Morphological Thermodynamics of Fluids: Shape Dependence of Free Energies

We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe fully the influence of an arbitrarily shaped container on the fluid. These three constraints can be understood as a more precise definition for the conventional term "extensive" and have as a consequence that the surface tension and other thermodynamic quantities contain, beside a constant term, only contributions linear in the mean and Gaussian curvature of the container and not an infinite number of curvatures as generally assumed before. We verify this numerically in the entropic system of hard spheres bounded by a curved wall.Comment: 4 pages, 3 figures, accepted for publication in PR

Density functional theory for hard-sphere mixtures: the White-Bear version Mark II

In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter, accepte

Effects of Noise on Galaxy Isophotes

The study of shapes of the images of objects is an important issue not only because it reveals its dynamical state but also it helps to understand the object's evolutionary history. We discuss a new technique in cosmological image analysis which is based on a set of non-parametric shape descriptors known as the Minkowski Functionals (MFs). These functionals are extremely versatile and under some conditions give a complete description of the geometrical properties of objects. We believe that MFs could be a useful tool to extract information about the shapes of galaxies, clusters of galaxies and superclusters. The information revealed by MFs can be utilized along with the knowledge obtained from currently popular methods and thus could improve our understanding of the true shapes of cosmological objects.Comment: 3 pages, 1 figure, to appear in "The IGM/Galaxy Connection - The Distribution of Baryons at z=0" Conference Proceeding

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Morphological fluctuations of large-scale structure: the PSCz survey

In a follow-up study to a previous analysis of the IRAS 1.2Jy catalogue, we quantify the morphological fluctuations in the PSCz survey. We use a variety of measures, among them the family of scalar Minkowski functionals. We confirm the existence of significant fluctuations that are discernible in volume-limited samples out to 200Mpc/h. In contrast to earlier findings, comparisons with cosmological N-body simulations reveal that the observed fluctuations roughly agree with the cosmic variance found in corresponding mock samples. While two-point measures, e.g. the variance of count-in-cells, fluctuate only mildly, the fluctuations in the morphology on large scales indicate the presence of coherent structures that are at least as large as the sample

Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids

Control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials, in particular those with negative Poisson’s ratio. This article sheds light on the old question of the relationship between geometric microstructure and mechanical response, by comparison of the deformation properties of bar-and-joint-frameworks with those of their realisation as a cellular solid made from linear-elastic material. For ordered planar tessellation models, we find a classification in terms of the number of degrees of freedom of the framework model: first, in cases where the geometry uniquely prescribes a single deformation mode of the framework model, the mechanical deformation and Poisson’s ratio of the linearly-elastic cellular solid closely follow those of the unique deformation mode; the result is a bending-dominated deformation with negligible dependence of the effective Poisson’s ratio on the underlying material’s Poisson’s ratio and small values of the effective Young’s modulus. Second, in the case of rigid structures or when geometric degeneracy prevents the bending-dominated deformation mode, the effective Poisson’s ratio is material-dependent and the Young’s modulus View the MathML sourceE˜cs large. All analysed structures of this type have positive values of the Poisson’s ratio and large values of View the MathML sourceE˜cs. Third, in the case, where the framework has multiple deformation modes, geometry alone does not suffice to determine the mechanical deformation. These results clarify the relationship between mechanical properties of a linear-elastic cellular solid and its corresponding bar-and-joint framework abstraction. They also raise the question if, in essence, auxetic behaviour is restricted to the geometry-guided class of bending-dominated structures corresponding to unique mechanisms, with inherently low values of the Young’s modulus

Imbibition in mesoporous silica: rheological concepts and experiments on water and a liquid crystal

We present, along with some fundamental concepts regarding imbibition of liquids in porous hosts, an experimental, gravimetric study on the capillarity-driven invasion dynamics of water and of the rod-like liquid crystal octyloxycyanobiphenyl (8OCB) in networks of pores a few nanometers across in monolithic silica glass (Vycor). We observe, in agreement with theoretical predictions, square root of time invasion dynamics and a sticky velocity boundary condition for both liquids investigated. Temperature-dependent spontaneous imbibition experiments on 8OCB reveal the existence of a paranematic phase due to the molecular alignment induced by the pore walls even at temperatures well beyond the clearing point. The ever present velocity gradient in the pores is likely to further enhance this ordering phenomenon and prevent any layering in molecular stacks, eventually resulting in a suppression of the smectic phase in favor of the nematic phase.Comment: 18 pages, 8 figure

Adsorption Isotherms of Hydrogen: The Role of Thermal Fluctuations

It is shown that experimentally obtained isotherms of adsorption on solid substrates may be completely reconciled with Lifshitz theory when thermal fluctuations are taken into account. This is achieved within the framework of a solid-on-solid model which is solved numerically. Analysis of the fluctuation contributions observed for hydrogen adsorption onto gold substrates allows to determine the surface tension of the free hydrogen film as a function of film thickness. It is found to decrease sharply for film thicknesses below seven atomic layers.Comment: RevTeX manuscript (3 pages output), 3 figure

Disentangling the Cosmic Web I: Morphology of Isodensity Contours

We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to test global properties of the density field. Furthermore, we identify coherent objects at various threshold levels and calculate their partial Minkowski functionals. We propose a set of two derived dimensionless quantities, planarity and filamentarity, which reduce the morphological information in a simple and intuitive way. Several simulations of the gravitational evolution of initial power-law spectra provide a framework for systematic tests of our method.Comment: 26 pages including 12 figures. Accepted for publication in Ap