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Taylor dispersion or Taylor diffusion is an apparent or effective diffusion of some scalar field arising on the large scale due to the presence of a strong, confined, zero-mean shear flow on the small scale. Essentially, the shear acts to smear out the concentration distribution in the direction of the flow, enhancing the rate at which it ...
That is, the Taylor series diverges at x if the distance between x and b is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions ...
In fluid dynamics, the Taylor microscale, which is sometimes called the turbulence length scale, is a length scale used to characterize a turbulent fluid flow. [1] This microscale is named after Geoffrey Ingram Taylor .
In mathematics, Itô's lemma or Itô's formula is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process.It serves as the stochastic calculus counterpart of the chain rule.
In calculus, Taylor's theorem gives an approximation of a -times differentiable function around a given point by a polynomial of degree , called the -th-order Taylor polynomial. For a smooth function , the Taylor polynomial is the truncation at the order k {\textstyle k} of the Taylor series of the function.
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g.
However, for sufficiently low concentrations of ions, a first-order Taylor series expansion approximation for the exponential function may be used (+ for <) to create a linear differential equation. [14]: Section 2.4.2 D&H say that this approximation holds at large distances between ions, [21]: 227 which is the same as saying that the ...
Determining the parameters of the Michaelis–Menten equation typically involves running a series of enzyme assays at varying substrate concentrations , and measuring the initial reaction rates , i.e. the reaction rates are measured after a time period short enough for it to be assumed that the enzyme-substrate complex has formed, but that the ...