<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">jamt</journal-id><journal-title-group><journal-title xml:lang="ru">Journal of Advanced Materials and Technologies</journal-title><trans-title-group xml:lang="en"><trans-title>Journal of Advanced Materials and Technologies</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2782-2192</issn><issn pub-type="epub">2782-2206</issn><publisher><publisher-name>ФГБОУ ВО «ТГТУ»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17277/jamt-2025-10-04-329-341</article-id><article-id custom-type="elpub" pub-id-type="custom">jamt-80</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Наноструктурированные наноматериалы и наноустройства</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>Nanostructured, nanoscale materials and nanodevices</subject></subj-group></article-categories><title-group><article-title>Топологическая лазерная термодинамика в технологиях управления функциональными характеристиками высокоэнтропийных сплавов с поверхностными дендритными структурами</article-title><trans-title-group xml:lang="en"><trans-title>Topological laser thermodynamics in technologies for controlling the functional characteristics of high-entropy alloys with dendritic surface structures</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0007-5496-4234</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Тумаркина</surname><given-names>Д. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Tumarkina</surname><given-names>D. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Тумаркина Дарья Денисовна, ассистент</p><p>ул. Горького, 87, Владимир, 600000, Российская Федерация</p></bio><bio xml:lang="en"><p>Darya D. Tumarkina, Teaching Assistant</p><p>87, Gorky St., Vladimir, 600000, Russian Federation</p></bio><email xlink:type="simple">tumarkina.darya@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-6052-666X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бутковский</surname><given-names>О. Я.</given-names></name><name name-style="western" xml:lang="en"><surname>Butkovsky</surname><given-names>O. Ya.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Бутковский Олег Ярославович, доктор физико-математических наук, профессор</p><p>ул. Горького, 87, Владимир, 600000, Российская Федерация</p></bio><bio xml:lang="en"><p>Oleg Ya. Butkovsky, D. Sc. (Phys. and Math.), Professor</p><p>87, Gorky St., Vladimir, 600000, Russian Federation</p></bio><email xlink:type="simple">OYButkovskiy@fa.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4536-8576</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бухаров</surname><given-names>Д. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Bukharov</surname><given-names>D. N.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Бухаров Дмитрий Николаевич, кандидат физико-математических наук, доцент</p><p>ул. Горького, 87, Владимир, 600000, Российская Федерация</p></bio><bio xml:lang="en"><p>Dmitry N. Bukharov, Cand. Sc. (Phys. and Math.), Associate Professor</p><p>87, Gorky St., Vladimir, 600000, Russian Federation</p></bio><email xlink:type="simple">buharovdn@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0850-9365</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Буракова</surname><given-names>И. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Burakova</surname><given-names>I. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Буракова Ирина Владимировна, кандидат технических наук, доцент</p><p>ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация</p></bio><bio xml:lang="en"><p>Irina V. Burakova, Cand. Sc. (Eng.), Associate Professor</p><p>Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation</p></bio><email xlink:type="simple">iris_tamb68@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4871-3504</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Бураков</surname><given-names>А. Е.</given-names></name><name name-style="western" xml:lang="en"><surname>Burakov</surname><given-names>A. E.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Бураков Александр Евгеньевич, кандидат технических наук, доцент, и. о. заведующего кафедрой</p><p>ул. Советская, 106/5, пом. 2, Тамбов, 392000, Российская Федерация</p></bio><bio xml:lang="en"><p>Alexander E. Burakov, Cand. Sc. (Eng.), Associate Professor, Acting Head of the Department</p><p>Bld. 2, 106/5, Sovetskaya St., Tambov, 392000, Russian Federation</p></bio><email xlink:type="simple">m-alex1983@yandex.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6323-7123</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Аракелян</surname><given-names>C. М.