Special courses of Magister education program


Optics of Fractals

Lecturer: Dr. S.D. Andreev (68 hours)

The basic task of this course is acquaintance of students, specialising in the field of physics of aerosols, theory of energy transfer, with bases of the theory of dispersion of electromagnetic radiation, methods and particular results of experimental researches of optical properties of atmospheric aerosols, with basic physical and technical problems resulting in rather rigid restrictions of existing nowadays opportunities of researches and modern knowledge  about perspectives of development of this part of atmospheric physics.
As basis for the present course have served the own works of the author (experimental researches of aerosol  attenuation and its constituents in nature conditions, researches of spectral absorption of  aerosols, modelling of the optical characteristics of aerosols, researches of temporary and spatial variations of the optical characteristics of the atmosphere), carried out largely together with L.S. Ivlev.


Optics of fractal clasters

Lecturer: Dr. S.D. Andreev (32 hours)

The theory of fractal systems, nowadays one of most active  developing  direction of researches in the field of natural sciences finds the widest application in physics, allowing at a new level to describe many well investigated processes and phenomena, and in many cases to explain some effects, earlier, within the framework of traditional knowledge remaining not clear. One of the most perspective areas of application of the theory, physics of small particles agglomerates, in particular their optical properties, that represents doubtless interest for researches of optical properties of aerosols in connection with a wide distribution of similar formations in atmospheric conditions.
The basic task of an offered course is acquaintance of the post-graduate students specialising in the field of physics of aerosols and the theories of energy transfer with real properties of small particles agglomerates, caused by the features of their structure, and modern methods of their study and description. A basis for an offered course are the literature data and results of own researches of the author. In connection with novelty of a considered material (for the first time given subjects have begun to be studied about 10 years ago), the accessible literature practically is absent (in Russian about ten articles, a little  more in English).


Atmospheric electricity

Lecturer : PhD S.S.Vlasenko (34 hours)

 The course is devoted to consideration of questions connected to passing of electrical processes in the atmosphere. The given direction in development of physics of the atmosphere historically was the first and keeps the actuality till now.


Experimental atmospheric dynamics

Lecturer: Ph.D N.M. Gavrilov; 6 cr
(see course details at lecturer's home page)

The basics of modern methods of observations of variations of atmospheric parameters by means of rockets, radars, lidars and satellite are considered. The basics of indicated modern methods of research of atmospheric dynamics are considered from uniform positions. Comparing to many similar courses the large attention is given to the analysis of accuracy and opportunities of various methods, connected with their space and temporary resolution. Accuracy and opportunities of various methods, as well as main results of measurements are analized. The lectures are recommended to students, specializing in the physics of atmosphere, ecology, geophysics, physics of ionosphere and radiophysics.


Introduction into chaotic atmospheric dynamics

Lecturer: P.I. Domnin (32 hours)

   The main goal of this course is to apply the concepts and methods of the dynamical system  theory  (DST) or deterministic chaos theory (DCT) to the atmospheric physics problems. The TDS basic notions ( as phase space, phase trajectory, regular and strange attractors, Lyapunov exponents etc.) are introduced and further used  analyzing the dynamics of simple low-dimensional systems (as Van der Paul or Duffing oscillators, the Rayleigh-Benard convection and others). The DST and DCT open the new perspectives for understanding nonlinear atmospheric dynamics.  This is illustrated by detailed analysis of Lorenz s three-dimensional atmospheric model. The important part of the course is devoted to the predictability problems of  nonlinear system dynamical evolution  generally and  atmospheric one in particular. Dynamics of error growth and role of scales on predictability and the necessity of a statistical approach to the forecasting of atmosphere dynamic evolution is explored. The passage from short-scale atmospheric dynamics to global climate dynamics is also outlined. Some ideas aiming to connect these two scales of atmospheric variability are  discussed.


Physical ecology

Lecture: prof. L.S. Ivlev.  (32 hours)

1. General notions about the physical ecology, biosphere. Monitoring of general physical parameters.
2. Energetics and environment. Stability of the biosphere like the main condition of environment preservation. The principle of Le-Chatelier in the biosphere. The role of artificial power sources in  changes of the biosphere.
3. Pollution in the environment. Pollution of the earth, water, atmosphere. Radioactive pollution. Electromagnetic and acoustic pollution. Pollution of flora and fauna.
4. Changes in the biosphere due to the human activity.
5. Changes of the Earth climate. Introduction in the physical climatology. The atmosphere composition and the climate. Influences on the climate. Nuclear winter.
6. Modelling and forecasting of the environment parameters. Problem of the liquid shorts purification. Catastrophes. Optimal planning of economy development. Urbanisation problems.


Local methods of monitoring of atmosphere

Lecturer: Dr., Prof.  L.S. Ivlev  (32 hours)

In this course the local methods of atmospheric monitoring used by various special departmental and research organisations are analysed.
Are considered the basic physical principles of action of devices for the control and analysis of concentration, chemical structure and other  characteristics of small atmospheric components and aerosols, and also radio-activity of air. The features of processing of results of local measurements and their opportunities are explicated. The examples of using the local mesurements in the solution of ecology problems are given.


