Relaxation Processes in Shock Waves

Multidimensional Delta-shock Waves and the Transportation and Concentration Processes

δ-Shock wave type solutions in the multidimensional system of conservation laws ρt +∇ · (ρF (U)) = 0, (ρU)t +∇ · (ρN(U)) = 0, x ∈ R , are studied, where F = (Fj) is a given vector field, N = (Njk) is a given tensor field, Fj , Nkj : R n → R, j, k = 1, . . . , n; ρ(x, t) ∈ R, U(x, t) ∈ R. The well-known particular cases of this system are zero-pressure gas dynamics in a standard form ρt +∇ · (ρU...

Shock Waves in Liquid

Asbtract The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by t...

Shock Waves in Medicine

Shock Waves

Shock wave theory was first studied for gas dynamics, for which shocks appear as compression waves. A shock wave is characterized as a sharp transition, even discontinuity in the flow. In fact, shocks appear in many different physical situation and represent strong nonlinearity of the physical processes. Important progresses have been made on shock wave theory in recent years. We will survey th...

Shock waves in trombones

Based on physical models of musical instruments and of the human voice, a new generation of sound synthesizers is born: virtual instruments. The models used for wind instruments are simple feedback loops in which a nonlinear sound source drives a linear filter representing the pipe of the instrument. While very rewarding musical sounds have been obtained with these models, it has become obvious...