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An invariant point is defined as a representation of an invariant system (0 degrees of freedom by Gibbs' phase rule) by a point on a phase diagram. A univariant line thus represents a univariant system with 1 degree of freedom. Two univariant lines can then define a divariant area with 2 degrees of freedom.
A phase diagram for a fictitious binary chemical mixture (with the two components denoted by A and B) used to depict the eutectic composition, temperature, and point. ( L denotes the liquid state.) A eutectic system or eutectic mixture ( / j uː ˈ t ɛ k t ɪ k / yoo- TEK -tik ) [ 1 ] is a type of a homogeneous mixture that has a melting point ...
Another type of binary phase diagram is a boiling-point diagram for a mixture of two components, i. e. chemical compounds. For two particular volatile components at a certain pressure such as atmospheric pressure , a boiling-point diagram shows what vapor (gas) compositions are in equilibrium with given liquid compositions depending on temperature.
The equilibrium phase diagram of a solid solution of made up of mixtures of α and β. The upper curve is the line of liquidus, and the lower curve is the line of solidus. The upper curve is the line of liquidus, and the lower curve is the line of solidus.
Some sink, source or node are equilibrium points. 2-dimensional case refers to Phase plane. In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems.
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
When is positive, there are two equilibrium points: that is, one saddle point and one node (either an attractor or a repellor). Other examples are in modelling biological switches. [ 4 ] Recently, it was shown that under certain conditions, the Einstein field equations of General Relativity have the same form as a fold bifurcation. [ 5 ]
The subset of the phase space of the dynamical system corresponding to the typical behavior is the attractor, also known as the attracting section or attractee. Invariant sets and limit sets are similar to the attractor concept. An invariant set is a set that evolves to itself under the dynamics. [3] Attractors may contain invariant sets.