Two-fluid hydrodynamic model for superfluids in fractal dimensions

Tayurskiı̆, D. A.; Lysogorskii, Yu. V.; Zvezdov, D Yu

doi:10.1088/1742-6596/150/3/032110

Cited by 4 publications

(7 citation statements)

References 10 publications

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“…Structures of nail bed and periungual epithelium have been considered for the patient data within eight groups of diseases (Figure 3c Figure 4, the values of fractal dimension for the affected and unaffected parts of the nail bed and periungual epithelium for different types of diseases are presented. One can see the existence of the general laws in the behavior of the fractal dimension D for groups of diseases: (1,6,8) and (2,4,5). The self-similarity coefficientÀ1 ≤ K ≤ 1 provides the geometrical evidence for the difference of tested object surface from the ideal fractal one in terms of color code.…”

Section: The Study Of Fractal Structure Of the Image Of The Nail Bed mentioning

confidence: 98%

“…For example, the hydrodynamics of superfluid helium in a highly disordered porous media or nanoporous media with fractal dimension gives an important information about dynamics of a Bose-Einstein condensate in a disordered potential with a complex fractal geometry. Taking into account nonadditive thermodynamics methods, it is possible to develop the models for small particle numbers or strongly correlated systems [1][2][3].…”

Section: Dynamic Chaos and Fractalsmentioning

confidence: 99%

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The Fractal Analysis of the Images and Signals in Medical Diagnostics

Albertovich¹,

Aleksandrovna²

2017

Fractal Analysis - Applications in Health Sciences and Social Sciences

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In the present chapter, we summarize our results concerning fractal analysis of some medical data. The aim of this study is to identify the inherent human body "chaotic" dynamics and insufficient disclosure of the physical essence of the processes observed, depending on the extent of developing a pathology that is characterized by a decrease or increase in the degree of complexity and as a consequence-randomness, for which, in some cases, hidden fractal. The proposed approach based on identifying the presence of the properties of self-similarity can be useful in preliminary clinical trials for the diagnosis of cancerous epithelial diseases, blood, and liver in the initial stage, the analysis of digital images, the structure of correlations biomedical parameters, as well as in the study of pathologies of the central nervous system-the neurological, neurodegenerative disorders, psychiatric disorders, and may be the basis for the development of the interface "brain-computer", on the basis of electroencephalography and magnetoencephalography. Additional measures are proposed to study the presence of self-similar properties in the form of self-similarity and magnitude SRGB ratio (area of a triangle in the coordinate system of the properties).

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Section: The Study Of Fractal Structure Of the Image Of The Nail Bed mentioning

confidence: 98%

Section: Dynamic Chaos and Fractalsmentioning

confidence: 99%

The Fractal Analysis of the Images and Signals in Medical Diagnostics

Albertovich¹,

Aleksandrovna²

2017

Fractal Analysis - Applications in Health Sciences and Social Sciences

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“…So one has to apply a new physics to describe such systems with taking into account their complex nature. For example, last two years the attempts to develop the fractionalized two-fluid hydrodynamics for nanoporous media with fractal dimensions have been made [7,8].…”

Section: Introductionmentioning

confidence: 99%

Superfluid hydrodynamic in fractal dimension space

Tayurskiı̆¹,

Lysogorskiy²

2012

J. Phys.: Conf. Ser.

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The complex behavior of liquid 4 He and liquid 3 He in nanoporous media is determined by influence of randomly distributed geometrical confinement as well as by significant contribution from the atoms near walls. In the present paper fractional Schrodinger equation has been used for deriving two-fluid hydrodynamical equations for describing the motion of superfluid helium in the fractal dimension space. Nonlinear equations for oscillations of pressure and temperature are obtained and coupling of pressure and temperature oscillations is observed. Moreover coupling should disappear at very low temperatures which provide an experimental test for this theory.

