanger and Hayes [Int. J. Non-Linear Mech. 36 (2001) 399–420]. We showed that the procedure of the decomposition could be simplified by considering its rotation tensor. Our method is illustrated by examples.     

Residual lignin inhibits thermal degradation of cellulosic fiber sheets

The market for cellulosic fiber based food packaging applications is growing together with the importance of improving the thermal durability of these fibers. To shed light on this, we investigated the role of residual lignin in pulp on the thermal stability of refined pulp sheets. The unbleached, oxygen delignified, and fully bleached pulp sheets were studied after four separate refining degrees. Comparison by Gurley air resistance, Bendtsen porosity, and the oxygen transmission rate tests showed that lignin containing sheets had better air and oxygen barrier properties than fully bleached sheets. Sheet density and light scattering coefficient measurements further confirmed that the lignin containing pulps underwent more intense fibrillation upon refining that changed the barrier properties of the sheets. Thermal treatments (at 225 °C, 20 and 60 min, in water vapor atmospheres of 1 and 75 v/v %) were applied to determine the thermal durability of the sheets. The results revealed that the residual lignin in pulps improved the thermal stability of the pulp sheets in the hot humid conditions. This effect was systematically studied by tensile strength, brightness, and light absorption coefficient measurements. The intrinsic viscosity results support the findings and suggest that lignin is able to hinder the thermal degradation of pulp polysaccharides. In spite of the fact that lignin is known to enhance the thermal yellowing of paper, no significant discoloration of the pulp sheets containing residual lignin was observed in the hot humid conditions (75 v/v %). Our results support the idea of lignin strengthening the thermal durability of paper.