Skip to main content
SpringerLink
Log in

Classical geometry of matter in the state of fractional dimension

  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

Complementing Euclidean geometry by the notion of a point that is able to disappear and appear again makes it possible to describe the space of matter in the state of fractional dimension in the classical context and, thus, opens up new prospects in the development of chemistry as a scientific field inseparable from the principle of atomism. In particular, taking into account the nonarithmetic character of any transformation, it becomes possible to distinctly define the interests of chemistry in the era of nanotechnologies owing to the physically clear interpretation of various notions such as matter, a body, and the boundary between the body and matter that is at the stage of becoming. The subject of these interests can be actions that can affect not only the divisibility of initial reactants and reaction products but also the number system of a chemical process in combination with selection rules on the way from states of fractional dimension to states of integer dimension.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Klyucharev, V. and Arkhangel’skii, I., Materials Science in a Classical University, Vyssh. Obraz. Ross., 2002, no. 2, pp. 43–47.

  2. Gladyshev, G.P., Termodinamika i makrokinetika prirodnykh ierarkhicheskikh protsessov (Thermodynamics and Macrokinetics of Hierarchical Processes in Nature), Moscow: Nauka, 1988 [in Russian].

    Google Scholar 

  3. Whitesides, G.M. and Grzybowski, B., Self-Assembly at All Scales, Science (Washington), 2002, vol. 295, no. 5564, pp. 2418–2421.

    Article  ADS  CAS  Google Scholar 

  4. Lebesgue, H., Sur la Mesure des grandeurs, Enseign. Math., 1932, vol. 31, pp. 173–206.

    Google Scholar 

  5. Lebesgue, H., La Mesure des grandeurs, Paris: Librairie Albert Blanchard, 1975. Translated under the title Ob izmerenii velichin, Moscow: Komkniga, 2005 [in French and in Russian].

    MATH  Google Scholar 

  6. Klyucharev, V.V., Fractal Images of Chemical Transformations, Dokl. Akad. Nauk, 2003, vol. 390, no. 3, pp. 355–358 [Dokl. Chem. (Engl. transl.), 2003, vol. 390, nos. 1–3, pp. 127–130].

    MATH  Google Scholar 

  7. Klyucharev, V.V., Dimensions of Becoming of Self-Propagating Chemical Processes, Dokl. Akad. Nauk, 2006, vol. 410, no. 3, pp. 347–353 [Dokl. Chem. (Engl. transl.), 2006, vol. 410, part 1, pp. 158–164].

    Google Scholar 

  8. Shenker, O.R., Fractal Geometry is Not the Geometry of Nature, Stud. Hist. Philos. Sci. A, 1994, vol. 25, no. 6, pp. 967–981.

    Article  MathSciNet  Google Scholar 

  9. Danilov, Yu.A., Lektsii po nelineinoi dinamike: Elementarnoe vvedenie (Lectures on Nonlinear Dynamics: An Elementary Introduction), Moscow: Postmarket, 2001 [in Russian].

    Google Scholar 

  10. Mandelbrot, B.B., The Fractal Geometry of Nature, New York: Freeman, 1983.

    Google Scholar 

  11. Lauterborn, W., Acoustical Turbulence, Lect. Notes Phys., 1985, vol. 235, pp. 188–198.

    Article  ADS  MathSciNet  Google Scholar 

  12. Kleiser, T. and Bocek, M., The Fractal Nature of Slip in Crystals, Z. Metallkd., 1986, vol. 77, no. 9, pp. 582–587.

    CAS  Google Scholar 

  13. Batunin, A.V., Fractal Analysis and Feigenbaum Universality in Hadron Physics, Usp. Fiz. Nauk, 1995, vol. 165, no. 6, pp. 645–660 [Phys.—Usp. (Engl. transl.), 1995, vol. 38, no. 6, pp. 609–622].

    CAS  Google Scholar 

  14. Polikarpov, M.I., Fractals, Topological Defects, and Confinement in Lattice Gauge Theories, Usp. Fiz. Nauk, 1995, vol. 165, no. 6, pp. 627–644 [Phys.—Usp. (Engl. transl.), 1995, vol. 38, no. 6, pp. 591–607].

    Article  Google Scholar 

  15. Jan, N., Stauffer, D., and Aharony, A., An Infinite Number of Effectively Infinite Clusters in Critical Percolation, J. Stat. Phys., 1998, vol. 92, nos. 1–2, pp. 325–328.

    Article  MATH  Google Scholar 

  16. Timashev, S.F., A New Dialog with Nature: A Law of Evolution of Natural Systems, Time Arrow, and Copenhagen Interpretation of Quantum Mechanics, Zh. Fiz. Khim., 2000, vol. 74, no. 1, pp. 16–30 [Russ. J. Phys. Chem. (Engl. transl.), 2000, vol. 74, no. 1, pp. 11–23].