</given-names></name><name name-style="western" xml:lang="en"><surname>Arakelian</surname><given-names>S. M.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Аракелян Сергей Мартиросович, доктор физико-математических наук, профессор, независимый исследователь</p><p>ул. Горького, 87, Владимир, 600000, Российская Федерация</p></bio><bio xml:lang="en"><p>Sergey M. Arakelian, D. Sc. (Phys. and Math.), Professor, Independent Researcher</p><p>87, Gorky St., Vladimir, 600000, Russian Federation</p></bio><email xlink:type="simple">arak@vlsu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Владимирский государственный университет имени Александра Григорьевича и Николая Григорьевича Столетовых</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Vladimir State University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Тамбовский государственный технический университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Tambov State Technical University</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>24</day><month>02</month><year>2026</year></pub-date><volume>10</volume><issue>4</issue><fpage>329</fpage><lpage>341</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Тумаркина Д.Д., Бутковский О.Я., Бухаров Д.Н., Буракова И.В., Бураков А.Е., Аракелян C.М., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Тумаркина Д.Д., Бутковский О.Я., Бухаров Д.Н., Буракова И.В., Бураков А.Е., Аракелян C.М.</copyright-holder><copyright-holder xml:lang="en">Tumarkina D.D., Butkovsky O.Y., Bukharov D.N., Burakova I.V., Burakov A.E., Arakelian S.M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://jamt.elpub.ru/jour/article/view/80">https://jamt.elpub.ru/jour/article/view/80</self-uri><abstract><p>Рассматривается лазерная термодинамика топологических структур – дендритов, полученных при воздействии лазерных импульсов на поверхность ряда высокоэнтропийных сплавов в процессе лазерной абляции. Рассмотрены схемы лазерного экспериментального синтеза и его параметры для получения дендритных структур высокоэнтропийных сплавов различного характера. Для разных конфигураций таких структур в рамках нанокластерных/островковых топологических моделей проанализированы возможности управления функциональными характеристиками образцов с дендритами (электрофизика и оптика) для возможных технологических применений. Смоделированы и оценены термодинамические условия направленного синтеза дендритов при разных условиях эксперимента с лазерным воздействием от Гауссового источника излучения в рамках приближения Matlab Laser Toolbox. Проведено исследование особенностей термодинамических условий синтеза дендритных систем, образованных из высокоэнтропийных сплавов на основе аналитических оценок поля температуры. Проведенная процедура позволила оценить реальные температуры плавления для компонент наноструктурированного высокоэнтропийного сплава. Предложены модели дендритных структур в диффузионном приближении в рамках диффузионно-ограниченной агрегации, для которых приведена оценка их электропроводимости с помощью моделирования вольтамперных характеристик в рамках туннельного и прыжкового приближений, а также усиления электрического поля на неоднородных границах фрактальных структур. Разработанные модели реализованы в среде MATLAB и имеют непосредственную связь с параметрами реальной схемы синтеза. Оценки, выполненные с их помощью, не противоречат реальным величинам.  </p></abstract><trans-abstract xml:lang="en"><p>This paper examines the laser thermodynamics of topological structures – dendrites – obtained by laser ablation of several high-entropy alloys using laser pulses. Laser experimental synthesis schemes and parameters for producing dendritic structures in various high-entropy alloys are discussed. For various configurations of such structures, the possibilities for controlling the functional characteristics of dendritic samples (electrophysics and optics) for potential technological applications are analyzed within nanocluster/island topological models. Thermodynamic conditions for targeted dendritic synthesis are modeled and evaluated under various experimental conditions with laser irradiation from a Gaussian radiation source using the Matlab Laser Toolbox approximation. The thermodynamic conditions for the synthesis of dendritic systems formed from high-entropy alloys are studied using analytical estimates of the temperature field. The procedure performed allowed us to estimate the actual melting temperatures for the components of the nanostructured high-entropy alloy. Models of dendritic structures in the diffusion approximation under diffusion-limited aggregation were proposed. Their electrical conductivity was estimated using simulations of the current-voltage characteristics within the tunneling and hopping approximations, as well as the enhancement of the electric field on fractal structures at their inhomogeneous boundaries. The developed models were implemented in MATLAB and were directly related to the parameters of the actual synthesis scheme, and the estimates obtained using them were consistent with the actual values.  </p></trans-abstract><kwd-group xml:lang="ru"><kwd>лазерная термодинамика</kwd><kwd>высокоэнтропийные сплавы</kwd><kwd>топологические поверхностные структуры</kwd><kwd>направленный синтез дендритов</kwd><kwd>управляемые функциональные характеристики</kwd></kwd-group><kwd-group xml:lang="en"><kwd>laser thermodynamics</kwd><kwd>high-entropy alloys</kwd><kwd>topological surface structures</kwd><kwd>directed synthesis of dendrites</kwd><kwd>controlled functional characteristics</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Panchenko VYa. Laser technologies of materials processing: modern problems of fundamental research and applied developments. Moscow: FIZMALIT; 2009. 664 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Panchenko VYa. Laser technologies of materials processing: modern problems of fundamental research and applied developments. Moscow: FIZMALIT; 2009. 664 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Grigor′yants AG, Shiganov IN, Misyurov AI. Technological processes of laser processing: Studies. Handbook for universities. Moscow: BMSTU Publ. House; 2006. 664 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Grigor′yants AG, Shiganov IN, Misyurov AI. Technological processes of laser processing: Studies. Handbook for universities. Moscow: BMSTU Publ. House; 2006. 664 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Römer GRBE, Huis In ’T Veld AJ. Matlab laser toolbox. Physics Procedia. 2010;5:413-419. DOI:10.1016/j.phpro.2010.08.068</mixed-citation><mixed-citation xml:lang="en">Römer GRBE, Huis In ’T Veld AJ. Matlab laser toolbox. Physics Procedia. 2010;5:413-419. DOI:10.1016/j.phpro.2010.08.068</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Kandidov VP, Chesnokov SS, Shlenov SA. Discrete Fourier transform. Study guide. Moscow: Lomonosov MSU Publ. House; 2019. 88 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Kandidov VP, Chesnokov SS, Shlenov SA. Discrete Fourier transform. Study guide. Moscow: Lomonosov MSU Publ. House; 2019. 88 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Bukharov DN, Osipov AV, Arakelyan SM, Kucherik AO. Graph-analytical model of the electrical conductivity of a semiconductor island plumbum telluride nanofilm. Journal of Physics: Conference Series. 2019; 1331:012008. DOI:10.1088/1742-6596/1331/1/012008</mixed-citation><mixed-citation xml:lang="en">Bukharov DN, Osipov AV, Arakelyan SM, Kucherik AO. Graph-analytical model of the electrical conductivity of a semiconductor island plumbum telluride nanofilm. Journal of Physics: Conference Series. 2019; 1331:012008. DOI:10.1088/1742-6596/1331/1/012008</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Arakelyan SM, Khudaberganov TA, Istratov AV, Osipov AV, Khor′kov KS. Topological laser-induced quantum states in nanocluster structures: fundamental effects and possible applications (electrophysics and optics). Optika i spektroskopiya = Optics and Spectroscopy. 2019;127(7):125-136. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Arakelyan SM, Khudaberganov TA, Istratov AV, Osipov AV, Khor′kov KS. Topological laser-induced quantum states in nanocluster structures: fundamental effects and possible applications (electrophysics and optics). Optika i spektroskopiya = Optics and Spectroscopy. 2019;127(7):125-136. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Garnov SV, Abramov DV, Bukharov DN, Khudaiberganov TA, et al. Electrophysics of carbon 1d structures obtained in a laser experiment: models and demonstration. Uspekhi Fizicheskih Nauk = PhysicsUspekhi. 2024;194(2):115-137. DOI:10.3367/UFNr.2023.12.039620 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Garnov SV, Abramov DV, Bukharov DN, Khudaiberganov TA, et al. Electrophysics of carbon 1d structures obtained in a laser experiment: models and demonstration. Uspekhi Fizicheskih Nauk = PhysicsUspekhi. 