Visualization during Crystallization in Minkowski Spacetime

Abstract:

It was achieved a visual representation of information about the crystallization process in the multidimensional space, which creates prerequisites for the development of software systems to solve a wide class of problems. With the geometric interpretation Minkowski space-time, quasi-Lorentz and Einstein's concept concerning the concept of giving time physical sense, simulated the process of formation of crystals in the four-dimensional space. The 4D model space combines the physical three-dimensional space of the factors affecting the formation of crystals, and time. Visualization of the crystallization process in spacetime plays an important role, as having great cognitive and probative value, and contributes to a better understanding of crystallization processes, creates conditions to control the properties of materials in the process of crystallization.

• Periodical: Solid State Phenomena (Volume 269)
• Pages: 7-13
• DOI: https://doi.org/10.4028/www.scientific.net/SSP.269.7
• Online since: November 2017
• Authors: Vitaliy S. Borovik*, Vitaliy V. Borovik, Dmitry A. Skorobogatchenko
• Keywords: Formation of Crystals, Lorenz Quasi-Transformation, Minkowski Space, Multi-Dimensional Space

References

[1] Yu.N. Maslovsky, S.V. Slipushenko, A.V. Tur, V.V. Yanovsky, 3D composite particles, Funct. Mater. 22 (2015) 69-78.

[2] I.I. Smolyaninov, V.N. Smolyaninova, Experimental observation of melting of the effective Minkowski spacetime in cobalt -based ferofluids, Rev. Plasmon. 3 (2017) 137-158.

DOI: 10.1007/978-3-319-48081-7_7

[3] 3D & 4D Technology Market by Technology – 2022. Markets and Markets on http: /www. marketsandmarkets. com (2016).

[4] Y. Golovin, Impulse radio emission in the crystallization of water, Nat. Tech. Sci. 1(1996) 158-160.

[5] Y. -H. Jiang, F. Liu, K. Huang, S. -H. Liang, Applying Vogel-Fulcher-Tammann relationship in crystallization kinetics of amorphous alloys, Thermochim. Acta. 607 (2015) 9-18.

DOI: 10.1016/j.tca.2015.03.019

[6] S. Schorsch, T. Vetter, M. Mazzotti, Measuring multidimensional particle size distributions during crystallization, Chem. Eng. Sci. 77 (2012) 130-142.

DOI: 10.1016/j.ces.2011.11.029

[7] T. Vetter, C.L. Burcham, M.F. Doherty, Attainable Regions in Crystallization Processes: Their Construction and the Influence of Parameter Uncertainty, Comp. Aid. Chem. Eng. 34 (2014) 465-470.

[8] Y. Sakai, S. Hashimoto, Four-dimensional Mathematical Data Visualization via Embodied Four-dimensional Space Display System, Forma. 26 (2011) 11-18.

[9] C. Moshe, Group Theory and General Relativity, Representations of the Lorentz Group and Their Applications to the Gravitational Field, McGraw-Hill, New York, (1977).

DOI: 10.1142/9781848160187_0002

[10] Encyclopedia of Mathematics, Vol. 4, Soviet Encyclopedia Publisher, Moscow, (1984).

[11] A. Einstein, The essence of the theory of relativity, Foreign Literature Publishing House, Moscow, (1955).

[12] A. Einstein, The basic ideas and problems of the theory of relativity: Collection of scientific works, Vol. 2. Nauka, Moscow, (1966).

[13] Encyclopedia of Mathematics, Vol. 2, Publisher Soviet Encyclopedia, Moscow, (1984).

[14] I.V. Melikhov, Crystallization as the process of self-organization of matter, VIII International scientific conference Kinetics and mechanism of crystallization: Crystallization as a form of self-organization of matter, Ivanovo, (2014).

[15] N.E. Kornienko, A.D. Rud, Resonant vibrational self-organization of diamond-graphite states in Multidimensional carbon, VIII International scientific conference Kinetics and mechanism of crystallization: Crystallization as a form of self-organization of matter, Ivanovo, (2014).