Continuous Restricted Radial Motion of a Gas under the Action of a Piston

The possibility of continuous conjugation of the straightline radial motion of a gas sphere toward the center and away from the center with the motion where the gas in the entire sphere stops simultaneously is shown. The motion is described by an invariant submodel of rank 1. Time reflections allow one to construct a solution that describes a periodic continuous restricted motion of the gas sphere under the action of a piston.     

Simple waves of a seven-dimensional subalgebra of all translations in gas dynamics

A differentially invariant solution of rank 1 for gas dynamics equations is considered in a seven-dimensional subalgebra of all translations including Galilean translations. Exact solutions with a uniformly accelerated plane of the level of invariant functions are obtained. A nonisentropic wave depends on two arbitrary functions and constants. A general solution of an isentropic simple wave depends on the constants only.     

Contact Transformation Group Classification of Nonlinear Wave Equations

Interest in nonlinear wave equations has been stimulated bynumerous physical applications, such as telecommunication (e.g.nonlinear telegrapher equation), gasdynamics, anisotropic plasticity andnonlinear elasticity, etc. Mathematical models of these phenomena canoften be reduced to particular types of the equation u _tt = f(x, u _x ) u _xx + g(x, u _x ). In this paper, the problem ofclassification of the latter equation with respect to admitted contacttransformation groups is reduced to the investigation of pointtransformation groups of the equivalent system of first-orderquasi-linear equations v _t =a(x, v)w _x , w _t = b(x,v)v _x .     

Gas flows with helical surfaces of the level

Some properties of the invariant gas-dynamic submodel of rank 2 with spiral surfaces of the level are reported. Invariant and isobaric solutions of the submodel are considered. Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 34–39, March–April, 1999.     

Partially invariant solutions for a submodel of radial motions of a gas

All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found. The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but different functions of different independent variables. The solutions predict different continuous unsteady convergence or expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles simultaneously, a collapse or an explosion occurs. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 26–34, September–October, 2007.     

Irregular Partially Invariant Solutions of Rank 2 and Defect 1 to Equations of Gas Dynamics

We consider three-dimensional subalgebras admitted by the equations of gas dynamics having time as an invariant and containing no rotation operator. For such subalgebras we seek for irregular partially invariant solutions of rank 2 and defect 1. The representation for solutions has the form which generalizes motion of a gas with a linear velocity field. We show that partially invariant solutions exist for each subalgebra. We describe the set of these solutions. We find solutions with the indicated representation that are not partially invariant. The solutions reducible to invariant solutions are generalized to new submodels.     

Study of the thermal decomposition of nitropyrroles at low pressures using field mass spectrometry

Conclusions During high-vacuum pyrolysis the-nitropyrroles decompose with the cleavage of the OH particle, while the-nitropyrroles decompose with the cleavage of NO₂.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 447–450, February, 1977.     

Gas pressure equalization in a porous medium filling a pipe with a closed end under shock loading

The problem of gas pressure equalization in a porous medium filling a pipe with a closed end under shock loading is solved. In this case, the initial filtration velocity behind the shock wave should be specified as initial data, in addition to the shock pressure. It is shown that the shock decays at a finite distance and pressure equalization occurs in a finite time. Approximate submodels of discontinuous and smooth solutions are obtained.     

The non-stationary invariant solution of the equations of gas dynamics describing the spreading of a gas into a vacuum

An invariant solution of the equations of gas dynamics, constructed on a one-dimensional subgroup (according to the classification in /1/) which is only allowed in the case of a polytropic gas with a special adiabatic index, is considered. The gas spreads out into a vacuum after a finite time. New solutions are constructed which describe one-dimensional flows from a source into a vacuum and the focussing of the gas within a sphere or a cylinder with shock waves. The spreading of a concentration of the gas with an arbitrary boundary when there is a contact discontinuity is also considered.

One-dimensional flows have been treated in detail in /2, 3/, mainly in the case of extended subgroups.     

Gas-dynamic helical motions with pressure and density depending on time alone

For the submodel of helical motions invariant with respect to the sum of rotation and translation, we consider solutions with pressure and density depending on time alone. Consistency of the system is studied by proceeding to Lagrangian variables. Equivalence of solutions is determined in terms of the five-dimensional admissible group. All solutions of the form described are calculated to within equivalence.Translated fromMatematicheskie Zametki, Vol. 59, No. 1, pp. 133–141, January, 1996.The work was financially supported by the Russian Foundation for Basic Research under grant No. 93-013-17326.