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Basic sums as parameters characterizing

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Języki publikacji
EN
Abstrakty
EN
We discuss the method of distributions’ characterization of geometric objects on the plane. The method is based on the basic sums. These basic sums perform the same role in description of image as the n-point correlation functions. In this paper we present some applications of this theory.
Rocznik
Strony
85--96
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Institute of Computer Science, Pedagogical University, Kraków, Poland
Bibliografia
  • 1. Bergman D.J, Dunn K.J.: Bulk effective dielectric constant of a composite with periodic micro-geometry. Phys. Rev. Ser. B 45 (1992), 13262–13271.
  • 2. Berlyand L., Mityushev V.V.: Generalized Clausius-Mossotti formula for random composite with circular fibers. J. Stat. Phys. 102 (2001), 115–145.
  • 3. Berlyand L., Mityushev V.V.: Increase and decrease of the effective conductivity of two phase composites due to polydispersity. J. Stat. Phys. 118 (2005), 481–509.
  • 4. Czapla R.: Random sets of stadiums in square and collective behavior of bacteria. IEEE/ACM Transactions on Computational Biology and Bioinformatics (in print).
  • 5. Czapla R., Mityushev V.V.: A criterion of collective behavior of bacteria. Math. Biosci. Eng. 14 (2017), 277–287.
  • 6. Czapla R., Mityushev V.V., Nawalaniec W.: Effective conductivity of random twodimensional composites with circular nonoverlapping inclusions. Comput. Mater. Sci. 63 (2012), 118-126.
  • 7. Czapla R., Mityushev V.V., Nawalaniec W.: Simulation of representative volume elements for random 2D composites with circular nonoverlapping inclusions. Theor. Appl. Inform. 24 (2012), 227-242.
  • 8. Hurwitz A., Courant R.: Theory of Functions. Moscow, Nauka 1968.
  • 9. Mityushev V.V: Transport properties of doubly periodic arrays of circular cylinders and optimal design problems. Appl. Math. Optim. 44 (2001), 17– 31.
  • 10. Mityushev V.V: Representative cell in mechanics of composites and generalized Eisenstein-Rayleigh sums. Complex Var. Elliptic Equ. 51 (2006), 1033-1045.
  • 11. Mityushev V.V., Nawalaniec W.:, Basic sums and their random dynamic changes in description of microstructure of 2D composites. Comput. Mater. Sci. 97 (2015), 64–74.
  • 12. Nawalaniec W.: Algorithms for computing symbolic representations of basic esums and their application to composites. J. Symbolic Comput. 74 (2016), 328–345.
  • 13. Rylko N.: Representative volume element in 2D for disks and in 3D for balls. J. Mech. Mater. Struct. 9 (2014), 427-439.
  • 14. Sokolov A., Aranson I.S., Kessler J.O., Goldstein R.E.: Concentration dependence of the collective dynamics of swimming bacteria. Phys. Rev. Lett. 98, 158102 (2007), 1–4.
  • 15. Szczepkowski J., Malevich A.E., Mityushev V.V.: Macroscopic properties of similar arrays of cylinders. Quart. J. Appl. Math. Mech. 56 (2003), 617-628.
  • 16. Torquato S.: Random Hetrogeneous Materials: Microstructure and Macroscopic Properties. Spinger-Verlag, New York 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9ad7f42b-8429-41d8-b66e-c381988a3638
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