181 research outputs found
Extension de la méthode de cholesky pour la synthèse d'un signal 2-D à incréments autosimilaires 1
- Dans un contexte de synthèse de profil routier, cet article présente l'extension d'une méthode de synthèse monodimensionnelle à la génération d'un terrain fractal auto-similaire 2-D. L'objectif est de fournir un terrain dont la dimension fractale est isotrope en terme d'évolution spatiale. La méthode de synthèse s'appuie sur une décomposition de Cholesky. Nous montrons en outre le lien qu'il existe entre les matrices issues de la décomposition selon l'élongation longitudinale et transversale
Power laws in microrheology experiments on living cells: comparative analysis and modelling
We compare and synthesize the results of two microrheological experiments on
the cytoskeleton of single cells. In the first one, the creep function J(t) of
a cell stretched between two glass plates is measured after applying a constant
force step. In the second one, a micrometric bead specifically bound to
transmembrane receptors is driven by an oscillating optical trap, and the
viscoelastic coefficient is retrieved. Both and
exhibit power law behavior: and , with the same exponent
. This power law behavior is very robust ; is
distributed over a narrow range, and shows almost no dependance on the cell
type, on the nature of the protein complex which transmits the mechanical
stress, nor on the typical length scale of the experiment. On the contrary, the
prefactors and appear very sensitive to these parameters. Whereas
the exponents are normally distributed over the cell population, the
prefactors and follow a log-normal repartition. These results are
compared with other data published in the litterature. We propose a global
interpretation, based on a semi-phenomenological model, which involves a broad
distribution of relaxation times in the system. The model predicts the power
law behavior and the statistical repartition of the mechanical parameters, as
experimentally observed for the cells. Moreover, it leads to an estimate of the
largest response time in the cytoskeletal network: s.Comment: 47 pages, 14 figures // v2: PDF file is now Acrobat Reader 4 (and up)
compatible // v3: Minor typos corrected - The presentation of the model have
been substantially rewritten (p. 17-18), in order to give more details -
Enhanced description of protocols // v4: Minor corrections in the text : the
immersion angles are estimated and not measured // v5: Minor typos corrected.
Two references were clarifie
Geometry and field theory in multi-fractional spacetime
We construct a theory of fields living on continuous geometries with
fractional Hausdorff and spectral dimensions, focussing on a flat background
analogous to Minkowski spacetime. After reviewing the properties of fractional
spaces with fixed dimension, presented in a companion paper, we generalize to a
multi-fractional scenario inspired by multi-fractal geometry, where the
dimension changes with the scale. This is related to the renormalization group
properties of fractional field theories, illustrated by the example of a scalar
field. Depending on the symmetries of the Lagrangian, one can define two
models. In one of them, the effective dimension flows from 2 in the ultraviolet
(UV) and geometry constrains the infrared limit to be four-dimensional. At the
UV critical value, the model is rendered power-counting renormalizable.
However, this is not the most fundamental regime. Compelling arguments of
fractal geometry require an extension of the fractional action measure to
complex order. In doing so, we obtain a hierarchy of scales characterizing
different geometric regimes. At very small scales, discrete symmetries emerge
and the notion of a continuous spacetime begins to blur, until one reaches a
fundamental scale and an ultra-microscopic fractal structure. This fine
hierarchy of geometries has implications for non-commutative theories and
discrete quantum gravity. In the latter case, the present model can be viewed
as a top-down realization of a quantum-discrete to classical-continuum
transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and
improved (especially section 4.5), typos corrected, references added; v4:
further typos correcte
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