Physics of fractals

Lecturer:  Dr. E.F. Mihailov (34 hours)

The basic task of the course - acquaintance of students, specialised in the field of physics of the atmosphere with bases of the theory of fractal analysis and methods of its using in practical tasks. The special attention is given to application of a method in optics and aerodynamics of atmospheric aerosols.
Basis of the course are the fundamental works in the field of the theory of fractal systems, original literature on application  of fractal analysis in applied researches, own works of the author and his colleagues.


The energy transfer in atmospheres

Lecturer: Prof. D.I. Nagirner; 6 cr

In a course of lectures the exact analytical and numerical methods of the emission energy transfer in planetary atmospheres are considered. The theory of energy transfer with frequency redistribution is stated in detail.


Mathematics of the remote soundings

( Prof., Dr. Yu.M.Timofeyev )

Direct and inverse problems of mathematical physics. Direct and inverse problems of atmospheric optics. Examples of the inverse problems of atmospheric optics. Correctness of the mathematical tasks ( Hadamard, Tikhonov ). Incorrectness of the inverse problems. Fredholm integral equation of the first kind. Variational derivatives and linearization of nonlinear problems. Formulation of real inverse problems of atmospheric optics. Different sources of errors in the solution. Regularization principles. A priori information. Different types of the a priori information. Root mean square solution of the inverse problems and its instability. Coefficient of amplifying the measurement errors. Deterministic methods of solving the integral equation.
Statistical methods of the solution. Derivation of the inverse operator. Error matrix of the solution. Iterative methods of solving the inverse problems. Problem of a convergence. Information content of indirect measurements. Optimal conditions of the measurements. Vertical resolution of the indirect measurements and averaging operator. Examples of solving different inverse problems of atmospheric optics.
Practice. Numerical realization and analysis of inverse problems of atmospheric optics: retrieval of the temperature, humidity, trace gases content, aerosol and etc.


Spectroscopy of atmospheric gases

Lecturer: Prof. Michael V. Tonkov. 4 cr.

The course is conventionally delivered to fourth year students whose speciality is physics of atmosphere.

  1. The first part deals with the spectra of non-interacting molecules. Harmonic oscillator and rigid rotor models. The anharmonicity effects on vibrational and rotational motion and the centrifugal distortion for diatomic molecules. Polyatomic molecules: methods of vibrational problem solution, the anharmonicity effects including Fermi-resonance, elementary information on group theory. The vibration-rotation spectra of linear molecules, symmetrical, asymmetrical, and spherical tops. The evidences of vibrational-rotational interactions (Coriolis interaction and l-doubling) in such spectra.
  2. The second part of the course deals with line broadening processes and effects of molecular interactions on IR absorption spectra. The radiation field, Doppler, and molecular collisional broadening. The Anderson theory of collisional broadening. Line mixing effect. Collision-induced spectra.

Geomagnetic phenomena and physics of ionosphere

lecturer : A. V. Usmanov

 Physics of geomagnetic phenomena is studied as a constituent of the solar-terrestrial physics. The basic facts about the sun, solar corona, and solar wind. Chapman’s static and Parker’s dynamic models of the solar corona. Analytical representation of the Earth’s magnetic field. Interaction of the solar wind with the geomagnetic field in the MHD approximation. The magnetosphere of the Earth, its structure. Distribution and properties of the magnetospheric plasma, adiabatic invariants. Radiation belts, ring current. Ionosphere, ionospheric conductivity, ionospheric current systems. Geomagnetic disturbances and magnetospheric storms. Indices of geomagnetic activity. (32 hours).


Circulation and energetics of the atmosphere

Lecturer: prof. G.M. Shved; 5 cr.; 54 hr.

Mechanisms of heating and cooling of the planetary atmospheres. Transformation of energy forms. Lorenz energy cicle. Special features of the vertical profiles of temperature in the planetary atmospheres. Geostrophic adjustment. Equations of absolute and potential vorticities. Convection in the planetary atmospheres, meso-scale Rayleigh-Benard convection, conditional instability of the second kind, macro-scale Hadley circulation. Barotropic and baroclinic instability, Rossby regime of circulation, baroclinic adjustment. Motions in midlatitude synoptic systems, cyclones and anticyclones, fronts. Tropical cyclones.


Waves in the atmosphere

Lecturer: prof. G.M. Shved; 5 cr.; 32 hr.

Classification of wave types. Linear theory acoustic-gravity waves (AGW). Equation of the wave energy. Sources and propagation of AGW. Observations of AGW. Inertio-gravity waves. Observations of global waves. Normal Rossby modes. Lunar and solar atmospheric tides and there sources. Equatorial waves and there sources. Gravity-wave breaking, forcing zonal-mean circulation by waves. Quasi-biennial oscillation of zonal wind in the equatorial stratosphere.