When an avalanche occurs, the PN junction is flooded with charge carriers and trap levels between the valence and conduction band become occupied to a degree that is much greater than that expected in a thermal-equilibrium distribution of charge carriers.
22.
A discrete time Markov chains ( DTMC ) with transition matrix " P " and equilibrium distribution \ pi is said to be in detailed balance if for all pairs " i " and " j ",
23.
The equilibrium and non-equilibrium distributions satisfy the following relations to their macroscopic variables ( these will be used later, once the particle distributions are in the " correct form " in order to scale from the particle to macroscopic level ):
24.
This formalism has been applied not only to parametric arrays [ 15 ], but also to other nonlinear acoustic effects, such as the absorption of sound by sound and to the equilibrium distribution of sound intensity spectra in cavities [ 18 ].
25.
Where " C " is a normalizing constant chosen to make the equilibrium state probabilities sum to 1 and \ scriptstyle { \ pi _ i ( \ cdot ) } represents the equilibrium distribution for queue " i ".
26.
The "'global balance equations "'( also known as "'full balance equations "') are a set of equations that characterize the equilibrium distribution ( or any stationary distribution ) of a Markov chain, when such a distribution exists.
27.
For a discrete time Markov chain with transition matrix " Q " and equilibrium distribution \ pi, the global balance equation has the same form as above, except that q _ { ij } should be interpreted as the transition probability and not the transition rate.
28.
In a 2012 study Pigolotti et al . conducted a thorough study of the unique bid auction in the grand canonical ensemble, finding a theoretical expression for the Nash equilibrium distribution and showing that real-world players play according to this distribution when the number of players in the auction is low.
29.
Along with detailed balancing, at temperature we may use our knowledge of the equilibrium energy distribution of the atoms, as stated in the Maxwell Boltzmann distribution, and the equilibrium distribution of the photons, as stated in Planck's law of black body radiation to derive universal relationships between the Einstein coefficients.
30.
As a result, the transition probabilities of the simulated annealing algorithm do not correspond to the transitions of the analogous physical system, and the long-term distribution of states at a constant temperature T need not bear any resemblance to the thermodynamic equilibrium distribution over states of that physical system, at any temperature.