    CAS  MathSciNet  Google Scholar 

  17. Frigg, R., Self-Organised Criticality-What It Is and What It Isn’t, Stud. Hist. Philos. Sci. A, 2003, vol. 34, no. 3, pp. 613–632.

    Article  Google Scholar 

  18. Lorenzen, S., Können Fraktale dem Naturverständnis? in Fraktale im Unterricht: Zur didaktischen Bedeutung des Fraktalbegriffs, Komorek, M., Duit, R., and Schenegelberger, M., Eds., Kiel: IPN, 1998, pp. 295–308.

    Google Scholar 

  19. Sokolov, I.M., Dimensionalities and Other Geometric Critical Exponents in Percolation Theory, Usp. Fiz. Nauk, 1986, vol. 150, no. 2, pp. 221–255 [Sov. Phys.—Usp. (Engl. transl.), 1986, vol. 29, no. 10, pp. 924–945].

    CAS  Google Scholar 

  20. Morozov, A.D., Vvedenie v teoriyu fraktalov (Introduction to the Fractal Theory), Nizhni Novgorod: Nizhni Novgorod University, 1999 [in Russian].

    Google Scholar 

  21. J. Feder, Fractals, New York: Plenum, 1988. Translated under the title Fraktaly, Moscow: Mir, 1991.

    MATH  Google Scholar 

  22. Suzuki, M., Phase Transition and Fractals, Prog. Theor. Phys., 1983, vol. 69, no. 1, pp. 65–76.

    Article  MATH  ADS  Google Scholar 

  23. Pfeifer, P. and Avnir, D., Chemistry in Non-Integer Dimensions between Two and Three: I. Fractal Theory of Heterogeneous Surfaces, J. Chem. Phys., 1983, vol. 79, no. 7, pp. 3558–3565.

    Article  ADS  CAS  MathSciNet  Google Scholar 

  24. Pfeifer, P. and Avnir, D., Chemistry in Non-Integer Dimensions Between Two and Three: II. Fractal Surfaces of Adsorbents, J. Chem. Phys., 1983, vol. 79, no. 7, pp. 3566–3571.

    Article  ADS  MathSciNet  Google Scholar 

  25. Lehn, J.M., Toward Complex Matter: Supramolecular Chemistry and Self-Organization, Proc. Nat. Acad. Sci. USA, 2002, vol. 99, no. 8, pp. 4763–4768.

    Article  PubMed  ADS  CAS  Google Scholar 

  26. Lehn, J.M., Toward Self-Organization and Complex Matter, Science (Washington), 2002, vol. 295, no. 5564, pp. 2400–2403.

    Article  ADS  CAS  Google Scholar 

  27. Lehn, J.M., Supramolecular Polymer Chemistry: Scope and Perspectives, Polym. Int., 2002, vol. 51, no. 10, pp. 825–839.

    Article  CAS  Google Scholar 

  28. Lehn, J.M., Supramolecular Chemistry: From Molecular Information towards Self-Organization and Complex Matter, Rep. Prog. Phys., 2004, vol. 67, no. 3, pp. 249–265.

    Article  ADS  Google Scholar 

  29. Lehn, J.M., Dynamers: Dynamic Molecular and Supramolecular Polymers, Prog. Polym. Sci., 2005, vol. 30, nos. 8–9, pp. 814–831.

    Article  CAS  Google Scholar 

  30. Lehn, J.M., From Supramolecular Chemistry towards Constitutional Dynamic Chemistry and Adaptive Chemistry, Chem. Soc. Rev., 2007, vol. 36, no. 2, pp. 151–160.

    Article  PubMed  CAS  MathSciNet  Google Scholar 

  31. Mendeleev, D.I., Issledovanie vodnykh rastvorov po udel’nomu vesu (Investigation of the Specific Weight of Aqueous Solutions), St. Petersburg: V. Demakov, 1887 [in Russian].

    Google Scholar 

  32. Smirnov, B.M., A Tangle of Fractal Fibers as a New State of Matter, Usp. Fiz. Nauk, 1991, vol. 161, no. 8, pp. 141–153. [Sov. Phys.—Usp. (Engl. transl.), 1991, vol. 34, no. 8, pp. 711–716].

    CAS  Google Scholar 

  33. Spehar, B., Clifford, C.W.G., Newell, B.R., and Taylor, R.T., Universal Aesthetic of Fractals, Comput. Graphics, 2003, vol. 27, no. 5, pp. 813–820.

    Article  Google Scholar 

  34. Daniell, P.J., The Theory of Flame Motion, Proc. R. Soc. London, Ser. A, 1930, vol. 126, no. 208, pp. 393–405.

    Article  ADS  CAS  Google Scholar 

  35. Knyazeva, A.G. and Sorokova, S.N., Steady Regimes of Conversion in a Viscoelastic Medium, Fiz. Goreniya Vzryva, 2006, vol. 42, no. 5, pp. 63–75 [Combust., Explos. Shock Waves (Engl. transl.), 2006, vol. 42, no. 5, pp. 549–558].

