A noisy linear map underlies oscillations in cell size and gene expression in bacteria.

During bacterial growth, a cell approximately doubles in size before division, after which it splits into two daughter cells. This process is subjected to the inherent perturbations of cellular noise and thus requires regulation for cell-size homeostasis. The mechanisms underlying the control and dynamics of cell size remain poorly understood owing to the difficulty in sizing individual bacteria over long periods of time in a high-throughput manner. Here we measure and analyse long-term, single-cell growth and division across different Escherichia coli strains and growth conditions. We show that a subset of cells in a population exhibit transient oscillations in cell size with periods that stretch across several (more than ten) generations. Our analysis reveals that a simple law governing cell-size control-a noisy linear map-explains the origins of these cell-size oscillations across all strains. This noisy linear map implements a negative feedback on cell-size control: a cell with a larger initial size tends to divide earlier, whereas one with a smaller initial size tends to divide later. Combining simulations of cell growth and division with experimental data, we demonstrate that this noisy linear map generates transient oscillations, not just in cell size, but also in constitutive gene expression. Our work provides new insights into the dynamics of bacterial cell-size regulation with implications for the physiological processes involved.

A finite volume approach to geometrically non-linear stress analysis

In this past decade finite volume (FV) methods have increasingly been used for the solution of solid mechanics problems. This contribution describes a cell vertex finite volume discretisation approach to the solution of geometrically nonlinear (GNL) problems. These problems, which may well have linear material properties, are subject to large deformation. This requires a distinct formulation, which is described in this paper together with the solution strategy for GNL problem. The competitive performance for this procedure against the conventional finite element (FE) formulation is illustrated for a three dimensional axially loaded column.

A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and threedimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

Efficient Non-Linear Idealisations of Aircraft Fuselage Panels in Compression

Aircraft fuselages are complex assemblies of thousands of components and as a result simulation models are highly idealised. In the typical design process, a coarse FE model is used to determine loads within the structure. The size of the model and number of load cases necessitates that only linear static behaviour is considered. This paper reports on the development of a modelling approach to increase the accuracy of the global model, accounting for variations in stiffness due to non-linear structural behaviour. The strategy is based on representing a fuselage sub-section with a single non-linear element. Large portions of fuselage structure are represented by connecting these non-linear elements together to form a framework. The non-linear models are very efficient, reducing computational time significantly

Non-linear conductance of disordered quantum wires

The self-consistent electron potential in a current-carrying disordered quantum wire is spatially inhomogeneous due to the formation of resistivity dipoles across scattering centres. In this paper it is argued that these inhomogeneities in the potential result in a suppression of the differential conductance of such a wire at finite applied voltage. A semi-classical argument allows this suppression, quadratic in the voltage, to be related directly to the amount of intrinsic defect scattering in the wire. This result is then tested against numerical calculations.

Non-linear electronic transport in Pt nanowires deposited by focused ion beam

Electrical transport and structural properties of platinum nanowires, deposited using the focussed ion beam method have been investigated. Energy dispersive X-ray spectroscopy reveals metal-rich grains (atomic composition 31% Pt and 50% Ga) in a largely non-metallic matrix of C, O and Si. Resistivity measurements (15-300 K) reveal a negative temperature coefficient with the room-temperature resistivity 80-300 times higher than that of bulk Pt. Temperature dependent current-voltage characteristics exhibit non-linear behaviour in the entire range investigated. The conductance spectra indicate increasing non-linearity with decreasing temperature, reaching 4% at 15 K. The observed electrical behaviour is explained in terms of a model for inter-grain tunnelling in disordered media, a mechanism that is consistent with the strongly disordered nature of the nanowires observed in the structure and composition analysis.