14,554 research outputs found
Geometric partition functions of cellular systems: Explicit calculation of the entropy in two and three dimensions
A method is proposed for the characterisation of the entropy of cellular
structures, based on the compactivity concept for granular packings.
Hamiltonian-like volume functions are constructed both in two and in three
dimensions, enabling the identification of a phase space and making it possible
to take account of geometrical correlations systematically. Case studies are
presented for which explicit calculations of the mean vertex density and
porosity fluctuations are given as functions of compactivity. The formalism
applies equally well to two- and three-dimensional granular assemblies.Comment: 14 pages, 4 figures, to appear in The European Physical Journal E -
Soft Matte
Stress in planar cellular solids and isostatic granular assemblies: Coarse-graining the constitutive equation
A recent theory for stress transmission in isostatic granular and cellular
systems predicts a constitutive equation that couples the stress field to the
local microstructure. The theory could not be applied to macroscopic systems
because the constitutive equation becomes trivial upon straightforward
coarse-graining. This problem is resolved here for arbitrary planar structures.
The solution is based on the observation that staggered order makes it possible
to couple the stress to a reduced geometric tensor that can be coarse-grained.
The method proposed here makes it possible to apply this idea to realistic
systems whose staggered order is generally 'frustrated'. This is achieved by a
renormalization procedure which removes the frustration and enables the use of
the upscalable reduced tensor. As an example we calculate the stress due to a
defect in a periodic solid foam
Modifying continuous-time random walks to model finite-size particle diffusion in granular porous media
The continuous-time random walk (CTRW) model is useful for alleviating the
computational burden of simulating diffusion in actual media. In principle,
isotropic CTRW only requires knowledge of the step-size, , and
waiting-time, , distributions of the random walk in the medium and it then
generates presumably equivalent walks in free space, which are much faster.
Here we test the usefulness of CTRW to modelling diffusion of finite-size
particles in porous medium generated by loose granular packs. This is done by
first simulating the diffusion process in a model porous medium of mean
coordination number, which corresponds to marginal rigidity (the loosest
possible structure), computing the resulting distributions and as
functions of the particle size, and then using these as input for a free space
CTRW. The CTRW walks are then compared to the ones simulated in the actual
media.
In particular, we study the normal-to-anomalous transition of the diffusion
as a function of increasing particle size. We find that, given the same
and for the simulation and the CTRW, the latter predicts incorrectly the
size at which the transition occurs. We show that the discrepancy is related to
the dependence of the effective connectivity of the porous media on the
diffusing particle size, which is not captured simply by these distributions.
We propose a correcting modification to the CTRW model -- adding anisotropy
-- and show that it yields good agreement with the simulated diffusion process.
We also present a method to obtain and directly from the porous
sample, without having to simulate an actual diffusion process. This extends
the use of CTRW, with all its advantages, to modelling diffusion processes of
finite-size particles in such confined geometries.Comment: 9 pages, 7 figure
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