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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 ...
Morphology problem. How are neural tissues formed in specific ways in different species? The formation of neural tissues in a certain way is necessary for the formation of certain goal-directed behavior for certain species.
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 ...
In a large class of singularly perturbed problems, the domain may be divided into two or more subdomains. In one of these, often the largest, the solution is accurately approximated by an asymptotic series [2] found by treating the problem as a regular perturbation (i.e. by setting a relatively small parameter to zero). The other subdomains ...
Pulmonary contusion due to trauma is an example of a condition that can be asymptomatic with half of people showing no signs at the initial presentation. The CT scan shows a pulmonary contusion (red arrow) accompanied by a rib fracture (purple arrow).
Apart from modelling melting of solids, Stefan problem is also used as a model for the asymptotic behaviour (in time) of more complex problems. For example, Pego [10] uses matched asymptotic expansions to prove that Cahn-Hilliard solutions for phase separation problems behave as solutions to a non-linear Stefan problem at an intermediate time ...
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.
For example, a disease with a known low asymptomatic rate may lead to increased surveillance of symptomatic cases, whereas a higher asymptomatic rate could lead to more aggressive methods such as travel bans and compulsory quarantines, since the number of infectious, asymptomatic cases would be unknown.