    CAS  Google Scholar 

  36. Amzallag, G.N., Critical Periods as Fundamental Events in Life, Theory Biosci., 2004, vol. 123, no. 1, pp. 17–32.

    Article  PubMed  Google Scholar 

  37. De Donder, T. and van Rysselberghe, P., Thermodynamic Theory of Affinity: A Book of Principles, Stanford: Stanford University Press, 1936.

    Google Scholar 

  38. De Donder, T. and van Rysselberghe, P., Thermodynamic Theory of Affinity: A Book of Principles, Stanford: Stanford University Press, 1936. Translated under the title Termodinamicheskaya teoriya srodstva. Kniga printsipov, Izhevsk: NITs “Regulyarnaya i Khaoticheskaya Dinamika,” 2002.

    Google Scholar 

  39. Zel’dovich, Ya.B. and Frank-Kamenetskii, D.A., A Theory of Thermal Propagation of Flame, Zh. Fiz. Khim., 1938, vol. 12, no. 1, pp. 100–105 [Acta Physicochim. URSS (Engl. transl.), 1938, vol. 9, pp. 341–350].

    Google Scholar 

  40. Novozhilov, B.V., Combustion of Energetic Materials in an Acoustic Field (Review), Fiz. Goreniya Vzryva, 2005, vol. 41, no. 6, pp. 116–136 [Combust., Explos. Shock Waves (Engl. transl.), 2005, vol. 41, no. 6, pp. 709–726].

    CAS  MathSciNet  Google Scholar 

  41. Merzhanov, A.G., Nonequilibrium Theory of Flame Propagation, Prog. Astronaut. Aeronaut., 1997, vol. 173, pp. 37–59.

    CAS  Google Scholar 

  42. Rogachev, A.S., Macrokinetics of Gasless Combustion: Old Problems and New Approaches, Int. J. Self-Propag. High-Temp. Synth., 1997, vol. 6, no. 2, pp. 215–242.

    CAS  Google Scholar 

  43. Gardiner, W.C., Introduction to Combustion Modeling, in Combustion Chemistry, Gardiner, W.C., Ed., New York: Springer, 1984, Chapter I. Translated under the title Khimiya goreniya, Moscow: Mir, 1988.

    Google Scholar 

  44. Merzhanov, A.G., The Chemistry of Self-Propagating High-Temperature Synthesis, J. Mater. Chem., 2004, vol. 14, no. 12, pp. 1779–1786.

    Article  CAS  Google Scholar 

  45. Schummer, J., The Notion of Nature in Chemistry, Stud. Hist. Philos. Sci. A, 2003, vol. 34, no. 4, pp. 705–736.

    Article  Google Scholar 

  46. The New Encyclopaedia Britannica: Macropaedia, Chicago: Encyclopaedia Britannica, 1993, vol. 25, pp. 845–850.

  47. Lisichkin, G.V. and Leenson, I.A., Natural Science Instead of Physics, Chemistry, and Biology, Khim. Shk., 2007, no. 6, pp. 2–5.

  48. Allcock, D., Carlson, J.A., and Toledo, D., Non-Arithmetic Uniformization of Some Real Moduli Spaces, Geometriae Dedicata, 2006, vol. 122, no. 1, pp. 159–169.

    Article  MathSciNet  Google Scholar 

  49. Lehn, J.-M., Supramolecular Chemistry Concepts and Perspectives, New York: Wiley, 1995. Translated under the title Supramolekulyarnaya khimiya: Kontseptsii i perspektivy, Novosibirsk: Nauka, 1998.

    Google Scholar 

  50. Giuseppone, N. and Lehn, J.M., Electric-Field Modulation of Component Exchange in Constitutional Dynamic Liquid Crystals, Angew. Chem., 2006, vol. 45, no. 28, pp. 4619–4624.

    Article  CAS  Google Scholar 

  51. Klyucharev, V.V., The Substance of Fractotechnology, in Book of Abstracts of Papers of the International Conference “HighMatTech-2007,” Kiev, Ukraine, 2007, Skorokhod, V.V., Ed., Kiev: Akademperiodika, 2007, p. 79.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Problems of Chemical Physics, Russian Academy of Sciences, pr. Akademika Semenova 1, Chernogolovka, Moscow oblast, 142432, Russia

    V. V. Klyucharev

Authors
  1. V. V. Klyucharev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Klyucharev.

Additional information

Original Russian Text © V.V. Klyucharev, 2008, published in Fizika i Khimiya Stekla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klyucharev, V.V. Classical geometry of matter in the state of fractional dimension. Glass Phys Chem 34, 660–665 (2008). https://doi.org/10.1134/S1087659608060023

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1087659608060023

Keywords

Search

Navigation