34 research outputs found
Controlling the interfacial and bulk concentrations of spontaneously charged colloids in non-polar media
Stabilization and dispersion of electrical charge by colloids in non-polar
media, such as nano-particles or inverse micelles, is significant for a variety
of chemical and technological applications, ranging from drug delivery to
e-ink. Many applications require knowledge about concentrations near the
solid|liquid interface and the bulk, particularly in media where colloids
exhibit spontaneous charging properties. By modification of the mean field
equations to include the finite size effects that are typical in concentrated
electrolytes along with disproportionation kinetics, and by considering high
potentials, it is possible to evaluate the width of the condensed double layers
near planar electrodes and the bulk concentrations of colloids at steady state.
These quantities also provide an estimate of the minimum initial colloid
concentration that is required to support electroneutrality in the dispersion
bulk, and thus provide insights into the quasi-steady state currents that have
been observed in inverse micellar media.Comment: 13 pages, 5 figure
Stationary peaks in a multivariable reaction--diffusion system: Foliated snaking due to subcritical Turing instability
An activator-inhibitor-substrate model of side-branching used in the context
of pulmonary vascular and lung development is considered on the supposition
that spatially localized concentrations of the activator trigger local
side-branching. The model consists of four coupled reaction-diffusion equations
and its steady localized solutions therefore obey an eight-dimensional spatial
dynamical system in one dimension (1D). Stationary localized structures within
the model are found to be associated with a subcritical Turing instability and
organized within a distinct type of foliated snaking bifurcation structure.
This behavior is in turn associated with the presence of an exchange point in
parameter space at which the complex leading spatial eigenvalues of the uniform
concentration state are overtaken by a pair of real eigenvalues; this point
plays the role of a Belyakov-Devaney point in this system. The primary foliated
snaking structure consists of periodic spike or peak trains with identical
equidistant peaks, , together with cross-links consisting of
nonidentical, nonequidistant peaks. The structure is complicated by a multitude
of multipulse states, some of which are also computed, and spans the parameter
range from the primary Turing bifurcation all the way to the fold of the
state. These states form a complex template from which localized physical
structures develop in the transverse direction in 2D.Comment: 30 pages, 14 figure
Front propagation and global bifurcations in a multi-variable reaction-diffusion model
We study the existence and stability of propagating fronts in Meinhardt's
reaction-diffusion model of branching in one spatial dimension. We identify a
saddle-node-infinite-period (SNIPER) bifurcation of fronts that leads to
episodic front propagation in the parameter region below propagation failure
and show that this state is stable. Stable constant speed fronts exist only
above this parameter value. We use numerical continuation to show that
propagation failure is a consequence of the presence of a T-point corresponding
to the formation of a heteroclinic cycle in a spatial dynamics description.
Additional T-points are identified that are responsible for a large
multiplicity of different traveling front-peak states. The results indicate
that multivariable models may support new types of behavior that are absent
from typical two-variable models but may nevertheless be important in
developmental processes such as branching and somitogenesis.Comment: 18 pages, 12 figure