Asymptotic Models for Studying Kinetics of Formation of Compact Objects with Strong Internal Bonds


An asymptotic method has been developed for investigation of kinetics of formation of compact objects with strong internal bonds. The method is based on the uncertainty relation for a coordinate and a momentum in space of sizes of objects (clusters) with strongly pronounced collective quantum properties resulted from exchange interactions of various physical nature determined by spatial scales of the processes under consideration. The proposed phenomenological approach has been developed by analogy with the all-known ideas about coherent states of quantum mechanical oscillator systems for which a product of coordinate and momentum uncertainties (dispersions) accepts the value, which is minimally possible within uncertainty relations. With such an approach the leading processes are oscillations of components that make up objects, mainly: collective nucleon oscillations in a nucleus and phonon excitations in a mesostructure crystal lattice. This allows us to consider formation and growth of subatomic and mesoscopic objects in the context of a single formalism. The proposed models adequately describe characteristics of formation processes of nuclear matter clusters as well as mesoscopic crystals having covalent and quasi-covalent bonds between atoms.

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Lin, E. (2014) Asymptotic Models for Studying Kinetics of Formation of Compact Objects with Strong Internal Bonds. World Journal of Mechanics, 4, 170-196. doi: 10.4236/wjm.2014.46019.

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The authors declare no conflicts of interest.


[1] Morokhov, I.D., Petinov, V.P., Turusov, L.P. and Petrunin, V.F. (1981) Structure and Properties of Fine Metallic Particles. Soviet Physics Uspekhi, 24, 295-334.
[2] Kadomtsev, B.B. (1994) Dynamics and Information. Soviet Physics Uspekhi, 37, 425-499.
[3] Von Oppen, G. (1994) Objects and Environment. Physics-Uspekhi, 39, 617-620.
[4] Smirnov, B.M. (2011) Processes Involving Clusters and Small Particles in Buffer Gas. Physics-Uspekhi, 54, 691-721.
[5] Pool, C.P. and Owens, F.J. (2003) Introduction to Nanotechnology. John Wiley & Sons Inc., London.
[6] Imry, Y. (2002) Introduction to Mesoscopic Physics. Oxford University Press, Oxford.
[7] Bording, J.K. and Taft, J. (2000) Molecular-Dynamics Simulation of Growth of Nanocrystals in Amorphous Matrix. Physical Review B, 62, 8098-8103.
[8] Hellen, E.K. and Alava, M.J. (2002) Persistence in Cluster-Cluster Aggregation. Physical Review E, 66, 026120.
[9] Hecker, S.S. (2000) Plutonium and Its Alloys: From Atoms to Microstructures. In: Cooper, N.G., Buican, I.G. and Schecker, J.A., Eds., Challenges in Plutonium Science, Los Alamos Science, Los Alamos, 290-334.
[10] Malygin, G.A. (2008) Nanoscope Size Effects on Martensitic Transformation in Shape Memory Alloys. Physics of the Solid State, 50, 1538-1543.
[11] Lin, E.E. (1993) Kinetics of the Formation of Compact Quantum Clusters in Stochastic Conservative Systems. Technical Physics Letters, 19, 165-166.
[12] Suzdalev, I.P. (2006) Nanotechnology: Physics-Chemistry of Nanoparticles, Nanostructures and Nanomaterials. Synergetics: From the Past to Future, Komkniga, Moscow. (in Russian)
[13] Vanossi, A., Manini, N., Urbakh, M., Zapetti, S. and Tosatti, E. (2013) Modeling Friction: From Nanoscale to Mesoscale. Review of Modern Physics, 85, 529-562.
[14] Lin, E.E. (2012) Calculating the Mass Numbers of Cluster Nuclides on the Basis of the Asymptotic Model. Bulletin of the Russian Academy of Sciences: Physics, 76, 881-883.
[15] Lin, E.E. (2010) Mesokinetics of Growth of Nanostructured Objects with Strong Interatomic Bonds. In: Taylor, J., Ed., Advances in Chemistry Research, Nova Science Publishers, New York, 5, 171-190.
[16] Fermi, E. (1960) Notes on Quantum Mechanics. The University of Chicago Press, Chicago.
