Atomic strings and fabric of spacetime

С.Ю. Еременко

Atomic strings and fabric of spacetime

research article UDC 517.95; 518:517; 537.874; 530.1; 539.120.4:5 Pages: 45-61

¹ д.т.н., профессор, директор Soliton Scientific Pty Ltd (Сидней, Австралия)

Keywords: atomic string atomic function atomic soliton soliton non-Archimedean calculus spacetime quantum spacetime warp spacetime curvature cosmic strings atomic computer

Abstract

AStrings as the generalizations of atomic functions can be used to model flat and curve spacetime composed from quanta, describe gravity and metric of cosmic strings and be the candidates for new atomic solitons and strings as fundamental blocks of spacetime fabric and matter expanding the theory of atomic functions to new possible applications in lattice physics, soliton and string theory, quantum gravity, astronomy, multiverse, and dark matter.

How to cite

Еременко С.Ю. Атомарные струны и структура пространства-времени // Успехи современной радиоэлектроники. 2018. № 6. С. 45–61.

References

Rvachev V.L. From the Special Theory of Relativity to Mathematics without the Archimedean Axiom and Back. Radiotekn. Elektron. 1995. № 1–2. P. 58–68; № 6. P. 39–50.
Kravchenko V.F., Rvachev V.L., Shevchenko A.N., Sheiko T.I. The interpretation of Certain Phenomena Observed in Deep Space by Using Non-Archimedean Calculi. Radiotekn. Elektron. 1995. № 7. P. 1076–1094.
Eremenko S.Yu. Combined Non-Archimedean Calculi. Foreign Radioelectronics: Achievements of modern radioelectronics. 1996. № 8. P. 57–65. https://www.researchgate.net/publication/320616255.
Eremenko S.Yu., Kravchenko V.F., Rvachev V.L. Combined Non-Archimedean Calculi and New Models of Relativistic Mechanics. Foreign Radioelectronics: Achievements of modern radioelectronics. 1997. № 9. P. 26–38. https://www.researchgate.net/publication/ 320616269.
Kravchenko V.F., Rvachev V.A. Application of atomic functions for solutions of boundary value problems in mathematical physics. Foreign Radioelectronics: Achievements of modern radioelectronics. 1996. №8. P. 6–22.
Rvachev V.L., Rvachev V.A. About one Finite Function, DAN URSR. A (6). 1971. P. 705–707.
Rvachev V.L. Theory of R-functions and their applications. Kiev: Naukova Dumka. 1982.
Rvachev V.L., Rvachev V.A. Non-classical methods in the theory of approximations in boundary value problems. Kiev: Naukova Dumka. 1982.
Kravchenko V.F., Kravchenko O.V., Pustovoit V.I., Pavlikov V.V. Atomic Functions Theory: 45 Years Behind. DOI 10.1109/MSMW.2016.7538216. https://www.researchgate.net/publication/308749839.
Kravchenko V.F. Lectures on the theory of atomic functions and their applications. Moscow: Radiotechnika. 2003.
Kravchenko V.F., Rvachev V.L. Logic Algebra, atomic functions and wavelets in physical applications. Moscow: Fizmatlit. 2009.
Eremenko S.Yu. Natural Vibrations and Dynamics of Composite Materials and Constructions. Kiev: Naukova Dumka. 1992.
Eremenko S.Yu. Finite Element Methods in Mechanics of Deformable Bodies. Kharkov: Osnova. 1991. https://www.researchgate.net/publication/321171685.
Eremenko S.Yu., Rvachev V.L. A survey of variants of the structural finite-element method. Journal of Mathematical Sciences. 1998. V. 90. № 2. P. 1917–1922.
Filippov A.T. The Versatile Soliton. Modern Birkhauser Classics. 2000.
Braun O.M., Kivshar Yu.S. The Frenkel-Kontorova Model: Concepts, Methods, and Applications. Springer. 2004.
Novikov S.P., Manakov S.V., Pitaevskii L.P., Zakharov V.E. Theory of Solitons: The Inverse Scattering Method. Springer-Verlag. 1984.
Rvachev V.L., Avinash K. Quadratic redshift law and the non-Archimedean universe. Radio Physics and Radio Astronomy. 2001. V. 6. № 2. P. 534–536.
Greene B. The fabric of the cosmos: space, time and texture of reality. New York: Vintage Books. 2004.
Kaku M. Introduction to Superstring and M-Theory (2nd ed.). New York: Springer-Verlag. 1999.
Pasachoff J.M., Filippenko A. The Cosmos: Astronomy in the New Millennium. Cambridge: https://en.wikipedia.org/wiki/England Cambridge University Press. 2014.
Taylor E.F., Wheeler J.A. Spacetime Physics: Introduction to Special Relativity. New York: W. H. Freeman. 1992.
Hawking S., Mlodinov L. The Grand Design. New York: Bantam Books. 2010.
The Collected Papers of Albert Einstein. Princeton, New Jersey: Princeton University Press. 1989.
Veinik A.I. Thermodynamics of real processes. Minsk: Nauka i Technika. 1991.
Niedermann F, Schneider R. Radially stabilized inflating cosmic strings. Phys.Rev. D. 91 (6): 064010
Smit J. Introduction to Quantum Fields on a Lattice. Cambridge: Cambridge University Press. 2002.
Rothe H. Lattice Gauge Theories, An Introduction. World Scientific. 2005.
DeGrand T., DeTar C. Lattice Methods for Quantum Chromodynamics. World Scientific. 2006.
Gattringer C., Lang C.B. Quantum Chromodynamics on the Lattice. Springer. 2010.
Scheglov E.G., Arutynov P.A. Non-Archimedean Calculus in the Mathematical Modelling of Digital ICs. Russian Microelectronics. 2002. V. 31. № 6. P. 384–395.
Arutynov P.A. Non-Archimedean Calculi in Theoretical Metrology. Izm. Tekh. (Metrologia). 2001. № 2. P. 3–18.
Bale R., Grossman J.P., Margrave G., Lamoureux M.P. Multidimensional partitions of unity and Gaussian terrains. CREWES Research Report. V. 14. 2002. https://www.researchgate.net/publication/265182366.

