The models mainly involve the following three parameters: the phonon mean free path (l), the characteristic size of the constriction (a), and the dominant phonon wavelength (λd).
Morrison [58] has shown that in the limits of κL > > 1 (κ inverse of Debye length, and L the characteristic length of the particle) the Smoluchowsky formula is applicable for particles irrespective of their morphologies.
The magnetic Reynolds number characterizes the importance of magnetic advection versus magnetic diffusion and is defined as Re m = vL/η, where v is the characteristic velocity, L the characteristic length (the thickness of the convective shell, D = L), and η the magnetic diffusivity.
Their study represented the Kurile Trench with a one-degree-of-freedom spring-slider system, and estimated (a−b)σeff, aσeff and L (L is the characteristic length (Eqs. (1)–(2)).
In serum, the method detection limit was 2 ng l-1, the characteristic mass was 0.22 (± 0.07) pg and the accuracy ranged from 95to100%0%.
In blood, the detection limit was 7 ng l-1, the characteristic mass was 0.20 (± 0.02) pg and the accuracy ranged from 99 to 101%.
where c e is the equilibrium concentration of the metal ion (mg/dm3), q e is the adsorption capacity at equilibrium (mg/g), and the constants q 0 (mg/g) and K L are the characteristics of the Langmuir equation (dm3/mg) which can be determined from its linearized form (plots of c e /q e versus c e ).
To analyze the relative contribution of advection and diffusive transport we utilize a dimensionless number, the Péclet number (P), that represents the ratio between the contribution of advection and diffusion: (12) P = v L D Where v is the interstitial flow rate, D is the diffusion coefficient and L is the characteristic length scale.
On the other hand, macroscopic gravity-driven motion of landslides and debris flows evolves over a characteristic time scale (L/g)1/2, where g is the magnitude of gravitational acceleration and L is the characteristic length of the moving mass.
where L is the characteristic length of the stretching/shrinking surface.
where u c = g β Δ T L is the characteristic velocity of natural convection.
