Since 1973 till 1989, V.V. Uchaikin 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 atmospheric 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 based on it sensitivity analysis. 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 "Concept of Stochastical Importance 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 the new class of statistical distributions called "fractional 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. About 50 articles have been published in these direction including the book "CHANCE AND STABILITY: Stable Distributions and their Applications" (V.V. Uchaikin and V.M. Zolotarev, series Modern Probability and Statistics, VSP, Utrecht, 1999, 570 p.).

PUBLICATIONAL ACTIVITY

Main scientific papers (1997-2003)

1. V. V. Uchaikin,
   Fractal Walk and Walk on Fractal ,
   Technical Physics, 49, No. 7, 927-932 (2004).
2. V. V. Uchaikin,
   The mesofractal Universe Driven by Raeleigh-Levy Walks ,
   General Relativity and Gravitation, 36, No. 7, 1689-1717 (2004).
3. V. V. Uchaikin, D.A. Korobko,
   Fractal Model of Transport: Low-angle Approximation, ,
   Technical Physics, 49, No. 5, 532-539 (2004).
4. V. V. Uchaikin, R.T. Sibatov,
   One-dimensional Fractal Walk at a Finite Free Motion Velocity, ,
   Tecnical Physics Letters, 30, No. 4, 316-318 (2004).
5. V. V. Uchaikin,
   Relaxation processes and fractional differential equations,
   International Journal of Theoretical Physics, 42, No. 1, 121-134 (2003).
6. V. V. Uchaikin,
   Anomalous Diffusion and Fractional Stable Distributions,
   Journal of Experimental and Theoretical Physics, 97, No. 4, 810-825 (2003).
7. V. V. Uchaikin,
   Self-similar anomalous diffusion and Levy-stable laws,
   Physics-Uspekhi, 46 (8), (2003).
8. A.A. Lagutin, V.V. Uchaikin,
   Anomalous diffusion equation: Application to cosmic ray transport,
   Nuclear Instr. And Meth. In Physics Researth B., p.212-216 (2003).
9. V. V. Uchaikin and I. V. Yarovikova,
   Numerical Solution of the Time-Dependent Problem of Anomalous Finite-Velocity Diffusion by the Moment Method,
   Computational Mathematics and Mathematical Physics, 43, No. 10, 1478 (2003)
10. V.V.Uchaikin,
    Monte-Carlo method for numerical investigations of fractal kinetics,
    CD-Disk XXIII Seminar on stability problems for stochastic model, 2003.
11. V.E. Bening, V. Yu. Korolev, V. N. Kolokoltsov, V.V. Saenko, V.V. Uchaikin, V.M Zolotarev,
    Estimation of Parameters of Fractional Stable Distributions,
    Nottingham Trent University Preprint No.4/03 (Nottingham Trent University, 2003).
12. V.V. Uchaikin, V.V. Saenko,
    Stochastic solution to partial differential equations of fractional orders,
    Sibirian Journal of Computational Mathematics, 6, №2, 197-203 (2003).
13. V.V. Uchaikin,
    Subordinated Levy-Feldheim Motion as a Model of Anomalous Self-Similar Diffusion,
    Physica A 305, 205-208 (2002).
14. V.V. Uchaikin,
    Multidimensional Symmetric Anomalous Diffusion,
    J. Chem. Phys. 88, 1141-1155 (2002).
15. V.V. Uchaikin,
    Anomalous Diffusion on a one-dimensional Fractal Lorentz Gas with Trapping Atoms,
    in: Emergent Nature, Editor M. Novak, World Scientific, New Jersey, 411-421 (2002).
16. V.V. Uchaikin, V.V. Saenko,
    On the Theory of Classic Mesodiffusion,
    J. Techn. Physics, 46, 139-146 (2001).
17. V. Kolokoltsov, V. Korolev and V. Uchaikin,
    Fractional Stable Distributions,
    J. Math. Sciences, 105, 2569-2576 (2001).
18. A.A. Lagutin, Yu.A. Nikulin, V.V. Uchaikin,
    The "Knee" in the Primary Cosmic Ray Spectrum as Consequence of the Anomalous Diffusion of the Particles in the Fractal Interstellar Medium,
    Nuclear Physics B 97, 267-270 (2001).
19. V. Yu. Korolev, V. V. Uchaikin,
    Some Limit Theorems for Compound Renewal Processes with Heavy Tails,
    Theory Probab. Appl. 45, 809-811 (2000).
20. V.V. Uchaikin, V.V. Saenko,
