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In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium.For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N): [1] [2] [3]: 123–125
Phase reduction is a method used to reduce a multi-dimensional dynamical equation describing a nonlinear limit cycle oscillator into a one-dimensional phase equation. [1] [2] Many phenomena in our world such as chemical reactions, electric circuits, mechanical vibrations, cardiac cells, and spiking neurons are examples of rhythmic phenomena, and can be considered as nonlinear limit cycle ...
It breaks down an apparently unimolecular reaction into two elementary steps, with a rate constant for each elementary step. The rate law and rate equation for the entire reaction can be derived from the rate equations and rate constants for the two steps. The Lindemann mechanism is used to model gas phase decomposition or isomerization reactions
As an example, consider the gas-phase reaction NO 2 + CO → NO + CO 2.If this reaction occurred in a single step, its reaction rate (r) would be proportional to the rate of collisions between NO 2 and CO molecules: r = k[NO 2][CO], where k is the reaction rate constant, and square brackets indicate a molar concentration.
Figure 5: Bode gain plot to find phase margin; scales are logarithmic, so labeled separations are multiplicative factors. For example, f 0 dB = βA 0 × f 1. Next, the choice of pole ratio τ 1 /τ 2 is related to the phase margin of the feedback amplifier. [9] The procedure outlined in the Bode plot article is followed. Figure 5 is the Bode ...
Each point within the triangle represents a possible composition of a mixture of the three components or pseudo-components, which may consist (ideally, according to the Gibbs' phase rule) of one, two or three phases. These points combine to form regions with boundaries between them, which represent the "phase behavior" of the system at constant ...
There are many correct collections of "Schreinemaker's rules" and the choice to use a given set of rules depends on the nature of the phase diagrams being created. Due to the phrasing of the Morey–Schreinemaker coincidence theorem, only one rule is essential to the Schreinemaker's rules. This is the so-called metastable extensions rule: [1]
The possible results of Phase I are either that a basic feasible solution is found or that the feasible region is empty. In the latter case the linear program is called infeasible. In the second step, Phase II, the simplex algorithm is applied using the basic feasible solution found in Phase I as a starting point.