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In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and physics. But asymptotic methods ...
In many cases, the asymptotic expansion is in power of a small parameter, ε: in the boundary layer case, this is the nondimensional ratio of the boundary layer thickness to a typical length scale of the problem. Indeed, applications of asymptotic analysis in mathematical modelling often [3] center around a nondimensional parameter which has ...
Asymptotic safety, if realized in Nature, has far reaching consequences in all areas where quantum effects of gravity are to be expected. Their exploration, however, is still in its infancy. By now there are some phenomenological studies concerning the implications of asymptotic safety in particle physics, astrophysics and cosmology, for instance.
As an example, asymptotic safety in combination with the Standard Model allows a statement about the mass of the Higgs boson and the value of the fine-structure constant. [32] Furthermore, it provides possible explanations for particular phenomena in cosmology and astrophysics , concerning black holes or inflation , for instance. [ 32 ]
A perturbed problem whose solution can be approximated on the whole problem domain, whether space or time, by a single asymptotic expansion has a regular perturbation.Most often in applications, an acceptable approximation to a regularly perturbed problem is found by simply replacing the small parameter by zero everywhere in the problem statement.
A manifold is asymptotically simple if it admits a conformal compactification ~ such that every null geodesic in has future and past endpoints on the boundary of ~.. Since the latter excludes black holes, one defines a weakly asymptotically simple manifold as a manifold with an open set isometric to a neighbourhood of the boundary of ~, where ~ is the conformal compactification of some ...
From earthquakes to hurricanes, volcanoes and floods, nature ha Wildfires continue to rage in the area, and the death toll now stands at at least 27. Around 12,000 structures have burned to the ...
In mathematics and statistics, an asymptotic distribution is a probability distribution that is in a sense the "limiting" distribution of a sequence of distributions. One of the main uses of the idea of an asymptotic distribution is in providing approximations to the cumulative distribution functions of statistical estimators .