Transient wave processes in block and elastic media. Analytical and numerical methods in solid mechanics. Special functions in solid mechanics.

Nadezhda Ivanovna Aleksandrova (maiden name Pinchukova) was born on January 10, 1957 in Russia, in the village of Severnoye, Severny District, Novosibirsk Region. Her parents, Ivan Nikiforovich Pinchukov (1921–2003) and Anna Mikhailovna Pinchukova (1923–2002; maiden name Eremina), were teachers at the Severnoye Secondary School. Nadezhda had two older sisters, Olga and Galina, and an older brother, Vladimir.

In 1973, she graduated from Severnoye Seconady School and became a student of the Department of Mechanics and Mathematics of Novosibirsk State University (NSU). In 1978, she graduated from NSU with honors and was hired as an intern researcher at the Institute of Mining of the Siberian Branch of the Academy of Sciences of the Soviet Union. In this Institute, which is located in Novosibirsk, Russia and is now called the N.A. Chinakal Institute of Mining of the Siberian Branch of the Russian Academy of Sciences, Nadezhda worked until the end of her life, consistently helding all scientific positions from an intern to chief researcher.

In 1983, Nadezhda defended her dissertation for the degree of Candidate of Physical and Mathematical Sciences (majoring in Solid Mechanics), which corresponds to Ph.D. in Solid Mechanics. The scientific supervisor was Dr. Mark V. Stepanenko. The dissertation was defended at the M.A. Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Academy of Sciences of the Soviet Union in Novosibirsk.

In 1986, Nadezhda married mathematician Victor A. Alexandrov and accepted her husband’s surname. The family had a son, Alexey, who became a programmer.

From 1992 to 2009 Nadezhda taught students at the Higher Mathematics Chair of the Physics Department at NSU. Working part-time, she successively held the positions equivalent to Assistant Professor and Associate Professor. In 2004, the Higher Attestation Commission (in Moscow) awarded Nadezhda the Docent academic rank.

In 2015, Nadezhda defended her dissertation for the degree of Doctor of Physical and Mathematical Sciences (with major in Solid Mechanics), which corresponds to habilitation in Solid Mechanics. Dr. Evgeny N. Sher served as the scientific consultant. The dissertation was defended at the at the M.A. Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences in Novosibirsk.

Nadezhda died on December 20, 2023 in Novosibirsk after a four-year battle with cancer. She is buried in Novosibirsk at the Southern Cemetery.

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Nadezhda's main scientific interests lay in the study of the propagation of waves in elastic shells, as well as elastic and block media. But sometimes the results she obtained went beyond the scope of solid mechanics itself, and then she published articles on computational mathematics or special functions. In particular, she found new asymptotic representations of the Lommel function and its derivative through the Scorer function.

In her work, Nadezhda sometimes used classical models (for example, that of an elastic shell or of an elastic medium), and sometimes she proposed her own model (primarily when she studied block media). Usually Nadezhda solved the problem numerically, and, when analyzing the finite-difference solution obtained, used either known exact solutions, or asymptotic estimates of exact solutions obtained by herself. To find numerical solutions, Nadezhda have never used ready-made software products for engineering calculations. She always chose the finite-difference algorithm for solving the problem herself and coded it “from scratch” in order to know exactly how the calculations were carried out and to be able to monitor the accuracy of the calculations. Nadezhda was always interested in finding asymptotic estimates for exact solutions of mechanical problems under study. She used them to test finite difference algorithms which she proposed. She sometimes also compared the results of numerical calculations with the results of laboratory or field experiments, performed by her colleagues, who in this case became her co-authors.

From 1978 to 1996 Nadezhda studied mainly various types of waves arising on elastic shells (often immersed in a liquid or filled with a liquid) as a result of external (for example, shock) loads. During this period of time, not all results of Nadezhda's research were published in the form of articles in scientific journals (most of those articles are put on the list of publications on her page on this site). Some of her results were published in technical reports, information about which is currently not possible to find. In general, we can say that the research carried out by Nadezhda from 1978 to 1996 are close to the topic of her Ph.D. thesis.

From 1997 to 2023 Nadezhda mainly studied various types of waves arising in block media and on their boundaries, including studying Rayleigh surface waves at the boundary of a block medium. For example, her article “Seismic waves in a three-dimensional block medium” (2016) is devoted to studying the differences in the behavior of a block medium and a homogeneous elastic medium. Among other things, this article shows that, in a block medium, waves propagate with dispersion, which is absent in a homogeneous elastic medium, and that on the bounadry of a block medium, low-frequency longitudinal and Rayleigh waves propagate at velocities much lower than the corresponding velocities in the blocks. In this paper, the propagation of seismic waves in a three-dimensional block medium was studied numerically, and then the obtained numerical solutions were compared with known analytical solutions for an elastic medium. In general, we can say that the research carried out by Nadezhda from 1998 to 2023 are close to the topic of her habilitation dissertation.

Considering the constant interest of Nadezhda to finding asymptotic solutions and asymptotic estimates of exact solutions for the mechanics problems she studied, it is not surprising that sometimes she had a desire to share her discoveries not only with mechanics, but also with mathematicians. In these cases, she published articles in mathematical journals and gave talks at mathematical seminars and conferences. For example, by using special functions to solve problems in solid mechanics, she found new asymptotic representations of the Lommel function and its derivative through the Scorer function.

As part of her teaching activities, Nadezhda published two textbooks for first-year students of the Physics Department at NSU (namely, “Seminars on Higher Algebra and Analytic Geometry” and “Seminars on Linear Algebra and Differential Geometry”) and one textbook for Ph.D. students majoring in geomechanics (namely, “Lectures on topic `Pendulum waves' within the course `Nonlinear geomechanics'").

The reader can learn more about Nadezhda's scientific and teaching activities using the list of her publications on her page on this site.

Victor A. Alexandrov, December 31, 2023

1. N. I. Aleksandrova, “Seismic waves in a three-dimensional block medium”, Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences, 472:2192 (2016), Article ID 20160111, 16 p
2. N. I. Aleksandrova, “Asymptotic formulae for the Lommel and Bessel functions and their derivatives”, Royal Society Open Science, 1:140176 (2014), 16 p.
3. N. I. Aleksandrova, “The discrete Lamb problem: Elastic lattice waves in a block medium”, Wave motion, 51:5 (2014), 818-832
4. N. I. Aleksandrova, “Asymptotic solution of the anti-plane problem for a two-dimensional lattice”, Doklady Physics, 59:3 (2014), 129-132
5. N. I. Aleksandrova, “Elastic wave propagation in block medium under impulse loading”, Journal of Mining Science, 39:6 (2003), 556-564

• Novosibirsk State University, Physics Department
• Institute of Mining, Siberian Branch of the Russian Academy of Sciences