869 research outputs found
The topological structure of 2D disordered cellular systems
We analyze the structure of two dimensional disordered cellular systems
generated by extensive computer simulations. These cellular structures are
studied as topological trees rooted on a central cell or as closed shells
arranged concentrically around a germ cell. We single out the most significant
parameters that characterize statistically the organization of these patterns.
Universality and specificity in disordered cellular structures are discussed.Comment: 18 Pages LaTeX, 16 Postscript figure
Asymptotic statistics of the n-sided planar Poisson-Voronoi cell. I. Exact results
We achieve a detailed understanding of the -sided planar Poisson-Voronoi
cell in the limit of large . Let be the probability for a cell to
have sides. We construct the asymptotic expansion of up to
terms that vanish as . We obtain the statistics of the lengths of
the perimeter segments and of the angles between adjoining segments: to leading
order as , and after appropriate scaling, these become independent
random variables whose laws we determine; and to next order in they have
nontrivial long range correlations whose expressions we provide. The -sided
cell tends towards a circle of radius (n/4\pi\lambda)^{\half}, where
is the cell density; hence Lewis' law for the average area of
the -sided cell behaves as with . For
the cell perimeter, expressed as a function of the polar
angle , satisfies , where is known Gaussian
noise; we deduce from it the probability law for the perimeter's long
wavelength deviations from circularity. Many other quantities related to the
asymptotic cell shape become accessible to calculation.Comment: 54 pages, 3 figure
The perimeter of large planar Voronoi cells: a double-stranded random walk
Let be the probability for a planar Poisson-Voronoi cell to have
exactly sides. We construct the asymptotic expansion of up to
terms that vanish as . We show that {\it two independent biased
random walks} executed by the polar angle determine the trajectory of the cell
perimeter. We find the limit distribution of (i) the angle between two
successive vertex vectors, and (ii) the one between two successive perimeter
segments. We obtain the probability law for the perimeter's long wavelength
deviations from circularity. We prove Lewis' law and show that it has
coefficient 1/4.Comment: Slightly extended version; journal reference adde
From one cell to the whole froth: a dynamical map
We investigate two and three-dimensional shell-structured-inflatable froths,
which can be constructed by a recursion procedure adding successive layers of
cells around a germ cell. We prove that any froth can be reduced into a system
of concentric shells. There is only a restricted set of local configurations
for which the recursive inflation transformation is not applicable. These
configurations are inclusions between successive layers and can be treated as
vertices and edges decorations of a shell-structure-inflatable skeleton. The
recursion procedure is described by a logistic map, which provides a natural
classification into Euclidean, hyperbolic and elliptic froths. Froths tiling
manifolds with different curvature can be classified simply by distinguishing
between those with a bounded or unbounded number of elements per shell, without
any a-priori knowledge on their curvature. A new result, associated with
maximal orientational entropy, is obtained on topological properties of natural
cellular systems. The topological characteristics of all experimentally known
tetrahedrally close-packed structures are retrieved.Comment: 20 Pages Tex, 11 Postscript figures, 1 Postscript tabl
Topological correlations in soap froths
Correlation in two-dimensional soap froth is analysed with an effective
potential for the first time. Cells with equal number of sides repel (with
linear correlation) while cells with different number of sides attract (with
NON-bilinear) for nearest neighbours, which cannot be explained by the maximum
entropy argument. Also, the analysis indicates that froth is correlated up to
the third shell neighbours at least, contradicting the conventional ideas that
froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure
Analysis of signalling pathways using continuous time Markov chains
We describe a quantitative modelling and analysis approach for signal transduction networks.
We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable
On Random Bubble Lattices
We study random bubble lattices which can be produced by processes such as
first order phase transitions, and derive characteristics that are important
for understanding the percolation of distinct varieties of bubbles. The results
are relevant to the formation of topological defects as they show that infinite
domain walls and strings will be produced during appropriate first order
transitions, and that the most suitable regular lattice to study defect
formation in three dimensions is a face centered cubic lattice. Another
application of our work is to the distribution of voids in the large-scale
structure of the universe. We argue that the present universe is more akin to a
system undergoing a first-order phase transition than to one that is
crystallizing, as is implicit in the Voronoi foam description. Based on the
picture of a bubbly universe, we predict a mean coordination number for the
voids of 13.4. The mean coordination number may also be used as a tool to
distinguish between different scenarios for structure formation.Comment: several modifications including new abstract, comparison with froth
models, asymptotics of coordination number distribution, further discussion
of biased defects, and relevance to large-scale structur
Description of Fischer Clusters Formation in Supercooled Liquids Within Framework of Continual Theory of Defects
Liquid is represented as complicated system of disclinations according to
defect description of liquids and glasses. The expressions for the linear
disclination field of an arbitrary form and energy of inter-disclination
interaction are derived in the framework of gauge theory of defects. It allows
us to describe liquid as a disordered system of topological moments and reduce
this model to the Edwards--Anderson model with large-range interaction. Within
the framework of this approach vitrifying is represented as a "hierarchical"
phase transition. The suggested model allows us to explain the process of the
Fischer clusters formation and the slow dynamics in supercooled liquids close
to the liquid--glass transition point
Computer investigation of the energy landscape of amorphous silica
The multidimensional topography of the collective potential energy function
of a so-called strong glass former (silica) is analyzed by means of classical
molecular dynamics calculations. Features qualitatively similar to those of
fragile glasses are recovered at high temperatures : in particular an intrinsic
characteristic temperature K is evidenced above which the
system starts to investigate non-harmonic potential energy basins. It is shown
that the anharmonicities are essentially characterized by a roughness appearing
in the potential energy valleys explored by the system for temperatures above
.Comment: 5 pages; accepted for publication in PR
DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction
We discuss the perturbative approach a` la Dyson to a quantum field theory
with nonlocal self-interaction :phi*...*phi:, according to Doplicher,
Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction
of non locally time--ordered products of Wick monomials can be performed as
usual, and we discuss a very simple Dyson diagram.Comment: 15 pages, pdf has active hyperlinks. To appear in the proceedings of
the conference on "Rigorous quantum Field Theory", held at Saclay on July
19-21, 2004, on the occasion of Jacques Bros' 70th birthda
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