Snaking and isolas of localised states in bistable discrete lattices

We consider localised states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The existence of stable localised states is made possible by pinning to the underlying lattice; they do not exist in the equivalent continuum equation. In particular we address the existence of 'isolas': closed curves of solutions in the bifurcation diagram. Isolas appear for some non-periodic boundary conditions in one spatial dimension but seem to appear generically in two dimensions. We point out how features of the bifurcation diagram in 1D help to explain some (unintuitive) features of the bifurcation diagram in 2D.Comment: 14 page

Effects of dissolved gases on partial anodic passivation phenomena at copper microelectrodes immersed in aqueous NaCl

Anodic passivation for copper exposed to aqueous NaCl (model seawater) is rate limited by diffusion of a poorly soluble Cu(I) chloro species. As a result, a protective layer of CuCl forms on copper metal (with approx. 1 μm thickness) that is then put under strain at more positive applied potentials with explosive events causing current spikes and particulate product expulsion. In this report, the mechanism for this explosive film rupture and particle expulsion process is shown to occur (i) in the absence of underlying anodic gas evolution, and (ii) linked to the presence/nature of gaseous solutes. The film rupture event is proposed to be fundamentally dependent on gas bubble nucleation (triggered by the release of interfacial stress) with surface tension effects by dissolved gases affecting the current spike pattern. Oxygen O2, hydrogen H2, and helium He suppress current spikes and behave differently to argon Ar, nitrogen N2, and carbon dioxide CO2, which considerably enhance current spikes. Vacuum-degassing the electrolyte solution results in behaviour very similar to that observed in the presence of helium. The overall corrosion rate for copper microelectrodes is compared and parameters linked to passivation and corrosion processes are discussed.</p

Forecasting resilience profiles of the run-up to regime shifts in nearly-one-dimensional systems

The forecasting of sudden, irreversible shifts in natural systems is a challenge of great importance, whose realization could allow pre-emptive action to be taken to avoid or mitigate catastrophic transitions, or to help systems adapt to them. In recent years, there have been many advances in the development of such early warning signals. However, much of the current toolbox is based around the tracking of statistical trends and therefore does not aim to estimate the future time scale of transitions or resilience loss. Metric-based indicators are also difficult to implement when systems have inherent oscillations which can dominate the indicator statistics. To resolve these gaps in the toolbox, we use additional system properties to fit parsimonious models to dynamics in order to predict transitions. Here, we consider nearly-one-dimensional systems-higher dimensional systems whose dynamics can be accurately captured by one-dimensional discrete time maps. We show how the nearly one-dimensional dynamics can be used to produce model-based indicators for critical transitions which produce forecasts of the resilience and the time of transitions in the system. A particularly promising feature of this approach is that it allows us to construct early warning signals even for critical transitions of chaotic systems. We demonstrate this approach on two model systems: of phosphorous recycling in a shallow lake, and of an overcompensatory fish population.</p

Demographic noise slows down cycles of dominance

We study the phenomenon of cyclic dominance in the paradigmatic Rock--Paper--Scissors model, as occurring in both stochastic individual-based models of finite populations and in the deterministic replicator equations. The mean-field replicator equations are valid in the limit of large populations and, in the presence of mutation and unbalanced payoffs, they exhibit an attracting limit cycle. The period of this cycle depends on the rate of mutation; specifically, the period grows logarithmically as the mutation rate tends to zero. We find that this behaviour is not reproduced in stochastic simulations with a fixed finite population size. Instead, demographic noise present in the individual-based model dramatically slows down the progress of the limit cycle, with the typical period growing as the reciprocal of the mutation rate. Here we develop a theory that explains these scaling regimes and delineates them in terms of population size and mutation rate. We identify a further intermediate regime in which we construct a stochastic differential equation model describing the transition between stochastically-dominated and mean-field behaviour.Comment: 25 pages, 11 figure

Effects of dissolved gases on partial anodic passivation phenomena at copper microelectrodes immersed in aqueous NaCl

