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Comparative analysis of one-particle mathematical models in materials science and oncology. I. Mathematical models

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Powder Metallurgy and Metal Ceramics Aims and scope

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Abstract

The mathematical formalism is studied for medium — foreign spherical inclusion models (in materials science) and body tissue — spherical tumor models (in oncology). It is established that they are similar, which is a frequently encountered phenomenon for general laws in mathematical descriptions of very different types of processes (for example, diffusion and thermal conductivity, electromagnetic oscillations and sound, statistical mechanics and population dynamics). A typical process occurring with powders in metals technology and nature is a complex process including diffusion and chemical reaction. Such a process sometimes relates to diffusion in the active medium. Special cells in the body (lymphocytes) appear outside tumors, move toward them, penetrate into them, and trap tumor cells. It is suggested that the lymphocytes can be considered as analogs of diffusing particles (the diffusant) while the tumor cells can be considered as analogs of traps in the case of diffusion in an active medium. An equation is also proposed that describes the behavior of an ensemble of tumor cells under the influence of a magnetic field.

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Authors and Affiliations

  1. Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Kiev

    A. I. Raichenko

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  1. A. I. Raichenko
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Translated from Poroshkovaya Metallurgiya, Nos. 11–12(446), pp. 72–78, November–December, 2005.

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Raichenko, A.I. Comparative analysis of one-particle mathematical models in materials science and oncology. I. Mathematical models. Powder Metall Met Ceram 44, 578–582 (2005). https://doi.org/10.1007/s11106-006-0028-7

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  • DOI: https://doi.org/10.1007/s11106-006-0028-7

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