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The equivalence of power laws with a particular scaling exponent can have a deeper origin in the dynamical processes that generate the power-law relation. In physics, for example, phase transitions in thermodynamic systems are associated with the emergence of power-law distributions of certain quantities, whose exponents are referred to as the ...
The wind profile power law relationship is. where is the wind speed (in metres per second) at height (in metres), and is the known wind speed at a reference height . The exponent ( ) is an empirically derived coefficient that varies dependent upon the stability of the atmosphere. For neutral stability conditions, is approximately 1/7, or 0.143.
Power-law fluid. In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time-independent non-Newtonian fluid) for which the shear stress, τ, is given by. where: ∂ u / ∂ y is the shear rate or the velocity gradient perpendicular to the plane of shear (SI unit s −1), and.
A central-force problem is said to be "integrable" if this integration can be solved in terms of known functions. If the force is a power law, i.e., if F(r) = α r n, then u can be expressed in terms of circular functions and/or elliptic functions if n equals 1, -2, -3 (circular functions) and -7, -5, -4, 0, 3, 5, -3/2, -5/2, -1/3, -5/3 and -7/ ...
The Wiener process is scale-invariant. In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation).
Calculus. In calculus, the power rule is used to differentiate functions of the form , whenever is a real number. Since differentiation is a linear operation on the space of differentiable functions, polynomials can also be differentiated using this rule. The power rule underlies the Taylor series as it relates a power series with a function's ...
Kohlrausch–Williams–Watts function Fourier transform of stretched exponential function. Curie–von Schweidler law This shows the response of dielectrics to an applied DC field to behave according to a power law, which can be expressed as an integral over weighted exponential functions. Djordjevic–Sarkar approximation
Stevens' power law is an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the stimulus. It is often considered to supersede the Weber–Fechner law, which is based on a logarithmic relationship between stimulus and sensation ...