Two-dimensional plasmons in the random impedance network model of disordered thin-film nanocomposites

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric nanocomposites. In order to study thin films, two-dimensional networks are often used despite the fact that such networks correspond to a two-dimensional electrodynamics [J.P. Clerc et al, J. Phys. A 29, 4781 (1996)]. In the present work, we propose a model of two-dimensional systems with three-dimensional Coulomb interaction and show that this model is equivalent to a planar network with long-range capacitive connections between sites. In a case of a metal film, we get a known dispersion $\omega \propto \sqrt{k}$ of plane-wave two-dimensional plasmons. In the framework of the proposed model, we study the evolution of resonances with decreasing of metal filling factor. In the subcritical region with metal filling $p$ lower than the percolation threshold $p_c$, we observe a gap with Lifshitz tails in the spectral density of states (DOS). In the supercritical region $p>p_c$, the DOS demonstrates a crossover between plane-wave two-dimensional plasmons and resonances associated with small clusters.Comment: 8 pages, 3 figures, revtex; references adde

Examples of clusters of <i>E</i>. <i>coli</i> cells showing oscillatory behaviour.

<p>The <i>gfp</i> expression in clusters of cells transformed with both the repressilator and the communication plasmid was followed in a time-lapse microscope for 1080 min (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180155#pone.0180155.s003" target="_blank">S3 Video</a>). Snapshots of five growing clusters of cells were taken periodically both in fluorescence (A) and bright-field (B). Each coloured line represents a different cluster of cells (C). Pictures in (A) and (B) correspond to the representative cluster of cells plotted as a green line in (C). Images were acquired every 20 min and the fluorescence intensity of each cluster of cells was determined using the ImageJ software.</p

Cellular synchronization.

<p>Standard deviation of GFP proteins per cell indicates how the system evolves to a synchronized state. SD is calculated for all cells in a 5 h interval basis.</p

Temporal evolution of GFP in 500 cells.

<p><b>(A)</b> Oscillations after 2 days. <b>(B)</b> Oscillations after 30 days.</p

Model prediction for typical temporal oscillations of GFP in different cells.

<p>Various colours denote various cells. Black solid line represents arithmetic mean of the modelled 200 cells. Black dashed line represents weighted arithmetic mean.</p