Full text, PDF 350 ₽

[1] Rvachev V.L. From the Special Theory of Relativity to Mathematics without the Archimedean Axiom and Back. Radiotekn. Elektron. 1995. № 1–2. P. 58–68; № 6. P. 39–50.

[2] Kravchenko V.F., Rvachev V.L., Shevchenko A.N., Sheiko T.I. The interpretation of Certain Phenomena Observed in Deep Space by Using Non-Archimedean Calculi. Radiotekn. Elektron. 1995. № 7. P. 1076–1094.

[3] Eremenko S.Yu. Combined Non-Archimedean Calculi. Foreign Radioelectronics: Achievements of modern radioelectronics. 1996. № 8. P. 57–65. https://www.researchgate.net/publication/320616255.

[4] Eremenko S.Yu., Kravchenko V.F., Rvachev V.L. Combined Non-Archimedean Calculi and New Models of Relativistic Mechanics. Foreign Radioelectronics: Achievements of modern radioelectronics. 1997. № 9. P. 26–38. https://www.researchgate.net/publication/ 320616269.

[5] Kravchenko V.F., Rvachev V.A. Application of atomic functions for solutions of boundary value problems in mathematical physics. Foreign Radioelectronics: Achievements of modern radioelectronics. 1996. №8. P. 6–22.

[6] Rvachev V.L., Rvachev V.A. About one Finite Function, DAN URSR. A (6). 1971. P. 705–707.

[7] Rvachev V.L. Theory of R-functions and their applications. Kiev: Naukova Dumka. 1982.

