Globally anisotropic high porosity silica aerogels

We discuss two methods by which high porosity silica aerogels can be engineered to exhibit global anisotropy. First, anisotropy can be introduced with axial strain (i.e. axial compression). In addition, intrinsic anisotropy can result during growth and drying stages and, suitably controlled, it can be correlated with preferential radial shrinkage in cylindrical samples. We have performed small angle X-ray scattering (SAXS) to characterize these two types of anisotropy. We show that global anisotropy originating from either strain or shrinkage leads to optical birefringence and that optical cross-polarization studies are a useful characterization of the uniformity of the imposed global anisotropy.     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

An algorithm for three-way data analysis that alternatively minimizes coupled vector (COV) resolution error and PARAFAC error.

A novel algorithm, alternatively minimizing coupled vector (COV) resolution error and PARAFAC error algorithm, is proposed in this paper. This algorithm can overcome the problem of slow convergence and is insensitive to the estimation of component number, such problems are unavoidable while using the traditional parallel factors analysis (PARAFAC) algorithm. In other words, this algorithm is capable of improving the computing speed and providing accurate resolutions provided that the number of factors used in the computation is no less than that of the actual underlying ones. The characteristic performances were demonstrated with a novel fluorescence data array.