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Stokes' law is important for understanding the swimming of microorganisms and sperm; also, the sedimentation of small particles and organisms in water, under the force of gravity. [ 5 ] In air, the same theory can be used to explain why small water droplets (or ice crystals) can remain suspended in air (as clouds) until they grow to a critical ...
An illustration of Stokes' theorem, with surface Σ, its boundary ∂Σ and the normal vector n.The direction of positive circulation of the bounding contour ∂Σ, and the direction n of positive flux through the surface Σ, are related by a right-hand-rule (i.e., the right hand the fingers circulate along ∂Σ and the thumb is directed along n).
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, [1] is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
Stokes's law is an expression for the frictional force exerted on spherical objects with very small Reynolds numbers, named for George Gabriel Stokes (1819–1903). Stokes's law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid's viscosity.
X is a Brownian motion with respect to P, i.e., the law of X with respect to P is the same as the law of an n-dimensional Brownian motion, i.e., the push-forward measure X ∗ (P) is classical Wiener measure on C 0 ([0, ∞); R n). both X is a martingale with respect to P (and its own natural filtration); and
Download as PDF; Printable version; In other projects ... move to sidebar hide. Stokes law can refer to: Stokes' law, for friction force; Stokes' law (sound ...
Professor of biology Jerry Coyne sums up biological evolution succinctly: [3]. Life on Earth evolved gradually beginning with one primitive species – perhaps a self-replicating molecule – that lived more than 3.5 billion years ago; it then branched out over time, throwing off many new and diverse species; and the mechanism for most (but not all) of evolutionary change is natural selection.
Gause's law or the competitive exclusion principle, named for Georgy Gause, states that two species competing for the same resource cannot coexist at constant population values. The competition leads either to the extinction of the weaker competitor or to an evolutionary or behavioral shift toward a different ecological niche .