Differential invariants of generic hyperbolic Monge--Amp\`ere equations

In this paper basic differential invariants of generic hyperbolic Monge--Amp\`ere equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.Comment: 25 page

Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films

A theoretical study of a dielectrophoretic force, i.e. the force acting on an electrically neutral particle in the inhomogeneous electric field, which is produced by a ferroelectric domain pattern, is presented. It has been shown by several researchers that artificially prepared domain patterns with given geometry in ferroelectric single crystals represent an easy and flexible method for patterning dielectric nanoobjects using dielectrophoretic forces. The source of the dielectrophoretic force is a strong and highly inhomogeneous (stray) electric field, which exists in the vicinity of the ferroelectric domain walls at the surface of the ferroelectric film. We analyzed dielectrophoretic forces in the model of a ferroelectric film of a given thickness with a lamellar 180${}^\circ$ domain pattern. The analytical formula for the spatial distribution of the stray field in the ionic liquid above the top surface of the film is calculated including the effect of free charge screening. The spatial distribution of the dielectrophoretic force produced by the domain pattern is presented. The numerical simulations indicate that the intersection of the ferroelectric domain wall and the surface of the ferroelectric film represents a trap for dielectric nanoparticles in the case of so called positive dielectrophoresis. The effects of electrical neutrality of dielectric nanoparticles, free charge screening due to the ionic nature of the liquid, domain pattern geometry, and the Brownian motion on the mechanism of nanoparticle deposition and the stability of the deposited pattern are discussed.Comment: Accepted in the Journal of Applied Physics, 10 pages, 5 figure