Dynamics in the boundary layer of a flat particle

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

“…Substituting (25) into (20) and separating the real and the imaginary parts, up to an arbitrary phase factor, which may be set to zero by a suitable choice of the phase of ψ, we obtain:…”

“…This topic was developed within scale relativity theory (SRT) [6,7] and non-standard scale relativity theory (NSSRT) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In this case, we assume that the movements of complex system entities take place on continuous, but non-differentiable, curves (fractal curves), so that all physical phenomena involved in the dynamics depend not only on space-time coordinates, but also on space-time scale resolution.…”

“…Moreover, the entities of the complex system may be reduced to and identified with their own trajectories, so that the complex system will behave as a special fluid lacking interaction (via their geodesics in a non-differentiable (fractal) space). We have called such fluid a "fractal fluid" [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Some Aspects Concerning the "Memorization Effect" in Complex Fluid

“…A great variety of materials are categorized as complex uids: colloidal uids, polymers (elastomers, thermoplastics and composites), biological uids (DNA, proteins, cells, dispersions of biopolymers and cells, human blood), foams, emulsions, gels, suspensions, micelar and liquid-crystal phases, molten materials. In this case the uids do not obey to the hydrodynamic laws [13].…”

“…Correspondingly, theoretical models of dynamics in complex uids can become sophisticated and ambiguous [13]. However, such situation can be standardized if we consider that complexities in interaction processes impose various time resolution scales while the evolution pattern leads to dierent freedom degrees [58].…”