Global Hopf bifurcation in the ZIP regulatory system

Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor. For certain parameter choices the steady state of this model becomes unstable upon variation in the external zinc concentration. Numerical results show periodic orbits emerging between two critical values of the external zinc concentration. Here we show the existence of a global Hopf bifurcation with a continuous family of stable periodic orbits between two Hopf bifurcation points. The stability of the orbits in a neighborhood of the bifurcation points is analyzed by deriving the normal form, while the stability of the orbits in the global continuation is shown by calculation of the Floquet multipliers. From a biological point of view, stable periodic orbits lead to potentially toxic zinc peaks in plant cells. Buffering is believed to be an efficient way to deal with strong transient variations in zinc supply. We extend the model by a buffer reaction and analyze the stability of the steady state in dependence of the properties of this reaction. We find that a large enough equilibrium constant of the buffering reaction stabilizes the steady state and prevents the development of oscillations. Hence, our results suggest that buffering has a key role in the dynamics of zinc homeostasis in plant cells.Comment: 22 pages, 5 figures, uses svjour3.cl

Time-of-use and time-of-export tariffs for home batteries: Effects on low voltage distribution networks

Time-of-use electricity tariffs are gradually being introduced around the world to expose consumers to the time-dependency of demand, however their effects on peak flows in distribution networks, particularly in areas with domestic energy storage, are little understood. This paper presents investigations into the impact of time-of-use and time-of-export tariffs in residential areas with various penetrations of battery storage, rooftop solar PV, and heat pumps. By simulating battery operation in response to high resolution household-level electrical and thermal demand data, it is found that home batteries operating to maximise cost savings in houses signed up to time-dependent tariffs cause little reduction in import and export peaks at the low voltage level, largely because domestic import and export peaks are spread out over time. When operating to maximise savings from the first three-tier time-of-use tariff introduced in the UK, batteries could even cause increases in peak demand at low voltage substations, if many batteries in the area commence charging at the start of the overnight off-peak price band. Home batteries operating according to time-dependent electricity tariffs significantly miss out on the potential peak shaving that could otherwise be achieved through dedicated peak shaving incentives schemes and smarter storage control strategies

Bio-inspired nanocatalysts for the oxygen reduction reaction

Electrochemical conversions at fuel cell electrodes are complex processes. In particular, the oxygen reduction reaction has substantial overpotential limiting the electrical power output efficiency. Effective and inexpensive catalytic interfaces are therefore essential for increased performance. Taking inspiration from enzymes, earth-abundant metal centres embedded in organic environments present remarkable catalytic active sites. Here we show that these enzyme-inspired centres can be effectively mimicked in two-dimensional metal-organic coordination networks self-assembled on electrode surfaces. Networks consisting of trimesic acid and bis-pyridyl-bispyrimidine coordinating to single iron and manganese atoms on Au(111) effectively catalyse the reduction and reveal distinctive catalytic activity in alkaline media. These results demonstrate the potential of surface-engineered metal-organic networks for electrocatalytic conversions. Specifically designed coordination complexes at surfaces inspired by enzyme cofactors represent a new class of nanocatalysts with promising applications in electrocatalysis.Fil: Grumelli, Doris Elda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Max Planck Institute for Solid State Research; AlemaniaFil: Wurtser, Benjamin. Max Planck Institute for Solid State Research; AlemaniaFil: Stepanow, Sabastian. Max Planck Institute for Solid State Research; AlemaniaFil: Kern, Klaus. Max Planck Institute for Solid State Research; Alemania. Ecole Polytechnique Federale de Lausanne; Suiz

An advanced micro-bio-loop to produce biogas

The authors report an advanced micro-bio-loop that involves recycling through four steps; namely: microalgae culture; de-oxygenation; anaerobic digestion; and aerobic decomposition. The advanced micro-bio-loop operates under sunlight to produce a continuous stream of biogas without requiring any additional external input or internal output to its surrounds. In comparison to conventional biogas production process, it achieves a net positive energy balance at remarkably different level of 0.0224 kWh MJ−1, with less than 33% of environmental impacts, less than 0.57% of water demand, only 7.35% arable land-use and 0.041% of labor

