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  1. Free, publicly-accessible full text available June 1, 2024
  2. Free, publicly-accessible full text available June 1, 2024
  3. Abstract

    A simple equation modelling an inextensible elastic lining of an inner-lined tube subject to an imposed pressure difference is derived from a consideration of the idealised elastic properties of the lining and the pressure and soft-substrate forces. Two cases are considered in detail, one with prominent wrinkling and a second one in which wrinkling is absent and only buckling remains. Bifurcation diagrams are computed via numerical continuation for both cases. Wrinkling, buckling, folding, and mixed-mode solutions are found and organised according to system-response measures including tension, in-plane compression, maximum curvature and energy. Approximate wrinkle solutions are constructed using weakly nonlinear theory, in excellent agreement with numerics. Our approach explains how the wavelength of the wrinkles is selected as a function of the parameters in compressed wrinkling systems and shows how localised folds and mixed-mode states form in secondary bifurcations from wrinkled states. Our model aims to capture the wrinkling response of arterial endothelium to blood pressure changes but applies much more broadly.

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  4. Abstract

    We derive sparse bounds for the bilinear spherical maximal function in any dimension . When , this immediately recovers the sharp bound of the operator and implies quantitative weighted norm inequalities with respect to bilinear Muckenhoupt weights, which seems to be the first of their kind for the operator. The key innovation is a group of newly developed continuity improving estimates for the single‐scale bilinear spherical averaging operator.

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  5. Abstract

    There has been a steady rise in the use of dormant propagules to study biotic responses to environmental change over time. This is particularly important for organisms that strongly mediate ecosystem processes, as changes in their traits over time can provide a unique snapshot into the structure and function of ecosystems from decades to millennia in the past. Understanding sources of bias and variation is a challenge in the field of resurrection ecology, including those that arise because often‐used measurements like seed germination success are imperfect indicators of propagule viability. Using a Bayesian statistical framework, we evaluated sources of variability and tested for zero‐inflation and overdispersion in data from 13 germination trials of soil‐stored seeds ofSchoenoplectus americanus, an ecosystem engineer in coastal salt marshes in the Chesapeake Bay. We hypothesized that these two model structures align with an ecological understanding of dormancy and revival: zero‐inflation could arise due to failed germinations resulting from inviability or failed attempts to break dormancy, and overdispersion could arise by failing to measure important seed traits. A model that accounted for overdispersion, but not zero‐inflation, was the best fit to our data. Tetrazolium viability tests corroborated this result: most seeds that failed to germinate did so because they were inviable, not because experimental methods failed to break their dormancy. Seed viability declined exponentially with seed age and was mediated by seed provenance and experimental conditions. Our results provide a framework for accounting for and explaining variability when estimating propagule viability from soil‐stored natural archives which is a key aspect of using dormant propagules in eco‐evolutionary studies.

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