475 research outputs found
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
Second order analysis of geometric functionals of Boolean models
This paper presents asymptotic covariance formulae and central limit theorems
for geometric functionals, including volume, surface area, and all Minkowski
functionals and translation invariant Minkowski tensors as prominent examples,
of stationary Boolean models. Special focus is put on the anisotropic case. In
the (anisotropic) example of aligned rectangles, we provide explicit analytic
formulae and compare them with simulation results. We discuss which information
about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their
Applications in Stochastic Geometry and Imaging" in Lecture Notes in
Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second
version mainly resolves minor LaTeX problems.
Radial Distribution Function for Semiflexible Polymers Confined in Microchannels
An analytic expression is derived for the distribution of the
end-to-end distance of semiflexible polymers in external potentials
to elucidate the effect of confinement on the mechanical and statistical
properties of biomolecules. For parabolic confinement the result is exact
whereas for realistic potentials a self-consistent ansatz is developed, so that
is given explicitly even for hard wall confinement. The
theoretical result is in excellent quantitative agreement with fluorescence
microscopy data for actin filaments confined in rectangularly shaped
microchannels. This allows an unambiguous determination of persistence length
and the dependence of statistical properties such as Odijk's deflection
length on the channel width . It is shown that neglecting the
effect of confinement leads to a significant overestimation of bending
rigidities for filaments
Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter
Nuclear matter under the conditions of a supernova explosion unfolds into a
rich variety of spatially structured phases, called nuclear pasta. We
investigate the role of periodic network-like structures with negatively curved
interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock
simulations in periodic lattices. As the most prominent result, we identify for
the first time the {\it single gyroid} network structure of cubic chiral
symmetry, a well known configuration in nanostructured soft-matter
systems, both as a dynamical state and as a cooled static solution. Single
gyroid structures form spontaneously in the course of the dynamical
simulations. Most of them are isomeric states. The very small energy
differences to the ground state indicate its relevance for structures in
nuclear pasta.Comment: 7 pages, 4 figure
Deformation of grain boundaries in polar ice
The ice microstructure (grain boundaries) is a key feature used to study ice
evolution and to investigate past climatic changes. We studied a deep ice core,
in Dome Concordia, Antarctica, which records past mechanical deformations. We
measured a "texture tensor" which characterizes the pattern geometry and
reveals local heterogeneities of deformation along the core. These results
question key assumptions of the current models used for dating
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
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
Rejection-free Geometric Cluster Algorithm for Complex Fluids
We present a novel, generally applicable Monte Carlo algorithm for the
simulation of fluid systems. Geometric transformations are used to identify
clusters of particles in such a manner that every cluster move is accepted,
irrespective of the nature of the pair interactions. The rejection-free and
non-local nature of the algorithm make it particularly suitable for the
efficient simulation of complex fluids with components of widely varying size,
such as colloidal mixtures. Compared to conventional simulation algorithms,
typical efficiency improvements amount to several orders of magnitude
Shape Statistics of Sloan Digital Survey superclusters
We study the supercluster shape properties of the recently compiled SDSS
cluster catalog using an approach based on differential geometry. We detect
superclusters by applying the percolation algorithm to observed cluster
populations, extended out to in order to avoid selection
biases. We utilize a set of shapefinders in order to study the morphological
features of superclusters with cluster members and find that
filamentary morphology is the dominant supercluster shape feature, in agreement
with previous studies.Comment: 6 pages, 6 figures, accepted for publication in the MNRAS, (minor
changes
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