Hamiltonian finite-dimensional oscillator-type reductions of Lax-integrable superconformal hierarchies

For bi-Hamiltonian superconformal hierarchies of nonlinear Benny-Kaup and Kaup-Broer dynamical systems, we develop a method for reduction to nonlocal finite-dimensional invariant subspaces of Neumann and Bargmann types, respectively. We prove that there exist even supersymplectic structures on these spaces and that the reduced commuting vector fields generated by the hierarchies are integrable in the Lax-Liouville sense. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 15–30, January–March, 2006.     

On the development of a kinetic model for a gas with allowance for nonequilibrium processes

The problems of developing a kinetic model of a medium (gas and plasma) are considered from the viewpoint of choice of the most important physicochemical processes. For the problem of a direct shock wave propagating in the atmosphere, kinetic models are selected with allowance for the error in specifying reaction-rate constants. The investigation was performed using an automated system that incorporates structured bases of physicochemical data, a generator of kinetic equations, a complex of programs for direct calculation, and program modules for determining, from a set of admissible solutions, the one satisfying specified criteria. Institute of Mechanics, Moscow State University, Moscow 119899. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 36–43, July–August, 1999.     

Turbulent thermal in a stratified atmosphere

An approximate analytical model of a turbulent thermal in a stratified atmosphere is proposed. This model makes it possible to predict the dynamics of the ascent, suspension and oscillation processes of a buoyant cloud both within the troposphere and on entering the stratossphere. The values of the heat energy needed for the thermal to penetrate the tropopause in northern and southern latitudes are estimated. Estimates are obtained for the amount of material dumped into the stratosphere. A method of determining the thermal energy of volcanic eruptions of the explosive type is proposed. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 141–153, November–December, 1986.     

Mathematical models for the study of interactions in the system lake baikal-atmosphere of the region

The structure of mathematical models for studying the processes of thermodynamics and transfer of pollutants in a climatic system involving the atmosphere of an industrial region and a lake is presented. These models are used to solve the problems of climatic and ecological monitoring and prediction. The problems of constructing numerical schemes and simulation methods are discussed. An example for estimating the effect of pollutants from sources located in the northern hemisphere of the Earth on the Baikal region is given. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 137–147, March–April, 1999.     

Motion of thermics in a stratified atmosphere

Regular features of motion of thermics in a stratified atmosphere are considered. Thermics are single and multiple free volumes of floating gas, which successively arise with a certain frequency near a horizontal surface. In a real atmosphere, large-scale thermics of this type appear, for example, as a result of powerful pulse actions on the ambient medium that are successively produced at one point near the Earth surface. Deceased. Institute of Physicotechnical and Radiotechnical Measurements, Moscow Region, Mendeleevo 141570. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 33–39, September–October, 1999.     

Radiation mechanism of generation of geomagnetic signals from underground and contact explosions

A mechanism is proposed for the generation of geomagnetic perturbations by an atmospheric electrical dipole formed by the gamma radiation from contact and underground explosions accompanied by formation of a ground dome and escape of explosion products into the atmosphere. The gyrotropic E-layer of the ionosphere plays a determining role in the generation of geomagnetic fluctuations at long epicentral distances. The amplitude-frequency parameters of a geomagnetic signal at 1000 km from a contact explosion with an energy of 150 ktons are estimated. The possibility of recording such geomagnetic signals from explosions with emission of gamma radiation into the atmosphere is shown. Moscow Engineering-Physical Institute, Moscow 115409. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 21–26, November–December, 1998.     

