# A. V. Latyshev

## Contact Details

NameA. V. Latyshev |
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## Pubs By Year |
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## Pub CategoriesPhysics - Plasma Physics (30) Mathematical Physics (15) Mathematics - Mathematical Physics (15) Physics - Fluid Dynamics (8) Quantum Physics (7) Mathematics - Optimization and Control (1) Instrumentation and Methods for Astrophysics (1) |

## Publications Authored By A. V. Latyshev

Classical plasma with arbitrary degree of degeneration of electronic gas is considered. In plasma N (N>2) collinear electromagnatic waves are propagated. It is required to find the response of plasma to these waves. Read More

The boundary problem about behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with diffusion boundary conditions is analytically solved. The kinetic equation of Vlasov - Boltzmann with integral of collisions of type BGK (Bhatnagar, Gross, Krook) and Maxwell equation for electric field are applied. Distribution function for electrons and electric field in plasma in the form of expansion under eigen solutions of the initial system of equations are received. Read More

Quantum plasma with arbitrary degree of degeneration of electronic gas is considered. In plasma N (N>2) external electromagnetic waves are propagated. It is required to find the response of plasma to these waves. Read More

The analytical solution of the boundary problem on behaviour (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in a slab of the conducting medium is received. The kinetic Vlasov---Boltzmann equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and Maxwell equation for electric field are applied. Mirror (reflections) boundary conditions are used. Read More

One of classical boundary problems of the kinetic theory (a problem about thermal sliding) of the rarefied gas along a flat firm surface is considered. Kinetic Boltzmann equation with model integral of collisions BGK (Bhatnagar, Gross, Krook) is used. As boundary conditions the boundary Maxwell conditions (mirror-diffuse) are used. Read More

In the present work the second Stokes problem about behaviour of the rarefied gas filling half-space is formulated. A plane limiting half-space makes harmonious fluctuations with variable amplitude in the plane. The amplitude changes on the exponential law. Read More

The second Stokes problem about behavior of the viscous fluid (matter) filling half-space is considered. A flat surface limiting half-space makes harmonious oscillations in the eigen plane. The equations of mechanics of the continuous environment are used. Read More

Earlier electron influence on sound absorption in metal on basis of the assumption of deformation of Fermi-surfaces under the influence of a sound wave was considered. In the present work other approach to this problem will be considered. Our approach based on the account of dynamic (kinetic) interaction of electronic gas with lattice fluctuations. Read More

We prove that the differential equation for the null-curves of pseudo-Euclidean space R^{2,n} defines a flat dynamical system in the sense of optimal control theory. The connection with general gauge theories is briefly discussed. Read More

At present, the principal limitation on the resolution and contrast of astronomical imaging instruments comes from aberrations in the optical path, which may be imposed by the Earth's turbulent atmosphere or by variations in the alignment and shape of the telescope optics. These errors can be corrected physically, with active and adaptive optics, and in post-processing of the resulting image. A recently-developed adaptive optics post-processing technique, called kernel phase interferometry, uses linear combinations of phases that are self-calibrating with respect to small errors, with the goal of constructing observables that are robust against the residual optical aberrations in otherwise well-corrected imaging systems. Read More

Quantum plasma with arbitrary degree degeneration of electronic gas is considered. Plasma is in two external electromagnetic fields. It is required to find the plasma response on this fields. Read More

From kinetic Vlasov equation for collisional plasmas distribution function in square-law approximation on sizes of intensivities of electric fields is received. The known integral of collisions of relaxation type, so-called BGK (Bhatnagar, Gross, Krook) integral of collisions is considered. The formula for calculation electric current at any temperature (any degree of degeneration of electronic gas) is deduced. Read More

Classical plasma with any degree degeneration of electronic gas is considered. In plasma two external electromagnetic field are propagation. It is required to find the plasma response on these fields. Read More

Kinetic Vlasov equation for collisional Maxwellian plasmas is used. Collision integral of BGK (Bhatnagar, Gross and Krook) type is applied. From Vlasov equation we find distribution function of electrons in square-law approximation on size of transversal electric field. Read More

