227 research outputs found
A constitutive law for cross-linked actin networks by homogenization techniques
Inspired by experiments on the actin driven propulsion of micrometer sized
beads we develop and study a minimal mechanical model of a two-dimensional
network of stiff elastic filaments grown from the surface of a cylinder.
Starting out from a discrete model of the network structure and of its
microscopic mechanical behavior we derive a macroscopic constitutive law by
homogenization techniques. We calculate the axisymmetric equilibrium state and
study its linear stability depending on the microscopic mechanical properties.
We find that thin networks are linearly stable, whereas thick networks are
unstable. The critical thickness for the change in stability depends on the
ratio of the microscopic elastic constants. The instability is induced by the
increase in the compressive load on the inner network layers as the thickness
of the network increases. The here employed homogenization approach combined
with more elaborate microscopic models can serve as a basis to study the
evolution of polymerizing actin networks and the mechanism of actin driven
motion.Comment: 19 pages, 7 figure
Behavior of a net of fibers linked by viscous interactions: theory and mechanical properties
International audienceThis paper presents an investigation of the macroscopic mechanical behavior of highly concentrated fiber suspensions for which the mechanical behavior is governed by local fiber-fiber interactions. The problem is approached by considering the case of a net of rigid fibers of uniform length, linked by viscous point interactions of power-law type. Those interactions may result in local forces and moments located at the contacting point between two fibers, and respectively power-law functions of the local linear and angular velocity at this point. Assuming the existence of an elementary representative volume which size is small compared to the size of the whole structure, the fiber net is regarded as a periodic assembly of identical cells. Macroscopic equilibrium and constitutive equations of the equivalent continuum are then obtained by the discrete and periodic media homogenization method, based on the use of asymptotic expansions. Depending on the order of magnitude of local translational viscosities and rotational viscosities, three types of the equivalent continua are proved to be possible. One of them leads to an effective Cosserat medium, the other ones being usual Cauchy media. Lastly, formulations that enable an effective computation of constitutive equations are detailed. They show that the equivalent continuum behaves like an anisotropic power-law fluid
Some spaces are more equal than others
It has generally been thought that in perturbed
Friedmann-Lemaitre-Robertson-Walker models of the Universe, global topology
should not have any feedback effects on dynamics. However, a weak-field limit
heuristical argument, assuming a finite particle horizon for the transmission
of gravitational signals, shows that a residual acceleration effect can occur.
The nature of this effect differs algebraically between different constant
curvature 3-manifolds. This potentially provides a selection mechanism for the
3-manifold of comoving space.Comment: 4 pages, proceedings of the Grassmannian Conference in Fundamental
Cosmology, Szczecin, 14-19 Sep 2009, to be refereed by Annalen der Physi
The Neumann problem in thin domains with very highly oscillatory boundaries
In this paper we analyze the behavior of solutions of the Neumann problem
posed in a thin domain of the type with and , defined by smooth
functions and , where the function is supposed to be
-periodic in the second variable . The condition implies
that the upper boundary of this thin domain presents a very high oscillatory
behavior. Indeed, we have that the order of its oscillations is larger than the
order of the amplitude and height of given by the small parameter
. We also consider more general and complicated geometries for thin
domains which are not given as the graph of certain smooth functions, but
rather more comb-like domains.Comment: 20 pages, 4 figure
A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data
It has been suggested by Roukema and coworkers (hereafter R04) that the
topology of the Universe as probed by the ``matched circles'' method using the
first year release of the WMAP CMB data, might be that of the Poincar\'e
dodecahedral space (PDS) model. An excess in the correlation of the
``identified circles'' was reported by R04, for circles of angular radius of
~11 deg for a relative phase twist -36deg, hinting that this could be due to a
Clifford translation, if the hypothesized model were true.
R04 did not however specify the statistical significance of the correlation
signal.
We investigate the statistical significance of the signal using Monte Carlo
CMB simulations in a simply connected Universe, and present an updated analysis
using the three-year WMAP data. We find that our analyses of the first and
three year WMAP data provide results that are consistent with the simply
connected space at a confidence level as low as 68%.Comment: 8 pages, 6 figures, typo corrected/replaced to match version
published in A&
The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps
Several studies have proposed that the shape of the Universe may be a
Poincare dodecahedral space (PDS) rather than an infinite, simply connected,
flat space. Both models assume a close to flat FLRW metric of about 30% matter
density. We study two predictions of the PDS model. (i) For the correct model,
the spatial two-point cross-correlation function, \ximc, of temperature
fluctuations in the covering space, where the two points in any pair are on
different copies of the surface of last scattering (SLS), should be of a
similar order of magnitude to the auto-correlation function, \xisc, on a
single copy of the SLS. (ii) The optimal orientation and identified circle
radius for a "generalised" PDS model of arbitrary twist , found by
maximising \ximc relative to \xisc in the WMAP maps, should yield . We optimise the cross-correlation at scales < 4.0 h^-1 Gpc
using a Markov chain Monte Carlo (MCMC) method over orientation, circle size
and . Both predictions were satisfied: (i) an optimal "generalised" PDS
solution was found, with a strong cross-correlation between points which would
be distant and only weakly correlated according to the simply connected
hypothesis, for two different foreground-reduced versions of the WMAP 3-year
all-sky map, both with and without the kp2 Galaxy mask: the face centres are
\phi
\in [0,2\pi]$, is about 6-9%.Comment: 20 pages, 22 figures, accepted in Astronomy & Astrophysics, software
available at http://adjani.astro.umk.pl/GPLdownload/dodec/ and MCMCs at
http://adjani.astro.umk.pl/GPLdownload/MCM
There was movement that was stationary, for the four-velocity had passed around
Is the Doppler interpretation of galaxy redshifts in a
Friedmann-Lemaitre-Robertson-Walker (FLRW) model valid in the context of the
approach to comoving spatial sections pioneered by de Sitter, Friedmann,
Lemaitre and Robertson, i.e. according to which the 3-manifold of comoving
space is characterised by both its curvature and topology? Holonomy
transformations for flat, spherical and hyperbolic FLRW spatial sections are
proposed. By quotienting a simply-connected FLRW spatial section by an
appropriate group of holonomy transformations, the Doppler interpretation in a
non-expanding Minkowski space-time, obtained via four-velocity parallel
transport along a photon path, is found to imply that an inertial observer is
receding from herself at a speed greater than zero, implying contradictory
world-lines. The contradiction in the multiply-connected case occurs for
arbitrary redshifts in the flat and spherical cases, and for certain large
redshifts in the hyperbolic case. The link between the Doppler interpretation
of redshifts and cosmic topology can be understood physically as the link
between parallel transport along a photon path and the fact that the comoving
spatial geodesic corresponding to a photon's path can be a closed loop in an
FLRW model of any curvature. Closed comoving spatial loops are fundamental to
cosmic topology.Comment: 8 pages, 2 figures; v2: missing dot added to Defn 1, minor
corrections; submitted to MNRA
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