Systematic multiscale models for deep convection on mesoscales

This paper builds on recent developments of a unified asymptotic approach to meteorological modeling [ZAMM, 80: 765–777, 2000, SIAM Proc. App. Math. 116, 227–289, 2004], which was used successfully in the development of Systematic multiscale models for the tropics in Majda and Klein [J. Atmosph. Sci. 60: 393–408, 2003] and Majda and Biello [PNAS, 101: 4736–4741, 2004]. Biello and Majda [J. Atmosph. Sci. 62: 1694–1720, 2005]. Here we account for typical bulk microphysics parameterizations of moist processes within this framework. The key steps are careful nondimensionalization of the bulk microphysics equations and the choice of appropriate distinguished limits for the various nondimensional small parameters that appear. We are then in a position to study scale interactions in the atmosphere involving moist physics. We demonstrate this by developing two systematic multiscale models that are motivated by our interest in mesoscale organized convection. The emphasis here is on multiple length scales but common time scales. The first of these models describes the short-time evolution of slender, deep convective hot towers with horizontal scale ~ 1 km interacting with the linearized momentum balance on length and time scales of (10 km/3 min). We expect this model to describe how convective inhibition may be overcome near the surface, how the onset of deep convection triggers convective-scale gravity waves, and that it will also yield new insight into how such local convective events may conspire to create larger-scale strong storms. The second model addresses the next larger range of length and time scales (10 km, 100 km, and 20 min) and exhibits mathematical features that are strongly reminiscent of mesoscale organized convection. In both cases, the asymptotic analysis reveals how the stiffness of condensation/evaporation processes induces highly nonlinear dynamics. Besides providing new theoretical insights, the derived models may also serve as a theoretical devices for analyzing and interpreting the results of complex moist process model simulations, and they may stimulate the development of new, theoretically grounded sub-grid-scale parameterizations.     

Predicting the nonlinear hereditary viscoelasticity of polymers

A mathematical model for the nonlinear hereditary viscoelasticity of polymer materials is proposed to predict deformation processes of various complexity — from simple relaxation and simple creep to complex deformation-relaxation and reverse relaxation processes with alternative loading and unloading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 147–157, November–December, 2007.     

Mathematical treatment of the discharge of a laminar hot gas in a stagnant colder atmosphere

We study the boundary-layer approximation of the classical mathematical model that describes the discharge of a laminar hot gas in a stagnant colder atmosphere of the same gas. We prove the existence and uniqueness of solutions to a nondegenerate problem (without zones of stagnation of gas temperature or velocity). The asymptotic behavior of these solutions is also studied __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 192–205, July–August, 2008.     

Mathematical simulation of gas cloud motion following the atmospheric explosion of a meteoroid

The gasdynamic consequences of the explosion of a meteoroid in a dense atmosphere are studied. The gas motion is simulated on the basis of a high-accuracy numerical method using adaptive movable networks. Some effects which could not be reproduced using coarser networks are revealed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 29–37, January–February, 1998. The study was carried out with the support of the Russian Foundation for Fundamental Research (project No. 96-01-00448).     

Behavior of the unsteady jet of a mixture of a pressurized gas and dispersed particles discharged from a circular duct into the atmosphere

The unsteady axisymmetric jet produced by discharge of a mixture of a pressurized gas and dispersed particles from a circular duct into the atmosphere is studied within the framework of two-velocity, two-temperature gas dynamics. An attempt is undertaken to allow for the effective pressure due to random particle motion. The collision mechanism is found to be essential to radial expansion of the flow. Experimental data that support the results obtained are reported. Mozhaiskii Military Spacecraft Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 151–157, January–February, 1999.     

Optimization of the shape of a wing in a hypersonic nonequilibrium gas flow

A variational technique of obtaining the optimal shape of a low-aspect-ratio wing with allowance for the nonequilibrium character of the flow is developed. The technique is applied to the problem of determining optimal wing shapes under terrestrial atmosphere conditions. The real-gas effect on the optimal shapes and maximum lift-drag ratio is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–170, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00629).     

Some aspects of solving interrelated problems of ecology and climate

Special features of interrelated problems of ecology and climate are analyzed. The technique proposed for solving this class of problems is demonstrated by an example of evaluating the atmospheric quality and monitoring and predicting the ecological consequences of man’s impact. An approach based on variational principles in combination with methods of splitting and decomposition is developed. The structure of algorithms implementing Eulerian and Lagrangian formulations of the problems is described. Examples of simulation scenarios for particular cases are given. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 161–170, September–October, 2000.     

Charging and coagulation of water aerosols with a small admixture of highly radioactive droplets

The mechanism of electrocoagulation of water aerosols with a small admixture of highly radioactive droplets is examined. A corresponding mathematical model describing the processes of ionization, electrization and coagulation of radioactive water aerosols is developed. The time dependence of the ion concentration and the charge and concentration of the nonradioactive droplets and of the charge and radius of the radioactive droplets is numerically investigated for a number of typical aerosols. It is shown that the electrocoagulation process may lead to an increase in the radius of the droplets from 5–10 to 30–40μm in ≃10⁴ sec ≃3 h and, consequently, may play a significant part in the development of aerosols with a droplet radius of up to 20μm, when gravitational coagulation is unimportant. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 90–96, March–April, 1994.     

