A Hierarchy of Voids

We present a model for the distribution of void sizes and its evolution within the context of hierarchical scenarios of gravitational structure formation. For a proper description of the hierarchical buildup of the system of voids in the matter distribution, not only the "void-in-void" problem should be taken into account, but also that of the "void-in-cloud" issue. Within the context of the excursion set formulation of an evolving void hierarchy is one involving a "two-barrier" excursion problem, unlike the "one-barrier" problem for the dark halo evolution. This leads to voids having a peaked size distribution at any cosmic epoch, centered on a characteristic void size that evolves self-similarly in time, this in distinct contrast to the distribution of virialized halo masses which do not have a small-scale cut-off.Comment: 6 pages, 4 figures, to appear in the Proceedings of IAU Colloquium 195: "Outskirts of Galaxy Clusters: intense life in the suburbs", Torino Italy, March 200

Voids in the LCRS versus CDM Models

We have analyzed the distribution of void sizes in the two-dimensional slices of the Las Campanas Redshift Survey (LCRS). Fourteen volume-limited subsamples were extracted from the six slices to cover a large part of the survey and to test the robustness of the results against cosmic variance. Thirteen samples were randomly culled to produce homogeneously selected samples. We then studied the relationship between the cumulative area covered by voids and the void size as a property of the void hierarchy. We find that the distribution of void sizes scales with the mean galaxy separation, $\lambda$. In particular, we find that the size of voids covering half of the area is given by D_{med} \approx \lambda + (12\pm3) \h^{-2}Mpc. Next, by employing an environmental density threshold criterion to identify mock galaxies, we were able to extend this analysis to mock samples from dynamical $n$-body simulations of Cold Dark Matter (CDM) models. To reproduce the observed void statistics, overdensity thresholds of $\delta_{th} \approx 0 ... 1$ are necessary. We have compared standard (SCDM), open (OCDM), vacuum energy dominated ($\Lambda$CDM), and broken scale invariant CDM models (BCDM): we find that both the void coverage distribution and the two-point correlation function provide important and complementary information on the large-scale matter distribution. The dependence of the void statistics on the threshold criterion for the mock galaxy indentification shows that the galaxy biasing is more crucial for the void size distribution than are differences between the cosmological models.Comment: 10 pages, 8 eps figures, submitted to MNRA

Coupled visco-mechanical and diffusion void growth modelling during composite curing

Most critical processing step during long fiber reinforced epoxy matrix composite laminate manufacturing is the polymerization stage. If not optimized, it gives birth to defects in the bulk material, such as voids. These defects are considered as possible sources of damage in the composite parts. The aim of this work is to model the evolution of void growth in thermoset composite laminates after ply collation (autoclave processes) or resin impregnation (RTM, LCM process). A coupled mechanical and diffusion model is presented to better predict the final void size at the end of polymerization. Amongst the parameter investigated, onset of pressure application and diffusive species concentration where found to have a major effect on void size evolution during curing process

Extended Void Merging Tree Algorithm for Self-Similar Models

In hierarchical evolution, voids exhibit two different behaviors related with their surroundings and environments, they can merge or collapse. These two different types of void processes can be described by the two-barrier excursion set formalism based on Brownian random walks. In this study, the analytical approximate description of the growing void merging algorithm is extended by taking into account the contributions of voids that are embedded into overdense region(s) which are destined to vanish due to gravitational collapse. Following this, to construct a realistic void merging model that consists of both collapse and merging processes, the two-barrier excursion set formalism of the void population is used. Assuming spherical voids in the Einstein de Sitter Universe, the void merging algorithm which allows us to consider the two main processes of void hierarchy in one formalism is constructed. In addition to this, the merger rates, void survival probabilities, void size distributions in terms of the collapse barrier and finally, the void merging tree algorithm in the self-similar models are defined and derived.Comment: 26 pages, 19 figures, accepted in MNRA

Statistical Geometry of Packing Defects of Lattice Chain Polymer from Enumeration and Sequential Monte Carlo Method

Voids exist in proteins as packing defects and are often associated with protein functions. We study the statistical geometry of voids in two-dimensional lattice chain polymers. We define voids as topological features and develop a simple algorithm for their detection. For short chains, void geometry is examined by enumerating all conformations. For long chains, the space of void geometry is explored using sequential Monte Carlo importance sampling and resampling techniques. We characterize the relationship of geometric properties of voids with chain length, including probability of void formation, expected number of voids, void size, and wall size of voids. We formalize the concept of packing density for lattice polymers, and further study the relationship between packing density and compactness, two parameters frequently used to describe protein packing. We find that both fully extended and maximally compact polymers have the highest packing density, but polymers with intermediate compactness have low packing density. To study the conformational entropic effects of void formation, we characterize the conformation reduction factor of void formation and found that there are strong end-effect. Voids are more likely to form at the chain end. The critical exponent of end-effect is twice as large as that of self-contacting loop formation when existence of voids is not required. We also briefly discuss the sequential Monte Carlo sampling and resampling techniques used in this study.Comment: 29 pages, including 12 figure

Porometry, porosimetry, image analysis and void network modelling in the study of the pore-level properties of filters

We present fundamental and quantitative comparisons between the techniques of porometry (or flow permporometry), porosimetry, image analysis and void network modelling for seven types of filter, chosen to encompass the range of simple to complex void structure. They were metal, cellulose and glass fibre macro- and meso-porous filters of various types. The comparisons allow a general re-appraisal of the limitations of each technique for measuring void structures. Porometry is shown to give unrealistically narrow void size distributions, but the correct filtration characteristic when calibrated. Shielded mercury porosimetry can give the quaternary (sample-level anisotropic) characteristics of the void structure. The first derivative of a mercury porosimetry intrusion curve is shown to underestimate the large number of voids, but this error can be largely corrected by the use of a void network model. The model was also used to simulate the full filtration characteristic of each sample, which agreed with the manufacturer's filtration ratings. The model was validated through its correct a priori simulation of absolute gas permeabilities for track etch, cellulose nitrate and sintered powder filters. © 2011 Elsevier Ltd

The Cosmically Depressed: Life, Sociology and Identity of Voids

We review and discuss aspects of Cosmic Voids that form the background for our Void Galaxy Survey (see accompanying paper by Stanonik et al.). Following a sketch of the general characteristics of void formation and evolution, we describe the influence of the environment on their development and structure and the characteristic hierarchical buildup of the cosmic void population. In order to be able to study the resulting tenuous void substructure and the galaxies populating the interior of voids, we subsequently set out to describe our parameter free tessellation-based watershed void finding technique. It allows us to trace the outline, shape and size of voids in galaxy redshift surveys. The application of this technique enables us to find galaxies in the deepest troughs of the cosmic galaxy distribution, and has formed the basis of our void galaxy program.Comment: 10 pages, 4 figures, proceedings "Galaxies in Isolation" (May 2009, Granada, Spain), eds. L. Verdes-Montenegro, ASP (this is a colour, extended and combined version; accompanying paper to Stanonik et al., arXiv:0909.2869, in same volume