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Miller twist rule is a mathematical formula derived by American physical chemist and historian of science Donald G. Miller (1927-2012) to determine the rate of twist to apply to a given bullet to provide optimum stability using a rifled barrel. [1]
When both the standard enthalpy change and stability constant have been determined, the standard entropy change is easily calculated from the equation above. The fact that stepwise formation constants of complexes of the type ML n decrease in magnitude as n increases may be partly explained in terms of the entropy factor.
In addition to determining the stability of the system, the root locus can be used to design the damping ratio and natural frequency (ω n) of a feedback system. Lines of constant damping ratio can be drawn radially from the origin and lines of constant natural frequency can be drawn as arccosine whose center points coincide with the origin.
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
The dimensionless equilibrium constant = = [] [] can be used to determine the conformational stability by the equation Δ G o = − R T ln K e q {\displaystyle \Delta G^{o}=-RT\ln K_{eq}} where R {\displaystyle R} is the gas constant and T {\displaystyle T} is the absolute temperature in kelvin .
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
Since absolute aggregation rates are difficult to measure, one often refers to the dimensionless stability ratio W, defined as = where k fast is the aggregation rate coefficient in the fast regime, and k the coefficient at the conditions of interest. The stability ratio is close to unity in the fast regime, increases in the slow regime, and ...
In mathematics, and especially differential and algebraic geometry, K-stability is an algebro-geometric stability condition, for complex manifolds and complex algebraic varieties. The notion of K-stability was first introduced by Gang Tian [ 1 ] and reformulated more algebraically later by Simon Donaldson . [ 2 ]