[17] Man’ko, V.I. (1990) Coherent State. In: Prokhorov, A.M., Ed., Physical Encyclopedia, Soviet Encyclopedia, Moscow, 392-394. (in Russian)
[18] Wagner, P. and Zhong, Y.M. (1995) Cluster Formation in Disordered Systems and Nuclear Fragmentation. Nuclear Physics A, 592, 385-412.
[19] Okun, L.B. (1998) Current Status of Elementary Particle Physics. Physics-Uspekhi, 41, 553-557.
[20] Dremin, I.M. (2010) The Quark-Gluon Medium. Physics-Uspekhi, 53, 123-1149.
[21] Lozovik, Y.E. and Popov, A.M. (1997) Formation and Growth of Carbon Nanostructures: Fullerens, Nanoparticles, Nanotubes and Cones. Physics Uspekhi, 40, 717-737.
[22] Mukhin, K.N. and Patarakin, O.O. (2000) Exotic Processes in Nuclear Physics. Physics-Uspekhi, 43, 799-839.
[23] Lin, E.E. (2010) Asymptotical Model of the Formation of Nuclear Matter Clusters. In: Il’kaev, R.I., Ed., Proceedings of International Conference 12th Khariton Thematic Scientific Readings, Problems of High Density Energy Physics, 19-23 April 2010, Sarov, 262-267. (in Russian)
[24] Panov, I.V. and Thielemann, F.K. (2004) Fission and the r-Process: Competition between Neutron-Induced and Beta-Delayed Fission. Astronomic Letters, 30, 647-655.
[25] Lin, E.E. (2011) Qualitative Kinetic Models of Formation of Compact Objects with Strong Internal Bonds. Monograph, Russian Federal Nuclear Center-VNIIEF, Sarov. (in Russian)
[26] Pugachev, V.C. and Sinitsyn, I.N. (1990) Stochastic Differential Systems: Analysis and Filtration. Nauka, Moscow. (in Russian)
[27] Reissland, J.A. (1973) The Physics of Phonons. John Wiley and Sons LTD., London; New York; Sydney; Toronto.
[28] Kulakov, V.M. (1991) Nuclear Properties of Nuclides. In: Grigor’ev, S. and Meilikhov, E.Z., Eds., Physical Quantities Handbook, Energoatomizdat, Moscow, 993-1054. (in Russian)
[29] Ishanov, B.S., Kapitonov, I.M. and Yudin, N.P. (2007) Particles and Atomic Nuclei. LKI, Moscow. (in Russian)
[30] Kadmenskii, S.G., Kurgalin, S.D. and Tchuvil’sky, Y.M. (2012) Cluster States in Atomic Nuclei and Cluser-Decay Processes. Physics of Particles and Nuclei, 38, 699-742.
[31] Zamyatnin, Y.S., Kadmensky, S.S., Kurgalin, S.D. and Tchuvil’sky, Y.M. (1994) Where the New Examples of Nuclei Cluster Decay Can Be Seek? Physics of Atomic Nuclei, 57, 1905-1918.
[32] Vandenbosch, R. and Huisenga, J.R. (1973) Nuclear Fission. Academic Press, New York; London.
[33] Obukhov, A.I. and Grigor’ev, I.S. (1991) Fissionof Nuclei. In: Grigor’ev, I.S. and Meilikhov, E.Z., Eds., Physical Quantities Handbook, Energoatomizdat, Moscow, 1087-1098. (in Russian)
[34] Panov, I.V., Korneev, I.Y. and Thielemann, F.K. (2009) Superheavy Elements and r-Process. Physics of Atomic Nuclei, 72, 1026-1033.
[35] Olkhovsky, V.S. (1984) On Investigation of Nuclear Reactions and Decays with the Help of Analysis of Theirs Durations. Soviet Journal of Particles and Nuclei, 15, 130-148.
[36] Olkhovsky, V.S., Recami, E. and Maydanuyk, S.P. (2012) Time as Quantum Observable, Canonical Conjugated to Energy. In: Pahlavani, M.R., Ed., Measurements in Quantum Mechanics, In Tech, Shaghai, 18-56.
[37] Segre, E. (1964) Nuclei and Particles, an Introduction to Nuclear and Subnuclear Physics. W. A. Benjamin Inc., New York.
[38] Segre, E. (1977) Nuclei and Particles. 2nd Edition, W. A. Benjamin Inc., New York.
