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

Recursion operator for stationary Nizhnik--Veselov--Novikov equation

We present a new general construction of recursion operator from zero curvature representation. Using it, we find a recursion operator for the stationary Nizhnik--Veselov--Novikov equation and present a few low order symmetries generated with the help of this operator.Comment: 6 pages, LaTeX 2

Zero curvature representation for a new fifth-order integrable system

In this brief note we present a zero-curvature representation for one of the new integrable system found by Mikhailov, Novikov and Wang in nlin.SI/0601046.Comment: 2 pages, LaTeX 2e, no figure

Why nonlocal recursion operators produce local symmetries: new results and applications

It is well known that integrable hierarchies in (1+1) dimensions are local while the recursion operators that generate them usually contain nonlocal terms. We resolve this apparent discrepancy by providing simple and universal sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions to generate a hierarchy of local symmetries. These conditions are satisfied by virtually all known today recursion operators and are much easier to verify than those found in earlier work. We also give explicit formulas for the nonlocal parts of higher recursion operators, Poisson and symplectic structures of integrable systems in (1+1) dimensions. Using these two results we prove, under some natural assumptions, the Maltsev--Novikov conjecture stating that higher Hamiltonian, symplectic and recursion operators of integrable systems in (1+1) dimensions are weakly nonlocal, i.e., the coefficients of these operators are local and these operators contain at most one integration operator in each term.Comment: 10 pages, LaTeX 2e, final versio

On the relation between standard and μ\mu-symmetries for PDEs

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.

A unified approach to computation of integrable structures

We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based approach and aim to provide a tutorial to the computations.Comment: 19 pages, based on a talk on the SPT 2011 conference, http://www.sptspt.it/spt2011/ ; v2, v3: minor correction

Sex-specific reproductive behaviours and paternity in free-ranging Barbary macaques (Macaca sylvanus)

In a wide variety of species, male reproductive success is determined by contest for access to females. Among multi-male primate groups, however, factors in addition to male competitive ability may also influence paternity outcome, although their exact nature and force is still largely unclear. Here, we have investigated in a group of free-ranging Barbary macaques whether paternity is determined on the pre- or postcopulatory level and how male competitive ability and female direct mate choice during the female fertile phase are related to male reproductive success. Behavioural observations were combined with faecal hormone analysis for timing of the fertile phase (13 cycles, 8 females) and genetic paternity analysis (n = 12). During the fertile phase, complete monopolisation of females did not occur. Females were consorted for only 49% of observation time, and all females had ejaculatory copulations with several males. Thus, in all cases, paternity was determined on the postcopulatory level. More than 80% of infants were sired by high-ranking males, and this reproductive skew was related to both, male competitive ability and female direct mate choice as high-ranking males spent more time in consort with females than low-ranking males, and females solicited copulations mainly from dominant males. As most ejaculatory copulations were female-initiated, female direct mate choice appeared to have the highest impact on male reproductive success. However, female preference was not directly translated into paternity, as fathers were not preferred over non-fathers in terms of solicitation, consortship and mating behaviour. Collectively, our data show that in the Barbary macaque, both sexes significantly influence male mating success, but that sperm of several males generally compete within the female reproductive tract and that therefore paternity is determined by mechanisms operating at the postcopulatory level