76 research outputs found
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 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
On complete integrability of the Mikhailov-Novikov-Wang system
We obtain compatible Hamiltonian and symplectic structure for a new
two-component fifth-order integrable system recently found by Mikhailov,
Novikov and Wang (arXiv:0712.1972), and show that this system possesses a
hereditary recursion operator and infinitely many commuting symmetries and
conservation laws, as well as infinitely many compatible Hamiltonian and
symplectic structures, and is therefore completely integrable. The system in
question admits a reduction to the Kaup--Kupershmidt equation.Comment: 5 pages, no figure
Scalar second order evolution equations possessing an irreducible sl-valued zero curvature representation
We find all scalar second order evolution equations possessing an
sl-valued zero curvature representation that is not reducible to a proper
subalgebra of sl. None of these zero-curvature representations admits a
parameter.Comment: 10 pages, requires nath.st
Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation
In this paper we classify Weingarten surfaces integrable in the sense of
soliton theory. The criterion is that the associated Gauss equation possesses
an sl(2)-valued zero curvature representation with a nonremovable parameter.
Under certain restrictions on the jet order, the answer is given by a third
order ordinary differential equation to govern the functional dependence of the
principal curvatures. Employing the scaling and translation (offsetting)
symmetry, we give a general solution of the governing equation in terms of
elliptic integrals. We show that the instances when the elliptic integrals
degenerate to elementary functions were known to nineteenth century geometers.
Finally, we characterize the associated normal congruences
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
On the Invariant Theory of Weingarten Surfaces in Euclidean Space
We prove that any strongly regular Weingarten surface in Euclidean space
carries locally geometric principal parameters. The basic theorem states that
any strongly regular Weingarten surface is determined up to a motion by its
structural functions and the normal curvature function satisfying a geometric
differential equation. We apply these results to the special Weingarten
surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of
constant Gauss curvature.Comment: 16 page
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 -symmetries for PDEs
We give a geometrical interpretation of the notion of -prolongations of
vector fields and of the related concept of -symmetry for partial
differential equations (extending to PDEs the notion of -symmetry for
ODEs). We give in particular a result concerning the relationship between
-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 -symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.
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