Porphyrinic compounds are of increasing interest to the materials science community, yet little attention has been paid to crystallographically controlled voids and channels in these materials. We have conducted an initial survey of the voids and channels in a random subset of 1000 porphyrinic compounds with known crystal structures. From calculations using a rolling-probe subroutine, we have found that about 5% of these compounds have line-of-sight channels, which differ in their topology depending on the crystallography. A small but significant number of porphyrinic compounds have calculated void contents of >25 volume %. We discuss in detail the void and channel characteristics, including pore-size distribution, of four representative compounds, with technological implications.

The main aim of this research was investigation of the processing-structure-property relationship for polymer blends. The paper presents the results of tests on the structure, basic physical and porous properties of polymer films blend of low density polyethylene (LDPE) with poly(4-methyl-1-pentene) (PMP). Studies utilizing LDPE/PMP blends were undertaken to investigate a three-stage process: melt-extrusion/annealing/uniaxial-stretching (MEAUS), and a two-stage process: melt-extrusion/uniaxial and biaxial stretching (MEUS and MEUBS), used to produce porous films. The permeability and porosity results coupled with small-angle x-ray scattering data provide a direct connection between changes in microstructure to the observed changes in gas transport properties.

The present paper is concerned with an in-depth study of the effects of rotation, two-temperature parameter and voids on the magneto-thermoelastic interactions in a homogeneous, isotropic, generalized half-space with gravity field. The formulation is applied within the frame-work of two-temperature generalized thermoelasticity based on the hyperbolic heat conduction model with one relaxation time. Using normal mode analysis technique for the physical variables appearing in the governing equations, we get the analytical expressions for displacement components, stress, thermodynamic temperature, conductive temperature and change in volume fraction field. The general solution obtained is then applied to a specific problem of an infinite half-space having isothermal boundary subjected to mechanical load. Variations of the considered variables through the vertical distance are illustrated graphically.

Voids form a prominent aspect of the Megaparsec distribution of galaxies and matter. Not only do they represent a key constituent of the Cosmic Web, they also are one of the cleanest probes and measures of global cosmological parameters. The shape and evolution of voids are highly sensitive to the nature of dark energy, while their substructure and galaxy population provides a direct key to the nature of dark matter. Also, the pristine environment of void interiors is an important testing ground for our understanding of environmental influences on galaxy formation and evolution. In this paper, we review the key aspects of the structure and dynamics of voids, with a particular focus on the hierarchical evolution of the void population. We demonstrate how the rich structural pattern of the Cosmic Web is related to the complex evolution and buildup of voids.

The Cosmic Web is a complicated highly-entangled geometrical object. Remarkably it has formed from practically Gaussian initial conditions, which may be regarded as the simplest departure from exactly uniform universe in purely deterministic mapping. The full complexity of the web is revealed neither in configuration no velocity spaces considered separately. It can be fully appreciated only in six-dimensional (6D) phase space. However, studies of the phase space is complicated by the fact that every projection of it on a three-dimensional (3D) space is multivalued and contained caustics. In addition phase space is not a metric space that complicates studies of geometry. We suggest to use Lagrangian submanifold i.e., x = x(q), where both x and q are 3D vectors instead of the phase space for studies the complexity of cosmic web in cosmological N-body dark matter simulations. Being fully equivalent in dynamical sense to the phase space it has an advantage of being a single valued and also metric space.

Bulk flows of galaxies moving with respect to the cosmic microwave background are well established observationally and seen in the most recent ΛCDM simulations. With the aid of an idealised Gadget-2 simulation, we show that void asymmetries in the cosmic web can exacerbate local bulk flows of galaxies. The {\it Cosmicflows-2} survey, which has mapped in detail the 3D structure of the Local Universe, reveals that the Local Group resides in a “local sheet” of galaxies that borders a “local void” with a diameter of about 40 Mpc. The void is emptying out at a rate of 16 km s-1 Mpc-1. In a co-moving frame, the Local Sheet is found to be moving away from the Local Void at ∼ 260 km s-1. Our model shows how asymmetric collapse due to unbalanced voids on either side of a developing sheet or wall can lead to a systematic movement of the sheet. We conjectured that asymmetries could lead to a large-scale separation of dark matter and baryons, thereby driving a dependence of galaxy properties with environment, but we do {\it not} find any evidence for this effect.

We have used the technique of in situ electron microscopy to study the oxidation and reduction of the palladium (Pd) catalysts. In this study, we have subjected a Pd catalyst to oxidation and reduction cycles and studied the changes in particle structure and morphology with in situ electron diffraction and imaging. The PdO particles can be reduced to Pd metal in situ at temperatures as low as 200°C in an atmosphere of a few Torr of both H2 and O2. We also found that essentially the same reduction occurred in the vacuums of 10−6 to 10−7 Torr in two different electron microscopes. Our in situ reduction studies show that many of the oxide particles form voids when reduced to Pd metal. The decrease in volume that occurs during reduction is often accommodated by a combination of particle shrinkage and void formation. The production of voids does not seem to depend on either the reducing atmosphere or the rate of reduction, although the voids appear to be unstable above 500°C.

After some reminiscences about the founding of the Applied Probability journals the author discusses three open problems concerned respectively with:

(i) the prehistory of applied probability

(ii) Poisson–Delauney Simplexes

(iii) voids and pancakes in the universe.