2024;194(2):115-137. DOI:10.3367/UFNr.2023.12.039620 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Bukharov DN, Tumarkina DD, Kucherik AO, Tkachev AG, et al. Structure control of metal-carbon composites with different nanotopological configurations and electrical conductivity characteristics in a laser experiment. Journal of Advanced Materials and Technologies. 2024;9(3):207-235. DOI:10.17277/jamt.2024.03.pp.207-235</mixed-citation><mixed-citation xml:lang="en">Bukharov DN, Tumarkina DD, Kucherik AO, Tkachev AG, et al. Structure control of metal-carbon composites with different nanotopological configurations and electrical conductivity characteristics in a laser experiment. Journal of Advanced Materials and Technologies. 2024;9(3):207-235. DOI:10.17277/jamt.2024.03.pp.207-235</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Bukharov DN, Kucherik AO, Arakelian SM. Nanocluster fractal electrical conductivity in thin films on a solid surface: dimensional model of different configurations and demonstration of results in a laser experiment. Journal of Advanced Materials and Technologies. 2023;8(3):227-251. DOI:10.17277/jamt.2023.03.pp.227-251</mixed-citation><mixed-citation xml:lang="en">Bukharov DN, Kucherik AO, Arakelian SM. Nanocluster fractal electrical conductivity in thin films on a solid surface: dimensional model of different configurations and demonstration of results in a laser experiment. Journal of Advanced Materials and Technologies. 2023;8(3):227-251. DOI:10.17277/jamt.2023.03.pp.227-251</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Trakhtenberg LI, Mel′nikova MYa. Metal/semiconductor containing nanocomposites. Moscow: Technosphere; 2019. 624 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Trakhtenberg LI, Mel′nikova MYa. Metal/semiconductor containing nanocomposites. Moscow: Technosphere; 2019. 624 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Arakelyan SM, Kucherik AO, Prokoshev VG, Rau VG, Sergeyev AG. Introduction to femtonanophotonics: fundamental principles and laser methods for the controlled production and diagnosis of nanostructured materials: a textbook. Moscow: Logos; 2020. 744 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Arakelyan SM, Kucherik AO, Prokoshev VG, Rau VG, Sergeyev AG. Introduction to femtonanophotonics: fundamental principles and laser methods for the controlled production and diagnosis of nanostructured materials: a textbook. Moscow: Logos; 2020. 744 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Practical recommendations for the development of printed circuit boards. Available from: https://btpit36.ru/pluginfile.php/5733/mod_resource/content/2/samspcbguide_ce_1.1.pdf [Accessed 21 June 2025]</mixed-citation><mixed-citation xml:lang="en">Practical recommendations for the development of printed circuit boards. Available from: https://btpit36.ru/pluginfile.php/5733/mod_resource/content/2/samspcbguide_ce_1.1.pdf [Accessed 21 June 2025]</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Shumilin AV, Bel′tyukov YaM. The effect of nonequilibrium correlations on the effective resistance between centers in the theory of hopping conduction. Fizikat verdogo tela = Physics of the Solid State. 2019; 61(11):2116-2121. DOI:10.21883/FTT.2019.11.48416.509 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Shumilin AV, Bel′tyukov YaM. The effect of nonequilibrium correlations on the effective resistance between centers in the theory of hopping conduction. Fizikat verdogo tela = Physics of the Solid State. 2019; 61(11):2116-2121. DOI:10.21883/FTT.2019.11.48416.509 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Kuvayskova YuE. Algorithms of discrete mathematics: a textbook. Ulyanovsk: UlGTU Publ. House; 2017. 99 p. ISBN 978-5-9795-1635-6 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Kuvayskova YuE. Algorithms of discrete mathematics: a textbook. Ulyanovsk: UlGTU Publ. House; 2017. 99 p. ISBN 978-5-9795-1635-6 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Korchagin SA, Terin DV, Klinayev YuV. Modeling of a fractal composite and investigation of its electrical characteristics. Matematicheskoye modelirovaniye i chislennyye metody. 2017;13(1):22-31. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Korchagin SA, Terin DV, Klinayev YuV. Modeling of a fractal composite and investigation of its electrical characteristics. Matematicheskoye modelirovaniye i chislennyye metody. 2017;13(1):22-31. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Bonch-Bruyevich VL. Problems of the electron theory of disordered semiconductors. Uspekhi fizicheskikh nauk = Physics-Uspekhi. 1983;140(4):583-637. DOI: 10.3367/UFNr.0140.198308b.0583 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Bonch-Bruyevich VL. Problems of the electron theory of disordered semiconductors. Uspekhi fizicheskikh nauk = Physics-Uspekhi. 