Abstract
Together with the Darcy filtration model, another model of beta-radiation filtering is considered. This model is related to the heap paradox problem and to numeration theory. The phase transition from liquid to amorphous solid, which changes with temperature and preserves the numeration of particles, is described.
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V. P. Maslov, “My Dear Ludvig,” Mat. Zametki 101 (6), 803–806 (2017) [Math. Notes 101 (6), 925–927 (2017)].
V. P. Maslov, V. P. Myasnikov, and V. G. Danilov, Mathematical Modeling of the Accident Block of Chernobyl Atomic Station (Nauka, Moscow, 1987) [in Russian].
V. P. Maslov and I. A. Molotkov, “High-Temperature Processes in a Porous Medium,” High Temperature 47 (2), 223–227 (2009).
V. P. Maslov and I. A. Molotkov, “Steady Cooling and Global Overheating Process in a Hazardous Reactor,” Journal of Applied Mathematics and Mechanics 72, 689–693 (2008).
Yu. L. Ershov, Numeration Theory (Nauka, Moscow, 1977).
G. L. Litvinov, “Maslov Dequantization, Idempotent and Tropical Mathematics: a Brief Introduction,” J. Math. Sci. 140 (3), 426–444 (2007).
E. M. Lifshits and L. P. Pitaevskii, Theoretical Physics, vol. X, Physical Kinetics (Fizmatlit, Moscow, 2007).
M. de Gosson, “On the Leray–Maslov Quantization of Lagrangian Submanifolds,” J. Geom. Phys. 13 (2), 158–168 (1994).
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non- Relativistic Theory, 2nd ed. (Nauka, Moscow, 1964; translation of the 1st ed., Pergamon Press, London–Paris and Addison-Wesley Publishing Co., Inc., Reading, Mass., 1958).
V. P. Maslov, “Mathematical Aspects of Weakly Nonideal Bose and Fermi Gases on a Crystal Base,” Funktsional. Anal. i Prilozhen. 37 (2), 16–27 (2003) [Functional Anal. Appl. 37 (2), (2003)].
V. P. Maslov, Quantum Economics (Nauka, Moscow, 2006) [in Russian].
N. Bohr and F. Kalckar “On the Transmution of Atomic Nuclei by Impact of Material Particles, I.” Kgl. Danske Vidensk Selskab Mat. Fys. Medd. 14 (10), 1–40 (1937) [Uspekhi Fiz. Nauk 20 (3), 317–340 (1938)].
F. C. Auluck and D. S. Kothari, “Statistical Mechanics and the Partitions of Numbers,” Math. Proc. Cambridge Philos. Soc. 42, 272–277 (1946).
B. K. Agarwala and F. C. Auluck, “Statistical Mechanics and the Partitions Into Non-Integral Powers of Integers,” Math. Proc. Cambridge Philos. Soc. 47 (1), 207–216 (1951).
A. Rovenchak, Statistical Mechanics Approach in the Counting of Integer Partitions arXiv:1603.01049v1 [math-ph] 3 Mar 2016.
A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971) [in Russian].
L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1976) [in Russian].
W.-S. Dai and M. Xie, “Gentile Statistics with a Large Maximum Occupation Number,” Annals of Physics 309, 295–305 (2004).
V. P. Maslov, “Analytical Number Theory and the Energy of Transition of the Bose Gas to the Fermi Gas. Critical Lines as Boundaries of the Noninteracting Gas (an Analog of the Bose Gas) in Classical Thermodynamics,” Russian J. Math. Phys., 25 (2), 220–232 (2018).
V. P. Maslov, “New Insight into the Partition Theory of Integers Related to Problems of Thermodynamics and Mesoscopic Physics,” Math. Notes 102 (2), 234–251 (2017).
A. Weinstein, “The Maslov cycle as a Legendre singularity and projection of a wavefront set,” Bulletin of the Brazilian Math. Society, New Series 44 (4), 593–610 (2013).
V. Guillemin, S. Sternerg, Geometric asymptotics (Amer. Math. soc., Providence, Rhode Island, 1977).
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Maslov, V.P. On Mathematical Investigations Related to the Chernobyl Disaster. Russ. J. Math. Phys. 25, 309–318 (2018). https://doi.org/10.1134/S1061920818030044
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DOI: https://doi.org/10.1134/S1061920818030044