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This paper continues previous investigation of Galilean-invariant equations of mathematical physics, which was begun with the use of the Clebsch– Gordan coefficients from the theory of products of the represented group SO(3). Complex systems of conservation laws and thermodynamic identities are constructed. Concrete examples are given.

Exact solutions of Euler equations that
describe the motion of an ideal
incompressible fluid with quadratic
pressure are studied. The solutions are
described by explicit formulas and can
be physically interpreted. The dynamics
of a spherical fluid volume is studied
for specified initial velocity fields.
It is shown that under certain initial
conditions, the spherical volume can
evolve into a torus-shaped body, thereby
changing the connectivity of the region
occupied by the fluid.

The one-velocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with continuous addition of energy to the gas phase is studied.

The problem of explosion in a hole surrounded by a porous medium is considered. Integral equations describing pressure relaxation in the hole due to gas filtration into the surrounding porous space are obtained within the framework of plane one-dimensional, radial, and spherical formulations. An analysis of numerical solutions of these equations shows that the characteristic time of pressure relaxation in the hole depends weakly on its initial value.
Key words: pressure relaxation, explosion in a hole, porous medium, filtration of explosion products, bottom-hole cleaning.

Simple estimates of the coefficient of dynamic viscosity of some metals are considered. Experimental results on shock loading of aluminum, copper, and steel plane specimens are given. It is shown that the coefficient of dynamic viscosity depends on the characteristic size of the structural level of plastic strain at which loading-energy dissipation is considered. It was found that the main level that determines the viscosity of materials under high-velocity loading is the mesoscopic level with a characteristic size of ≈10 μm.
Key words: viscosity, high-velocity loading, mesoscopic level, interferogram.

A three-dimensional phase diagram of carbon has been built in the coordinates "pressure

The paper considers a physical model for the explosive synthesis of ultrafine aluminum oxide, which assumes that in a compression wave the starting material is divided into layers with different states of aggregation and grain-size compositions. The relationship between the synthesis conditions and the properties of the product is studied. It is shown that the yield of the ultrafine fraction in the synthesized powder depends on the conditions of metal oxidation during dispersion, shock-wave parameters, and the velocity of dispersion of the starting material into the gas medium of the explosion chamber. Experimental data are used to determine the layer sizes and the constants characterizing the possibility of vapor-phase oxidation of aluminum during explosive synthesis. In the coordinates corresponding to the process parameters (yield of the ultrafine fraction and the masses of the explosive and the starting metal), a synthesis surface is constructed and optimum parameters for production of ultrfine material are determined.
Key words: ultrafine aluminum oxide, explosive synthesis, layer-by-layer separation of material in a compression wave, conditions of synthesis, properties of material.

Despite all safety measures in handling objects containing explosives, the probability of their accidental explosion is not completely eliminated. Effective environmental protection against explosions is achieved by localization of an explosion in the closed volume of an explosion-proof container. The use of such containers can considerably improve safety in operation of ammunition and other explosive devices.
Key words: container, charge, high explosive, fiberglass plastic, composite material, shell, fracture, strain, strength.

An analysis is made of the main kinematic parameters that determine the beginning of weld formation near the lower boundary of the region of explosion welding. The welding of aluminum with steel is considered. The paper reports experimental results for the flow of material in the gap under oblique collision of metal plates.
Key words: oblique collision, particle flow, explosion welding.

Experimental data on the kinetics of preexplosion conduction of silver azide in the early stage of explosive decomposition initiated by a pulse action were obtained for the first time. It is found that the kinetics of conduction in the early stage is more complex than that at later stages. In the early stages, the difference between kinetic curves for various samples is greater than that for the steady process.
Key words: silver azide, explosion, chain reactions, conduction, kinetics, pulse photolysis.