1983;140(4):583-637. DOI: 10.3367/UFNr.0140.198308b.0583 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Cao M, Chen J, Sun X, Xie F, Li B. Theoretical predictions and experimental verifications of SERS detection in colorants. RSC Advances. 2023;13(22):15086-15098. DOI: 10.1039/D3RA01584J</mixed-citation><mixed-citation xml:lang="en">Cao M, Chen J, Sun X, Xie F, Li B. Theoretical predictions and experimental verifications of SERS detection in colorants. RSC Advances. 2023;13(22):15086-15098. DOI: 10.1039/D3RA01584J</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Detecting and identifying food colorants with SERS. Spectroscopy online. Available from: https://www.spectroscopyonline.com/view/detecting-andidentifying-food-colorants-sers [Accessed 21 June 2025]</mixed-citation><mixed-citation xml:lang="en">Detecting and identifying food colorants with SERS. Spectroscopy online. Available from: https://www.spectroscopyonline.com/view/detecting-andidentifying-food-colorants-sers [Accessed 21 June 2025]</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Tkachenko LA, Repina AV. The theory of unsteady heat transfer: A textbook. Kazan: Kazan University Publ. House; 2017. 139 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Tkachenko LA, Repina AV. The theory of unsteady heat transfer: A textbook. Kazan: Kazan University Publ. House; 2017. 139 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Rykalin NN, Uglov AA, Zuyev IV, Kokora AN. Laser electron beam processing of materials: A reference book. Moscow: Mashinostroyeniye; 1985. 496 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Rykalin NN, Uglov AA, Zuyev IV, Kokora AN. Laser electron beam processing of materials: A reference book. Moscow: Mashinostroyeniye; 1985. 496 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Libenson MN, Yakovlev EB, Shandybina GD. Interaction of laser radiation with matter (power optics). Part II. Laser heating and destruction of materials. Study guide. Saint-Petersburg: ITMO Publ. House; 2014. 181 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Libenson MN, Yakovlev EB, Shandybina GD. Interaction of laser radiation with matter (power optics). Part II. Laser heating and destruction of materials. Study guide. Saint-Petersburg: ITMO Publ. House; 2014. 181 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Antonov DN, Burtsev AA, Butkovskiy OYa. Distribution of dendrites produced on the surface of steel as a result of exposure to laser radiation. Zhurnal tekhnicheskoy fiziki = Technical Physics. 2016;86(1):110-115. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Antonov DN, Burtsev AA, Butkovskiy OYa. Distribution of dendrites produced on the surface of steel as a result of exposure to laser radiation. Zhurnal tekhnicheskoy fiziki = Technical Physics. 2016;86(1):110-115. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Unutulmazsoy Y, Merkle R, Fischer D, Mannhart J, Maie, J. The oxidation kinetics of thin nickel films between 250 and 500 °C. Physical Chemistry Chemical Physics. 2017;19(13):9045-9052. DOI:10.1039/C7CP00476A</mixed-citation><mixed-citation xml:lang="en">Unutulmazsoy Y, Merkle R, Fischer D, Mannhart J, Maie, J. The oxidation kinetics of thin nickel films between 250 and 500 °C. Physical Chemistry Chemical Physics. 2017;19(13):9045-9052. DOI:10.1039/C7CP00476A</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Vorobev AH. Diffusion problems in chemical kinetics. Study guide. Moscow: Lomonosov MSU Publ. House; 2003. 98 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Vorobev AH. Diffusion problems in chemical kinetics. Study guide. Moscow: Lomonosov MSU Publ. House; 2003. 98 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">AISI 304 Stainless steel characteristics. Available from: https://inoxtrade.ru/info/commoninfo/item100590/aisi-304/ [Accessed 21 June 2025]</mixed-citation><mixed-citation xml:lang="en">AISI 304 Stainless steel characteristics. Available from: https://inoxtrade.ru/info/commoninfo/item100590/aisi-304/ [Accessed 21 June 2025]</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Special functions. Available from: https://www.tutorialspoint.com/python/special_functions.htm [Accessed 21 June 2025]</mixed-citation><mixed-citation xml:lang="en">Special functions. Available from: https://www.tutorialspoint.com/python/special_functions.htm [Accessed 21 June 2025]</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Sergeyev NA, Ryabushkin DS. Physics of nanosystems: monograph. Moscow: Logos; 2016. 