| Summary: | Determining the isothermal and adiabatic nonlinearity parameters of liquids and soft matter is crucially important for a variety of engineering applications requiring operations under high pressures, nondestructive testing, exploring the propagation of finite amplitude and shock waves, etc. It has been shown recently that mathematically this problem can be reduced to the initial value problem for an ODE build based on the linear response theory for thermodynamic equalities. The required initial conditions should be determined from thermodynamic measurements at ambient pressure (or along the saturation curve). From the physical point of view, the required regression leading to the determining nonlinearity parameters originates from certain regularities in the response of molecular oscillations to the density changes. In this work, we explore how this regression procedure should be optimized computationally with respect to temperature ranges, which exclude anomalies affecting parameters of equations used for the required predictive calculations under high pressures. The validity of the proposed approach is tested by case studies of the propagation of weakly non-linear waves with finite amplitudes and density changes due to shock waves under the Rankine–Hugoniot jump conditions.
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