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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]

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is fallacious on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena. [ABSTRACT FROM AUTHOR]

So-called ‘distinctively mathematical explanations’ (DMEs) are said to explain physical phenomena, not in terms of contingent causal laws, but rather in terms of mathematical necessities that constrain the physical system in question. Lange argues that the existence of four or more equilibrium positions of any double pendulum has a DME. Here we refute both Lange’s claim itself and a strengthened and extended version of the claim that would pertain to any n-tuple pendulum system on the ground that such explanations are actually causal explanations in disguise and their associated modal conditionals are not general enough to explain the said features of such dynamical systems. We argue and show that if circumscribing the antecedent for a necessarily true conditional in such explanations involves making a causal analysis of the problem, then the resulting explanation is not distinctively mathematical or non-causal. Our argument generalises to other dynamical systems that may have purported DMEs analogous to the one proposed by Lange, and even to some other counterfactual accounts of non-causal explanation given by Reutlinger and Rice. [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]

Background: Advanced imaging in patients with shoulder instability can be variable. MRI offers visualization of soft tissue injuries including capsulolabral injuries, however may not be ideal to assess osseous injuries. CT examination may often be desired as the accepted standard for assessment of glenoid and humeral bone loss, the extent of which can dictate surgical management in the adolescent age group in which bone loss is common. Hypothesis/Purpose: Our hypothesis, MRI bone sequence/method (FRACTURE: FFE Resembling A CT Using Restricted Echo-spacing) can provide measurements comparable to standard CT for glenoid bone loss. The objective of this study was to validate this technique in a cadaveric glenoid bone loss model using 2D-CT as the reference standard. Methods: Glenoid fractures of varying sizes were arthroscopically created in 10 cadaveric shoulders. 2D-CT and MRI FRACTURE on 3T Philips Ingenia; Philips Healthcare, Best, Netherlands) were performed on all 10 shoulders. FRACTURE is a 3D-gradient echo pulse sequence with restricted echo-spacing combined with an automated post-processing is a technical innovation which provides superior cortical and trabecular bone contrast on MRI. The CT and MRI were presented in a blinded fashion to 2 experienced musculoskeletal radiologists for independent measurement of the glenoid fracture length, width, as well as % glenoid bone loss using the best-fit circle method. Paired t-tests were performed to compare the measurements obtained on CT with those obtained on the MR FRACTURE images. Intraclass correlation coefficient was used to measure interobserver reliability. Results: There was no statistically significant difference between CT and MRI in terms of the measured glenoid fracture length(P-value=0.54) or fracture width(P-value=0.86). The mean length measured on CT was 23.40 mm ± 6.87 and on MRI was 22.96 mm ± 7.38. The mean width on CT measured 7.96 mm ± 3.51 and on MRI measured 7.89 mm ± 3.18. There was also no statistically significant difference between CT and MRI in terms of measured glenoid bone loss (P-value=0.65). Intraclass correlation coefficients for interobserver reliability ranged from 0.95 to 0.99 for measurements performed on CT and MRI. Conclusion: Measurements of glenoid fracture and associated % bone loss on CT were comparable with measurements obtained using the MR FRACTURE technique. Inter-observer reproducibility for these measurements was excellent. MRI FRACTURE technique may obviate preoperative CT in patients with anterior shoulder instability. [ABSTRACT FROM AUTHOR]

Glacier ice flow is shaped and defined by several properties, including the bedrock elevation profile and the basal slip distribution. The effect of these two basal properties can be present in similar ways in the surface. For bedrock recovery, this makes distinguishing between them an interesting and complex problem. The results of this paper show that in some synthetic test cases it is indeed possible to distinguish and recover both bedrock elevation and basal slip given free surface elevation and free surface velocity. The unidirectional shallow ice approximation is used to compute steady-state surface data for a number of synthetic cases with different bedrock profiles and basal slip distributions. A simple inversion method based on Newton's method is applied to the known surface data to return the bedrock profile and basal slip distribution. In each synthetic test case, the inversion was successful in recovering both the bedrock elevation profile and the basal slip distribution variables. These results imply that there are a unique bedrock profile and basal slip which give rise to a unique combination of free surface velocity and free surface elevation. [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]