On the arrangement of tidal turbines in rough and oscillatory channel flow

Fast tidal streams are a promising source of clean, predictable power, but the task of arranging tidal turbines for maximum power capture is complicated. Actuator disc models, such as the two-scale actuator disc theory, have proven useful in seeking optimal turbine arrangements, yet these models assume flows that are frictionless and steady, and thus quite unlike the channel flow conditions that actual tidal turbines experience. In this paper, we use numerical methods to relax these assumptions and explore how optimal turbine arrangements change as the flow transitions from frictionless and steady to rough and oscillatory. In so doing, we show that, under certain conditions, the assumption of quasi-steady flow in models of tidal turbines may neglect leading-order physics. When the ratio of drag to inertial forces in the unexploited channel is very low, for instance, the optimal turbine arrangements are found to be quite different, and the potential for enhanced power capture is found to be much greater than predicted by two-scale actuator disc theory

Heat transfer in the seabed boundary layer

We present a theoretical model of the temperature distribution in the boundary layer region close to the seabed. Using a perturbation expansion, multiple scales and similarity variables, we show how free-surface waves enhance heat transfer between seawater and a seabed with a solid, horizontal, smooth surface. Maximum heat exchange occurs at a fixed frequency depending on ocean depth, and does not increase monotonically with the length and phase speed of propagating free-surface waves. Close agreement is found between predictions by the analytical model and a finite-difference scheme. It is found that free-surface waves can substantially affect the spatial evolution of temperature in the seabed boundary layer. This suggests a need to extend existing models that neglect the effects of a wave field, especially in view of practical applications in engineering and oceanography.</jats:p

Effects of support structures in an LES actuator line model of a tidal turbine with contra-rotating rotors

Computational fluid dynamics is used to study the impact of the support structure of a tidal turbine on performance and the downstream wake characteristics. A high-fidelity computational model of a dual rotor, contra-rotating tidal turbine in a large channel domain is presented, with turbulence modelled using large eddy simulation. Actuator lines represent the turbine blades, permitting the analysis of transient flow features and turbine diagnostics. The following four cases are considered: the flow in an unexploited, empty channel; flow in a channel containing the rotors; flow in a channel containing the support structure; and flow in a channel with both rotors and support structure. The results indicate that the support structure contributes significantly to the behaviour of the turbine and to turbulence levels downstream, even when the rotors are upstream. This implies that inclusion of the turbine structure, or some parametrisation thereof, is a prerequisite for the realistic prediction of turbine performance and reliability, particularly for array layouts where wake effects become significant

Quantifying multiple uncertainties in modelling shallow water-sediment flows: A stochastic Galerkin framework with Haar wavelet expansion and an operator-splitting approach

The interactive processes of shallow water flow, sediment transport, and morphological evolution constitute a hierarchy of multi-physical problems of significant interests in a spectrum of engineering and science areas. To date, modelling shallow water hydro-sediment-morphodynamic (SHSM) processes is subject to multiple sources of uncertainty arising from input data and incomplete understanding of the underlying physics. A stochastic SHSM model with multiple uncertainties has yet to be developed as most SHSM models still concern deterministic problems and only one has been recently extended to a stochastic setting, but is restricted to a single source of uncertainty. Here we first present a new probabilistic SHSM model incorporating multiple uncertainties within the stochastic Galerkin framework using a multidimensional tensor product of Haar wavelet expansion to capture local, nonlinear variations in joint probability distributions and an operator-splitting-based method to ensure that the modelling system remains hyperbolic. Then, we verify the proposed model via benchmark probabilistic numerical tests with joint uncertainties introduced in initial and boundary conditions, matching established experiments of flow-sediment-bed evolutions driven by a sudden dam break and by a landslide dam failure and large-scale rapid flow-sediment-bed evolution in response to flash flood. The present work facilitates a promising modelling framework for quantifying multiple uncertainties in practical shallow water hydro-sediment-morphodynamic modelling applications