1. knowledge of the main principles and ideas of the percolation theory;
2. skills in the application of the percolation theory to the analysis of transport phenomena;
3. knowledge of the main principles and ideas of the fractal analysis;
4. skills in the application of the fractal analysis in scientific investigations;
5. knowledge of the main ideas of the deterministic chaos theory;
6. knowledge of the main principles and concepts of the theory of solitons formation, particularly in solids.

absent

In the frames of the discipline the basic theories of percolation, fractal analysis, the deterministic chaos and solitons formation that are used for the transport phenomena analysis, are considered. The objective of the discipline is the introduction of the young scientists to the approaches of simulation and modeling of the transport phenomena as well as to the peculiarities of the existing models. Lections: 1. The elements of percolation theory. The principal points. The clusters. The percolation threshold. The task of the nodes. The task of the connections. The covering lattice. The including lattice. The white and the black percolation. Dual lattice. The oriented percolation. 2. The percolation thresholds for volume lattices. Ferromagnetic with long-range interaction and the task of the spheres. The electrical conductivity of doped semiconductors. Mott transition. The structure of the infinite cluster. Shklovskii – de Gennes model. The hopping conductivity; the description of the phenomena in the frames of the percolation theory. 3. The fractal analysis. The concept of the fractal. The coastline paradox. The Hausdorff – Bezikovich dimension. The triadic Koch curve. The similarity and scaling. The dimension of similarity. Examples of the fractals. The fractal dimension of the clusters. Diffusion-limited aggregation. 4. The formation of the fractal structures during the percolation. Self-similarity of the percolation clusters. The finite clusters of the percolation. The cluster radius of gyration. The fractal diffusion front. The relationship between the perimeter and the area. Fractals in solids. Airgels. The formation of fractal structures during the deformation. 5. Phase points and phase trajectories. The phase portrait of the system. Attractors. The strange attractors and deterministic chaos. Lorenz attractor. The fractal dimension of the strange attractors. Solitons. The solitary Russel wave, its main properties. The Korteweg–de Vries equation, its soliton solutions. Frenkel – Kontorova soliton. Sine – Gordon equation, its soliton solutions. Dislocations and anti-dislocations, their soliton properties. Breathers.

Basic
1. Mott N.F., Davis E.A., Electronic Processes in Non-Crystalline Materials, OUP Oxford, 2012.
2. Shkovskii B.I., Efros A.L., Electronic Properties of Doped Semiconductors, Moscow, 1979 (in Russian).
3. Zaiman J.M., Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems. Cambridge University Press, 1979.
4. Efros A.L., Physics and Geometry of Disorder. Moscow, 1982 (in Russian).
5. Feder J. Fractals. Springer, 1988.
6. Mandelbrot B.B., The Fractal Geometry of Nature. New York, W.H. Freeman and Company, 1983.
7. Lamb G.L., jr., Elements of Soliton Theory. New York?Chichester?Brisbane?Toronto, John Wiley & Sons, 1980.
8. Philippov A.T. The Many-faced soliton. Мoscow, Science, 1990 (in Russian).
9. Gleick J., Chaos: Making a New Science. Penguin (Non-Classics), 2008.
Additional
1. Sokolov I.M., Dimensions and other geometric critical indicators in percolation theory. Physics-Uspekhi (Advances in Physical Sciences) , 1986, vol. 150, p. 221 (in Russian).
2. Schroeder M..R. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York, W.H. Freeman and Company, 1992.
3. Fractals in Physics. Proceedings of 6th International Symposium on Fractals in Physics, 1985, Moscow, Mir, 1988 (in Russian).
4. Peitgen H.-O., Richter P.H., The Beauty of Fractals. Springer–Verlag, 1986.
5. Nicolis G., Prigogine I., Exploring Complexity: an Introduction. New York, W.H. Freeman and Company, 1989.
6. Prigogine I., Stengers I., Order out of Chaos. Man’s New Dialog with Nature. London, Heinemann, 1984.
8. Information resources
The sites dedicated to fractals: http://fraktalz.narod.ru/, http://ns1.npkgoi.ru/r_1251/investigations/fractal_opt/data3/data3.html, http://fractals.nsu.ru/, http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html, etc.

Ongoing monitoring is carried out for determination of the readiness for the class in the following forms:
• selective oral questioning before the class;
• frontal standardized questioning by the cards, tests during 5-10 minutes;
• the estimation of the activity during the class, proposals, original solutions, clarifications and definitions, additions to the previous answers, etc.
The control questions are divided into:
• test tasks – choose correct answers;
• problematic – creation of the situation of problematic character;
• questions-lines – to reveal the causal links.
The final control is carried out in accordance with the results of ongoing monitoring and the results of exam.