Methodological derivation of the eikonal equation

Usually, when working with the eikonal equation, reference is made to its derivation in the monograph by Born and Wolf. The derivation of this equation was done rather carelessly. Understanding this derivation requires a certain number of implicit assumptions. For a better understanding of the eikonal approximation and for methodological purposes, the authors decided to repeat the derivation of the eikonal equation, explicating all possible assumptions. Methodically, the following algorithm for deriving the eikonal equation is proposed. The wave equation is derived from Maxwell’s equation. In this case, all conditions are explicitly introduced under which it is possible to do this. Further, from the wave equation, the transition to the Helmholtz equation is carried out. From the Helmholtz equation, with the application of certain assumptions, a transition is made to the eikonal equation. After analyzing all the assumptions and steps, the transition from the Maxwell’s equations to the eikonal equation is actually implemented. When deriving the eikonal equation, several formalisms are used. The standard formalism of vector analysis is used as the first formalism. Maxwell’s equations and the eikonal equation are written as three-dimensional vectors. After that, both the Maxwell’s equations and the eikonal equation use the covariant 4-dimensional formalism. The result of the work is a methodically consistent description of the eikonal equation

Arctic Museum Collections--Special Issue The Beringian Coevolution Project: Holistic Collections of Mammals and Associated Parasites Reveal Novel Perspectives on Evolutionary and Environmental Change in the North

The Beringian Coevolution Project (BCP), a field program underway in the high northern latitudes since 1999, has focused on building key scientific infrastructure for integrated specimen-based studies on mammals and their associated parasites. BCP has contributed new insights across temporal and spatial scales into how ancient climate and environmental change have shaped faunas, emphasizing processes of assembly, persistence, and diversification across the vast Beringian region. BCP collections also represent baseline records of biotic diversity from across the northern high latitudes at a time of accelerated environmental change. These specimens and associated data form an unmatched resource for identifying hidden diversity, interpreting past responses to climate oscillations, documenting contemporary conditions, and anticipating outcomes for complex biological systems in a regime of ecological perturbation. Because of its dual focus on hosts and parasites, the BCP record also provides a foundation for comparative analyses that can document the effects of dynamic change on the geographic distribution, transmission dynamics, and emergence of pathogens. By using specific examples from carnivores, shrews, lagomorphs, rodents and their associated parasites, we demonstrate how broad, integrated field collections provide permanent infrastructure that informs policy decisions regarding human impact and the effect of climate change on natural populations.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author