Nonlinear metasurfaces have been enabling unprecedented control over light generation and wave mixing, dem-onstrating enhanced wavefront control, beam shaping and steering of nonlinear light …

In this paper, we study the nonlinear stability of 2-D compressible Couette flow in Sobolev space at high Reynolds numbers. Moreover, we also show the enhanced dissipation phenomenon and stability …

The topic of Nonlinear Elasticity is foundational to our understanding of the behaviour of soft matter under various forces. Yet, it remains a challenging area for many undergraduate students because it …

In this section, based on the theory of critical function spaces, we establish the well-posedness theory for (1.1), and for this purpose, we start by proving an associated nonlinear estimate.

A globally optimal nonlinear feedback controller and a Kalman estimator are then designed within the eigenfunction space and compared to traditional and gain-scheduled proportional-integral controllers, …

We have summarized briefly some basic results of Sobolev spaces and nonlinear functional analysis, and basic theory of elliptic equations, in the two appendices.

Abstract This research develops a novel geometri-cally nonlinear aeroelastic model of a cantilevered flexible wing capable of capturing unsteady aerody-namics with finite span effects.

Using a nonlinear model changes the control problem from a convex quadratic program to a nonconvex nonlinear problem, which is much more difficult to solve and provides no guarantee that the global …

The first example involves typical nonlinear systems, including the van der Pol system, Duffing system, and nonlinear pendulum system. The second example considers a 40-degrees-of-freedom system …

We note that our result includes nonlinear instability in the L2 energy norm which we claim is the natural norm in which to consider issues of stability and instability. The technique we employ to prove our …