New Theoretical Approach of the Physical Processes in Nanostructures

Agop, Maricel; Forna, Norin; Casian-Botez, I.; Bejenariu, Constantin

doi:10.1166/jctn.2008.2489

Cited by 29 publications

(38 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we divide by dτ and neglect the terms that contain differential factors, using the method from [5][6][7][8][9][10][11], we obtain:…”

Section: Consequences Of Non-differentiability On a Space-time Manifoldmentioning

confidence: 99%

“…In order to eliminate this contradiction, we will assume that the temporal coordinate of the fractal curve is also a fractal one. Thus, most elements of the non-relativistic approach of scale relativity theory with arbitrary constant fractal dimension, as described in [5][6][7][8][9][10][11], remain valid, but the time differential element dt is now replaced by the proper time differential element dτ . In this way, not only the space, but the entire space-time continuum is considered to be non-differentiable and, therefore, fractal.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Implications of Non-Differentiable Entropy on a Space-Time Manifold

Agop

Gavriluţ

Ştefan³

et al. 2015

Entropy

View full text Add to dashboard Cite

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-time manifold in the hydrodynamic version and its correspondence with motion variables (energy, momentum, etc.) are established. Moreover, for the same non-differentiability type, through a scale resolution dependence of a fundamental length and wave function independence with respect to the proper time, a non-differentiable Klein-Gordon-type equation in the wave function version is obtained. For a phase-amplitude functional dependence on the wave function, the non-differentiable spontaneous symmetry breaking mechanism implies pattern generation in the form of Cooper non-differentiable-type pairs, while its non-differentiable topology implies some fractal logic elements (fractal bit, fractal gates, etc.).

show abstract

“…If we divide by dτ and neglect the terms that contain differential factors, using the method from [5][6][7][8][9][10][11], we obtain:…”

Section: Consequences Of Non-differentiability On a Space-time Manifoldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Implications of Non-Differentiable Entropy on a Space-Time Manifold

Agop

Gavriluţ

Ştefan³

et al. 2015

Entropy

View full text Add to dashboard Cite

show abstract

“…the fractal space [23][24][25][26]. Once such a space admitted, the following consequences result: iv1) The dynamics of physical system are described through fractal functions that depend both on space-time coordinates and on the de Broglie scale resolution.…”

Section: Non-differentiability Of the Motion Curves In The Wd Non-relmentioning

confidence: 99%

Holographic-Type Gravitation via Non-Differentiability in Weyl-Dirac Theory

Pricop¹,

Răuţ²,

Borsos³

et al. 2013

JMP

View full text Add to dashboard Cite

In the Weyl-Dirac non-relativistic hydrodynamics approach, the non-linear interaction between sub-quantum level and particle gives non-differentiable properties to the space. Therefore, the movement trajectories are fractal curves, the dynamics are described by a complex speed field and the equation of motion is identified with the geodesics of a fractal space which corresponds to a Schrödinger non-linear equation. The real part of the complex speed field assures, through a quantification condition, the compatibility between the Weyl-Dirac non-elativistic hydrodynamic model and the wave mechanics. The mean value of the fractal speed potential, identifies with the Shanon informational energy, specifies, by a maximization principle, that the sub-quantum level "stores" and "transfers" the informational energy in the form of force. The wave-particle duality is achieved by means of cnoidal oscillations modes of the state density, the dominance of one of the characters, wave or particle, being put into correspondence with two flow regimes (non-quasi-autonomous and quasi-autonomous) of the Weyl-Dirac fluid. All these show a direct connection between the fractal structure of space and holographic principle.

show abstract

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Agop

Gavriluţ

Crumpei³

et al. 2014

Entropy

View full text Add to dashboard Cite

Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced.First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The last one gives a specific fractal potential, which generates uncertainty relations through non-differentiable entropy. Next, the correlation between informational non-differentiable entropy and informational non-differentiable energy implies specific uncertainty relations through a maximization principle of the informational non-differentiable entropy and for a constant value of the informational non-differentiable energy. Finally, for a harmonic oscillator, the constant value of the informational non-differentiable energy is equivalent to a quantification condition. Keywords:non-differentiable entropy; informational non-differentiable entropy; informational non-differentiable energy; uncertainty relations Entropy 2014, 16 6043

show abstract

New Theoretical Approach of the Physical Processes in Nanostructures

Cited by 29 publications

References 0 publications

Implications of Non-Differentiable Entropy on a Space-Time Manifold

Implications of Non-Differentiable Entropy on a Space-Time Manifold

Holographic-Type Gravitation via Non-Differentiability in Weyl-Dirac Theory

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

Contact Info

Product

Resources

About