87 research outputs found
Effects of finite curvature on soliton dynamics in a chain of nonlinear oscillators
We consider a curved chain of nonlinear oscillators and show that the
interplay of curvature and nonlinearity leads to a number of qualitative
effects. In particular, the energy of nonlinear localized excitations centered
on the bending decreases when curvature increases, i.e. bending manifests
itself as a trap for excitations. Moreover, the potential of this trap is
double-well, thus leading to a symmetry breaking phenomenon: a symmetric
stationary state may become unstable and transform into an energetically
favorable asymmetric stationary state. The essentials of symmetry breaking are
examined analytically for a simplified model. We also demonstrate a threshold
character of the scattering process, i.e. transmission, trapping, or reflection
of the moving nonlinear excitation passing through the bending.Comment: 13 pages (LaTeX) with 10 figures (EPS
Curvature-induced symmetry breaking in nonlinear Schrodinger models
We consider a curved chain of nonlinear oscillators and show that the
interplay of curvature and nonlinearity leads to a symmetry breaking when an
asymmetric stationary state becomes energetically more favorable than a
symmetric stationary state. We show that the energy of localized states
decreases with increasing curvature, i.e. bending is a trap for nonlinear
excitations. A violation of the Vakhitov-Kolokolov stability criterium is found
in the case where the instability is due to the softening of the Peierls
internal mode.Comment: 4 pages (LaTex) with 6 figures (EPS
Solitons in anharmonic chains with ultra-long-range interatomic interactions
We study the influence of long-range interatomic interactions on the
properties of supersonic pulse solitons in anharmonic chains. We show that in
the case of ultra-long-range (e.g., screened Coulomb) interactions three
different types of pulse solitons coexist in a certain velocity interval: one
type is unstable but the two others are stable. The high-energy stable soliton
is broad and can be described in the quasicontinuum approximation. But the
low-energy stable soliton consists of two components, short-range and
long-range ones, and can be considered as a bound state of these components.Comment: 4 pages (LaTeX), 5 figures (Postscript); submitted to Phys. Rev.
Localization of nonlinear excitations in curved waveguides
Motivated by the example of a curved waveguide embedded in a photonic
crystal, we examine the effects of geometry in a ``quantum channel'' of
parabolic form. We study the linear case and derive exact as well as
approximate expressions for the eigenvalues and eigenfunctions of the linear
problem. We then proceed to the nonlinear setting and its stationary states in
a number of limiting cases that allow for analytical treatment. The results of
our analysis are used as initial conditions in direct numerical simulations of
the nonlinear problem and localized excitations are found to persist, as well
as to have interesting relaxational dynamics. Analogies of the present problem
in contexts related to atomic physics and particularly to Bose-Einstein
condensation are discussed.Comment: 14 pages, 4 figure
Effects of spin-elastic interactions in frustrated Heisenberg antiferromagnets
The Heisenberg antiferromagnet on a compressible triangular lattice in the
spin- wave approximation is considered. It is shown that the interaction
between quantum fluctuations and elastic degrees of freedom stabilizes the low
symmetric L-phase with a collinear Neel magnetic ordering. Multi-stability in
the dependence of the on-site magnetization on an unaxial pressure is found.Comment: Revtex, 4 pages, 2 eps figure
Numerical study of breathers in a bent chain of oscillators with long-range interaction
Most of the studies of breathers in networks of oscillators are limited to nextneighbour
interaction. However, long-range interaction becomes critical when
the geometry of the chain is taken into account, as the distance between
oscillators and, therefore, the coupling, depends on the shape of the system.
In this paper we analyse the existence and stability of breathers, i.e. localized
oscillations in a simple model for a bent chain of oscillators with long-range
interaction.European Union HPRN–CT–1999–0016
Moving breathers in a DNA model with competing short and long range dispersive interactions
Moving breathers is a means of transmitting information in DNA. We study the
existence and properties of moving breathers in a DNA model with short range
interaction, due to the stacking of the base pairs, and long range interaction, due
to the finite dipole moment of the bond within each base pair.
In our study, we have found that mobile breathers exist for a wide range of
the parameter values, and the mobility of these breathers is hindered by the long
range interaction. This fact is manifested by: (a) an increase of the effective mass
of the breather with the dipole–dipole coupling parameter; (b) a poor quality of
the movement when the dipole–dipole interaction increases; and (c) the existence
of a threshold value of the dipole–dipole coupling above which the breather is not
movable.
An analytical formula for the boundaries of the regions where breathers are movable
is calculated. Concretely, for each value of the breather frequency, it can be
obtained the maximum value of the dipole–dipole coupling parameter and the maximum
and minimum values of the stacking coupling parameter where breathers are
movable. Numerical simulations show that, although the necessary conditions for
the mobility are fulfilled, breathers are not always movable.
Finally, the value of the dipole–dipole coupling constant is obtained through quantum
chemical calculations. They show that the value of the coupling constant is
small enough to allow a good mobility of breathers.European Commission under the RTN project LOCNET, HPRN-CT-1999-0016
Stationary and moving breathers in a simplified model of curved alpha--helix proteins
The existence, stability and movability of breathers in a model for
alpha-helix proteins is studied. This model basically consists a chain of
dipole moments parallel to it. The existence of localized linear modes brings
about that the system has a characteristic frequency, which depends on the
curvature of the chain. Hard breathers are stable, while soft ones experiment
subharmonic instabilities that preserve, however the localization. Moving
breathers can travel across the bending point for small curvature and are
reflected when it is increased. No trapping of breathers takes place.Comment: 19 pages, 11 figure
Kink propagation in a two-dimensional curved Josephson junction
We consider the propagation of sine-Gordon kinks in a planar curved strip as
a model of nonlinear wave propagation in curved wave guides. The homogeneous
Neumann transverse boundary conditions, in the curvilinear coordinates, allow
to assume a homogeneous kink solution. Using a simple collective variable
approach based on the kink coordinate, we show that curved regions act as
potential barriers for the wave and determine the threshold velocity for the
kink to cross. The analysis is confirmed by numerical solution of the 2D
sine-Gordon equation.Comment: 8 pages, 4 figures (2 in color
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