On the other hand, near the interface, application of voltage " v D " reduces the step in band edges and increases minority carrier densities by a Boltzmann factor exp ( " v D / V th " ) above the bulk values.
22.
This relationship is described by the Boltzmann factor, where " E " is activation energy in electronvolts or joules, " T " is absolute temperature in kelvins, and " k " is the Boltzmann constant in eV / K or J / K:
23.
It depends on the Boltzmann factors e ^ {-\ frac { m g h } { k T } } where m is the atomic ( or molecular ) mass, g is the gravitational acceleration, h is the height, k is Boltzmann's constant, and T is the temperature.
24.
Where \ beta \; = 1 / kT, k is Boltzmann's constant, T is the absolute temperature, " e " \ scriptstyle-\ beta E _ R is called the Boltzmann factor, and the summation is over all possible states R'of the many-particle system.
25.
Historically, this occurred because the original idea was to use Metropolis Hastings algorithm to compute averages on a system in contact with a heat bath where the weight is given by the Boltzmann factor, P ( \ boldsymbol { x } ) \ propto \ exp (-\ beta E ( \ boldsymbol { r } ) ).
26.
The motivation to use the non-extensive statistics from Tsallis [ 5 ] comes from the results obtained ` by Bediaga et al . [ 6 ] They showed that with the substitution of the Boltzmann factor in Hagedorn's theory by the q-exponential function, it was possible to recover good agreement between calculation and experiment, even at energies as high as those achieved at the LHC, with q > 1.
27.
The density of each gas is proportional to this Boltzmann factor ( with the specific atomic mass ), so you can calculate the height at which the ratio of the Boltzmann factors e ^ { \ frac { ( m _ { Xe }-m _ { He } ) g h } { k T } } becomes 2 ( about 1385 m ) . talk ) 15 : 13, 13 December 2011 ( UTC)
28.
The density of each gas is proportional to this Boltzmann factor ( with the specific atomic mass ), so you can calculate the height at which the ratio of the Boltzmann factors e ^ { \ frac { ( m _ { Xe }-m _ { He } ) g h } { k T } } becomes 2 ( about 1385 m ) . talk ) 15 : 13, 13 December 2011 ( UTC)
29.
So, you can express this dimensionless number as the volume divided by an effective volume VQ . Obviously the physical interpreation of VQ is the volume at which one particle would have effectively just one state available when taking into account the penalty in the form the Boltzmann factor that disfavours states with energy much higher than k T, so 1 / Vq is the effective density of available quantum states per particle . talk ) 12 : 36, 22 May 2013 ( UTC)
30.
In statistical mechanics applications prior to the introduction of the Metropolis algorithm, the method consisted of generating a large number of random configurations of the system, computing the properties of interest ( such as energy or density ) for each configuration, and then producing a weighted average where the weight of each configuration is its Boltzmann factor, exp ( " " E " / " kT " ), where " E " is the energy, " T " is the temperature, and " k " is Boltzmann's constant.
