629 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
Microscopic theory for interface fluctuations in binary liquid mixtures
Thermally excited capillary waves at fluid interfaces in binary liquid
mixtures exhibit simultaneously both density and composition fluctuations.
Based on a density functional theory for inhomogeneous binary liquid mixtures
we derive an effective wavelength dependent Hamiltonian for fluid interfaces in
these systems beyond the standard capillary-wave model. Explicit expressions
are obtained for the surface tension, the bending rigidities, and the coupling
constants of compositional capillary waves in terms of the profiles of the two
number densities characterizing the mixture. These results lead to predictions
for grazing-incidence x-ray scattering experiments at such interfaces.Comment: 23 pages, 11 figure
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.
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
Local orientations of fluctuating fluid interfaces
Thermal fluctuations cause the local normal vectors of fluid interfaces to
deviate from the vertical direction defined by the flat mean interface
position. This leads to a nonzero mean value of the corresponding polar tilt
angle which renders a characterization of the thermal state of an interface.
Based on the concept of an effective interface Hamiltonian we determine the
variances of the local interface position and of its lateral derivatives. This
leads to the probability distribution functions for the metric of the interface
and for the tilt angle which allows us to calculate its mean value and its mean
square deviation. We compare the temperature dependences of these quantities as
predicted by the simple capillary wave model, by an improved phenomenological
model, and by the microscopic effective interface Hamiltonian derived from
density functional theory. The mean tilt angle discriminates clearly between
these theoretical approaches and emphasizes the importance of the variation of
the surface tension at small wave lengths. Also the tilt angle two-point
correlation function is determined which renders an additional structural
characterization of interfacial fluctuations. Various experimental accesses to
measure the local orientational fluctuations are discussed.Comment: 29 pages, 12 figure
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
Using the filaments in the LCRS to test the LambdaCDM model
It has recently been established that the filaments seen in the Las Campanas
Redshift Survey (LCRS) are statistically significant at scales as large as 70
to 80 Mpc/h in the slice, and 50 to 70 Mpc/h in the five other
LCRS slices. The ability to produce such filamentary features is an important
test of any model for structure formation. We have tested the LCDM model with a
featureless, scale invariant primordial power spectrum by quantitatively
comparing the filamentarity in simulated LCRS slices with the actual data. The
filamentarity in an unbiased LCDM model, we find, is less than the LCRS.
Introducing a bias b=1.15, the model is in rough consistency with the data,
though in two of the slices the filamentarity falls below the data at a low
level of statistical significance. The filamentarity is very sensitive to the
bias parameter and a high value b=1.5, which enhances filamentarity at small
scales and suppresses it at large scales, is ruled out. A bump in the power
spectrum at k~0.05 Mpc/h is found to have no noticeable effect on the
filamentarity.Comment: 16 pages, 3 figures; Minor Changes, Accepted to Ap
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
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