192 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Sergeyev NA, Ryabushkin DS. Physics of nanosystems: monograph. Moscow: Logos; 2016. 192 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Borlakov KhSh, Kochkarova PA. Fractal dimension as a thermodynamic parameter. Izvestiya vuzov. Severo-Kavkazskiy region. Yestestvennyye nauki. 2006;3:50-52. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Borlakov KhSh, Kochkarova PA. Fractal dimension as a thermodynamic parameter. Izvestiya vuzov. Severo-Kavkazskiy region. Yestestvennyye nauki. 2006;3:50-52. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Aleshin MP, Tumarkina DD, Oparin ES, Bukharov DN, et al. Models and structures in the electrophysics of high-entropy alloys with laser-induced fractal surface objects. Physics of Metals and Metallography. 2024;125(9):970-985. DOI:10.1134/S0031918X24601574</mixed-citation><mixed-citation xml:lang="en">Aleshin MP, Tumarkina DD, Oparin ES, Bukharov DN, et al. Models and structures in the electrophysics of high-entropy alloys with laser-induced fractal surface objects. Physics of Metals and Metallography. 2024;125(9):970-985. DOI:10.1134/S0031918X24601574</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Suzdalev IP. Nanotechnology: Physico-chemistry of nanoclusters, nanostructures and nanomaterials. Moscow: LIBROKOM Publ. House; 2019. 592 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Suzdalev IP. Nanotechnology: Physico-chemistry of nanoclusters, nanostructures and nanomaterials. Moscow: LIBROKOM Publ. House; 2019. 592 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Tumarkina DD, Butkovskiy OY, Bolachkov AV, Burtsev AA. Surface topology of mixing entropy resulting from two-pulse laser ablation of stainless steel. Fizikokhimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov. 2023;15:869-878. DOI:10.26456/pcascnn/2023.15.869 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Tumarkina DD, Butkovskiy OY, Bolachkov AV, Burtsev AA. Surface topology of mixing entropy resulting from two-pulse laser ablation of stainless steel. Fizikokhimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov. 2023;15:869-878. DOI:10.26456/pcascnn/2023.15.869 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Rekhviashvili SH, Kishtikova EV. On the melting temperature of nanoparticles and nanostructured substances. Pis′ma v zhurnal tekhnicheskoy fiziki = Technical Physics Letters. 2006;32(10):50-55. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Rekhviashvili SH, Kishtikova EV. On the melting temperature of nanoparticles and nanostructured substances. Pis′ma v zhurnal tekhnicheskoy fiziki = Technical Physics Letters. 2006;32(10):50-55. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Atomic radii. Available from: https://dpva.ru/Guide/GuidePhysics/Length/AtomicRadius [Accessed 21 June 2025]</mixed-citation><mixed-citation xml:lang="en">Atomic radii. Available from: https://dpva.ru/Guide/GuidePhysics/Length/AtomicRadius [Accessed 21 June 2025]</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Spivak LV, Shchepina NE. Polymorphic transformations in iron and zirconium. Technical Physics. 2020;65:1100-1105. DOI:10.1134/S1063784220070221</mixed-citation><mixed-citation xml:lang="en">Spivak LV, Shchepina NE. Polymorphic transformations in iron and zirconium. Technical Physics. 2020;65:1100-1105. DOI:10.1134/S1063784220070221</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Pochtenny AE. Jump conductivity under direct current in intrinsic and doped organic semiconductors: monograph. Minsk: BGTU Publ. House; 2016. 171 p. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Pochtenny AE. Jump conductivity under direct current in intrinsic and doped organic semiconductors: monograph. Minsk: BGTU Publ. House; 2016. 171 p. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Blinova NA, Filippov MV. Method of finding a path in a labyrinth in the presence of interference. Novyye informatsionnyye tekhnologii v avtomatizirovannykh sistemakh. 2019;22:46-50. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Blinova NA, Filippov MV. Method of finding a path in a labyrinth in the presence of interference. Novyye informatsionnyye tekhnologii v avtomatizirovannykh sistemakh. 2019;22:46-50. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Krevchik VD, Semenov MB, Krevchik PV. Quantum tunneling with dissipation: an application to tunnel transport for semiconductor quantum dots in a combined AFM / STM system under external electric field conditions (review). Part II. