Scaling state of dry two-dimensional froths: universal angle deviations and structure

We characterize the late-time scaling state of dry, coarsening, two-dimensional froths using a detailed, force-based vertex model. We find that the slow evolution of bubbles leads to systematic deviations from 120degree angles at three-fold vertices in the froth, with an amplitude proportional to the vertex speed, v ~ sqrt(t), but with a side-number dependence that is independent of time. We also find that a significant number of T1 side-switching processes occur for macroscopic bubbles in the scaling state, though most bubble annihilations involve four-sided bubbles at microscopic scales.Comment: 7 pages, 7 figure

Von-Neumann's and related scaling laws in Rock-Paper-Scissors type models

We introduce a family of Rock-Paper-Scissors type models with $Z_N$ symmetry ($N$ is the number of species) and we show that it has a very rich structure with many completely different phases. We study realizations which lead to the formation of domains, where individuals of one or more species coexist, separated by interfaces whose (average) dynamics is curvature driven. This type of behavior, which might be relevant for the development of biological complexity, leads to an interface network evolution and pattern formation similar to the ones of several other nonlinear systems in condensed matter and cosmology.Comment: 5 pages, 6 figures, published versio

Arresting bubble coarsening: A two-bubble experiment to investigate grain growth in presence of surface elasticity

Many two-phase materials suffer from grain-growth due to the energy cost which is associated with the interface that separates both phases. While our understanding of the driving forces and the dynamics of grain growth in different materials is well advanced by now, current research efforts address the question of how this process may be slowed down, or, ideally, arrested. We use a model system of two bubbles to explore how the presence of a finite surface elasticity may interfere with the coarsening process and the final grain size distribution. Combining experiments and modelling in the analysis of the evolution of two bubbles, we show that clear relationships can be predicted between the surface tension, the surface elasticity and the initial/final size ratio of the bubbles. We rationalise these relationships by the introduction of a modified Gibbs criterion. Besides their general interest, the present results have direct implications for our understanding of foam stability

Glassy behaviour in a simple topological model

In this article we study a simple, purely topological, cellular model which is allowed to evolve through a Glauber-Kawasaki process. We find a non-thermodynamic transition to a glassy phase in which the energy (defined as the square of the local cell topological charge) fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate. We investigate a correlation function which exhibits aging behaviour, and follows a master curve in the stationary regime when time is rescaled by a factor of the relaxation time t_r. This master curve can be fitted by a von Schweidler law in the late beta-relaxation regime. The relaxation times can be well-fitted at all temperatures by an offset Arrhenius law. A power law can be fitted to an intermediate temperature regime; the exponent of the power law and the von Schweidler law roughly agree with the relationship predicted by Mode-coupling Theory. By defining a suitable response function, we find that the fluctuation-dissipation ratio is held until sometime later than the appearance of the plateaux; non-monotonicity of the response is observed after this ratio is broken, a feature which has been observed in other models with dynamics involving activated processes.Comment: 11 pages LaTeX; minor textual corrcetions, minor corrections to figs 4 & 7

Diffusive transport of light in three-dimensional disordered Voronoi structures

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: a constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for transport-mean-free path fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in {dry} foams.Comment: 8 pages, 8 figure

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

Cluster Persistence: a Discriminating Probe of Soap Froth Dynamics

The persistent decay of bubble clusters in coarsening two-dimensional soap froths is measured experimentally as a function of cluster volume fraction. Dramatically stronger decay is observed in comparison to soap froth models and to measurements and calculations of persistence in other systems. The fraction of individual bubbles that contain any persistent area also decays, implying significant bubble motion and suggesting that T1 processes play an important role in froth persistence.Comment: 5 pages, revtex, 4 eps figures. To appear in Europhys. Let

Glass transition in self organizing cellular patterns

We have considered the dynamical evolution of cellular patterns controlled by a stochastic Glauber process determined by the deviations of local cell topology from that of a crystalline structure. Above a critical temperature evolution is towards a common equilibrium state from any initial configuration, but beneath this temperature there is a dynamical phase transition, with a start from a quasi-random state leading to non-equilibrium glassy freezing whereas an ordered start rests almost unchanged. A temporal persistence function decays exponentially in the high temperature equilibrating state but has a characteristic slow non-equilibrium aging-like behaviour in the low temperature glassy phase.Comment: Added references, text minor change

Bubble kinematics in a sheared foam

We characterize the kinematics of bubbles in a sheared two-dimensional foam using statistical measures. We consider the distributions of both bubble velocities and displacements. The results are discussed in the context of the expected behavior for a thermal system and simulations of the bubble model. There is general agreement between the experiments and the simulation, but notable differences in the velocity distributions point to interesting elements of the sheared foam not captured by prevalent models

Structure of Optimal Transport Networks Subject to a Global Constraint

The structure of pipe networks minimizing the total energy dissipation rate is studied analytically. Among all the possible pipe networks that can be built with a given total pipe volume (or pipe lateral surface area), the network which minimizes the dissipation rate is shown to be loopless. Furthermore, such an optimal network is shown to contain at most N-2 nodes in addition to the N sources plus sinks that it connects. These results are valid whether the possible locations for the additional nodes are chosen freely or from a set of nodes (such as points of a grid). Applications of these results to various physical situations and to the efficient computation of optimal pipe networks are also discussed