147 research outputs found
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
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
Topological model of soap froth evolution with deterministic T2-processes
We introduce a topological model for the evolution of 2d soap froth. The
topological rearrangements (T2 processes) are deterministic (unlike the
standard stochastic model): the final topology depends on the areas of the
neighboring cells. The new model gives agreement with experiments in the
transient regime, where the previous models failed qualitatively, and also
improves agreement in the scaling state.Comment: latex, 12 pages, 2 figure
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
Bubble kinetics in a steady-state column of aqueous foam
We measure the liquid content, the bubble speeds, and the distribution of
bubble sizes, in a vertical column of aqueous foam maintained in steady-state
by continuous bubbling of gas into a surfactant solution. Nearly round bubbles
accumulate at the solution/foam interface, and subsequently rise with constant
speed. Upon moving up the column, they become larger due to gas diffusion and
more polyhedral due to drainage. The size distribution is monodisperse near the
bottom and polydisperse near the top, but there is an unexpected range of
intermediate heights where it is bidisperse with small bubbles decorating the
junctions between larger bubbles. We explain the evolution in both bidisperse
and polydisperse regimes, using Laplace pressure differences and taking the
liquid fraction profile as a given.Comment: 7 pages, 3 figure
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
Topology of Cell-Aggregated Planar Graphs
We present new algorithm for growth of non-clustered planar graphs by
aggregation of cells with given distribution of size and constraint of
connectivity k=3 per node. The emergent graph structures are controlled by two
parameters--chemical potential of the cell aggregation and the width of the
cell size distribution. We compute several statistical properties of these
graphs--fractal dimension of the perimeter, distribution of shortest paths
between pairs of nodes and topological betweenness of nodes and links. We show
how these topological properties depend on the control parameters of the
aggregation process and discuss their relevance for the conduction of current
in self-assembled nanopatterns.Comment: 8 pages, 5 figure
Selection of the scaling solution in a cluster coalescence model
The scaling properties of the cluster size distribution of a system of
diffusing clusters is studied in terms of a simple kinetic mean field model. It
is shown that a one parameter family of mathematically valid scaling solutions
exists. Despite this, the kinetics reaches a unique scaling solution
independent of initial conditions. This selected scaling solution is marginally
physical; i.e., it is the borderline solution between the unphysical and
physical branches of the family of solutions.Comment: 4 pages, 5 figure
A Phase Front Instability in Periodically Forced Oscillatory Systems
Multiplicity of phase states within frequency locked bands in periodically
forced oscillatory systems may give rise to front structures separating states
with different phases. A new front instability is found within bands where
(). Stationary fronts shifting the
oscillation phase by lose stability below a critical forcing strength and
decompose into traveling fronts each shifting the phase by . The
instability designates a transition from stationary two-phase patterns to
traveling -phase patterns
Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
We study the nonequilibrium dynamics of the -state Potts model following a
quench from the high temperature disordered phase to zero temperature. The time
dependent two-point correlation functions of the order parameter field satisfy
dynamic scaling with a length scale . In particular, the
autocorrelation function decays as . We illustrate these
properties by solving exactly the kinetic Potts model in . We then analyze
a Langevin equation of an appropriate field theory to compute these correlation
functions for general and . We establish a correspondence between the
two-point correlations of the -state Potts model and those of a kinetic
Ising model evolving with a fixed magnetization . The dynamics of this
Ising model is solved exactly in the large q limit, and in the limit of a large
number of components for the order parameter. For general and in any
dimension, we introduce a Gaussian closure approximation and calculate within
this approximation the scaling functions and the exponent . These
are in good agreement with the direct numerical simulations of the Potts model
as well as the kinetic Ising model with fixed magnetization. We also discuss
the existing and possible experimental realizations of these models.Comment: TeX, Vanilla.sty is needed. [Admin note: author contacted regarding
missing figure1 but is unable to supply, see journal version (Nov99)
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