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In 2020, after New Zealand emerged from its short-lived lockdown and students returned to university campuses, mathematicians Jeanette McLeod and Phil Wilson from the University of Canterbury taught a final-year mathematics course using craft. A part of most lectures included a hands-on craft activity to explore a key concept and to foster curiosity. This article describes the design and delivery of the course and reflects on the overwhelmingly positive student feedback. We suggest that the creation of, and interaction with, mathematical craft objects played a significant role in shaping these responses by generating feelings of engagement, reducing stress, and allowing tangible access to mathematical ideas.

Invasive tree species pose a grave global threat to biodiversity, particularly impacting vulnerable grassland ecosystems. This paper presents a novel approach to simulate the invasion of ecosystems by these aggressive species. Our innovative coupled ODE-PDE model offers explicit invasion simulations, a significant leap beyond traditional integro-difference matrix models. With robust theoretical properties, including solution positivity, and drawing upon PDE theory, our model offers deeper insights into invasion behavior. Our model reveals that invasions undergo a prolonged quiescent phase before rapidly transitioning to a consistent rate of advancement after a critical point. This study not only sheds light on invasion dynamics but also charts a course for future exploration and potential model extensions. [ABSTRACT FROM AUTHOR]

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread. [ABSTRACT FROM AUTHOR]

In 2020, after New Zealand emerged from its short-lived lockdown and students returned to university campuses, mathematicians Jeanette McLeod and Phil Wilson from the University of Canterbury taught a final-year mathematics course using craft. A part of most lectures included a hands-on craft activity to explore a key concept and to foster curiosity. This article describes the design and delivery of the course and reflects on the overwhelmingly positive student feedback. We suggest that the creation of, and interaction with, mathematical craft objects played a significant role in shaping these responses by generating feelings of engagement, reducing stress, and allowing tangible access to mathematical ideas. [ABSTRACT FROM AUTHOR]

In this work, the flow conditions are numerically investigated inside uniform and non-uniform street canyons well within the atmospheric boundary layer. The numerical simulations use the steady-RANS method with the near-wall modelling approach to simulate wall roughness at the boundary. With the aim of investigating both flow structure in broad terms and pedestrian comfort in the street canyon between parallel buildings, we test different canyon configurations with varied street width, building width and building height. Turbulent conditions are broadly expected to hold within the physically realistic range of Reynolds number of order 10 6 considered here, where we take the building height to be a characteristic length scale and the free stream velocity as the characteristic velocity. In addition to discussing the features of the canyon and wake flow, we investigate the effects of canyon geometry on pedestrian comfort by using the Extended Land Beaufort Scale for this purpose. We present and compare pedestrian comfort 'maps' for each of our geometries. [ABSTRACT FROM AUTHOR]

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism—aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium–ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD—vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization—found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease. [ABSTRACT FROM AUTHOR]