7,125 research outputs found
Modelling the Fluid Mechanics of Cilia and Flagella in Reproduction and Development
Cilia and flagella are actively bending slender organelles, performing
functions such as motility, feeding and embryonic symmetry breaking. We review
the mechanics of viscous-dominated microscale flow, including time-reversal
symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the
fundamental force singularity, higher order multipoles, and the method of
images, providing physical insight and forming a basis for computational
approaches. Two biological problems are then considered in more detail: (1)
left-right symmetry breaking flow in the node, a microscopic structure in
developing vertebrate embryos, and (2) motility of microswimmers through
non-Newtonian fluids. Our model of the embryonic node reveals how particle
transport associated with morphogenesis is modulated by the gradual emergence
of cilium posterior tilt. Our model of swimming makes use of force
distributions within a body-conforming finite element framework, allowing the
solution of nonlinear inertialess Carreau flow. We find that a three-sphere
model swimmer and a model sperm are similarly affected by shear-thinning; in
both cases swimming due to a prescribed beat is enhanced by shear-thinning,
with optimal Deborah number around 0.8. The sperm exhibits an almost perfect
linear relationship between velocity and the logarithm of the ratio of zero to
infinite shear viscosity, with shear-thickening hindering cell progress.Comment: 20 pages, 24 figure
Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis
We propose a strategy for approximating Pareto optimal sets based on the
global analysis framework proposed by Smale (Dynamical systems, New York, 1973,
pp. 531-544). The method highlights and exploits the underlying manifold
structure of the Pareto sets, approximating Pareto optima by means of
simplicial complexes. The method distinguishes the hierarchy between singular
set, Pareto critical set and stable Pareto critical set, and can handle the
problem of superposition of local Pareto fronts, occurring in the general
nonconvex case. Furthermore, a quadratic convergence result in a suitable
set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure
The singularities as ontological limits of the general relativity
The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete.
After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views.
DOI: 10.58679/TW6232
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
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