Mathematical modeling of the electrical properties of temporal nanocomposites with a complex structure

During the research, a new modeling method was developed that makes it possible to adapt the electromagnetic response of the environment of a spontaneously ordered nanocomposite in time, using the concept of a temporarily effective environment, which can be used to create new nanostructured materials with specified electrical properties. Using computer technology and mathematical methods, modeling of the dielectric constant of temporal nanocomposites with a complex structure was carried out. A mathematical model developed to describe the dielectric constant of temporal nanocomposites is presented. The model takes into account various factors, such as the geometric parameters of nanoparticles, their concentration, orientation and characteristics of the dielectric matrix. Using the proposed model, numerical experiments were carried out to evaluate the influence of structural features on the dielectric constant of temporal nanocomposites. The work studied the distribution of the electric field in the time domain for nanocomposites with complex configurations and having a dielectric constant that varies periodically with time. The study demonstrated the possibility of using the effective medium model in problems of designing temporal nanocomposites of complex configurations. The research results can be used in practice-oriented problems related to the design of metamaterials with specified electrical properties.

1. Sukhonosov V.Ya. The classical model of matter with weak nonlinearity and dissipation. Vestnik nauki. 2023;2(3):249–263. (In Russ.).

2. Streltsov O.V. Analysis of features of prediction the characteristics of electromagnetic waves. Modelirovanie, optimizatsiya i informatsionnye tekhnologii = Modeling, Optimization and Information Technology. 2013;1(1). (In Russ.). URL: https://moitvivt.ru/ru/journal/article?id=46.

3. Erofeev V.I., Pavlov I.S. Metamaterials: engineering applications and mathematical modelling. Mashinostroenie i inzhenernoe obrazovanie = Mechanical Engineering and Engineering Education. 2021;(1-2):28–45. (In Russ.).

4. Pacheco-Peña V., Engheta N. Effective medium concept in temporal metamaterials. Nanophotonics. 2020;9(2):379–391. https://doi.org/10.1515/nanoph-2019-0305.

5. Ryazantsev R.O., Salomatov Y.P., Polenga S.V. Metamaterial absorber and antenna ground plane. Pis'ma v Zhurnal tekhnicheskoi fiziki = Technical Physics Letters. 2021;47(23):19–21. (In Russ.). https://doi.org/10.21883/TPL.2022.15.53812.18947.

6. Zheng X., Zhang X., Chen T.-T., Watanabe I. Deep Learning in Mechanical Metamaterials: From Prediction and Generation to Inverse Design. Advanced Materials. 2023;35(45):e2302530. https://doi.org/10.1002/adma.202302530.

7. Choi S., Choi J., Landig R., et al. Observation of discrete time-crystalline order in a disordered dipolar many-body system. Nature. 2017;543(7644):221–225. https://doi.org/10.1038/nature21426.

8. Dolgal A.S., Petrosyan R.N. Solution of the Inverse Problem of Gravity Exploration for 2D Prismatic Bodies by the Statistical Tests Method. Vestnik Permskogo universiteta. Geologiya = Bulletin of Perm University. Geology. 2021;20(4):334–343. (In Russ.). https://doi.org/10.17072/psu.geol.20.4.334.

9. Korchagin S.A., Terin D.V. A Method for Modeling the Dielectric Constant of an Anisotropic Hierarchically Constructed Nanocomposite with a Periodic Structure. Pis'ma v Zhurnal tekhnicheskoi fiziki = Technical Physics Letters. 2021;47(16):3–5. https://doi.org/10.1134/S1063785021080198.

10. Tashkinov M.A., Dobrydneva A.D., Matveenko V.P., Silberschmidt V.V. Modeling the effective conductive properties of polymer nanocomposites with a random arrangement of graphene oxide particles. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Mekhanika = PNRPU Mechanics Bulletin. 2021;(2):167–180. (In Russ.). https://doi.org/10.15593/perm.mech/2021.2.15.

11. Mukhutdinova M.A., Yurasov A.N. Modeling of the magnetorefractive effect in CO Al2O3 nanocomposites in the framework of the Bruggeman approximation. In: Perspektivnye materialy i tekhnologii (PMT-2023): Sbornik dokladov Natsional'noi nauchno-tekhnicheskoi konferentsii «Perspektivnye materialy i tekhnologii» s mezhdunarodnym uchastiem Instituta perspektivnykh tekhnologii i industrial'nogo programmirovaniya RTU MIREA, 10-15 April 2023, Moscow, Russia. Moscow: MIREA – Russian Technological University, 2023. P. 100–109. (In Russ.).

12. Koutserimpas T.T., Fleury R. Electromagnetic Waves in a Time Periodic Medium With Step-Varying Refractive Index. IEEE Transactions on Antennas and Propagation. 2018;66(10):5300–5307. https://doi.org/10.1109/TAP.2018.2858200.