Understanding strain gradient phenomena is of paramount importance in diverse areas condensed matter physics. This effect responsible for flexoelectricity dielectric materials, and it plays a crucial role the mechanical behavior nanoscale-sized specimens. In magnetoelectric composites, which comprise piezoelectric or ferroelectric (FE) materials coupled to magnetostrictive (MS) phases, can add ...

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

Received February 11, 1992; revised manuscript received July 24, 1992; accepted October 21, 1992 In previous research (Tech. Rep. 172, University of Southern California, Los Angeles, Calif., 1991) we developed an iterative shape-from-shading (SFS) algorithm that uses a single image, by combining a triangular-element surface model with a linearized reflectance map. In the current research we gen...

Motivated by mirror symmetry, we consider the Lagrangian fibration R → R and Lagrangian maps f : L →֒ R → R, exhibiting an unstable singularity, and study how the bifurcation locus of gradient lines, the integral curves of ∇fx, for x ∈ B, where fx(y) = f(y) − x · y, changes when f is slightly perturbed. We consider the cases when f is the germ of a fold, of a cusp and, particularly, of an ellipt...

We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations governing fluid motion, followed by a multiscale asymptotic expansion in the distance away from threshold. Close to onset, the asymptotic expansion yields an amplit...