Abstract A diffuse interface model for tumour growth in the presence of a nutrient consumed by is considered. The system equations consists Cahn–Hilliard equation with source terms cells and reaction–diffusion nutrient. We introduce fully-discrete finite element approximation prove stability bounds discrete scheme. Moreover, we show that solutions exist depend continuously on initial boundary d...

F or normal growth and optimum production, fruit the quantities that they are in certain annual crops. Generally, nitrogen is the only macronutrient that must be consistently supplied to fruit trees in California. Under certain conditions, other nutrient deficiencies can develop. Toxicities can also become a problem. These will be discussed in the sections for individual nutrients. trees requir...

Rock colonization by plant roots and their associated microbiota is one of the major drivers of mineral weathering, nutrient cycling, soil formation and ecosystem stability. Yet the mechanisms of biouptake of lithogenic elements from rocks with differential nutrient availabilities and limitations are yet to be established. Here we present results from a mesocosm experiment that examined lithoge...

We report results from a series of studies coevolving players for simple Rock–Paper–Scissors games. These results demonstrate that “Current Individual versus Ancestral Opponent” (CIAO) plots, which have been proposed as a visualization technique for detecting both coevolutionary progress and coevolutionary cycling, suffer from ambiguity with respect to an important but rarely discussed class of...

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The diversity and composition of ecological communities often co-vary with ecosystem productivity. However, the relative importance of productivity, or resource abundance, versus the spatial distribution of resources in shaping those ecological patterns is not well understood, particularly for the bacterial communities that underlie most important ecosystem functions. Increasing ecosystem produ...

Nutrient cycling is a ubiquitous feature of ecosystems at all scales, allowing productivity to rise beyond the limits set by external nutrient inputs. Nutrient cycling occurs as a side-effect of the metabolism of a diverse set of species that each performs a step in the recycling loop. Recycling loops can be large and involve many steps. At each step the possibility exists for ‘side-reactions’ ...

The emergence of third-generation, technology-based public bikeshare schemes offers new opportunities for researching cycling behaviour. In this study, data from one such scheme, the London Cycle Hire Scheme (LCHS), are analysed. Algorithms are developed for summarising and labelling cyclists’ usage behaviours and tailored visual analysis applications are designed for exploring their spatiotemp...