3,443 research outputs found
Sharp interface limit of an energy modelling nanoparticle-polymer blends
We identify the -limit of a nanoparticle-polymer model as the number
of particles goes to infinity and as the size of the particles and the phase
transition thickness of the polymer phases approach zero. The limiting energy
consists of two terms: the perimeter of the interface separating the phases and
a penalization term related to the density distribution of the infinitely many
small nanoparticles. We prove that local minimizers of the limiting energy
admit regular phase boundaries and derive necessary conditions of local
minimality via the first variation. Finally we discuss possible critical and
minimizing patterns in two dimensions and how these patterns vary from global
minimizers of the purely local isoperimetric problem.Comment: Minor changes. Rephrased introduction. This version is to appear in
Interfaces and Free Boundarie
Efficient fetal-maternal ECG signal separation from two channel maternal abdominal ECG via diffusion-based channel selection
There is a need for affordable, widely deployable maternal-fetal ECG monitors
to improve maternal and fetal health during pregnancy and delivery. Based on
the diffusion-based channel selection, here we present the mathematical
formalism and clinical validation of an algorithm capable of accurate
separation of maternal and fetal ECG from a two channel signal acquired over
maternal abdomen
Stochastic spectral-spatial permutation ordering combination for nonlocal morphological processing
International audienceThe extension of mathematical morphology to mul-tivariate data has been an active research topic in recent years. In this paper we propose an approach that relies on the consensus combination of several stochastic permutation orderings. The latter are obtained by searching for a smooth shortest path on a graph representing an image. The construction of the graph can be based on both spatial and spectral information and naturally enables patch-based nonlocal processing
Unifying particle-based and continuum models of hillslope evolution with a probabilistic scaling technique
Relationships between sediment flux and geomorphic processes are combined
with statements of mass conservation, in order to create continuum models of
hillslope evolution. These models have parameters which can be calibrated using
available topographical data. This contrasts the use of particle-based models,
which may be more difficult to calibrate, but are simpler, easier to implement,
and have the potential to provide insight into the statistics of grain motion.
The realms of individual particles and the continuum, while disparate in
geomorphological modeling, can be connected using scaling techniques commonly
employed in probability theory. Here, we motivate the choice of a
particle-based model of hillslope evolution, whose stationary distributions we
characterize. We then provide a heuristic scaling argument, which identifies a
candidate for their continuum limit. By simulating instances of the particle
model, we obtain equilibrium hillslope profiles and probe their response to
perturbations. These results provide a proof-of-concept in the unification of
microscopic and macroscopic descriptions of hillslope evolution through
probabilistic techniques, and simplify the study of hillslope response to
external influences.Comment: 28 pages, 8 figure
Convective nonlocal Cahn-Hilliard equations with reaction terms
We introduce and analyze the nonlocal variants of two Cahn-Hilliard type
equations with reaction terms. The first one is the so-called
Cahn-Hilliard-Oono equation which models, for instance, pattern formation in
diblock-copolymers as well as in binary alloys with induced reaction and type-I
superconductors. The second one is the Cahn-Hilliard type equation introduced
by Bertozzi et al. to describe image inpainting. Here we take a free energy
functional which accounts for nonlocal interactions. Our choice is motivated by
the work of Giacomin and Lebowitz who showed that the rigorous physical
derivation of the Cahn-Hilliard equation leads to consider nonlocal
functionals. The equations also have a transport term with a given velocity
field and are subject to a homogenous Neumann boundary condition for the
chemical potential, i.e., the first variation of the free energy functional. We
first establish the well-posedness of the corresponding initial and boundary
value problems in a weak setting. Then we consider such problems as dynamical
systems and we show that they have bounded absorbing sets and global
attractors
Minimality via second variation for a nonlocal isoperimetric problem
We discuss the local minimality of certain configurations for a nonlocal
isoperimetric problem used to model microphase separation in diblock copolymer
melts. We show that critical configurations with positive second variation are
local minimizers of the nonlocal area functional and, in fact, satisfy a
quantitative isoperimetric inequality with respect to sets that are
-close. The link with local minimizers for the diffuse-interface
Ohta-Kawasaki energy is also discussed. As a byproduct of the quantitative
estimate, we get new results concerning periodic local minimizers of the area
functional and a proof, via second variation, of the sharp quantitative
isoperimetric inequality in the standard Euclidean case. As a further
application, we address the global and local minimality of certain lamellar
configurations.Comment: 35 page
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