[39] Valentin, L. (1982) Physique Subatomique: Noyaux Et Particles. Nouvelle Edition Entirement Refondue, Hermann, Paris.
[40] Jacob, M. and Landshoff, P. (1982) The Inner Structure of Proton. Scientific American, 242, 66-75.
[41] Kane, G. (1987) Modern Elementary Particle Physics. University of Michigan, Addison-Wesley Publishing Company Inc., Michigan.
[42] Neufeld, R.B. and Mueller, B. (2009) Sound Produced by a Fast Parton in a Guark-Gluon Plasma Is a “Crescendo”. Physical Review Letters, 103, 043201.
[43] Selinov, I.P. (1990) Atomic Nuclei: Structure and Systematic. Nauka, Moscow. (in Russian)
[44] Nadezin, D.K. (1992) Neutron Stars. In: Prokhorov, A.M., Ed., Physical Encyclopedia, Big Russian Encyclopedia, Moscow, 280-283. (in Russian)
[45] Utrobin, V.P. (1994) Supernovae. In: Prokhorov, A.M., Ed., Physical Encyclopedia, Big Russian Encyclopedia, Moscow, Vol. 4, 433-435. (in Russian)
[46] Ponomarev, L.I. (1992) Uncertainty Relations. In: Prokhorov, A.M., Ed., Physical Encyclopedia, Big Russian Encyclopedia, Moscow, 321-322. (in Russian)
[47] Vereshchagin, A.L., Sakovich, G.V., Brylyakov, P.M., Zolotukhina, I.I., Petrova, L.A. and Novoselov, N.N. (1990) The Structure of Carbon Diamond-Like Phase of Detonated Synthesis. Soviet Physics Doklady, 35, 851-852.
[48] Lin, E.E. (2003) On the Growth Kinetics of a Single-Wall Carbon Nanotube. Doklady Physics, 48, 180-181.
[49] Badiali, J.P. (1999) Fractal Behavior in Quantum Statistical Physics. Physical Review E, 60, 2533-2539.
[50] Vollmer, M. (1983) Kinetics of New Phase Formation. Plenum, New York. (Kinetic der Phasenbildung. T. Steinkopf, Dresden, 1939)
[51] Syue-sen’, T. (1965) Physical Mechanics. Mir, Moscow. (Translated from Chinese)
[52] Yakubov, T.S. (1990) On Specific Heat of Solids Revealing Fractal Character. Doklady Academii Nauk SSSR, 310, 145-149.
[53] Lin, E.E. (2000) On the Cluster Mechanism of Diamond Synthesis from Different Solid Carbon Forms. Physics of the Solid State, 42, 1946-1951.
[54] Lin, E.E. (1994) Aggregation of Crystalline Clusters in the Shock Wave Front Propagating through Condensed Species. Soviet Journal of Chemical Physics, 12, 404-409.
[55] Lin, E.E. (1997) Shock-Induced Growth of Crystals in a Porous Medium of Diamond Nanoparticles. Chemical Physics Reports, 16, 2241-2244.
[56] Lin, E.E. (2000) Shock-Induced Coalescence of Nanodiamonds. Bulletin of the Russian Academy of Sciences: Physics, 64, 1215-1216.
[57] Lin, E.E. (2005) Pulsed Loading of Objects during Intense Expansion of Products of Solid Explosives (Review). Combustion, Explosion, and Shock Waves, 41, 241-263.
[58] Lin, E.E. (2009) Determining the Growth Rate of Nanostructured Particles of Light Actinide at High and Moderate Temperatures. Technical Physics Letters, 35, 418-420.
[59] Van Bueren, H.G. (1960) Imperfections in Crystals. North-Holland Publishing Company, Amsterdam.
[60] Lin, E.E. (2010) Influence of Size Factors on the Character of Size Transformations in Light Actinides. Physics of the Solid State, 52, 153-157.
[61] Janke, E., Emde, F. and Losch, F. (1960) Tafeln Hoherer Funktionen. (Neubearbeitet von F. Losch), B. G. Verlagsgesellschaft, Stuttgart.
[62] Louson, E.S., Martinez, B., Roberts, J.A., Richardson, J.U. and Benne, B.I. (2000) Oscillations of Atoms and Plutonium Melting. In: Cooper, N.G., Buican, I.G. and Schecker, J.A., Eds., Challenges in Plutonium Science, Los Alamos Science, Los Alamos, 190-199.
