380 research outputs found
Magnetoelastic nature of solid oxygen epsilon-phase structure
For a long time a crystal structure of high-pressure epsilon-phase of solid
oxygen was a mistery. Basing on the results of recent experiments that have
solved this riddle we show that the magnetic and crystal structure of
epsilon-phase can be explained by strong exchange interactions of
antiferromagnetic nature. The singlet state implemented on quaters of O2
molecules has the minimal exchange energy if compared to other possible singlet
states (dimers, trimers). Magnetoelastic forces that arise from the spatial
dependence of the exchange integral give rise to transformation of 4(O2)
rhombuses into the almost regular quadrates. Antiferromagnetic character of the
exchange interactions stabilizes distortion of crystal lattice in epsilon-phase
and impedes such a distortion in long-range alpha- and delta-phases.Comment: 11 pages, 4 figures, Changes: corrected typos, reference to the
recent paper is adde
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
Long-range effects on superdiffusive solitons in anharmonic chains
Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam
(FPU)-like lattices were recently generalized to the case of dispersive
long-range interactions (LRI) of the Kac-Baker form. The position variance of
the soliton shows a stronger than linear time-dependence (superdiffusion) as
found earlier for lattice solitons on FPU chains with nearest neighbour
interactions (NNI). In contrast to the NNI case where the position variance at
moderate soliton velocities has a considerable linear time-dependence (normal
diffusion), the solitons with LRI are dominated by a superdiffusive mechanism
where the position variance mainly depends quadratic and cubic on time. Since
the superdiffusion seems to be generic for nontopological solitons, we want to
illuminate the role of the soliton shape on the superdiffusive mechanism.
Therefore, we concentrate on a FPU-like lattice with a certain class of
power-law long-range interactions where the solitons have algebraic tails
instead of exponential tails in the case of FPU-type interactions (with or
without Kac-Baker LRI). A collective variable (CV) approach in the continuum
approximation of the system leads to stochastic integro-differential equations
which can be reduced to Langevin-type equations for the CV position and width.
We are able to derive an analytical result for the soliton diffusion which
agrees well with the simulations of the discrete system. Despite of
structurally similar Langevin systems for the two soliton types, the algebraic
solitons reach the superdiffusive long-time limit with a characteristic
time-dependence much faster than exponential solitons. The soliton
shape determines the diffusion constant in the long-time limit that is
approximately a factor of smaller for algebraic solitons.Comment: 7 figure
Soliton dynamics in damped and forced Boussinesq equations
We investigate the dynamics of a lattice soliton on a monatomic chain in the
presence of damping and external forces. We consider Stokes and hydrodynamical
damping. In the quasi-continuum limit the discrete system leads to a damped and
forced Boussinesq equation. By using a multiple-scale perturbation expansion up
to second order in the framework of the quasi-continuum approach we derive a
general expression for the first-order velocity correction which improves
previous results. We compare the soliton position and shape predicted by the
theory with simulations carried out on the level of the monatomic chain system
as well as on the level of the quasi-continuum limit system. For this purpose
we restrict ourselves to specific examples, namely potentials with cubic and
quartic anharmonicities as well as the truncated Morse potential, without
taking into account external forces. For both types of damping we find a good
agreement with the numerical simulations both for the soliton position and for
the tail which appears at the rear of the soliton. Moreover we clarify why the
quasi-continuum approximation is better in the hydrodynamical damping case than
in the Stokes damping case
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
Kinks in the discrete sine-Gordon model with Kac-Baker long-range interactions
We study effects of Kac-Baker long-range dispersive interaction (LRI) between
particles on kink properties in the discrete sine-Gordon model. We show that
the kink width increases indefinitely as the range of LRI grows only in the
case of strong interparticle coupling. On the contrary, the kink becomes
intrinsically localized if the coupling is under some critical value.
Correspondingly, the Peierls-Nabarro barrier vanishes as the range of LRI
increases for supercritical values of the coupling but remains finite for
subcritical values. We demonstrate that LRI essentially transforms the internal
dynamics of the kinks, specifically creating their internal localized and
quasilocalized modes. We also show that moving kinks radiate plane waves due to
break of the Lorentz invariance by LRI.Comment: 11 pages (LaTeX) and 14 figures (Postscript); submitted to Phys. Rev.
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