This paper investigates the role of viscosity in the error upper bounds of a consistent splitting scheme for the Navier–Stokes equations proposed by Huang and Shen [1]. In their original analysis the viscosity is fixed to unity. By following and extending their proof methodology while keeping the viscosity ν symbolic, we obtain an H1 velocity error bound that contains negative powers of ν, indicating that the scheme is not robust as ν → 0. To establish this bound we refine a theorem in [2] on the constant in the Stokes pressure estimate, which is crucial to the error analysis. A targeted numerical experiment based on a perturbation of the Kovasznay flow corroborates this analytical prediction: the scheme of [1] blows up at high Reynolds number, and a comparison with a fully implicit Newton solver and with the time-dependent Stokes counterpart of the same scheme localizes the failure to the explicit treatment of the convection term.
In seismic-prone regions, assessment of the risk of regional bridge networks is essential for quantifying resilience metrics. Ideally this assessment needs to rely on high-fidelity numerical simulation models and on a comprehensive quantification of the seismic hazard. Unfortunately, the computational burden associated with such a faithful assessment of risk across the bridge portfolio is prohibitive for larger networks. This study investigates the use of a Gaussian Process (GP)-based stochastic emulation framework to alleviate this burden. A single surrogate model is established across all bridges of the same typology in the network. The surrogate model development accounts for diverse bridge configurations, as well as aleatoric ground motion variability across different intensity levels. The implementation also addresses aleatoric correlations across different engineering demand parameters for each bridge. The framework is implemented for risk assessment of the Chilean bridge network, specifically for four different bridge typologies, representing the predominant configurations within the national bridge inventory. It also examines in detail the computational benefits of establishing a single surrogate model across each typology, by comparing its accuracy to an application that considers the development of separate surrogate models per bridge type. The case study validates the accuracy of the stochastic emulation framework and illustrates the computational benefits for regional risk assessment. The latter is accomplished by comparing the results to different approximate formulations with respect to the assumptions for modeling the bridges within the network or the fidelity for considering and propagating the different types of uncertainties impacting the risk estimation.
In this wok, the Cauchy problem on the line of the modified Korteweg-de Vries equation with higher-order dispersion is studied, and for data in Sobolev and analytic Gevrey spaces its optimal well-posedness is established. The proofs are based on the derivation of sharp trilinear estimates in Bourgain spaces suggested by the corresponding linear problem. Furthermore, for analytic initial data improved lower bounds for the radius of spatial analyticity of the solution are derived.
To holistically understand the biology of animals, we must unravel the complexities and specificities of host-microbe interactions across animal taxa. Birds represent enigmatic and scientifically compelling hosts in which to understand these interactions. Here, we present a brief summary of a series of conversations among avian microbiome researchers regarding methodological challenges facing the avian microbiome field, where most research to date has focused on bacterial communities of the gut. Collectively, we acknowledged a commonly shared but underreported issue facing the avian microbiome field: that of difficulty in obtaining high-quality and high-yield microbial DNA from avian fecal samples. We discuss some of the potential reasons underlying low DNA yields, such as inhibitory compounds and rapid DNA degradation, and provide recommendations for how researchers in the avian microbiome field might cope with these methodological challenges. Collective and dedicated efforts to address these challenges will be required for a robust understanding of host-microbe interactions in avian systems.
Recent research supports that Cognitive Behavioral Therapy for Insomnia (CBT-I) improves both insomnia and depression symptoms. The primary purpose of the current review was to summarize potential mechanistic pathways linking insomnia and depression while evaluating how improvements in sleep via CBT-I may lead to reduced depressive symptoms. The current literature supports that there are several potential biological, behavioral, and cognitive-affective mechanisms, including improved hypothalamic-pituitary-adrenal (HPA) axis and inflammatory functioning, behavioral activation, and emotion regulation, that may explain the antidepressant effects of CBT-I. Critically evaluating the potential mechanisms by which CBT-I improves depression (e.g., HPA-axis, inflammatory, behavioral, and emotional processes) will inform future efforts to enhance the overall effectiveness of CBT-I in patients with comorbid depression. Specifically, it will identify specific mechanisms that can be the focus of more targeted interventions or strategies to streamline CBT-I in patients with depression.
