Present field of interest:
Levy-stable and fractionally stable statistics; stochastic fractal structures and processes; integro-differential equations of fractional orders and their applications to anomalous diffusion, non-Debye relaxation, plasma turbulence, cosmic ray propagation, large scale structure of the Universe; Monte Carlo methods.
Scientific biography and main results:
The Ph.D. thesis of V.V. Uchaikin concerned application of the perturbation theory to theoretical
problems of radiation shielding and non-destructive testing. His main results of that period are the theory of images blurred by Compton scattering of radiation, the Monte Carlo algorithm of calculation of influence of local inhomogeneities, generalized perturbation theory applied to transition effects in cosmic ray physics.
Since 1973 till 1989, V.V. Uchaikin had been worked in the Altai State University (Barnaul, Russia). His scientific group became known through development of stochastic transport theory for high-energy particles in cosmic rays, introducing the adjoint approach to cascade theory, numerical investigation of the spatial distributions in electromagnetic component of extensive air showers (EAS), creation of the two-component model of stochastic fluctuations in EAS, the transport theory in random media, the variational method of interpolation of solutions of integro-differential equations and sensitivity analysis based on this theory. Some of the results are used now in different codes of processing of cosmic ray arrays data (in particular, in the code ”CORSIKA”).
His second, Sc.D. thesis was titled ”Stochastic Importance Concept and its Applications to Transport Problems” and defended at the meeting-point of two sciences: Nuclear Physics and Geophysics.
In 1995, V.V.Uchaikin found a new scientific direction in Ulyanovsk State University (Ulyanovsk, Russia): numerical simulation of stochastic fractals, fractal diffusion and diffusion on fractals. He developed conception of mesofractals applied to the large-scale structure of the Universe, calculated of penetration of light in such structures, offered a new model of non-Debye relaxation, investigated a new class of statistical distributions called ”fractionally stable distributions” and a new class of random processes - subordinated Levy motion, created the code for simulations of such distributions and processes, investigated new regimes of anomalous diffusion, stated the difference between fractal diffusion and diffusion on fractals. More than 50 articles have been published in these direction including the books ”CHANCE AND STABILITY: Stable Distributions and their Applications” (V.V. Uchaikin and
V.M. Zolotarev, series Modern Probability and Statistics, VSP, Utrecht, 1999, 570 pp.) and ”FRACTIONAL DERIVATIVES METHOD” ( V.V.Uchaikin, Artishock-Press, 2008, 500 pp., in Russian).