16,654 research outputs found
Multiphase shape optimization problems
This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as min (Formula presented.) where D â âd is a given bounded open set, |Ωi| is the Lebesgue measure of Ωi, and m is a positive constant. For a large class of such functionals, we analyze qualitative properties of the cells and the interaction between them. Each cell is itself a subsolution for a (single-phase) shape optimization problem, from which we deduce properties like finite perimeter, inner density, separation by open sets, absence of triple junction points, etc. As main examples we consider functionals involving the eigenvalues of the Dirichlet Laplacian of each cell, i.e., Fi = λki
A Multiphase Shape Optimization Problem for Eigenvalues: Qualitative Study and Numerical Results
We consider the multiphase shape optimization problem
where
is a given constant and is a bounded open set
with Lipschitz boundary. We give some new results concerning the qualitative
properties of the optimal sets and the regularity of the corresponding
eigenfunctions. We also provide numerical results for the optimal partitions
Free boundary regularity for a multiphase shape optimization problem
In this paper we prove a regularity result in dimension two
for almost-minimizers of the constrained one-phase Alt-Caffarelli and the
two-phase Alt-Caffarelli-Friedman functionals for an energy with variable
coefficients. As a consequence, we deduce the complete regularity of solutions
of a multiphase shape optimization problem for the first eigenvalue of the
Dirichlet-Laplacian up to the fixed boundary. One of the main ingredient is a
new application of the epiperimetric-inequality of Spolaor-Velichkov [CPAM,
2018] up to the boundary. While the framework that leads to this application is
valid in every dimension, the epiperimetric inequality is known only in
dimension two, thus the restriction on the dimension
A Note on Optimal Design of Multiphase Elastic Structures
The paper describes the first exact results in optimal design of three-phase
elastic structures. Two isotropic materials, the "strong" and the "weak" one,
are laid out with void in a given two-dimensional domain so that the compliance
plus weight of a structure is minimized. As in the classical two-phase problem,
the optimal layout of three phases is also determined on two levels: macro- and
microscopic. On the macrolevel, the design domain is divided into several
subdomains. Some are filled with pure phases, and others with their mixtures
(composites). The main aim of the paper is to discuss the non-uniqueness of the
optimal macroscopic multiphase distribution. This phenomenon does not occur in
the two-phase problem, and in the three-phase design it arises only when the
moduli of material isotropy of "strong" and "weak" phases are in certain
relation.Comment: 8 pages, 4 figure
Disjunctive Normal Level Set: An Efficient Parametric Implicit Method
Level set methods are widely used for image segmentation because of their
capability to handle topological changes. In this paper, we propose a novel
parametric level set method called Disjunctive Normal Level Set (DNLS), and
apply it to both two phase (single object) and multiphase (multi-object) image
segmentations. The DNLS is formed by union of polytopes which themselves are
formed by intersections of half-spaces. The proposed level set framework has
the following major advantages compared to other level set methods available in
the literature. First, segmentation using DNLS converges much faster. Second,
the DNLS level set function remains regular throughout its evolution. Third,
the proposed multiphase version of the DNLS is less sensitive to
initialization, and its computational cost and memory requirement remains
almost constant as the number of objects to be simultaneously segmented grows.
The experimental results show the potential of the proposed method.Comment: 5 page
Multiple NEA Rendezvous Mission: Solar Sailing Options
The scientific interest in near-Earth asteroids (NEAs) and the classification of some of those as potentially hazardous
asteroid for the Earth stipulated the interest in NEA exploration. Close-up observations of these objects will increase
drastically our knowledge about the overall NEA population. For this reason, a multiple NEA rendezvous mission through
solar sailing is investigated, taking advantage of the propellantless nature of this groundbreaking propulsion technology.
Considering a spacecraft based on the DLR/ESA Gossamer technology, this work focuses on the search of possible
sequences of NEA encounters. The effectiveness of this approach is demonstrated through a number of fully-optimized
trajectories. The results show that it is possible to visit five NEAs within 10 years with near-term solar-sail technology.
Moreover, a study on a reduced NEA database demonstrates the reliability of the approach used, showing that 58% of the
sequences found with an approximated trajectory model can be converted into real solar-sail trajectories. Lastly, this second
study shows the effectiveness of the proposed automatic optimization algorithm, which is able to find solutions for a large
number of mission scenarios without any input required from the user
Optimal partitions for Robin Laplacian eigenvalues
We prove the existence of an optimal partition for the multiphase shape
optimization problem which consists in minimizing the sum of the first Robin
Laplacian eigenvalue of mutually disjoint {\it open} sets which have a
-countably rectifiable boundary and are contained into a
given box in $R^d
A Novel Euler's Elastica based Segmentation Approach for Noisy Images via using the Progressive Hedging Algorithm
Euler's Elastica based unsupervised segmentation models have strong
capability of completing the missing boundaries for existing objects in a clean
image, but they are not working well for noisy images. This paper aims to
establish a Euler's Elastica based approach that properly deals with random
noises to improve the segmentation performance for noisy images. We solve the
corresponding optimization problem via using the progressive hedging algorithm
(PHA) with a step length suggested by the alternating direction method of
multipliers (ADMM). Technically, all the simplified convex versions of the
subproblems derived from the major framework of PHA can be obtained by using
the curvature weighted approach and the convex relaxation method. Then an
alternating optimization strategy is applied with the merits of using some
powerful accelerating techniques including the fast Fourier transform (FFT) and
generalized soft threshold formulas. Extensive experiments have been conducted
on both synthetic and real images, which validated some significant gains of
the proposed segmentation models and demonstrated the advantages of the
developed algorithm
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