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The well-known Rayleigh-Plesset (RP) equation is the base of nearly all hydrodynamical descriptions of the sonoluminescence phenomenon. A major deficiency of this equation is that it accounts for viscosity of an incompressible liquid and compressibility, separately. By removing this approximation, we have modified the RP equation, considering effects of liquid second viscosity. This modification exhibits its importance at the end of an intense collapse, so that the new model predicts the appearance of a new picosecond bouncing during high-amplitude sonoluminescence radiation. This new bouncing produces very sharp (sub-picosecond) peaks on the top of the sonoluminescence pulse. These new... 

The well-known Rayleigh-Plesset [Formula presented] equation is the basis of almost all hydrodynamical descriptions of single-bubble sonoluminescence [Formula presented]. A major deficiency of the [Formula presented] equation is that it accounts for viscosity of an incompressible liquid and compressibility, separately. By removing this approximation, a new modification of the [Formula presented] equation is presented considering effect of compressional viscosity of the liquid. This modification leads to addition of a new viscous term to the traditional bubble boundary equation. Influence of this new term in the dynamics of a sonoluminescing bubble has numerically been studied considering... 

Diffusivity equation which can provide us with the pressure distribution, is a Partial Differential Equation (PDE) describing fluid flow in porous media. The quadratic pressure gradient term in the diffusivity equation is nearly neglected in hydrology and petroleum engineering problems such as well test analysis. When a compressible liquid is injected into a well at high pressure gradient or when the reservoir possess a small permeability value, the effect of ignoring this term increases. In such cases, neglecting this parameter can result in high errors. Previous models basically focused on numerical and semi-analytical methods for semi-infinite domain. To the best of our knowledge, no...