1,478 research outputs found
Peaks and dips in Gaussian random fields: a new algorithm for the shear eigenvalues, and the excursion set theory
We present a new algorithm to sample the constrained eigenvalues of the
initial shear field associated with Gaussian statistics, called the `peak/dip
excursion-set-based' algorithm, at positions which correspond to peaks or dips
of the correlated density field. The computational procedure is based on a new
formula which extends Doroshkevich's unconditional distribution for the
eigenvalues of the linear tidal field, to account for the fact that halos and
voids may correspond to maxima or minima of the density field. The ability to
differentiate between random positions and special points in space around which
halos or voids may form (peaks/dips), encoded in the new formula and reflected
in the algorithm, naturally leads to a straightforward implementation of an
excursion set model for peaks and dips in Gaussian random fields - one of the
key advantages of this sampling procedure. In addition, it offers novel
insights into the statistical description of the cosmic web. As a first
physical application, we show how the standard distributions of shear
ellipticity and prolateness in triaxial models of structure formation are
modified by the constraint. In particular, we provide a new expression for the
conditional distribution of shape parameters given the density peak constraint,
which generalizes some previous literature work. The formula has important
implications for the modeling of non-spherical dark matter halo shapes, in
relation to their initial shape distribution. We also test and confirm our
theoretical predictions for the individual distributions of eigenvalues
subjected to the extremum constraint, along with other directly related
conditional probabilities. Finally, we indicate how the proposed sampling
procedure naturally integrates into the standard excursion set model,
potentially solving some of its well-known problems, and into the ellipsoidal
collapse framework. (abridged)Comment: 18 pages, 5 figures, MNRAS in pres
Cross-diffusion systems for image processing: II. The nonlinear case
In this paper the use of nonlinear cross-diffu\-sion systems to model image
restoration is investigated, theoretically and numerically. In the first case,
well-posedness, scale-space properties and long time behaviour are analyzed.
From a numerical point of view, a computational study of the performance of the
models is carried out, suggesting their diversity and potentialities to treat
image filtering problems. The present paper is a continuation of a previous
work of the same authors, devoted to linear cross-diffusion models.
\keywords{Cross-diffusion \and Complex diffusion \and Image restoration
Collective effects in cellular structure formation mediated by compliant environments: a Monte Carlo study
Compliant environments can mediate interactions between mechanically active
cells like fibroblasts. Starting with a phenomenological model for the
behaviour of single cells, we use extensive Monte Carlo simulations to predict
non-trivial structure formation for cell communities on soft elastic substrates
as a function of elastic moduli, cell density, noise and cell position
geometry. In general, we find a disordered structure as well as ordered
string-like and ring-like structures. The transition between ordered and
disordered structures is controlled both by cell density and noise level, while
the transition between string- and ring-like ordered structures is controlled
by the Poisson ratio. Similar effects are observed in three dimensions. Our
results suggest that in regard to elastic effects, healthy connective tissue
usually is in a macroscopically disordered state, but can be switched to a
macroscopically ordered state by appropriate parameter variations, in a way
that is reminiscent of wound contraction or diseased states like contracture.Comment: 45 pages, 7 postscript figures included, revised version accepted for
publication in Acta Biomateriali
Highly accurate schemes for PDE-based morphology with general structuring elements
The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology
Pattern formation on the surface of cationic-anionic cylindrical aggregates
Charged pattern formation on the surfaces of self--assembled cylindrical
micelles formed from oppositely charged heterogeneous molecules such as
cationic and anionic peptide amphiphiles is investigated. The net
incompatibility among different components results in the formation of
segregated domains, whose growth is inhibited by electrostatics. The transition
to striped phases proceeds through an intermediate structure governed by
fluctuations, followed by states with various lamellar orientations, which
depend on cylinder radius and . We analyze the specific heat,
susceptibility , domain size and morphology as a
function of and .Comment: Sent to PRL 11Jan05 Transferred from PRL to PRE 10Jun0
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