156 research outputs found
Shaping liquid drops by vibration
We present and analyze a minimal hydrodynamic model of a vertically vibrated
liquid drop that undergoes dynamic shape transformations. In agreement with
experiments, a circular lens-shaped drop is unstable above a critical vibration
amplitude, spontaneously elongating in horizontal direction. Smaller drops
elongate into localized states that oscillate with half of the vibration
frequency. Larger drops evolve by transforming into a snake-like structure with
gradually increasing length. The worm state is long-lasting with a potential to
fragmentat into smaller drops
Morphology changes in the evolution of liquid two-layer films
We consider two thin layers of immiscible liquids on a heated solid
horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such
a two-layer (or bilayer) liquid film may be unstable due to effective molecular
interactions or the Marangoni effect. Using a long wave approximation we derive
coupled evolution equations for the interafce profiles for a general
non-isothermal situation allowing for slip at the substrate. Linear and
nonlinear analyses are performed for isothermal ultrathin layers below 100 nm
thickness under the influence of destabilizing long-range and stabilizing
short-range interactions. Flat films may be unstable to varicose, zigzag or
mixed modes. During the long-time evolution the nonlinear mode type can change
via switching between two different branches of stable stationary solutions or
via coarsening along a single such branch.Comment: 14 eps figures and 1 tex fil
Rectification of self-propelled particles by symmetric barriers
The motion of self-propelled particles can be rectified by asymmetric or
ratchet-like periodic patterns in space. Here we show that a non-zero average
drift can already be induced in a periodic potential with symmetric barriers
when the self-propulsion velocity is also symmetric and periodically modulated
but phase-shifted against the potential. In the adiabatic limit of slow
rotational diffusion we determine the mean drift analytically and discuss the
influence of temperature. In the presence of asymmetric barriers modulating the
self-propulsion can largely enhance the mean drift or even reverse it
Coarsening modes of clusters of aggregating particles
There are two modes by which clusters of aggregating particles can coalesce:
The clusters can merge either (i) by the Ostwald ripening process in which
particles diffuse from one cluster to the other whilst the cluster centres
remain stationary, or (ii) by means of a cluster translation mode, in which the
clusters move towards each other and join. To understand in detail the
interplay between these different modes, we study a model system of hard
particles with an additional attraction between them. The particles diffuse
along narrow channels with smooth or periodically corrugated walls, so that the
system may be treated as one-dimensional. When the attraction between the
particles is strong enough, they aggregate to form clusters. The channel
potential influences whether clusters can move easily or not through the system
and can prevent cluster motion. We use Dynamical Density Functional theory to
study the dynamics of the aggregation process, focusing in particular on the
coalescence of two equal size clusters. As long as the particle hard-core
diameter is non-zero, we find that the coalescence process can be halted by a
sufficiently strong corrugation potential. The period of the potential
determines the size of the final stable clusters. For the case of smooth
channel walls, we demonstrate that there is a cross-over in the dominance of
the two different coarsening modes, that depends on the strength of the
attraction between particles, the cluster sizes and the separation distance
between clusters
Excitable systems with noise and delay with applications to control: renewal theory approach
We present an approach for the analytical treatment of excitable systems with
noise-induced dynamics in the presence of time delay. An excitable system is
modeled as a bistable system with a time delay, while another delay enters as a
control term taken after [Pyragas 1992] as a difference between the current
system state and its state "tau" time units before. This approach combines the
elements of renewal theory to estimate the essential features of the resulting
stochastic process as functions of the parameters of the controlling term
Synchronization of a large number of continuous one-dimensional stochastic elements with time delayed mean field coupling
We study synchronization as a means of control of collective behavior of an ensemble
of coupled stochastic units in which oscillations are induced merely by external noise.
We determine the boundary of the synchronization domain of a large number of onedimensional
continuous stochastic elements with time delayed non-homogeneous
mean-field coupling. Exact location of the synchronization threshold is shown to
be a solution of the boundary value problem (BVP) which was derived from the
linearized Fokker-Planck equation. Here the synchronization threshold is found by
solving this BVP numerically. Approximate analytics is obtained by expanding the
solution of the linearized Fokker-Planck equation into a series of eigenfunctions of
the stationary Fokker-Planck operator. Bistable systems with a polynomial and
piece-wise linear potential are considered as examples. Multistability and hysteresis
is observed in the Langevin equations for finite noise intensity. In the limit of small
noise intensities the critical coupling strength was shown to remain finite
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