Space Time Physics and Fractality

Dynamics Behaviors of a Laser Produced Plasma: Theoretical Approach

“…Non-differentiability implies the following [10][11][12][13][14][15][16][17]: 1) A continuous and non-differentiable curve (or almost nowhere differentiable) is explicitly scale dependent. Moreover, its length tends to infinity, when the scale interval tends to zero.…”

“…3) Although the local differential time invariance is broken, it can still be recovered through the complex operator [15][16][17]:…”

“…their geodesics), so that the complex system should behave as a special "fluid" lacking interaction via geodesics in a non-differentiable (fractal) space. The equation of geodesics (a generalization of Newton's first principle for motion of fractal curves) can be written in the form [15][16][17]:…”

“…3) The fractal potential (8) results from non-differentiability and should be considered as a kinetic term and not as a potential one. Moreover, the fractal potential (8) can generate a viscosity stress tensor type [15][16][17].…”

“…where fractal continuity equation of density energy  was added [15][16][17]. With non-dimensional vario ables, , t (12a)…”