[8] Rvachev V.L., Rvachev V.A. Non-classical methods in the theory of approximations in boundary value problems. Kiev: Naukova Dumka. 1982.

[9] Kravchenko V.F., Kravchenko O.V., Pustovoit V.I., Pavlikov V.V. Atomic Functions Theory: 45 Years Behind. DOI 10.1109/MSMW.2016.7538216. https://www.researchgate.net/publication/308749839.

[10] Kravchenko V.F. Lectures on the theory of atomic functions and their applications. Moscow: Radiotechnika. 2003.

[11] Kravchenko V.F., Rvachev V.L. Logic Algebra, atomic functions and wavelets in physical applications. Moscow: Fizmatlit. 2009.

[12] Eremenko S.Yu. Natural Vibrations and Dynamics of Composite Materials and Constructions. Kiev: Naukova Dumka. 1992.

[13] Eremenko S.Yu. Finite Element Methods in Mechanics of Deformable Bodies. Kharkov: Osnova. 1991. https://www.researchgate.net/publication/321171685.

[14] Eremenko S.Yu., Rvachev V.L. A survey of variants of the structural finite-element method. Journal of Mathematical Sciences. 1998. V. 90. № 2. P. 1917–1922.

[15] Filippov A.T. The Versatile Soliton. Modern Birkhauser Classics. 2000.

[16] Braun O.M., Kivshar Yu.S. The Frenkel-Kontorova Model: Concepts, Methods, and Applications. Springer. 2004.

[17] Novikov S.P., Manakov S.V., Pitaevskii L.P., Zakharov V.E. Theory of Solitons: The Inverse Scattering Method. Springer-Verlag. 1984.

[18] Rvachev V.L., Avinash K. Quadratic redshift law and the non-Archimedean universe. Radio Physics and Radio Astronomy. 2001. V. 6. № 2. P. 534–536.

[19] Greene B. The fabric of the cosmos: space, time and texture of reality. New York: Vintage Books. 2004.

[20] Kaku M. Introduction to Superstring and M-Theory (2nd ed.). New York: Springer-Verlag. 1999.

[21] Pasachoff J.M., Filippenko A. The Cosmos: Astronomy in the New Millennium. Cambridge: https://en.wikipedia.org/wiki/England Cambridge University Press. 2014.

[22] Taylor E.F., Wheeler J.A. Spacetime Physics: Introduction to Special Relativity. New York: W. H. Freeman. 1992.

[23] Hawking S., Mlodinov L. The Grand Design. New York: Bantam Books. 2010.

[24] The Collected Papers of Albert Einstein. Princeton, New Jersey: Princeton University Press. 1989.

[25] Veinik A.I. Thermodynamics of real processes. Minsk: Nauka i Technika. 1991.

[26] Niedermann F, Schneider R. Radially stabilized inflating cosmic strings. Phys.Rev. D. 91 (6): 064010

[27] Smit J. Introduction to Quantum Fields on a Lattice. Cambridge: Cambridge University Press. 2002.

[28] Rothe H. Lattice Gauge Theories, An Introduction. World Scientific. 2005.

[29] DeGrand T., DeTar C. Lattice Methods for Quantum Chromodynamics. World Scientific. 2006.

[30] Gattringer C., Lang C.B. Quantum Chromodynamics on the Lattice. Springer. 2010.

[31] Scheglov E.G., Arutynov P.A. Non-Archimedean Calculus in the Mathematical Modelling of Digital ICs. Russian Microelectronics. 2002. V. 31. № 6. P. 384–395.

[32] Arutynov P.A. Non-Archimedean Calculi in Theoretical Metrology. Izm. Tekh. (Metrologia). 2001. № 2. P. 3–18.

[33] Bale R., Grossman J.P., Margrave G., Lamoureux M.P. Multidimensional partitions of unity and Gaussian terrains. CREWES Research Report. V. 14. 2002. https://www.researchgate.net/publication/265182366.

Abstract

How to cite

Related articles