|
|
Invariance of specific mass increment in the case of non-equilibrium growth |
L. M. Martyusheva b, A. P. Sergeevb, P. S. Terentieva |
a Ural Federal University, 19 Mira Str., Ekaterinburg 620002, Russia;
b Institute of Industrial Ecology, 20 S. Kovalevskoy Str., Ekaterinburg 620219, Russia |
|
|
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.
|
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
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|