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The action is defined by an integral, and the classical equations of motion of a system can be derived by minimizing the value of that integral. The action principle provides deep insights into physics, and is an important concept in modern theoretical physics .
[1] [2] The third law is also more generally stated as: "To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." [3] The attribution of which of the two forces is the action and which is the reaction is arbitrary. Either of the two can be ...
Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential ...
In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that of a smaller set of objects, together with a set of operations that can be applied to it, that result in the creation of a larger collection of objects, called the generated set .
Since the equations naturally split into direct and quadrature components, many reactances come in pairs, one for the direct axis (with the index d), one for the quadrature axis (with the index q). This is often using direct-quadrature-zero transformation.
The reaction term can be deduced by noting that particles can interact in () different ways, so that the probability that a pair annihilates is (), yielding a term († †) where number state n is replaced by number state n − 2 at site i {\displaystyle i} at a certain rate.
Dynamical properties of reaction networks were studied in chemistry and physics after the invention of the law of mass action.The essential steps in this study were introduction of detailed balance for the complex chemical reactions by Rudolf Wegscheider (1901), [1] development of the quantitative theory of chemical chain reactions by Nikolay Semyonov (1934), [2] development of kinetics of ...
Since a ψ, ψ pair is a commuting element of the Grassmann algebra, it does not matter what order the pairs are in. If more than one ψ, ψ pair have the same k, the integral is zero, and it is easy to check that the sum over pairings gives zero in this case (there are always an even number of them). This is the Grassmann analog of the higher ...