Conductive and Convective Types Behaviors at Nano-Time Scales

Botez, Irinel Casian; Agop, M.; Nica, P.; Pãun, Viorel-Puiu; Munceleanu, G. V.

doi:10.1166/jctn.2010.1608

Cited by 26 publications

(34 citation statements)

References 9 publications

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“…Moreover, the real parts of physical quantities are differentiable and independent on scale resolution the imaginary parts are non-differentiable and dependent on the resolution scale; iv2) The scale resolution reflects a certain degree of non-differentiability of the movement curve; iv3) The movement operatoris identified with the "covariant derivative" , whilê d dt ; iv4)The use of a generalized Newton principle turns the movement Equation (7) into geodesics of a fractal space; iv5) Chaoticity, either by turbulence as in the non-relativistic hydrodynamics approach, either by stochasticization as in the generalized Schrödinger approach, is achieved through non-differentiability of a fractal space. Indeed, by substituting (8a,b) in (7) and using the method described in [27,28], it results:…”

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

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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.

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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

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“…The differential of the "fractal part" components ξ i (t, dt), i = 1, 3, satisfies the relation (the fractal equation) [22][23][24] …”

Section: Non-differentiability Consequences In Drugmentioning

confidence: 99%

“…We formulate the following stipulation [22][23][24]: the mean value of the fractal concentration field Q and its derivatives coincide with themselves and the differentials d ± X i and dt are independent. Therefore, the average of their products coincides with the product of the averages.…”

Section: Covariant Total Derivative In Drug Release Processmentioning

confidence: 99%

Drug Release Kinetics from Polymer Matrix through Fractal Approximation of Motion

Bācāiţā

Urîtu²,

Popa

et al. 2012

Smart Materials Research

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The present paper analyzes the process of drug release from polymer matrix. This process has been considered as fractal polymer process. Since complexity of physical processes is replaced by fractality, the paper studies the process through fractal approach. In drug dynamics, fractal "diffusion" equation can be obtained through fractal approximation of motion. All experimental release curves have been best demonstrated by Weibull relation (which was, in its turn, also demonstrated). Weibull parameters are related to the fractal dimension of drug release kinetics from a polymer matrix. Such a dimension can characterize and measure the complexity of the system. In the above-mentioned context, some experimental results of our researchers are presented and analyzed by comparing them with Peppas relation, a basic law in the description of drug release kinetics. Consequently, experimental data for Weibull relation are better correlated with certain resulting factors. At the same time, some conclusions regarding the phenomena involved in the process are considered as being based on the approach.

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“…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

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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

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Conductive and Convective Types Behaviors at Nano-Time Scales

Cited by 26 publications

References 9 publications

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

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

Drug Release Kinetics from Polymer Matrix through Fractal Approximation of Motion

Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems

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