Non-linear behaviours in complex fluid dynamics via non-differentiability. Separation control of the solid components from heterogeneous mixtures

Solid components separation from heterogeneous mixtures through turbulence control

“…The present paper gives results extending those from [24,26], taking into account the convection, dissipation and dispersion effects that play an important role in the flow process of fluid-solid mixture. Two distinct approximations of motion of scale relativity in an arbitrary constant fractal dimension are considered: the dissipative approximation which implies the separation process of the solid components from heterogeneous mixtures through the "relevant dimensions" of the solid components and their positions in the fluid-solid mixture, and dispersive approximation which implies control of the separation process of solid components from heterogeneous mixtures through turbulence regimes of the fluid-solid mixtures.…”

“…This integration is, however, different from the procedures used in [24,26] on account the following facts:…”

“…Indeed, due to the fact that from Eq. (16) the turbulence is of a statistic nature (for details see [20,21,24,26]), we can evaluate it with the help of entropy and entropic current densities [10][11][12]45], in particular with the fractal entropy [57], S Q = ln N, and with the current densities associated to the fractal entropy, j Qξ = V ξ ln N and j Qη = V η ln N, respectively. In Fig.…”

“…This topic was systematically developed in [24][25][26] using the Scale Relativity Theory (SRT) [20,21]. According to SRT the motion along a streamline, followed by a jump from one streamline to another in a Euclidian space, is replaced by motions on continuous but nondifferentiable curves (fractal curves) in a fractal space [17][18][19][20][21][22][23]27].…”

Dynamics of Transient Plasmas Generated by ns Laser Ablation of Memory Shape Alloys

“…density, momentum, energy, etc. [8][9][10][11][12] and the processes which they define. The practicality of such methods can be accepted sequentially, on space-time domains for which the differentiability still respected.…”