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1

Fracton mediated superconductivity in the "net fractal" systems. Preliminaries and an overview of other fracton based models

Bąk Z

Materials Science Poland

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2008

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Vol. 26, No. 4

913--919

EN

Assuming that the force constants scale as σ(λx) = λ –α σ(x), we construct the model of elastic (linear) excitations on a fractal (fractons). We show that the fractons on a specific class of fractals, “net fractals”, can be assumed to be log-scale phonons. Further, we discuss the model of fracton mediated superconductivity in the “net fractal” systems). We show that with the use of logarithmic coordinates, the fracton mediated superconductivity can be described within a model which is reminiscent of the conventional BCS formulation.

2

Fracton oscillations in the net fractals

Bąk Z.

Materials Science Poland

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2007

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Vol. 25, No. 2

491--496

EN

Institute of Physics, Jan Długosz University of Częstochowa, al. Armii Krajowej 13/15, 42-201 Częstochowa, Poland Assuming that the force constants scale as d(Ax)=A-ed(x), we construct the model of elastic (linear) excitations on a fractal (fractons). We show that the fractons, a specific class of fractals, "net fractals", can be assumed as the log-scale phonons. Further, we discuss propagation of elastic medium perturbation in terms of fractional dynamics. Within this approach we find two different modes of vibrations, both expressed with the help of generalized Mittag-Leffler functions.

3

Classification of overlayer precipitates by novel hierarchical systems-superfractals

Bąk Z.

Prace Naukowe. Chemia i Ochrona Środowiska / Akademia im. Jana Długosza w Częstochowie

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2005

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Vol. 10

25--31

EN

The formalism introduced allows a new insight into the symmetry hidden in the mathematical formulation of fractals. We prove that application of the logarithmic scales uncovers hidden relation between fractals and crystals and prove that this symmetry can be classified according to symmetry groups of conventional crystallography. The latter result allows us to introduce the concept of superfractals, which generalizes the idea of conventional fractals. We show that idea of superfractals offers a new tool for characterization of surface precipitates.

4

Critical temperature in layered superconductors

Bąk Z.

Prace Naukowe. Chemia / Wyższa Szkoła Pedagogiczna w Częstochowie

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2003

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Vol. 8

115--119

EN

We consider Bose-Einstein condensation of preexisting Cooper pairs which are confined within quasi-2D laminar structure. We show that the spectral dimensionality ɑ of such systems should be described within fractional-dimensional scheme. From detailed calculations results that for ɑ > 3 results that one would expect enhancement of critical temperature up to the limit set by the Cooper pair binding energy. We show that in the laterally modulated systems there can arise ɑ > 3 case while for the optimally doped YBCO system there is experimental evidence that ɑ =4.

5

EPOGRAN - nowe kruszywo dla budownictwa

Jarema-Suchorowska S., Śliwińska-Serafin M., Bąk Z.

Energetyka

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2002

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nr 10-11

801-804

PL

Przedstawiono prace nad technologią wytwarzania kruszyw granulowanych z popiołu i żużla z Elektrowni Opole. W wyniku badań wyłowiono składy recepturowe oraz opracowano sposób wytwarzania granulatów spełniających wymagania kruszyw do betonów lekkich. Z partii badawczych kruszyw wytworzono betony klasy LB 30, odmiany 1,8 i 2,0, o nasiąkliwości od 9,7 do 11,3%, pełnej mrozoodporności co najmniej F 75, niewielkim skurczu od 0,36 do 0,56 mm/m.

EN

Presented are works concerning a production technology of granulated aggregates made of fly ashes and slag from the Opole Power Station. As a result of the investigations the were prepared recipe compositions and was worked out a production way of granulates fulfilling reguirements of the aggregates for concrete of LB 38 class (variety 1.8 and 2.8) with the absorbability from 9.7 to 11.3 %, full frost resistance at least F 75 and small shrinkage from 0.36 to 0.56 mm/m.

6

Influence of the interface roughness on the interlayer coupling in magnetic superlattices

Bąk Z.

Prace Naukowe. Chemia / Wyższa Szkoła Pedagogiczna w Częstochowie

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2001

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Vol. 5

109--113

EN

The interface roughness disturbs the planar geometry and the restraint conditions imposed (by interface potentials) on the motion of the mobile charge carriers create deviation from integral (spectral) dimensionality. In our contribution we calculate the interlayer coupling that accounts for the fractional dimensionality and show that effect interface roughness on the interlayer coupling can be accounted for by an exchange-like term which exhibits π/2 phase shift with respect to the conventional interlayer coupling derived for ideally fiat interfaces.

7

Interlayer coupling in magnetic superlattices with self-similar interfaces

Bąk Z., Gruhn W., Jaroszewicz R.

Electron Technology

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2000

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Vol. 33, No. 3

427-429

EN

In the metallic superlattices interface roughness and restraint conditions imposed on the motion of free electrons may result in nonintegral dimensionality of the system. In our contribution we will derive formulae for the interlayer coupling in a superlattices with self-similar interfaces, assuming, that the spectral dimension of electron gas within the metallic spacers is integral.

8

Vibrational states in a system of non-integral dimension

Gruhn W., Bąk Z., Jaroszewicz R.

Electron Technology

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1998

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Vol. 31, No. 3/4

369-372

EN

We give theoretical description of vibrational of vibronic excitations in the elastic system which exhibits fractional dimension. Using the fractional calculus formalism, we find eigenfunctons and eigenvalues of elementary vibronic excitation in a elastic system of non-integral dimension. Comparison with the prperties of the conventional integer dimension systems are well as applications in a superlattices in a superlattices are widely discussed.

9

RKKY interaction in the magnetic system of half-integer dimension

Bąk Z., Jaroszewicz R., Gruhn W.

Electron Technology

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1998

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Vol. 31, No. 3/4

381-383

EN

Experimental results shown that some metallic superlatices and overlayers exhabit dimensional cross-over behave as system of fractional dimension, when the layer thickness is increased. We derive formulae for thr RKKY-reminiscent interaction between localised magnetic moments in the metalic system of fractional dimension.

10

Magnetic interlayer coupling in the position mass dependet system

Jaroszewicz R., Bąk Z.

Electron Technology

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1998

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Vol. 31, No. 3/4

384-387

EN

The magnetic interlayer interaction in the magnetic superlattices for the case of variable effective mass and imperfect interface is considered. We calculate the influence of the effective mass on the oscillation period. Moreover, we have derived formulae for the coupling constant in the case when the effective potential within nonmagnetic spacer is position dependent.