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“…So one has to apply new physics to describe such systems with taking into account their complex nature. For example, last two years the attempts to develop the fractionalized two-fluid hydrodynamics for nanoporous media with fractal dimensions have been made [9,10]. The actuality of such new hydrodynamics becomes very clear because of numerous studies of quantum liquids inside nanoporous media [11,12] as well as because of last developments in chemical synthesis of aerogels with different network of strands (from fibrous to globular one [13]).…”

mentioning

confidence: 99%

“…The actuality of such new hydrodynamics becomes very clear because of numerous studies of quantum liquids inside nanoporous media [11,12] as well as because of last developments in chemical synthesis of aerogels with different network of strands (from fibrous to globular one [13]). One of the interesting obtained results is that density waves (the first sound) and temperature waves (the second sound) become strongly coupled even in the absence of viscosity, so it is purely geometric effect of fractal space of nanopores [9,10].In this paper we will review the procedure, results and discuss the issues for this approach. …”

mentioning

confidence: 99%

Quantum fluids in nanoporous media—Effects of the confinement and fractal geometry

Tayurskiı̆

Lysogorskiy

2011

Chin. Sci. Bull.

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The complex behavior of such quantum fluids like liquid 4 He and liquid 3 He in nanoporous media is determined by spatial quantization because of geometrical confinement as well as by significant contribution from the surface atoms. In the present report we will review the procedure, results and discuss the issues for fractionalized nonextensive hydrodynamical approach to describe the properties of quantum fluids inside nanopores and propose consideration of strong correlated quantum liquid by means of fractionalized Schrödinger equation. The zero-point energy of atoms of two stable isotopes of helium -4 He and 3 He -is high enough to prevent their solidification even at extremely low temperatures without application of external pressure. So they belong to the class of quantum fluids with strong correlations between atoms but their behavior is quite different at low temperatures. The first one represents a Bose-system and shows superfluid transition at 2.17 K while atoms of 3 He are governed by Fermi-statistics and superfluid transition can be observed only at much lower temperatures (about 1 mK) when the pairing of two atoms occurs. But even at liquid helium temperatures (1.5-4.2 K) the effects of quantum statistics for 3 He atoms become pronounceable especially in nanoscale confinement (nanoporous media, thin adsorbed layers on solid substrates) [1][2][3] and in the presence of nanoscale disorder induced for example by silica aerogel strands [4]. In recent years the problem of correct description of quantum fluids in the confined geometry at nanoscale length has emerged [5][6][7][8]. It has been recognized that the quantum fluids at these circumstances can be considered as a new state of quantum matter due to close values between characteristic lengths for these quantum liquids and the size of geometrical confinement and significant contri- *Corresponding author (email: dtayursk@gmail.com) bution from the surface atoms. So one has to apply new physics to describe such systems with taking into account their complex nature. For example, last two years the attempts to develop the fractionalized two-fluid hydrodynamics for nanoporous media with fractal dimensions have been made [9,10]. The actuality of such new hydrodynamics becomes very clear because of numerous studies of quantum liquids inside nanoporous media [11,12] as well as because of last developments in chemical synthesis of aerogels with different network of strands (from fibrous to globular one [13]). One of the interesting obtained results is that density waves (the first sound) and temperature waves (the second sound) become strongly coupled even in the absence of viscosity, so it is purely geometric effect of fractal space of nanopores [9,10]. In this paper we will review the procedure, results and discuss the issues for this approach. Theoretical models for bulk superfluid helium-4There are several approaches to describe the behavior of bulk superfluid helium-4. For example, two-fluid model [14,15],

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Two-fluid hydrodynamic model for superfluids in fractal dimensions

Cited by 4 publications

References 10 publications

The Fractal Analysis of the Images and Signals in Medical Diagnostics

The Fractal Analysis of the Images and Signals in Medical Diagnostics

Superfluid hydrodynamic in fractal dimension space

Quantum fluids in nanoporous media—Effects of the confinement and fractal geometry

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