Kinetic Vlasov-Boltzmann equation for degenerate collisional plasmas with integral of collisions of relaxation type BGK (Bhatnagar, Gross and Krook) is used. Square-law expansion on size of intensity of electric field for kinetic equation, Lorentz's force and integral of collisions is considered. It is shown, that nonlinearity leads to generation of the longitudinal electric current directed along a wave vector. Read More

Kinetic Vlasov equation for collisional plasmas with BGK (Bhatnagar-Gross-Krook) collision integral is used. The case of arbitrary temperature (i.e. Read More

The analysis of nonlinear interaction of transversal electromagnetic field with degenerate collisionless classical and quantum plasmas is carried out. Formulas for calculation electric current in degenerate collisionless classical and quantum plasmas are deduced. It has appeared, that the nonlinearity account leads to occurrence of longitudinal electric current directed along a wave vector. Read More

The analysis of nonlinear interaction of transversal electromagnetic field with Maxwellian collisionless classical and quntum plasmas is carried out. Formulas for calculation electric current in Maxwellian collisionless classical and quntum plasmas are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. Read More

From Vlasov kinetic equation for collisionless plasmas distribution function in square-law approximation on size of electromagnetic field is received. Formulas for calculation electric current at any temperature (any degree of degeneration of electronic gas) are deduced. The case of small values of the wave numbers is considered. Read More

The analysis of nonlinear interaction of transversal electromagnetic field with collisionless plasma is carried out. Formulas for calculation electric current in collisionless plasma with arbitrary degree of degeneration of electronic gas are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. Read More

Half-space boundary Kramers' problem about isothermal sliding of moderate dense gas with accomodation boundary conditions along a flat firm surface is solving. The new method of the solution of boundary problems of the kinetic theory is applied (see JVMMF, 2012, 52:3, 539-552). The method allows to receive the solution with arbitrary degree of accuracy. Read More

In the present work the classical problem of the kinetic theory of gases (the Smoluchowsky' problem about temperature jump in rarefied gas) is considered. The rarefied gas fills half-space over a flat firm surface. logarithmic gradient of temperature is set far from surface. Read More

We consider two classes of linear kinetic equations: with constant collision frequency and constant mean free path of gas molecules (i.e., frequency of molecular collisions, proportional to the modulus molecular velocity). Read More

For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function are linearize concerning the absolute Maxwellian, given far from a wall. Quantities of of temperature and concentration jumps are found. Read More

For the one-dimensional linear kinetic equations with collisional frequency of the molecules, proportional to the module velocity of molecules, analytical solutions of problems about temperature jump and weak evaporation (condensation) in rarefied gas are received. Quantities of temperature and concentration jumps are found. Distributions of concentration, mass velocity and temperature are constructed. Read More

For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and Krook) and constant frequency of collisions of molecules. Distribution of concentration, mass speed and temperature is received. Read More

For the one-dimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and Krook) and frequency of collisions of molecules, affine depending on the module molecular velocity. Read More

The analysis of nonlinear interaction of transversal electromagnetic field with quantum collisionless plasma is carried out. Formulas for calculation electric current in quantum collisionless plasma at any temperature are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. Read More

The one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and frequency of collisions affine depending on the module of molecular velocity is constructed. Laws of preservation of number of particles, momentum and energy at construction equation are used. Separation of variables leads to the characteristic equation. Read More

The analysis of nonlinear interaction of transversal electromagnetic field with quantum collisionless plasma is carried out. Formulas for calculation electric current in quantum collisionless plasma at any temperature are deduced. It has appeared, that the nonlinearity account leads to occurrence of the longitudinal electric current directed along a wave vector. Read More

The analytical solution of a problem on isothermal sliding of rarefied gas along a flat firm surface (the Kramers problem) for Holway-Shakhov equation is presented. Read More

The new generalized kinetic equation is offered. This equation represents a hybrid Shakhov's equation and ellipsoidal statistical Holway's equation. Equation constants are expressed through such physically significant quantities, as viscosity of gas, its heat conductivity and self-diffusion coefficient. Read More

The kinetic description of magnetic susceptibility and Landau diamagnetism of quantum collisional plasmas with any degeration of electronic gas is given. The correct expression of electric conductivity of quantum collisional plasmas with any degeration of electronic gas (see A. V. Read More

With the use of correct expression of the electric conductivity of quantum collisional plasmas (A. V. Latyshev and A. Read More

