An experimental study was carried out on a piezoelectric actuator in order to explore the benefits of a mathematical formula [1], that describes the output of the inverse compensation when an inverse Prandtl-Ishlinskii hysteresis model is applied as a feedforward compensator. The inverse Prandtl-Ishlinskii was first formulated and applied for compensation of hysteresis nonlinearities of a piezo...

The effects of weak breaking of the midplane reflection symmetry on the 1:2 steady state mode interaction in Rayleigh–Bénard convection are discussed in a PDE setting. Effects of this type arise from the inclusion of non-Boussinesq terms or due to small differences in the boundary conditions at the top and bottom of the convecting layer. The latter provides the simplest realization, and capture...

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within ε of a stable profile, then the unique solution of the C...

incompressible fluid between two infinite vertical parallel plates in the presence of constant temperature and mass diffusion has been investigated analytically. The method of Laplace transform is used to solve the dimensionless governing partial differential equations. The velocity, temperature and concentration profiles have been presented for different parameters like Prandtl number, Schmidt...

Theodor Meyer’s 1908 doctoral dissertation, with Ludwig Prandtl (1875–1953) as his advisor, introduced much of what has now become basic gas dynamics: not only the Prandtl–Meyer expansion but also the oblique-shock-wave theory as well. It is arguably the most influential dissertation in all of fluid dynamics. Yet no biography or even a photograph of Meyer has been available in the intervening c...

We find a new class of data for which the Prandtl boundary layer equations and the hydrostatic Euler equations are locally in time well-posed. In the case of the Prandtl equations, we assume that the initial datum u0 is monotone on a number of intervals (on some strictly increasing on some strictly decreasing) and analytic on the complement and show that the local existence and uniqueness hold....