Invariance of specific mass increment in the case of non-equilibrium growth

doi:10.1088/1674-1056/24/9/090502

Abstract

The invariance of specific mass increments of crystalline structures that co-exist in the case of non-equilibrium growth is grounded for the first time by using the maximum entropy production principle. Based on the hypothesis of the existence of a universal growth equation, and through the dimensional analysis, an explicit form of the time-dependent specific mass increment is proposed. The applicability of the obtained results for describing growth in animate nature is discussed.

Keywords: entropy production universal growth equation

Received: 27 January 2015
Revised: 23 March 2015
Accepted manuscript online:

PACS:	05.70.Ln	(Nonequilibrium and irreversible thermodynamics)
	81.10.Aj	(Theory and models of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation)
	87.19.lx	(Development and growth)

Corresponding Authors: L. M. Martyushev
E-mail: leonidmartyushev@gmail.com

Cite this article:

L. M. Martyushev, A. P. Sergeev, P. S. Terentiev Invariance of specific mass increment in the case of non-equilibrium growth 2015 Chin. Phys. B 24 090502

[1]	Martyushev L M and Terentiev P S 2012 Phys. Rev. E 85 041604
[2]	Martyushev L M and Terentiev P S 2013 Physica A 392 3819
[3]	The abbreviation uses the initial letters of “dendrite” and “seaweed”.
[4]	Currently, non-equilibrium thermodynamics is very actively and fruitfully used to obtain various interesting results relating to nonequilibrium systems (see, for example, Refs.).
[5]	Ziegler H 1963 Progress in Solid Mechanics (Vol. 4) (Sneddon I N and Hill R (eds.)) (Amsterdam: North Holland)
[6]	Ziegler H 1983 An Introduction to Thermomechanics (Amsterdam: North Holland)
[7]	Kleidon A and Lorenz R (eds.) 2005 Non-equilibrium Thermodynamics and Entropy Production: Life, Earth and Beyond (Heidelberg: Springer)
[8]	Martyushev L M and Seleznev V D 2006 Phys. Rep. 426 1
[9]	Dewar R C, Lineweaver C H, Niven R K and Regenauer-Lieb K (eds.) 2014 Beyond the Second Law. Entropy Production and Nonequilibrium Systems (Berlin, Heidelberg: Springer-Verlag)
[10]	Ben-Jacob E and Garik P 1990 Nature 343 523
[11]	Hill A 1990 Nature 348 426
[12]	Martiouchev L M, Seleznev V D and Kuznetsova I E 2000 J. Exper. Theor. Phys. 91 132
[13]	Huxley J 1932 Problems of Relative Growth (London: Methuen & Co)
[14]	Schmalhausen I 1927 Wilhelm Roux' Arch. Entwickl.-Mech. Org. 110 33
[15]	Schmalhausen I 1930 Wilhelm Roux' Arch. Entwickl.-Mech. Org. 123 153
[16]	Schmalhausen I 1930 Biolog. Zentralblatt 50 292
[17]	Martyushev L M and Terentiev P S 2014 ArXiv: q-bio/1404.4318
[18]	Bridgman P W 1922 Dimensional Analysis (New Haven: Yale University Press)
[19]	Therefore, for instance, a crystal growing in a solution accumulates impurities and other defects on its surface with time, which significantly influence the rate of growth.
[20]	Cao L, Ke P, Qiao L Y and Zheng Z G 2014 Chin. Phys. B 23 070501
[21]	Chen Q and Hou M Y 2014 Chin. Phys. B 23 074501

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Invariance of specific mass increment in the case of non-equilibrium growth

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