With the use of correct expression of the electric conductivity of quantum collisional degenerate plasmas (A. V. Latyshev and A. Read More

Formulas for transverse conductance and dielectric permeability in quantum non-degenerate and Maxwellian collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. The special case of frequency of collisions proportional to the module of a wave vector is considered. Read More

Formulas for transverse conductance and dielectric permeability in quantum degenerate collisional plasma with arbitrary variable collision frequency in Mermin's approach are deduced. Frequency of collisions of particles depends arbitrarily on a wave vector. For this purpose the kinetic Shr\"{o}dinger - Boltzmann equation with collision integral of relaxation type in momentum space is applied. Read More

Formulas for the longitudinal dielectric permeability in quantum degenerate collisional plasma with the frequency of collisions proportional to the module of the wave vector, in Mermin's approach, are received. Equation of Shr\"{o}dinger - Boltzmann with integral of collisions relaxation type in Mermin's approach is applied. It is spent numerical and graphic comparison of the real and imaginary parts of dielectric function of non-degenerate and maxwellian collisional quantum plasma with a constant and a variable frequencies of collisions. Read More

Formulas for the longitudinal dielectric permeability in quantum non-degenerate and maxwellian collisional plasma with the frequency of collisions proportional to the module of the wave vector, in Mermin's approach, are received. Equation of Shr\"{o}dinger - Boltzmann with integral of collisions relaxation type in Mermin's approach is applied. It is spent numerical and graphic comparison of the real and imaginary parts of dielectric function of non-degenerate and maxwellian collisional quantum plasma with a constant and a variable frequencies of collisions. Read More

The dependence of the chemical potential jump coefficient on the evaporation coefficient is analyzed for the case in which the evaporating component is a Bose gas. The concentration of the evaporating component is assumed to be much lower than the concentration of the carrier gas. The expression for the chemical potential jump is derived from the analytic solution of the problem for the case in which the collision frequency of molecules of the evaporating component is constant. Read More

The formula for dielectric function of non-degenerate and maxwellian collisional plasmas is transformed to the form, convenient for research. Graphic comparison of longitudinal dielectric functions of quantum and classical non-degenerate collisional plasmas is made. Read More

Detailed deducing of formulas for longitudinal electric conductivity and dielectric permeability in the quantum degenerate collisional plasma with constant collision frequency in Mermin' approach is given. The kinetic Schr\"{o}dinger-Boltzmann equation in momentum space in relaxation approximation is used. It is shown that when collision frequency of plasma particles tends to zero (plasma passes to collisionless one), the deduced formula for dielectric function passes to the known Lindhard' formula for collisionless plasmas. Read More

Formulas for longitudinal electric conductivity and dielectric permeability in the quantum non-degenerate collisional plasma with the frequency of collisions depending on momentum in Mermin' approach are received. The kinetic equation in momentum space in relaxation approximation is used. It is shown that when Planck's constant tends to zero, the deduced formula passes to the corresponding formula for classical plasma. Read More

The Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. On an example of Kramers' problem the new generalized method of a source of the decision of the boundary problems from the kinetic theory is developed. The method allows to receive the decision with any degree of accuracy. Read More

In the present work zero of dispersive function from Stokes' second problem are investigated. Stokes' second problem is a problem about behavior of the rarefied gas filling half-space. A plane, limiting half-space, makes harmonious oscillations in the plane. Read More

Second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane limiting half-space makes harmonious fluctuations in the plane. The kinetic equation with modelling integral collisions in form of ellipsoidal statistical model is used . Read More

Distribution of mass velocity of quantum Bose-gas in half-space is received. Far from half-space border the gradient of mass velocity is set. The mass velocity of Bose-gas directly at a wall is found also. Read More

Formulas for transverse conductance in quantum collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. Read More

Formulas for transverse conductance in quantum Maxwellian collisional plasma are deduced. The kinetic Von Neumann equation in momentum space with collision integral in the relaxation form is used. It is shown, that at Planck's constant tends to zero the derived formula transfers to the classical one. Read More

Formulas for transverse conductance in quantum non-degenerate collisional plasma are deduced. The kinetic equation in momentum space in the relaxation approach is used. It is shown, that at $\hbar\to 0$ the derived formula transfers to the classical one. Read More