Directed percolation in a two dimensional stochastic fire-diffuse-fire model

In this paper we establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains the both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a non-equilibrium phase-transition between propagating and non-propagating waves is obtained by an examination of the \textit{local slope} $\delta(t)$ of the survival probability, $\Pi(t) \propto \exp(- \delta(t))$, for a wave to propagate for a time $t$.

Controlling Pattern Formation in Nanoparticle Assemblies via Directed Solvent Dewetting

We have achieved highly localised control of pattern formation in two dimensional nanoparticle assemblies by direct modification of solvent dewetting dynamics. A striking dependence of nanoparticle organisation on the size of atomic force microscope-generated surface heterogeneities is observed and reproduced in numerical simulations. Nanoscale features induce rupture of the solvent-nanoparticle film, causing the local flow of solvent to carry nanoparticles into confinement. Microscale heterogeneities instead slow the evaporation of the solvent, producing a remarkably abrupt interface between different nanoparticle patterns.

Coerced Mechanical Coarsening of Nanoparticle Assemblies

Coarsening is a ubiquitous phenomenon [1-3] that underpins countless processes in nature, including epitaxial growth [1,3,4], the phase separation of alloys, polymers and binary fluids [2], the growth of bubbles in foams5, and pattern formation in biomembranes6. Here we show, in the first real-time experimental study of the evolution of an adsorbed colloidal nanoparticle array, that tapping-mode atomic force microscopy (TM-AFM) can drive the coarsening of Au nanoparticle assemblies on silicon surfaces. Although the growth exponent has a strong dependence on the initial sample morphology, our observations are largely consistent with modified Ostwald ripening processes [7-9]. To date, ripening processes have been exclusively considered to be thermally activated, but we show that nanoparticle assemblies can be mechanically coerced towards equilibrium, representing a new approach to directed coarsening. This strategy enables precise control over the evolution of micro- and nanostructures.

DNA charge neutralisation by linear polymers I: irreversible binding

We develop a deterministic mathematical model to describe the way in which polymers bind to DNA by considering the dynamics of the gap distribution that forms when polymers bind to a DNA plasmid. In so doing, we generalise existing theory to account for overlaps and binding cooperativity whereby the polymer binding rate depends on the size of the overlap The proposed mean-field models are then solved using a combination of numerical and asymptotic methods. We find that overlaps lead to higher coverage and hence higher charge neutralisations, results which are more in line with recent experimental observations. Our work has applications to gene therapy where polymers are used to neutralise the negative charges of the DNA phosphate backbone, allowing condensation prior to delivery into the nucleus of an abnormal cell.

DNA charge neutralisation by linear polymers II: reversible binding

We model the way in which polymers bind to DNA and neutralise its charged backbone by analysing the dynamics of the distribution of gaps along the DNA. We generalise existing theory for irreversible binding to construct new deterministic models which include polymer removal, movement along the DNA and allow for binding with overlaps. We show that reversible binding alters the capacity of the DNA for polymers by allowing the rearrangement of polymer positions over a longer timescale than when binding is irreversible. When the polymers do not overlap, allowing reversible binding increases the number of polymers adhered and hence the charge that the DNA can accommodate; in contrast, when overlaps occur, reversible binding reduces the amount of charge neutralised by the polymers.