    Telegraph Equation in Random Walk problem,
    J. Physical Studies 4, 371-379 (2000).
21. V.V. Uchaikin,
    Montroll-Weiss Problem, Fractional Equations and Stable Distributions,
    Intern. J. Theor Physics, 39, 2087-2105 (2000).
22. V.V. Uchaikin,
    Small-Angle Multiple Scattering on a Fractal System of Point Scatterers,
    in: Paradigms of Complexity, Editor M. Novak, World Scientific, Singapore, 41-49 (2000).
23. V.V. Uchaikin,
    Subdiffusion and Stable Laws,
    J. Exper. Theor. Physics, 88, 1155-1163 (1999).
24. V.M. Zolotorev, V.V. Uchaikin, V.V. Saenko,
    Superdiffusion and Stable Laws,
    J. Exper. Theor. Physics, 88, 780-787 (1999).
25. V.V. Uchaikin,
    Evolution Equations for Levy Stable Processes,
    Intern. J. Theor. Physics, 38, 2377-2388 (1999).
26. V.V. Uchaikin, D.A. Korobko,
    Theory of Multiple Scattering in a Fractal Medium,
    Techn. Physics Letters, 25, 6, 435-437 (1999).
27. V.V. Uchaikin,
    Anomalous Transport Equations and their Application to Fractal Walking,
    Physica A 255/1-2, 65-92 (1998).
28. V.V. Uchaikin, G.G. Gusarov, D.A. Korobko,
    Fractal Properties of Clusters Generated by Branching Processes,
    J. Math. Sciences 92, 3940-3948 (1998).
29. V.V. Uchaikin, D.A. Korobko,
    On Existence of Non-Zero Mass Density for Fractal Point-like Masses with a Power-Type Distribution,
    J. Math. Sciences 92, 4008-4012 (1998).
30. V.V.Uchaikin,
    Renewal Theory for Anomalous Transport Processes,
    J. Math. Sciences, 92, 4085-4096 (1998).
31. V.V. Uchaikin, G.G. Gusarov, I.F. Gismjatov, V.A. Svetukhin,
    Paired Levy-Mandelbrot Trajectory as a Homogeneous Fractal,
    Intern. J. Bifurcation and Chaos, 8, 977-984 (1998).
32. V.A. Slobodenyuk, V.V. Uchaikin,
    The Fractal Nature of the Asymptotic Solution of Integral Equation with Stable (in Levy's sense) Kernel,
    J. Math. Sciences, 89, 1570-1575 (1998).
33. V.V. Uchaikin,
    Anomalous Diffusion of Particles with a Finite Free-Motion Velocity,
    Theor. Math. Physics, 115, 496-501 (1998).
34. 
    V.V. Uchaikin, G.G. Gusarov,
    The Exactly Resolved Non-lattice Model of Random Media Based on Markov Walks with a Stable Law for Jumps,
    J. Math. Sciences, 83, 439-346 (1997).
35. V.V. Uchaikin,
    Mathematical Modelling of the Distribution of Galaxies in the Universe,
    J. Math. Sciences, 84, 1175-1178 (1997).
36. V.V. Uchaikin, G.G.Gusarov,
    Levy Flight Applied to Random Media Problems,
    J. Math. Physics, 38, 2453-2464 (1997).
37. V.V. Uchaikin,
    Similarity Relations for Space-Time Distributions in Inclined EMC in Atmosphere,
    Nuclear Physics B (Proc. Suppl.), 52B, 149-151 (1997).
38. A.A. Lagutin, Yu.A. Nikulin, V.A. Litvinov, V.V. Uchaikin,
    Sensitivity Theory in the Problem of Highest Energy EAS Simulation,
    Nucl. Physics B (Proc. Suppl.) 52B, 158-160 (1997).
39. V. Uchaikin and D. Korobko,
    Global Mass Density for a Fractal Model of the Universe,
    Gravitation and Cosmology, 3, 323-327 (1997).

Main Monographs

1. V.V. Uchaikin, V.M. Zolotarev,
   Chance and Stability. Stable Distributions and their Applications.
   Netherlands, Utrecht, VSP, - 570p. (1999).
2. V.V.Uchaikin, A.A.Lagutin, V.A. Litvinov,
   The Sensitivity Theory in Cosmic Ray Physics.
   Barnaul, Altaj State University Press, (1995) (in Russian).
3. V.V.Uchaikin, A.A.Lagutin,
   The Stochastic Importance.
   Moscow, Energoatomizdat (1993) (in Russian).
4. V.V.Uchaikin, V.V.Ryzhov,
   The Stochastic Theory of High Energy Particle Transport,
   Novosibirsk, Nauka, Siberian Branch (1988) (in Russian).
5. V.V. Uchaikin, A.V.Lappa,
   Probabilistic Problems in Transport theory,
   Tomsk, Tomsk University Press (1978) (in Russian).
6. A.M. Kolchuzhkin,V.V.Uchaikin.
   Introduction into the Theory of Particle Penetration through a Matter,
   Moscow, Atomizdat (1978) (in Russian).