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One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define. With SI electromagnetic units, called rationalized, [3] [4] Maxwell's equations have no explicit factors of 4π in the formulae, whereas the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
The Poisson–Boltzmann equation describes a model proposed independently by Louis Georges Gouy and David Leonard Chapman in 1910 and 1913, respectively. [3] In the Gouy-Chapman model, a charged solid comes into contact with an ionic solution, creating a layer of surface charges and counter-ions or double layer. [4]
[1] [2] The qualitative form of this connection is called Hamilton's optico-mechanical analogy. In mathematics, the Hamilton–Jacobi equation is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.
In physics, specifically electromagnetism, the Biot–Savart law (/ ˈ b iː oʊ s ə ˈ v ɑːr / or / ˈ b j oʊ s ə ˈ v ɑːr /) [1] is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current.
The phase-space formulation is a formulation of quantum mechanics that places the position and momentum variables on equal footing in phase space.The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.
In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: [1] + =. It is named after English mathematician James Joseph Sylvester. Then given matrices A, B, and C, the problem is to find the possible matrices X that obey this equation.
Erythritol tetranitrate (ETN) is an explosive compound chemically similar to PETN, [1] though it is thought to be slightly more sensitive to friction and impact.. Like many nitrate esters, ETN acts as a vasodilator, and was the active ingredient in the original "sustained release" tablets, made under a process patent in the early 1950s, called "nitroglyn".