479 research outputs found
Lubricating Bacteria Model for Branching growth of Bacterial Colonies
Various bacterial strains (e.g. strains belonging to the genera Bacillus,
Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns
during growth on poor semi-solid substrates. These patterns reflect the
bacterial cooperative self-organization. Central part of the cooperation is the
collective formation of lubricant on top of the agar which enables the bacteria
to swim. Hence it provides the colony means to advance towards the food. One
method of modeling the colonial development is via coupled reaction-diffusion
equations which describe the time evolution of the bacterial density and the
concentrations of the relevant chemical fields. This idea has been pursued by a
number of groups. Here we present an additional model which specifically
includes an evolution equation for the lubricant excreted by the bacteria. We
show that when the diffusion of the fluid is governed by nonlinear diffusion
coefficient branching patterns evolves. We study the effect of the rates of
emission and decomposition of the lubricant fluid on the observed patterns. The
results are compared with experimental observations. We also include fields of
chemotactic agents and food chemotaxis and conclude that these features are
needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.
Viscous fingering in liquid crystals: Anisotropy and morphological transitions
We show that a minimal model for viscous fingering with a nematic liquid
crystal in which anisotropy is considered to enter through two different
viscosities in two perpendicular directions can be mapped to a two-fold
anisotropy in the surface tension. We numerically integrate the dynamics of the
resulting problem with the phase-field approach to find and characterize a
transition between tip-splitting and side-branching as a function of both
anisotropy and dimensionless surface tension. This anisotropy dependence could
explain the experimentally observed (reentrant) transition as temperature and
applied pressure are varied. Our observations are also consistent with previous
experimental evidence in viscous fingering within an etched cell and
simulations of solidification.Comment: 12 pages, 3 figures. Submitted to PR
Fronts with a Growth Cutoff but Speed Higher than
Fronts, propagating into an unstable state , whose asymptotic speed
is equal to the linear spreading speed of infinitesimal
perturbations about that state (so-called pulled fronts) are very sensitive to
changes in the growth rate for . It was recently found
that with a small cutoff, for ,
converges to very slowly from below, as . Here we show
that with such a cutoff {\em and} a small enhancement of the growth rate for
small behind it, one can have , {\em even} in the
limit . The effect is confirmed in a stochastic lattice model
simulation where the growth rules for a few particles per site are accordingly
modified.Comment: 4 pages, 4 figures, to appear in Rapid Comm., Phys. Rev.
The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff
The concept of pulled fronts with a cutoff has been introduced to
model the effects of discrete nature of the constituent particles on the
asymptotic front speed in models with continuum variables (Pulled fronts are
the fronts which propagate into an unstable state, and have an asymptotic front
speed equal to the linear spreading speed of small linear perturbations
around the unstable state). In this paper, we demonstrate that the introduction
of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear
diffusion equation with a cutoff, we show that the longest relaxation times
that govern the convergence to the asymptotic front speed and profile,
are given by , for
.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.
The Future Evolution of White Dwarf Stars Through Baryon Decay and Time Varying Gravitational Constant
Motivated by the possibility that the fundamental ``constants'' of nature
could vary with time, this paper considers the long term evolution of white
dwarf stars under the combined action of proton decay and variations in the
gravitational constant. White dwarfs are thus used as a theoretical laboratory
to study the effects of possible time variations, especially their implications
for the future history of the universe. More specifically, we consider the
gravitational constant to vary according to the parametric relation , where the time scale is the same order as
the proton lifetime. We then study the long term fate and evolution of white
dwarf stars. This treatment begins when proton decay dominates the stellar
luminosity, and ends when the star becomes optically thin to its internal
radiation.Comment: 12 pages, 10 figures, accepted to Astrophysics and Space Scienc
Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts
We present a (heuristic) theoretical derivation for the scaling of the
diffusion coefficient for fluctuating ``pulled'' fronts. In agreement
with earlier numerical simulations, we find that as ,
approaches zero as , where is the average number of particles per
correlation volume in the stable phase of the front. This behaviour of
stems from the shape fluctuations at the very tip of the front, and is
independent of the microscopic model.Comment: Some minor algebra corrected, to appear in Rapid Comm., Phys. Rev.
ISML: an interface specification meta-language
In this paper we present an abstract metaphor model situated within a model-based user interface framework. The inclusion of metaphors in graphical user interfaces is a well established, but mostly craft-based strategy to design. A substantial body of notations and tools can be found within the model-based user interface design literature, however an explicit treatment of metaphor and its mappings to other design views has yet to be addressed. We introduce the Interface Specification Meta-Language (ISML) framework and demonstrate its use in comparing the semantic and syntactic features of an interactive system. Challenges facing this research are outlined and further work proposed
Fluctuating "Pulled" Fronts: the Origin and the Effects of a Finite Particle Cutoff
Recently it has been shown that when an equation that allows so-called pulled
fronts in the mean-field limit is modelled with a stochastic model with a
finite number of particles per correlation volume, the convergence to the
speed for is extremely slow -- going only as .
In this paper, we study the front propagation in a simple stochastic lattice
model. A detailed analysis of the microscopic picture of the front dynamics
shows that for the description of the far tip of the front, one has to abandon
the idea of a uniformly translating front solution. The lattice and finite
particle effects lead to a ``stop-and-go'' type dynamics at the far tip of the
front, while the average front behind it ``crosses over'' to a uniformly
translating solution. In this formulation, the effect of stochasticity on the
asymptotic front speed is coded in the probability distribution of the times
required for the advancement of the ``foremost bin''. We derive expressions of
these probability distributions by matching the solution of the far tip with
the uniformly translating solution behind. This matching includes various
correlation effects in a mean-field type approximation. Our results for the
probability distributions compare well to the results of stochastic numerical
simulations. This approach also allows us to deal with much smaller values of
than it is required to have the asymptotics to be valid.Comment: 26 pages, 11 figures, to appear in Phys. rev.
Instanton Contribution to the Pion Electro-Magnetic Formfactor at Q^2 > 1 GeV^2
We study the effects of instantons on the charged pion electro-magnetic
formfactor at intermediate momenta. In the Single Instanton Approximation
(SIA), we predict the pion formfactor in the kinematic region Q^2=2-15 GeV^2.
By developing the calculation in a mixed time-momentum representation, it is
possible to maximally reduce the model dependence and to calculate the
formfactor directly. We find the intriguing result that the SIA calculation
coincides with the vector dominance monopole form, up to surprisingly high
momentum transfer Q^2~10 GeV^2. This suggests that vector dominance for the
pion holds beyond low energy nuclear physics.Comment: 8 pages, 5 figures, minor revision
Universality in Bacterial Colonies
The emergent spatial patterns generated by growing bacterial colonies have
been the focus of intense study in physics during the last twenty years. Both
experimental and theoretical investigations have made possible a clear
qualitative picture of the different structures that such colonies can exhibit,
depending on the medium on which they are growing. However, there are
relatively few quantitative descriptions of these patterns. In this paper, we
use a mechanistically detailed simulation framework to measure the scaling
exponents associated with the advancing fronts of bacterial colonies on hard
agar substrata, aiming to discern the universality class to which the system
belongs. We show that the universal behavior exhibited by the colonies can be
much richer than previously reported, and we propose the possibility of up to
four different sub-phases within the medium-to-high nutrient concentration
regime. We hypothesize that the quenched disorder that characterizes one of
these sub-phases is an emergent property of the growth and division of bacteria
competing for limited space and nutrients.Comment: 12 pages, 5 figure
- …