The Mathematical Principles of Scale Relativity Physics

2019 ◽  
Author(s):  
Nicolae Mazilu ◽  
Maricel Agop ◽  
Ioan Mercheş
Keyword(s):  
Scale Relativity

scholarly journals Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 444
Author(s):  
Nicolae Dan Tesloianu ◽  
Lucian Dobreci ◽  
Vlad Ghizdovat ◽  
Andrei Zala ◽  
Adrian Valentin Cotirlet ◽  
...  
Keyword(s):  
Stochastic Processes ◽  
Standard Form ◽  
Momentum Conservation ◽  
Relativity Theory ◽  
Horizontal Pipe ◽  
Scale Transition ◽  
Theory Of Motion ◽  
Multifractal Theory ◽  
Scale Relativity ◽  
Specific Momentum

By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale’s theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable–non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the “stopping effect” associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal “pipe” with circular symmetry. Our model has been validated based on experimental clinical data.

scholarly journals The Pauli equation in scale relativity

2006 ◽  
Vol 39 (40) ◽  
pp. 12565-12585 ◽  
Author(s):  
Marie-Noëlle Célérier ◽  
Laurent Nottale
Keyword(s):  
Pauli Equation ◽  
Scale Relativity

Scale Relativity

1997 ◽  
pp. 249-261 ◽  
Author(s):  
Laurent Nottale
Keyword(s):  
Scale Relativity

scholarly journals Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 226
Author(s):  
Maricel Agop ◽  
Mitică Craus
Keyword(s):  
Complex System ◽  
Fractal Theory ◽  
Invariant Function ◽  
Hydrodynamic Type ◽  
Simultaneous Action ◽  
Systems Dynamics ◽  
Invariant Functions ◽  
Scale Relativity ◽  
The One ◽  
Joint Invariant

In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the S L ( 2 R ) type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved.

scholarly journals Scale relativity and gauge invariance

2001 ◽  
Vol 12 (9) ◽  
pp. 1577-1583 ◽  
Author(s):  
Laurent Nottale
Keyword(s):  
Gauge Invariance ◽  
Scale Relativity
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