The modified perturbation theory for calculation of transition effect in electromagnetic cascades; calculations of images in radiation introscopy; the basis of the stochastical theory of measurements in high-energy transport processes; adjoint equations for various kinds of stochastic importance and methods for their solution; numerical methods of solution of adjont equation by means of spline technique; simulation of fluctuations in multiplicative and cascade processes; the variational sensibility theory; simulations and investigations of stochastic fractals and corresponding transport processes; extended thermodinamics, anomalous diffusion and non-Debay relaxation; Levy-stable and subordinated Levy-stable distributions and processes; fractional differential equations.
Biography
Graduated Tomsk Polytechnic Institut. His first thesis was defended in 1969. It concerned to application of the perturbation theory to problems of radiation shielding and defectoscopy. Since 1970 till 1989 he worked on numerical methods for solving problems of stochastic transport theory (Barnaul). The scientific group created by V. V. Uchaikin becames known through their calculations of spatial distributions in electromagnetic component of extensive atmospheric showers. The results have been included in international code Corsica. Since 1995, V. V. Uchaikin formed a new scientific direction in Ulyanovsk State University: numerical simulation of stochastic fractals and diffusion in them. About 50 articles have been publicated in these direction icluding the book V. V. Uchaikin, V. M. Zolotarev, CHANCE AND STABILITY (ser. Modern Probability and Statistics, VSP, Utrecht, 1999, 570 p.). At present, he develop numerical methods for solving integrodifferential equations of fractional orders, theory of non-Debye relaxation and a model of the large structure of the Universe.
Main publications:
V. V. Uchaikin. Anomalous transport equations and their application to fractal walking // Physica A, 255/1–2, 65–92 (1998).
V. V. Uchaikin, V. M. Zolotarev. Chance and Stability. Stable Distributions and their Applications. The Netherlands, Utrecht, VSP, 570 p. (1999).
V. V. Uchaikin. Montroll–Weiss problem, fractional equations and stable distributions // Intern. Journal of Theor. Physics, 39 (2000).
V. V. Uchaikin. Multidimensional symmetric anomalous diffusion // J. Chem. Phys., v. 88, 1141–1155, (2002).
V. V. Uchaikin, V. A. Litvinov, “Spontaneous clustering in Markov chains. IV. Clustering in turbulent environments”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 228 (2023), 58–84
2.
V. V. Uchaikin, E. V. Kozhemyakina, “Spontaneous clustering in Markov chains. III. Monte Carlo Algorithms”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 222 (2023), 115–133
V. V. Uchaikin, “Spontaneous clustering in Markov chains. II. Mesofractal model”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 221 (2023), 128–147
V. V. Uchaikin, “Spontaneous clustering in Markov chains. I. Fractal Dust”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 220 (2023), 125–144
V. V. Uchaikin, A. D. Erlykin, R. T. Sibatov, “Nonlocal (fractional-differential) model of cosmic ray transport in the interstellar medium”, UFN, 193:3 (2023), 233–278; Phys. Usp., 66:3 (2023), 221–262
V. V. Uchaikin, V. A. Litvinov, E. V. Kozhemyakina, “On an algorithm for simulation of multiparticles events”, Chelyab. Fiz.-Mat. Zh., 7:4 (2022), 466–479
2021
7.
V. A. Litvinov, V. V. Uchaikin, “Method of variational interpolation in inverse problems of anomalous diffusion of fractional-differential type”, Sib. Zh. Vychisl. Mat., 24:4 (2021), 393–408; Num. Anal. Appl., 14:4 (2021), 343–356
2019
8.
V. V. Uchaikin, “Atoms and photons: kinetic equations with delay”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 167 (2019), 62–96
9.
V. V. Uchaikin, “Fractional models in hydromechanics”, Izvestiya VUZ. Applied Nonlinear Dynamics, 27:1 (2019), 5–40
V. V. Uchaikin, V. A. Litvinov, “Variational interpolation of functionals in transport theory inverse problems”, Sib. Zh. Vychisl. Mat., 22:3 (2019), 363–380; Num. Anal. Appl., 12:3 (2019), 297–310
V. A. Litvinov, V. V. Uchaikin, “Adjoint equation method for solving the inverse diffusion source problem”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 11:3 (2019), 20–27
V. V. Uchaikin, “Nonlocal Turbulent Diffusion Models”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 154 (2018), 113–122; J. Math. Sci. (N. Y.), 253:4 (2021), 573–582
V. V. Uchaikin, V. A. Litvinov, “Nonlinear perturbation theory based on the variational principle: Model examples”, Izvestiya VUZ. Applied Nonlinear Dynamics, 26:6 (2018), 82–98
2016
14.
