Scientific Seminar "Mathematical modeling"

The plan of the workshop on the 2014-2015

25.09.2014, 14:30

Rybakov Yury P. DrSci,prof., Head of Dept. of Theoretical Physics and Mechanics PFUR

Spin excitations in a chiral model of graphene


We consider the 8-spinor generalization of the chiral model of graphene, including spin and quasispin excitation. The interaction with the electromagnetic field is performed by lengthening derivatives. This leads to the electromagnetic current, comprising current conduction current and the current of the London Pauli polarization-magnetization. As an illustration of the model, the problem of the structure of the spin excitations in the presence of an external constant magnetic field.

23.10.2014, 14:30

Rudoy Yuri G., Department of Theoretical Physics and Mechanics, People’s Friendship University of Russia, Moscow, Russian Federation



This monograph presents a systematic, concise and modern view on some mathematical aspects of equilibrium thermodynamics and statistical mechanics and includes the main formal structures involved in this parts of physics — i.e., geometrical, probabilistic, algebraic and functional. Many attention is devoted to the geometrical structure which exploits the methods of contact geometry and differential forms. The evolution of ideas is presented in profound historical context from the very beginning — e.g., Carnot, Kelvin, Clausius, Planck, Gibbs.

To the first time in monographic literature a subsequent presentation of information geometry, or geometrostatistics, is given including it’s quantum, or non-commutative generalization. This method is applied to the problem of estimation of parameters which characterize the probability density function or density matrix. Some physical examples are considered, in particular classical and quantum ideal gas, quantum harmonic oscillator and also the spin paramagnetic. The special attention is given to the uncertainty relations – thermodynamic as well as quantum ones.

27.11.2014, 14:30

Podgainy Dmitry V. PhD, SR, Scientific secretary of LIT JINR

Maxwell's theory of electrodynamics in elastic compressive model of perfect vacuum


From the well-known analogy between Lame’s equations, that is the basis of the linear elasticity theory, and electrodynamics equations it follows that elastic continuum may play the role of a macroscopic model of perfect vacuum; i.e. the medium in which electromagnetic waves are distributed in the absence of matter. However, full correspondence between Lame and Maxwell’s equations is reached under the conditions of elastic continuum incompressibility. Accounting of compressibility of continuum leads to modification of Maxwell’s equations, particularly there is a need to introduce a new 3-dimensional scalar field into the electrodynamic equation system. The report provides one of way of introduction of such scalar field. In the extended electrodynamics this field exists along with electric and magnetic field, and may be propagated together with the electric field in elastic compressive vacuum as a compressional electro-scalar wave (i.e. waves in which the direction of its distribution and electrical vector are collinear). The solution of extended equations by means of potentials leads to the appearance of additional to the 4-vectorial electrodynamic potential new 4-scalar potential that, in terms of quantum-field concept, describes scalar massless particles with zero spin, the superposition of which implements Coulomb field.

11.12.2014, 14:30

Yudin Ivan P. PhD, SR Leading researcher of LHEP JINR

Direct and inverse problems of mathematical modeling in the physics of charged particle beams


The results of mathematical modeling related to the solution of inverse and direct problems of nonlinear ion optics, magnetostatic problems (finding the distribution of magnetic fields, as well as the configuration of the magnetic system for the realization of a given field distribution) for accelerators and experimental facilities, as well as the inverse problem - the problem of restoring momentum charged particles in the experimental physical units.

The study was conducted on the basis of the author developed new models, algorithms and software. Analyzed the role and the optimal ratio between the direct and inverse problems for mathematical modeling problems of accelerator physics.

The solution of a number of specific tasks beam physics (numerical simulation results planned and existing accelerators and experimental facilities (JINR) and IHEP (Protvino)).



15.01.2015, 14:30

Sorokin Leonid V.,  Ph.D, Associate Professor, Peoples’ Friendship University of Russia, Economic Faculty, Economic & mathematical modeling department

Estimation of the Global Mean Sea Level change as a function of the Global Surface Air Temperature (Natural Disaster scenarios)


During the pre-industrial period the variation of Global Surface Air Temperature on 1 °С change Global Mean Sea Level on 24,79 m (SL < 0) and in the modern time — 7,5 m (SL > 0). For the Global Warming period the rising rate of the Global Mean Sea Level will slowing down in 3,3 times simultaneously increases the Global Surface Air Temperature rate in 3,3 times. In the present time the Global Surface Air Temperature is 0,8 °С higher then pre-industrial level that will lead to the sea-level rise on 6 m. The EU Strategy on adaptation to climate change assume that the global warming must be limited to below 2 °C above pre-industrial level, that within some ages will lead to the sea-level rise on 15 m (15 times grater thanfor the A1B scenario, with the Sea-level rise up to 1 m). So in the future conditions the EU Strategy on adaptation to climate change do not assume rapid climate changes that will significantly increase the economic losses from Sea Level Rise.


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