[63] Dwight, H.B. (1961) Tables of Integrals and other Mathematical Data. The Macmillan Company, New York.
[64] Hecker, S.S., Harbur, D.R. and Zocco, T.G. (2004) Phase Stability and Phase Transformations in Pu-Ga Alloys. Progress in Materials Science, 49, 429-485.
[65] Kitching, S., Planterose, P.G. and Gill, D.C. (2003) Stabilized Plutonium. In: Jarvinen, G.D., Ed., Plutonium Futures— The Science, American Institute of Physics, New York, 79-81.
[66] Mitchell, J.N., Hecker, S.S., Freibert, F.J., Schwarts, D.S. and Bange, M.E. (2008) Inconventional Delta-Phase Stabilization in Pu-Ga Alloys. In: Fundamental Plutonium Properties, Proceedings of 8th International Workshop, 8-12 September 2008, Snezhinsk, 5-6.
[67] Leshli, D.S., Blau, M.S. and Moment, R.L. (2000) Manufacturing of Single Crystals of Plutonium. In: Cooper, N.G., Buican, I.G. and Schecker, J.A., Eds., Challenges in Plutonium Science, Los Alamos Science, Los Alamos, 233-245.
[68] Ginzburg, V.L. (1999) What Problems of Physics and Astrophysics Seem Now to Be Especially Important and Interesting (Thirty Years Later, Already on the Verge of XXI Century)? Physics-Uspekhi, 42, 353-373.
[69] Okun, L.B. (1985) Particle Physics: The Guest for the Substance of Substance. Hardwood Academic Publishers, Chur.
[70] Lin, E.E. (1993) Kinetics of Deep-Inelastic Heavy Ions Interaction. Technical Physics Letters, 19, 669-670.
[71] Whitham, G.B. (1974) Linear and Nonlinear Waves. A Wiley-Interscience Publication, Hoboken.
[72] Düllmann, C.E., Schadell, M. and Yakushev, A. (2010) Production and Decay of Element 114: High Cross Sections and New Nucleus 277Hs. Physical Review Letters, 104, 252701-252705.
[73] Wang, N. and Liu, M. (2011) Nuclear Mass Predictions with a Radial Basis Function Approach. Physical Review C, 84, 051303.
[74] Galimov, E.M., Kudin, A.M., Skorobogatskii, V.N., Plotnichenko, V.G., Bondarev, O.L., Zarubin, B.G., Strazdovskii, V.V., Aronin, A.S., Fisenko, A.V. and Bubov, I.V. (2004) Experimental Confirmation of the Diamond Synthesis during Cavitation. Doklady Physics, 395, 187-191.
[75] Khachatryan, A., Aloyan, S.S., May, P.W., Sargsyan, R., Khachatryan, V.A. and Bagdasaryan, V.S. (2008) Grafite-to-Diamond Transformation Induced by Ultrasound Cavitation. Diamond and Related Materials, 17, 931-936.
[76] Lin, E.E. (2011) Cluster Mechanism of Diamond Synthesis under Severe Cavitation Conditions. Technical Physics Letters, 37, 593-595.
[77] Lin, E.E. (2011) Detonation Zone Width Determination Based on Uncertainty Principle. Technical Physics Letters, 37, 449-450.
[78] Auchev, A.A., Ilyushkina, N.Y., Lin, E.E., Popov, N.N. and Tanakov, Z.V. (2013) Recrystallization in Aluminum Alloyes under Impact of Solids. In: Proceedings of International Conference 15th Khariton Topical Scientific Readings “Extreme States of Substance. Detonation. Shock Waves”, 18-22 March 2013, Sarov, 300-301. (in Russian)
[79] Hlopkin, M.N. (1991) Heat Capacity. In: Grigor’ev, S. and Meilikhov, E.Z., Eds., Physical Quantities Handbook, Energoatomizdat, Moscow, 205. (in Russian)
[80] Rubakov, V.A. (2012) Large Hadron Collider’s Discovery of a New Particle with Higgs Boson Properties. Physics-Uspekhi, 55, 949-957.
[81] Elsayed, A., Khalil, S. and Moretti, S. (2012) Higgs Mass Corrections in the SUSY B-L Model with Inverse Seesaw. Physics Letters B, 715, 208-213.

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