Learning physics by data for the motion of a sphere falling in a non-Newtonian fluid.

Highlights • A nonlinear DAE of the velocity v of a falling sphere in non-Newtonian fluid will be proposed by directly learning the data. Our model successfully simulates the sustaining oscillations and abrupt increase during the sedimentation of a sphere. It presents the behavior of a chaotic system which is highly sensitive to initial conditions and experimentally nonreproducible. The normalized representation covers both the classical physical laws and the nonuniform oscillations. The data-driven idea will provide scientists with more important tools to support their discovery in the future. Abstract In this paper, we will introduce a mathematical model of nonlinear jerk equation of velocity v = η 1 η 2 v ″ + 1 v ″ + η 3 v ″ to simulate the nonuniform oscillations of the motion of a falling sphere in the non-Newtonian fluid. This differential/algebraic equation is established only by learning the experimental data with the generalized Prony method and sparse optimization method. From the numerical results, our model successfully simulates the sustaining oscillations and abrupt increase during the sedimentation of a sphere through a non-Newtonian fluid. It presents the behavior of a chaotic system which is highly sensitive to initial conditions. More statistical and physical discussions about the dynamical features of the model are provided as well. Our model can be interpreted as a nonlinear elastic system, and includes both the uniform and nonuniform oscillatory motion of the falling sphere. [ABSTRACT FROM AUTHOR]