Anodic passivation for copper exposed to aqueous NaCl (model seawater) is rate limited by diffusion of a poorly soluble Cu(I) chloro species. As a result, a protective layer of CuCl forms on copper metal (with approx. 1 μm thickness) that is then put under strain at more positive applied potentials with explosive events causing current spikes and particulate product expulsion. In this report, the mechanism for this explosive film rupture and particle expulsion process is shown to occur (i) in the absence of underlying anodic gas evolution, and (ii) linked to the presence/nature of gaseous solutes. The film rupture event is proposed to be fundamentally dependent on gas bubble nucleation (triggered by the release of interfacial stress) with surface tension effects by dissolved gases affecting the current spike pattern. Oxygen O2, hydrogen H2, and helium He suppress current spikes and behave differently to argon Ar, nitrogen N2, and carbon dioxide CO2, which considerably enhance current spikes. Vacuum-degassing the electrolyte solution results in behaviour very similar to that observed in the presence of helium. The overall corrosion rate for copper microelectrodes is compared and parameters linked to passivation and corrosion processes are discussed.</p

How close is the nearest node in a wireless network?

The ability of small-cell wireless networks to self-organize is crucial for improving capacity and performance in modern communication networks. This paper considers one of the most basic questions: what is the expected distance to a cell's nearest neighbour in a spatially distributed network? We analyse a model problem in the asymptotic limit of large total received signal and compare the accuracy of different heuristics. We also analytically consider the effects of fading. Our analysis shows that the most naive heuristic systematically underestimates the distance to the nearest node; this is substantially corrected in cases of interest by inclusion of the next-order asymptotic term. We illustrate our theoretical results explicitly or several combinations of signal and path loss parameters and show that our theory is well supported by numerical simulations. </p

Cyclical fate restriction:A new view of neural crest cell fate specification

Neural crest cells are crucial in development, not least because of their remarkable multipotency. Early findings stimulated two hypotheses for how fate specification and commitment from fully multipotent neural crest cells might occur, progressive fate restriction (PFR) and direct fate restriction, differing in whether partially restricted intermediates were involved. Initially hotly debated, they remain unreconciled, although PFR has become favoured. However, testing of a PFR hypothesis of zebrafish pigment cell development refutes this view. We propose a novel ‘cyclical fate restriction’ hypothesis, based upon a more dynamic view of transcriptional states, reconciling the experimental evidence underpinning the traditional hypotheses.</p

Linking the Cu(II/I) potential to the onset of dynamic phenomena at corroding copper microelectrodes immersed in aqueous 0.5 M NaCl

Electrochemical studies have been conducted at copper microelectrodes (125, 50, and 25 μm in diameter) immersed in aqueous 0.5 M NaCl. Cyclic and linear sweep voltammetry were used to explore the corrosion of copper in chloride media. Cyclic voltammetry revealed the reversible Cu(I)/Cu(0) potential at approximately −0.11 V vs. SCE associated with the formation of a dense CuCl blocking layer (confirmed by in situ Raman and fluorescence measurements). Although continuous dissolution of Cu(I) occurs, only an increase in the driving potential into the region of the Cu(II)/Cu(I) potential at approximately +0.14 V vs. SCE started more rapid and stochastic dissolution/corrosion processes. The corrosion process is demonstrated to be linked to two distinct mechanisms based on (A) slow molecular dissolution and (B) fast colloidal dissolution. A polymer of intrinsic microporosity (PIM-EA-TB) is employed to suppress colloidal processes to reveal the underlying molecular processes.</p

Linking the Cu(II/I) potential to the onset of dynamic phenomena at corroding copper microelectrodes immersed in aqueous 0.5 M NaCl

Electrochemical studies have been conducted at copper microelectrodes (125, 50, and 25 μm in diameter) immersed in aqueous 0.5 M NaCl. Cyclic and linear sweep voltammetry were used to explore the corrosion of copper in chloride media. Cyclic voltammetry revealed the reversible Cu(I)/Cu(0) potential at approximately −0.11 V vs. SCE associated with the formation of a dense CuCl blocking layer (confirmed by in situ Raman and fluorescence measurements). Although continuous dissolution of Cu(I) occurs, only an increase in the driving potential into the region of the Cu(II)/Cu(I) potential at approximately +0.14 V vs. SCE started more rapid and stochastic dissolution/corrosion processes. The corrosion process is demonstrated to be linked to two distinct mechanisms based on (A) slow molecular dissolution and (B) fast colloidal dissolution. A polymer of intrinsic microporosity (PIM-EA-TB) is employed to suppress colloidal processes to reveal the underlying molecular processes.</p