V. V. Uchaikin, A. S. Ambrozevich, R. T. Sibatov, S. A. Ambrozevich, E. V. Morozova, “Memory and nonlinear transport effects in charging–discharging of a supercapacitor”, Zhurnal Tekhnicheskoi Fiziki, 86:2 (2016), 95–104; Tech. Phys., 61:2 (2016), 250–259
A. S. Ambrozevich, R. T. Sibatov, V. V. Uchaikin, E. V. Morozova, “Experimental study of charging-discharging currents in supercapacitors”, University proceedings. Volga region. Physical and mathematical sciences, 2014, no. 4, 164–175
2013
16.
R. T. Sibatov, Ju. V. Saenko, V. V. Uchajkin, V. V. Saenko, E. V. Morozova, V. V. Shulezhko, E. V. Kozhemjakina, A. N. Byzykchi, G. G. Gusarov, D. A. Korobko, I. V. Jarovikova, K. V. Saltykova, I. I. Kozhemjakin, V. M. Juravlev, A. V. Juravlev, N. K. Aynullova, “Statistical Analysis of Radiation-Induced Dynamics of Cancer Cell Transcriptome Using Dna-Microarray Data”, Mat. Biolog. Bioinform., 8:2 (2013), 520–528
17.
V. V. Uchaikin, “Fractional phenomenology of cosmic ray anomalous diffusion”, UFN, 183:11 (2013), 1175–1223; Phys. Usp., 56:11 (2013), 1074–1119
V. V. Uchaikin, “Fractional models of cosmic ray acceleration in the Galaxy”, Pis'ma v Zh. Èksper. Teoret. Fiz., 92:4 (2010), 226–232; JETP Letters, 92:4 (2010), 200–205
V. V. Uchaikin, “On the fractional derivative model of the transport of cosmic rays in the Galaxy”, Pis'ma v Zh. Èksper. Teoret. Fiz., 91:3 (2010), 115–120; JETP Letters, 91:3 (2010), 105–109
R. T. Sibatov, V. V. Uchaikin, “Fractional differential approach to dispersive transport in semiconductors”, UFN, 179:10 (2009), 1079–1104; Phys. Usp., 52:10 (2009), 1019–1043
V. V. Uchaikin, R. T. Sibatov, “Fractional differential kinetics of dispersive transport as the consequence of its self-similarity”, Pis'ma v Zh. Èksper. Teoret. Fiz., 86:8 (2007), 584–588; JETP Letters, 86:8 (2007), 512–516
V. V. Saenko, V. V. Uchaikin, “An algorithm of statistical estimation of the parameters of fractionally stable distributions”, Sistemy i Sredstva Inform., 2006, no. special issue, 226–237
2003
23.
V. V. Uchaikin, V. V. Saenko, “Stochastic solution to partial differential equations of fractional orders”, Sib. Zh. Vychisl. Mat., 6:2 (2003), 197–203
V. V. Uchaikin, I. V. Yarovikova, “Numerical solution to the non-stationary problem of anomalous kinetic by the method of momenta”, Zh. Vychisl. Mat. Mat. Fiz., 43:10 (2003), 1536–1548; Comput. Math. Math. Phys., 43:10 (2003), 1478–1490
V. V. Uchaikin, “Anomalous diffusion of particles with a finite free-motion velocity”, TMF, 115:1 (1998), 154–160; Theoret. and Math. Phys., 115:1 (1998), 496–501
V. V. Uchaikin, “Monte Carlo simulation of particle transport with multiplication”, Zh. Vychisl. Mat. Mat. Fiz., 16:3 (1976), 758–766; U.S.S.R. Comput. Math. Math. Phys., 16:3 (1976), 209–217
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