Elastic moduli of model random three-dimensional closed-cell cellular solids

Most cellular solids are random materials, while practically all theoretical results are for periodic models. To be able to generate theoretical results for random models, the finite element method (FEM) was used to study the elastic properties of solids with a closed-cell cellular structure. We have computed the density ($\rho$) and microstructure dependence of the Young's modulus ($E$) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law $E\propto\rho^n$ ($1 < n <2$), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data.Comment: 13 pages, 13 figure

Elastic properties of model porous ceramics

The finite element method (FEM) is used to study the influence of porosity and pore shape on the elastic properties of model porous ceramics. The Young's modulus of each model was found to be practically independent of the solid Poisson's ratio. At a sufficiently high porosity, the Poisson's ratio of the porous models converged to a fixed value independent of the solid Poisson's ratio. The Young's modulus of the models is in good agreement with experimental data. We provide simple formulae which can be used to predict the elastic properties of ceramics, and allow the accurate interpretation of empirical property-porosity relations in terms of pore shape and structure.Comment: 17 pages, 13 figure

Dimer percolation and jamming on simple cubic lattice

We consider site percolation of dimers (``neadles'') on simple cubic lattice. The percolation threshold is estimated as $p_c^\text{perc} \approx 0.2555 \pm 0.0001$. The jamming threshold is estimated as $p_c^\text{jamm} = 0.799 \pm 0.002$.Comment: 3 pages, 4 figures, submitted to EPJ

A reaction-diffusion model for the hydration/setting of cement

We propose a heterogeneous reaction-diffusion model for the hydration and setting of cement. The model is based on diffusional ion transport and on cement specific chemical dissolution/precipitation reactions under spatial heterogeneous solid/liquid conditions. We simulate the spatial and temporal evolution of precipitated micro structures starting from initial random configurations of anhydrous cement particles. Though the simulations have been performed for two dimensional systems, we are able to reproduce qualitatively basic features of the cement hydration problem. The proposed model is also applicable to general water/mineral systems.Comment: REVTeX (12 pages), 4 postscript figures, tarred, gzipped, uuencoded using `uufiles', coming with separate file(s). Figure 1 consists of 6 color plates; if you have no color printer try to send it to a black&white postscript-plotte

Elastic properties of a tungsten-silver composite by reconstruction and computation

We statistically reconstruct a three-dimensional model of a tungsten-silver composite from an experimental two-dimensional image. The effective Young's modulus ($E$) of the model is computed in the temperature range 25-1060^o C using a finite element method. The results are in good agreement with experimental data. As a test case, we have reconstructed the microstructure and computed the moduli of the overlapping sphere model. The reconstructed and overlapping sphere models are examples of bi-continuous (non-particulate) media. The computed moduli of the models are not generally in good agreement with the predictions of the self-consistent method. We have also evaluated three-point variational bounds on the Young's moduli of the models using the results of Beran, Molyneux, Milton and Phan-Thien. The measured data were close to the upper bound if the properties of the two phases were similar ($1/6 < E_1 /E_2 < 6$).Comment: 23 Pages, 12 Figure

Quantifying Shape of Star-Like Objects Using Shape Curves and A New Compactness Measure

Shape is an important indicator of the physical and chemical behavior of natural and engineered particulate materials (e.g., sediment, sand, rock, volcanic ash). It directly or indirectly affects numerous microscopic and macroscopic geologic, environmental and engineering processes. Due to the complex, highly irregular shapes found in particulate materials, there is a perennial need for quantitative shape descriptions. We developed a new characterization method (shape curve analysis) and a new quantitative measure (compactness, not the topological mathematical definition) by applying a fundamental principle that the geometric anisotropy of an object is a unique signature of its internal spatial distribution of matter. We show that this method is applicable to “star-like” particles, a broad mathematical definition of shape fulfilled by most natural and engineered particulate materials. This new method and measure are designed to be mathematically intermediate between simple parameters like sphericity and full 3D shape descriptions. For a “star-like” object discretized as a polyhedron made of surface planar elements, each shape curve describes the distribution of elemental surface area or volume. Using several thousand regular and highly irregular 3-D shape representations, built from model or real particles, we demonstrate that shape curves accurately encode geometric anisotropy by mapping surface area and volume information onto a pair of dimensionless 2-D curves. Each shape curve produces an intrinsic property (length of shape curve) that is used to describe a new definition of compactness, a property shown to be independent of translation, rotation, and scale. Compactness exhibits unique values for distinct shapes and is insensitive to changes in measurement resolution and noise. With increasing ability to rapidly capture digital representations of highly irregular 3-D shapes, this work provides a new quantitative shape measure for direct comparison of shape across classes of particulate materials

Deconfinement and Percolation

Using percolation theory, we derive a conceptual definition of deconfinement in terms of cluster formation. The result is readily applicable to infinite volume equilibrium matter as well as to finite size pre-equilibrium systems in nuclear collisions.Comment: 13 pages, latex, six figures include

Correlations in the T Cell Response to Altered Peptide Ligands

The vertebrate immune system is a wonder of modern evolution. Occasionally, however, correlations within the immune system lead to inappropriate recruitment of preexisting T cells against novel viral diseases. We present a random energy theory for the correlations in the naive and memory T cell immune responses. The non-linear susceptibility of the random energy model to structural changes captures the correlations in the immune response to mutated antigens. We show how the sequence-level diversity of the T cell repertoire drives the dynamics of the immune response against mutated viral antigens.Comment: 21 pages; 6 figures; to appear in Physica

Pressure dependence of the sound velocity in a 2D lattice of Hertz-Mindlin balls: a mean field description

We study the dependence on the external pressure $P$ of the velocities $v_{L,T}$ of long wavelength sound waves in a confined 2D h.c.p. lattice of 3D elastic frictional balls interacting via one-sided Hertz-Mindlin contact forces, whose diameters exhibit mild dispersion. The presence of an underlying long range order enables us to build an effective medium description which incorporates the radial fluctuations of the contact forces acting on a single site. Due to the non linearity of Hertz elasticity, self-consistency results in a highly non-linear differential equation for the "equation of state" linking the effective stiffness of the array with the applied pressure, from which sound velocities are then obtained. The results are in excellent agreement with existing experimental results and simulations in the high and intermediate pressure regimes. It emerges from the analysis that the departure of $v_{L}(P)$ from the ideal $P^{1/6}$ Hertz behavior must be attributed primarily to the fluctuations of the stress field, rather than to the pressure dependence of the number of contacts