Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS

Oceanographic and behavioural assumptions in models of the fate of coral and coral reef fish larvae

A predictive model of the fate of coral reef fish larvae in a reef system is proposed that combines the oceanographic processes of advection and turbulent diffusion with the biological process of horizontal swimming controlled by olfactory and auditory cues within the timescales of larval development. In the model, auditory cues resulted in swimming towards the reefs when within hearing distance of the reef, whereas olfactory cues resulted in the larvae swimming towards the natal reef in open waters by swimming against the concentration gradients in the smell plume emanating from the natal reef. The model suggested that the self-seeding rate may be quite large, at least 20% for the larvae of rapidly developing reef fish species, which contrasted with a self-seeding rate less than 2% for non-swimming coral larvae. The predicted self-recruitment rate of reefs was sensitive to a number of parameters, such as the time at which the fish larvae reach post-flexion, the pelagic larval duration of the larvae, the horizontal turbulent diffusion coefficient in reefal waters and the horizontal swimming behaviour of the fish larvae in response to auditory and olfactory cues, for which better field data are needed. Thus, the model suggested that high self-seeding rates for reef fish are possible, even in areas where the 'sticky water' effect is minimal and in the absence of long-term trapping in oceanic fronts and/or large-scale oceanic eddies or filaments that are often argued to facilitate the return of the larvae after long periods of drifting at sea