16 research outputs found
Oscillatory wave fronts in chains of coupled nonlinear oscillators
Wave front pinning and propagation in damped chains of coupled oscillators
are studied. There are two important thresholds for an applied constant stress
: for (dynamic Peierls stress), wave fronts fail to propagate,
for stable static and moving wave fronts coexist, and
for (static Peierls stress) there are only stable moving wave
fronts. For piecewise linear models, extending an exact method of Atkinson and
Cabrera's to chains with damped dynamics corroborates this description. For
smooth nonlinearities, an approximate analytical description is found by means
of the active point theory. Generically for small or zero damping, stable wave
front profiles are non-monotone and become wavy (oscillatory) in one of their
tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.
Tilt order parameters, polarity and inversion phenomena in smectic liquid crystals
The order parameters for the phenomenological description of the smectic-{\it
A} to smectic-{\it C} phase transition are formulated on the basis of molecular
symmetry and structure. It is shown that, unless the long molecular axis is an
axis of two-fold or higher rotational symmetry, the ordering of the molecules
in the smectic-{\it C} phase gives rise to more than one tilt order parameter
and to one or more polar order parameters. The latter describe the indigenous
polarity of the smectic-{\it C} phase, which is not related to molecular
chirality but underlies the appearance of spontaneous polarisation in chiral
smectics. A phenomenological theory of the phase transition is formulated by
means of a Landau expansion in two tilt order parameters (primary and
secondary) and an indigenous polarity order parameter. The coupling among these
order parameters determines the possibility of sign inversions in the
temperature dependence of the spontaneous polarisation and of the helical pitch
observed experimentally for some chiral smectic-{\it } materials. The
molecular interpretation of the inversion phenomena is examined in the light of
the new formulation.Comment: 12 pages, 5 figures, RevTe
Instabilities and Bifurcations of Nonlinear Impurity Modes
We study the structure and stability of nonlinear impurity modes in the
discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear
impurity emphasizing the effects of interplay between discreteness,
nonlinearity and disorder. We show how the interaction of a nonlinear localized
mode (a discrete soliton or discrete breather) with a repulsive impurity
generates a family of stationary states near the impurity site, as well as
examine both theoretical and numerical criteria for the transition between
different localized states via a cascade of bifurcations.Comment: 8 pages, 8 figures, Phys. Rev. E in pres
New types of instabilities in Liquid Crystals with Tilted Orientation
Theoretical consideration of a new kind of instability formed of rolls perpendicular to Williams' domains when the molecules are initially tilted with respect to the substrate plane is presented. The threshold voltage versus the tilt angle, dielectric constants, electroconductivity, viscosity coefficients and the frequency of an external field is calculated within the framework of the two-dimensional model. The contribution of electrokinetic processes observed in an isotropic liquid to the effect under consideration is discussed and the respective estimates for the threshold are given