Abbreviations [P.sub.i]: The pressure of inside the bubble, Pa [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]: The pressure of hydrogen inside the bubble, Pa [P.sub.o]: Ambient pressure, Pa [[gamma].sub.gl]: Gas-liquid surface tension, N x [m.sup.-1] R: Bubble radius, m [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]: The number of hydrogen molecules inside the bubble T: Ambient temperature, K k: Boltzmann's constant
, 1.038065 x [10.sup.-23] J x [K.sup.-1] [t.sub.n]: Nucleation time, s [t.sub.g]: Growth time, s.
where [rho] is the resistivity at temperature T(K), [E.sub.[mu]] is the conduction activation energy, R is the Boltzmann's constant
, and [[rho].sub.0] is the temperature-independent constant.
His explorations of ideas such as Boltzmann's constant
follows the notions of ancient to modern scientists and mathematicians, considering the meaning behind mathematics and its influence on physics, chemistry and astronomy.
Where [P.sub.t] is the transmitted signal power in watt, F is the noise figure in dB, K is the Boltzmann's constant
, T is the ambient temperature in [degrees]C, and [alpha] is the total attenuation coefficient in dB/km.
where [W.sub.M] is the effective barrier height, [k.sub.B] is Boltzmann's constant
([k.sub.B] = 86.13 [mu]e [VK.sup.1]), [[tau].sub.0] is the relaxation time, and T is the temperature.
Where, [k.sub.B] is the Boltzmann's constant
(1.38 x [10.sup.-23] [JK.sup.-1]), h the Planck constant (6.63 x [10.sup.-34] J s), and T the temperature (K).
Here h denotes Planck's constant, k Boltzmann's constant
, and [V.sub.a] atomic volume.
(Note the analogy with statistical mechanics where the exponential is--[E.sub.i]/kT where [E.sub.i] is the potential energy, and k is Boltzmann's constant