28 research outputs found
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.
Hard-Sphere Fluids in Contact with Curved Substrates
The properties of a hard-sphere fluid in contact with hard spherical and
cylindrical walls are studied. Rosenfeld's density functional theory (DFT) is
applied to determine the density profile and surface tension for wide
ranges of radii of the curved walls and densities of the hard-sphere fluid.
Particular attention is paid to investigate the curvature dependence and the
possible existence of a contribution to that is proportional to the
logarithm of the radius of curvature. Moreover, by treating the curved wall as
a second component at infinite dilution we provide an analytical expression for
the surface tension of a hard-sphere fluid close to arbitrary hard convex
walls. The agreement between the analytical expression and DFT is good. Our
results show no signs for the existence of a logarithmic term in the curvature
dependence of .Comment: 15 pages, 6 figure
Neuromorphometric characterization with shape functionals
This work presents a procedure to extract morphological information from
neuronal cells based on the variation of shape functionals as the cell geometry
undergoes a dilation through a wide interval of spatial scales. The targeted
shapes are alpha and beta cat retinal ganglion cells, which are characterized
by different ranges of dendritic field diameter. Image functionals are expected
to act as descriptors of the shape, gathering relevant geometric and
topological features of the complex cell form. We present a comparative study
of classification performance of additive shape descriptors, namely, Minkowski
functionals, and the nonadditive multiscale fractal. We found that the proposed
measures perform efficiently the task of identifying the two main classes alpha
and beta based solely on scale invariant information, while also providing
intraclass morphological assessment
Surface layering of liquids: The role of surface tension
Recent measurements show that the free surfaces of liquid metals and alloys
are always layered, regardless of composition and surface tension; a result
supported by three decades of simulations and theory. Recent theoretical work
claims, however, that at low enough temperatures the free surfaces of all
liquids should become layered, unless preempted by bulk freezing. Using x-ray
reflectivity and diffuse scattering measurements we show that there is no
observable surface-induced layering in water at T=298 K, thus highlighting a
fundamental difference between dielectric and metallic liquids. The
implications of this result for the question in the title are discussed.Comment: 5 pages, 4 figures, to appear in Phys. Rev. B. 69 (2004
Monte Carlo simulation of subsurface ordering kinetics in an fcc-alloy model
Within the atom-vacancy exchange mechanism in a nearest-neighbor interaction
model we investigate the kinetics of surface-induced ordering processes close
to the (001) surface of an fcc A_3B-alloy. After a sudden quench into the
ordered phase with a final temperature above the ordering spinodal, T_f > T_sp,
the early time kinetics is dominated by a segregation front which propagates
into the bulk with nearly constant velocity. Below the spinodal, T_f < T_sp,
motion of the segregation wave reflects a coarsening process which appears to
be slower than predicted by the Lifschitz-Allen-Cahn law. In addition, in the
front-penetrated region lateral growth differs distinctly from perpendicular
growth, as a result of the special structure of antiphase boundaries near the
surface. Our results are compared with recent experiments on the subsurface
ordering kinetics at Cu_3Au (001).Comment: 10 pages, 9 figures, submitted to Phys. Rev. B, in prin
Capillary Condensation and Interface Structure of a Model Colloid-Polymer Mixture in a Porous Medium
We consider the Asakura-Oosawa model of hard sphere colloids and ideal
polymers in contact with a porous matrix modeled by immobilized configurations
of hard spheres. For this ternary mixture a fundamental measure density
functional theory is employed, where the matrix particles are quenched and the
colloids and polymers are annealed, i.e. allowed to equilibrate. We study
capillary condensation of the mixture in a tiny sample of matrix as well as
demixing and the fluid-fluid interface inside a bulk matrix. Density profiles
normal to the interface and surface tensions are calculated and compared to the
case without matrix. Two kinds of matrices are considered: (i) colloid-sized
matrix particles at low packing fractions and (ii) large matrix particles at
high packing fractions. These two cases show fundamentally different behavior
and should both be experimentally realizable. Furthermore, we argue that
capillary condensation of a colloidal suspension could be experimentally
accessible. We find that in case (ii), even at high packing fractions, the main
effect of the matrix is to exclude volume and, to high accuracy, the results
can be mapped onto those of the same system without matrix via a simple
rescaling.Comment: 12 pages, 9 figures, submitted to PR
Dark Energy from structure: a status report
The effective evolution of an inhomogeneous universe model in any theory of
gravitation may be described in terms of spatially averaged variables. In
Einstein's theory, restricting attention to scalar variables, this evolution
can be modeled by solutions of a set of Friedmann equations for an effective
volume scale factor, with matter and backreaction source terms. The latter can
be represented by an effective scalar field (`morphon field') modeling Dark
Energy.
The present work provides an overview over the Dark Energy debate in
connection with the impact of inhomogeneities, and formulates strategies for a
comprehensive quantitative evaluation of backreaction effects both in
theoretical and observational cosmology. We recall the basic steps of a
description of backreaction effects in relativistic cosmology that lead to
refurnishing the standard cosmological equations, but also lay down a number of
challenges and unresolved issues in connection with their observational
interpretation.
The present status of this subject is intermediate: we have a good
qualitative understanding of backreaction effects pointing to a global
instability of the standard model of cosmology; exact solutions and
perturbative results modeling this instability lie in the right sector to
explain Dark Energy from inhomogeneities. It is fair to say that, even if
backreaction effects turn out to be less important than anticipated by some
researchers, the concordance high-precision cosmology, the architecture of
current N-body simulations, as well as standard perturbative approaches may all
fall short in correctly describing the Late Universe.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy, 59
pages, 2 figures; matches published versio
Microscopy on Thermal Capillary Waves in Demixed Colloid-Polymer Systems
Recently we have shown how to tune length- and timcscales in demixed colloid-polymer dispersions in such a way that thermal capillary waves at the free interface between demixed fluid phases can be studied directly by means of laser scanning confocal microscopy [Aarts, Schmidt and Lekkerkerker, Science 304, 847 (2004)]. Here, we focus on several static properties of the interface. We show that the probability of fluctuations of the local interface position around its equilibrium value is Gaussian. By comparing two-point correlations of these fluctuations as a function of distance with predictions from capillary wave theory, we obtain results for the interfacial tension and the capillary length. The presented technique enables us to measure also the probability distribution of the tilt angle of the local interface normal and the vertical direction. © Springer-Verlag Berlin Heidelberg 2005
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