Modeling of the catalytic properties of high-temperature surface insulation in a dissociated carbon dioxide — Nitrogen mixture

A model of the heterogeneous catalysis of a dissociated carbon dioxide — nitrogen mixture on high-temperature heat-shield coatings is developed; the model takes into account nonequilibrium adsorption-desorption reactions of nitrogen and oxygen atoms and carbon dioxide molecules and their recombination in the Eley-Rideal reactions. On the basis of a comparison of the calculated heat fluxes in dissociated carbon dioxide with those measured on the VGU-4 plasma generator of the Institute for Problems in Mechanics of the RAS, the parameters of the catalysis model in question are chosen for three modern oxidant-resistant coating materials. The performances of these coatings are compared for the conditions of Mars Miniprobe entry into the Martian atmosphere. Their usability for the entry path considered is shown. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 106–116, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00259) and the “Integratisya“ Federal Program (project No. 2.1–414).     

Specific features of explosive boiling of liquids on a film microheater

Explosive boiling of liquids on film heaters under the action of pulsed heat fluxes q = 10⁸–10⁹ W/m ² is considered. A technique of stroboscopic visualization of boiling stages with a time resolution of 100 nsec is used. Numerous scenarios of evolution of explosive boiling are demonstrated. Conditions of the thermal effect (magnitude of the heat flux, duration and repetition frequency of heat pulses) are found, which ensure single and repeated boiling, intermittent boiling, and boiling with formation of complicated multi-bubble structures. It is noted that homogeneous nucleation is a dominating mechanism of incipience of examined liquids for q > 10⁸ W/m ². __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 81–89, March–April, 2007.     

Some types of kinetic equations reducible to partial differential equations

The possibility of passing from the kinetic equation to a partial differential equations is rigorously mathematically proved for the case of nearly elastic scattering processes. Some examples are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 12–16, September–October, 2007.     

Diffusion-controlled melting and re-solidification of metal micro layers on a reactive substrate

The paper offers a theoretical approach to a prediction of residue formation inherent to melting and subsequent solidification of micro layers of molten aluminum alloys. The residue formation follows a reactive flow of a portion of the melt that is removed by a surface tension action. The residue portion solidifies in situ. The phenomenon studied is associated with materials’ processing during controlled atmosphere brazing of aluminum. The model assumes that diffusion of Silicon, present in an Al+Si clad of a brazing sheet, has a twofold role. First, a solid state Si diffusion prior to melting and across the clad–core interface of a composite brazing sheet takes place and modifies alloys’ composition on both sides of the interface. Subsequently, Si diffusion within clad controls the melting process. Both processes are essential for clad residue formation. The approach advocated in this paper leads to a prediction of the residue formation through a modeling of the non-equilibrium diffusion-controlled melting. A heuristic interpretation of physical mechanisms was discussed and a related mathematical model devised. The model was solved numerically in terms of Si concentration distributions for a moving boundary problem and corroborated with empirical data. Empirical data were gathered using an experimental controlled atmosphere brazing facility. The results of the modeling and their corroboration with the experimental data indicate a strong dependence of residue formations on the pre-melting state of the clad, in particular on the grain size within Al-clad matrix. A good agreement between numerically predicted residue mass and experimental findings is documented in detail.     

A New Coal-Permeability Model: Internal Swelling Stress and Fracture–Matrix Interaction

We have developed a new coal-permeability model for uniaxial strain and constant confining-stress conditions. The model is unique in that it explicitly considers fracture–matrix interaction during coal-deformation processes and is based on a newly proposed internal swelling stress concept. This concept is used to account for the impact of matrix swelling (or shrinkage) on fracture-aperture changes resulting from partial separation of matrix blocks by fractures that do not completely cut through the whole matrix. The proposed permeability model is evaluated using data from three Valencia Canyon coalbed wells in the San Juan Basin, where increased permeability has been observed during CH₄ gas production, as well as using published data from laboratory tests. Model results are generally in good agreement with observed permeability changes. The importance of fracture–matrix interaction in determining coal permeability, demonstrated in this study using relatively simple stress conditions, underscores the need for a dual-continuum (fracture and matrix) mechanical approach to rigorously capture coal-deformation processes under complex stress conditions, as well as the coupled flow and transport processes in coal seams.