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki. 2020;(4):132-185. DOI:10.21685/2072-3040-2020-4-9 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Krevchik VD, Semenov MB, Krevchik PV. Quantum tunneling with dissipation: an application to tunnel transport for semiconductor quantum dots in a combined AFM / STM system under external electric field conditions (review). Part II. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Fiziko-matematicheskie nauki. 2020;(4):132-185. DOI:10.21685/2072-3040-2020-4-9 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Simonyan ES, Medvedeva OA, Medvedev SN. Creation of maze with multiple solutions, search for all solutions and editing them. Modelirovaniye, optimizatsiya i informatsionnyye tekhnologii. 2019;7(2(25)):365-381. DOI:10.26102/2310-6018/2019.25.2.030 (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Simonyan ES, Medvedeva OA, Medvedev SN. Creation of maze with multiple solutions, search for all solutions and editing them. Modelirovaniye, optimizatsiya i informatsionnyye tekhnologii. 2019;7(2(25)):365-381. DOI:10.26102/2310-6018/2019.25.2.030 (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Krasnov ES. Methodology for evaluating pathfinding algorithms in a maze to select a mobile robot movement strategy. Izvestiya Tul′skogo gosudarstvennogo universiteta. Tekhnicheskiye nauki. 2012;11(2):179-187. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Krasnov ES. Methodology for evaluating pathfinding algorithms in a maze to select a mobile robot movement strategy. Izvestiya Tul′skogo gosudarstvennogo universiteta. Tekhnicheskiye nauki. 2012;11(2):179-187. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Moskalev PV. Analysis of the structure of a percolation cluster. Zhurnal tehnicheskoy fiziki = Technical Physics. 2009;79(6):1-7. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Moskalev PV. Analysis of the structure of a percolation cluster. Zhurnal tehnicheskoy fiziki = Technical Physics. 2009;79(6):1-7. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Moshnikov V.A., Nalimova S.S., Seleznev B.I. Gas-sensitive layers based on fractal-percolation structures. Semiconductors. 2014;48(11):1499-1503. DOI:10.1134/S1063782614110177</mixed-citation><mixed-citation xml:lang="en">Moshnikov V.A., Nalimova S.S., Seleznev B.I. Gas-sensitive layers based on fractal-percolation structures. Semiconductors. 2014;48(11):1499-1503. DOI:10.1134/S1063782614110177</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Montaldi J, Smolyanov OG. Feynman path integrals and Lebesgue–Feynman measures. Doklady Mathematics. 2017;96(1):368-372. DOI:10.1134/S1064562417040226</mixed-citation><mixed-citation xml:lang="en">Montaldi J, Smolyanov OG. Feynman path integrals and Lebesgue–Feynman measures. Doklady Mathematics. 2017;96(1):368-372. DOI:10.1134/S1064562417040226</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Tsitsiashvili GSh, Osipova MA, Losev AS. Derivation of asymptotic constants for the disconnection probability of a planar weighted graph. Prikladnaya diskretnaya matematika. 2014;2:97-100. (In Russ.)</mixed-citation><mixed-citation xml:lang="en">Tsitsiashvili GSh, Osipova MA, Losev AS. Derivation of asymptotic constants for the disconnection probability of a planar weighted graph. Prikladnaya diskretnaya matematika. 2014;2:97-100. (In Russ.)</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Kuznetsov VM, Khromov VI. Fractal representation of the Debye theory for studying the heat capacity of macro-and nanostructures. Technical Physics. 2008; 53(11):1401-1406. DOI:10.1134/S1063784208110029</mixed-citation><mixed-citation xml:lang="en">Kuznetsov VM, Khromov VI. Fractal representation of the Debye theory for studying the heat capacity of macro-and nanostructures. Technical Physics. 2008; 53(11):1401-1406. DOI:10.1134/S1063784208110029</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">Goryachev NS, Kukushkin VI, Belik AY, Rybkin AY, et al. Using SERS and SEF spectroscopy to detect fullerene-dye dyads in water and biological structures. Bulletin of the Russian Academy of Sciences: Physics. 2022;86(4):418-422. DOI:10.3103/S1062873822040116</mixed-citation><mixed-citation xml:lang="en">Goryachev NS, Kukushkin VI, Belik AY, Rybkin AY, et al. Using SERS and SEF spectroscopy to detect fullerene-dye dyads in water and biological structures. Bulletin of the Russian Academy of Sciences: Physics. 2022;86(4):418-422. DOI:10.3103/S1062873822040116</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
