Contemporary proliferation of renewable power generation is causing an overhaul in the topology, composition, and dynamics of electrical grids. These low-output, intermittent generators are widely distributed throughout the grid, including at the household level. It is critical for the function of modern power infrastructure to understand how this increasingly distributed layout affects network stability and resilience. This paper uses dynamical models, household power consumption, and photovoltaic generation data to show how these characteristics vary with the level of distribution. It is shown that resilience exhibits daily oscillations as the grid’s effective structure and the power demand fluctuate. This can lead to a substantial decrease in grid resilience, explained by periods of highly clustered generator output. Moreover, the addition of batteries, while enabling consumer self-sufficiency, fails to ameliorate these problems. The methodology identifies a grid’s susceptibility to disruption resulting from its network structure and modes of operation.

The Wilson–Cowan population model of neural activity has greatly influenced our understanding of the mechanisms for the generation of brain rhythms and the emergence of structured brain activity. As well as the many insights that have been obtained from its mathematical analysis, it is now widely used in the computational neuroscience community for building large-scale in silico brain networks that can incorporate the increasing amount of knowledge from the Human Connectome Project. Here, we consider a neural population model in the spirit of that originally developed by Wilson and Cowan, albeit with the added advantage that it can account for the phenomena of event-related synchronization and desynchronization. This derived mean-field model provides a dynamic description for the evolution of synchrony, as measured by the Kuramoto order parameter, in a large population of quadratic integrate-and-fire model neurons. As in the original Wilson–Cowan framework, the population firing rate is at the heart of our new model; however, in a significant departure from the sigmoidal firing rate function approach, the population firing rate is now obtained as a real-valued function of the complex-valued population synchrony measure. To highlight the usefulness of this next-generation Wilson–Cowan style model, we deploy it in a number of neurobiological contexts, providing understanding of the changes in power spectra observed in electro- and magnetoencephalography neuroimaging studies of motor cortex during movement, insights into patterns of functional connectivity observed during rest and their disruption by transcranial magnetic stimulation, and to describe wave propagation across cortex.

In this work, we consider the spatial homogenization of a coupled transport and fluid–structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The ‘active’ nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection–reaction–diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits.

A key question in neuroscience is to understand how a rich functional repertoire of brain activity arises within relatively static networks of structurally connected neural populations: elucidating the subtle interactions between evoked "functional connectivity" and the underlying "structural connectivity" has the potential to address this. These structural-functional networks (and neural networks more generally) are more naturally described using a multilayer or multiplex network approach, in favour of standard single-layer network analyses that are more typically applied to such systems. In this letter, we address such issues by exploring important structure-function relations in the Macaque cortical network by modelling it as a duplex network that comprises an anatomical layer, describing the known (macro-scale) network topology of the Macaque monkey, and a functional layer derived from simulated neural activity. We investigate and characterize correlations between structural and functional layers, as system parameters controlling simulated neural activity are varied, by employing recently described multiplex network measures. Moreover, we propose a novel measure of multiplex structure-function clustering which allows us to investigate the emergence of functional connections that are distinct from the underlying cortical structure, and to highlight the dependence of multiplex structure on the neural dynamical regime.

The growth of a cell population within a rigid porous scaffold in a perfusion bioreactor is studied, using a three-phase continuum model of the type presented by Lemon et al. (2006, Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol., 52, 571–594) to represent the cell population (and attendant extracellular matrix), culture medium and porous scaffold. The bioreactor system is modelled as a 2D channel containing the cell-seeded rigid porous scaffold (tissue construct) which is perfused with culture medium. The study concentrates on (i) the cell–cell and cell–scaffold interactions and (ii) the impact of mechanotransduction mechanisms on construct composition. A numerical and analytical analysis of the model equations is presented and, depending upon the relative importance of cell aggregation and repulsion, markedly different cell movement is revealed. Additionally, mechanotransduction effects due to cell density, pressure and shear stress-mediated tissue growth are shown to generate qualitative differences in the composition of the resulting construct. The results of our simulations indicate that this model formulation (in conjunction with appropriate experimental data) has the potential to provide a means of identifying the dominant regulatory stimuli in a cell population.