Quasi-Fractals: New Method of Description of a Structure of Disordered Media

Nigmatullin, Raoul R.; Alekhin, A. P.

doi:10.3182/20060719-3-pt-4902.00045

Cited by 3 publications

(2 citation statements)

References 3 publications

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“…while value of the radius R increases from zero to L x /2 with the step R 0 = 0.5 σ that is the radius of a particle. Here, f is the fractal parameter, which can take non-integer values within the range from 1 (for one-dimensional, linear structure) to 3 (for three-dimensional structure); whereas for the two-dimensional clusters on has f = 2 [40]. Thus, the morphology of the crystalline nucleus can be evaluated quantitatively from the found correspondence between log[N] and log[R/R 0 ].…”

Section: Estimation Of Nucleation and Morphological Characteristicsmentioning

confidence: 99%

Structure and morphology of crystalline nuclei arising in a crystallizing liquid metallic film

2019

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Control of the crystallization process at the microscopic level makes it possible to generate the nanocrystalline samples with the desired structural and morphological properties, that is of great importance for modern industry. In the present work, we study the influence of supercooling on the structure and morphology of the crystalline nuclei arising and growing within a liquid metallic film. The cluster analysis allows us to compute the diffraction patterns and to evaluate the morphological characteristics (the linear sizes of the homogeneous part and the thickness of the surface layer) of the crystalline nuclei emergent in the system at different levels of supercooling. We find that the liquid metallic film at the temperatures corresponded to low supercooling levels crystallizes into a monocrystal, whereas a polycrystalline structure forms at deep supercooling levels. We find that the temperature dependence of critical size of the crystalline nuclei contains two distinguishable regimes with the crossover temperature T/T g ≈ 1.15 (T g is the glass transition temperature), which appears due to the specific geometry of the system.

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Section: Estimation Of Nucleation and Morphological Characteristicsmentioning

confidence: 99%

Structure and morphology of crystalline nuclei arising in a crystallizing liquid metallic film

2019

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“…If the impedance is under an infinite diffusion layer, the Warburg impedance is given by: R where N represents the number of boxes with size η(N) resulting from the z subdivisions of the original structure. This is not the only description for the fractal geometry, but it is enough for the identification of groups Z(jω) = (j ωC ) 0.5 (7) with similar geometries. Some of the classical fractals adopted in this work where R is the diffusion resistance.…”

Section: Introductionmentioning

confidence: 99%

Development of fractional order capacitors based on electrolyte processes

2008

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In recent years, significant research in the field of electrochemistry was developed. The per-formance of electrical devices, depending on the processes of the electrolytes, was described and the physical origin of each parameter was established. However, the influence of the irregularity of the elec-trodes was not a subject of study and only recently this problem became relevant in the viewpoint of fractional calculus. This paper describes an electrolytic process in the perspective of fractional order capacitors. In this line of thought, are developed several experiments for measuring the electrical impedance of the devices. The results are analyzed through the frequency response, revealing capacitances of fractional order that can constitute an alternative to the classical integer order elements. Fractional order electric circuits are used to model and study the performance of the electrolyte processes.

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Modeling of generation and propagation of cardiac action potential using fractional capacitance

Wardhan¹,

Singh²

2015

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Quasi-Fractals: New Method of Description of a Structure of Disordered Media

Cited by 3 publications

References 3 publications

Structure and morphology of crystalline nuclei arising in a crystallizing liquid metallic film

Structure and morphology of crystalline nuclei arising in a crystallizing liquid metallic film

Development of fractional order capacitors based on electrolyte processes

Modeling of generation and propagation of cardiac action potential using fractional capacitance

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