https://www.selleckchem.com/products/2-d08.html The mechanism for singularity formation in an inviscid wall-bounded fluid flow is investigated. The incompressible Euler equations are numerically simulated in a cylindrical container. The flow is axisymmetric with the swirl. The simulations reproduce and corroborate aspects of prior studies reporting strong evidence for a finite-time singularity. The analysis here focuses on the interplay between inertia and pressure, rather than on vorticity. The linearity of the pressure Poisson equation is exploited to decompose the pressure field into independent contributions arising from the meridional flow and from the swirl, and enforcing incompressibility and enforcing flow confinement. The key pressure field driving the blowup of velocity gradients is that confining the fluid within the cylinder walls. A model is presented based on a primitive-variables formulation of the Euler equations on the cylinder wall, with closure coming from how pressure is determined from velocity. The model captures key features in the mechanics of the blowup scenario.We propose an iterative method to evaluate the feedback control kernel of a chaotic system directly from the system's attractor. Such kernels are currently computed using standard linear optimal control theory, known as linear quadratic regulator theory. This is however applicable only to linear systems, which are obtained by linearizing the system governing equations around a target state. In the present paper, we employ the preconditioned multiple shooting shadowing (PMSS) algorithm to compute the kernel directly from the nonlinear dynamics, thereby bypassing the linear approximation. Using the adjoint version of the PMSS algorithm, we show that we can compute the kernel at any point of the domain in a single computation. replaces the standard adjoint equation (that is ill-conditioned for chaotic systems) with a well-conditioned adjoint, producing reliable sensitivities which are u