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The damping ratio is a system parameter, denoted by ζ ("zeta"), that can vary from undamped (ζ = 0), underdamped (ζ < 1) through critically damped (ζ = 1) to overdamped (ζ > 1). The behaviour of oscillating systems is often of interest in a diverse range of disciplines that include control engineering , chemical engineering , mechanical ...
In the special case of overdamped dynamics, the inertia of the particle is negligible in comparison to the damping force, and the trajectory () is described by the overdamped Langevin equation = + () +, where is the damping constant.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
A simple harmonic oscillator is an oscillator that is neither driven nor damped.It consists of a mass m, which experiences a single force F, which pulls the mass in the direction of the point x = 0 and depends only on the position x of the mass and a constant k.
In graph theory, the outer boundary of a subset S of the vertices of a graph G is the set of vertices in G that are adjacent to vertices in S, but not in S themselves. The inner boundary is the set of vertices in S that have a neighbor outside S.
The graph shown here appears as a subgraph of an undirected graph if and only if models the sentence ,,,.. In the first-order logic of graphs, a graph property is expressed as a quantified logical sentence whose variables represent graph vertices , with predicates for equality and adjacency testing.
Forbidden graph characterizations may be used in algorithms for testing whether a graph belongs to a given family. In many cases, it is possible to test in polynomial time whether a given graph contains any of the members of the obstruction set, and therefore whether it belongs to the family defined by that obstruction set.
In graph theory, the strength of an undirected graph corresponds to the minimum ratio of edges removed/components created in a decomposition of the graph in question. It is a method to compute partitions of the set of vertices and detect zones of high concentration of edges, and is analogous to graph toughness which is defined similarly for vertex removal.