834 research outputs found
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
Statistical Mechanics of Two-dimensional Foams
The methods of statistical mechanics are applied to two-dimensional foams
under macroscopic agitation. A new variable -- the total cell curvature -- is
introduced, which plays the role of energy in conventional statistical
thermodynamics. The probability distribution of the number of sides for a cell
of given area is derived. This expression allows to correlate the distribution
of sides ("topological disorder") to the distribution of sizes ("geometrical
disorder") in a foam. The model predictions agree well with available
experimental data
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
Random walk on disordered networks
Random walks are studied on disordered cellular networks in 2-and
3-dimensional spaces with arbitrary curvature. The coefficients of the
evolution equation are calculated in term of the structural properties of the
cellular system. The effects of disorder and space-curvature on the diffusion
phenomena are investigated. In disordered systems the mean square displacement
displays an enhancement at short time and a lowering at long ones, with respect
to the ordered case. The asymptotic expression for the diffusion equation on
hyperbolic cellular systems relates random walk on curved lattices to
hyperbolic Brownian motion.Comment: 10 Pages, 3 Postscript figure
Soap Froths and Crystal Structures
We propose a physical mechanism to explain the crystal symmetries found in
macromolecular and supramolecular micellar materials. We argue that the packing
entropy of the hard micellar cores is frustrated by the entropic interaction of
their brush-like coronas. The latter interaction is treated as a surface effect
between neighboring Voronoi cells. The observed crystal structures correspond
to the Kelvin and Weaire-Phelan minimal foams. We show that these structures
are stable for reasonable areal entropy densities.Comment: 4 pages, RevTeX, 2 included eps figure
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
The Suprafroth (Superconducting Froth)
The structure and dynamics of froths have been subjects of intense interest
due to the desire to understand the behaviour of complex systems where
topological intricacy prohibits exact evaluation of the ground state. The
dynamics of a traditional froth involves drainage and drying in the cell
boundaries, thus it is irreversible. We report a new member to the froths
family: suprafroth, in which the cell boundaries are superconducting and the
cell interior is normal phase. Despite very different microscopic origin,
topological analysis of the structure of the suprafroth shows that statistical
von Neumann and Lewis laws apply. Furthermore, for the first time in the
analysis of froths there is a global measurable property, the magnetic moment,
which can be directly related to the suprafroth structure. We propose that this
suprafroth is a new, model system for the analysis of the complex physics of
two-dimensional froths
- …