Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system

Optimal wave reflection as a mechanism for seagrass self-organization

Ecosystems threatened by climate change can boost their resilience by developing spatial patterns. Spatially regular patterns in wave-exposed seagrass meadows are attributed to self-organization, yet underlying mechanisms are not well understood. Here, we show that these patterns could emerge from feedbacks between wave reflection and seagrass-induced bedform growth. We derive a theoretical model for surface waves propagating over a growing seagrass bed. Wave-induced bed shear stress shapes bedforms which, in turn, trigger wave reflection. Numerical simulations show seagrass pattern development once wave forcing exceeds a critical amplitude. In line with Mediterranean Sea field observations, these patterns have half the wavelength of the forcing waves. Our results raise the hypothesis that pattern formation optimizes the potential of seagrass meadows to reflect wave energy, and a clear direction for future field campaigns. If wave-reflecting pattern formation increases ecosystem resilience under globally intensifying wave climates, these ecosystems may inspire nature-based coastal protection measures.

Highlighting the Diversity of Desmoplastic Small Round Cell Tumor: A Case Series

Desmoplastic small round cell tumor (DSRCT) is a rare malignant tumor that occurs mainly in the retroperitoneum of children and young adults. In its prototypical form, DSCRT displays characteristic morphology with nested primitive small round cells in a desmoplastic stroma and a distinctive immunophenotype with polyphenotypic differentiation. However, DSCRT can also exhibit a broader clinical, histologic and immunohistochemical spectrum and, therefore, cause diagnostic difficulties. Given that DSCRT is an aggressive and nearly universally fatal disease, making the correct diagnosis is critically important. Herein, we report three patients with DSRCT and unusual clinical, morphologic or immunohistochemical characteristics, in order to highlight its remarkable diversity and increase awareness of this unusual, distinctive neoplasm.

Modern perspectives on near-equilibrium analysis of Turing systems

In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Nontrivial amplification below the threshold for excitable cell signaling

In many asymptotically stable fluid systems, arbitrarily small fluctuations can grow by orders of magnitude before eventually decaying, dramatically enhancing the fluctuation variance beyond the minimum predicted by linear stability theory. Here using influential quantitative models drawn from the mathematical biology literature, we establish that dramatic amplification of arbitrarily small fluctuations is found in excitable cell signaling systems as well. Our analysis highlights how positive and negative feedback, proximity to bifurcations, and strong separation of timescales can generate nontrivial fluctuations without nudging these systems across their excitation thresholds. These insights, in turn, are relevant for a broader range of related oscillatory, bistable, and pattern-forming systems that share these features. The common thread connecting all of these systems with fluid dynamical examples of noise amplification is non-normality.

Effect of small inclination on binary convection in elongated rectangular cells

We analyze the effect of a small inclination on the well-studied problem of two-dimensional binary fluid convection in a horizontally extended closed rectangular box with a negative separation ratio, heated from below. The horizontal component of gravity generates a shear flow that replaces the motionless conduction state when inclination is not present. This large-scale flow interacts with the convective currents resulting from the vertical component of gravity. For very small inclinations the primary bifurcation of this flow is a Hopf bifurcation that gives rise to chevrons and blinking states similar to those obtained with no inclination. For larger but still small inclinations this bifurcation disappears and is superseded by a fold bifurcation of the large-scale flow. The convecton branches, i.e., branches of spatially localized states consisting of counterrotating rolls, are strongly affected, with the snaking bifurcation diagram present in the noninclined system destroyed already at small inclinations. For slightly larger but still small inclinations we obtain small-amplitude localized states consisting of corotating rolls that evolve continuously when the primary large-scale flow is continued in the Rayleigh number. These localized states lie on a solution branch with very complex behavior strongly dependent on the values of the system parameters. In addition, several disconnected branches connecting solutions in the form of corotating rolls, counterrotating rolls, and mixed corotating and counterrotating states are also obtained.