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The global balance equations can then be partitioned to give a set of local balance equations (also known as partial balance equations, [2] independent balance equations [7] or individual balance equations [8]). [1] These balance equations were first considered by Peter Whittle. [8] [9] The resulting equations are somewhere between detailed
In mathematics, the method of dominant balance approximates the solution to an equation by solving a simplified form of the equation containing 2 or more of the equation's terms that most influence (dominate) the solution and excluding terms contributing only small modifications to this approximate solution.
Dirac equation in the algebra of physical space; Dirac–Kähler equation; Doppler equations; Drake equation (aka Green Bank equation) Einstein's field equations; Euler equations (fluid dynamics) Euler's equations (rigid body dynamics) Relativistic Euler equations; Euler–Lagrange equation; Faraday's law of induction; Fokker–Planck equation ...
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
This is illustrated in the image here, where the balanced equation is: CH 4 + 2 O 2 → CO 2 + 2 H 2 O. Here, one molecule of methane reacts with two molecules of oxygen gas to yield one molecule of carbon dioxide and two molecules of water. This particular chemical equation is an example of complete combustion. Stoichiometry measures these ...
The more general inhomogeneous case: + = is not a conservation equation but the general kind of balance equation describing a dissipative system. The dependent variable y is called a nonconserved quantity, and the inhomogeneous term s(y,x,t) is the-source, or dissipation.