Distribution of states

The distributions of states in conduction and valence bands are commonly described by the effective density of states. The concentration of electrons, n, in the conduction band can be calculated as... 

Finite temperature being reduced to zero Kelvin, i.e. the use of static structures to represent molecules, rather than treating them as an ensemble of molecules in a distribution of states (translational, rotational and vibrational) corresponding to a (macroscopic) temperature. 

If the sampling scheme is changed, C(I, J) can continue to be updated with an adjusted acc provided that the distribution of states within the macrostates does not change. This would not be the case, for example, if we were only monitoring transition probabilities between particle numbers and the temperature changed, as it would redistribute the microstate probabilities within each value of N. 

One of our main assumptions in the derivation of the Langmuir model [and implicitly made by Langmuir himself (1918)] is that the binding process does not affect the distribution of states of the adsorbent molecules. Removal of this assumption has a profound effect on the form of the BI of systems with more than a single site. 

Comparison of the integration of this last conservation equation with the direct simulation of an uncoupled neural population with a given distribution of states (v, u) at the initial time provides a validation for the simplified version of the model. Then adding the imposed flux accounting for connectivity allows us to simulate a large population of Izhikevich neurons with a given pattern of connectivity (number of afferents per neuron and delays kernel). 

The average behavior of a gas model during a motion of unlimited duration corresponds to the Maxwell-Boltz-mann distribution of state. 

The fundamental assumption underlying this investigation is the hypothesis that the gas models are ergodic systems (cf. Section 10). With the help of this hypothesis Boltzmann computed the time average of, for instance, the kinetic energy of each atom (the same value is obtained for all atoms ).108 Likewise he calculated the time average of other functions (q, p) which characterize the average distribution of state. 

If we accept the validity of Eq. (34), we can conclude from it more than just a statement about average behavior. In fact, it also determines essentially the relative time intervals that the gas spends in the various distributions of state. 

IX) Of all the various distributions of state Z which correspond to a certain "visible state Sn, there is a special one, Zb, such that a very much larger region in T-space belongs to this Z and to the Z s very near to it than to all other Z s belonging to Sn. 

At initial time tA this group of motions originates from all those phases which correspond to a given distribution of state Za, i.e., from that exact set to which statements (X) apply. It follows from (X) therefore that in the first time interval, i.e., from tA, to tA+At, the overwhelming majority of the motions under consideration will satisfy the Stosszahlansatz. 

Boltzmann One considers in T-space the shell of T-points which correspond to the given total energy Eo. The overwhelming majority of these phase points correspond closely to a Maxwell-Boltzmann distribution (Eq. 53 ) of the molecules of the gas model (cf. Section 13, I). Then from Eqs. (57 ), (60), etc., one calculates for this distribution of state the pressure and the other reactive forces, the kinetic energy per molecular degree of freedom, etc. 

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