2,179 research outputs found
Exact static solutions for discrete models free of the Peierls-Nabarro barrier: Discretized first integral approach
We propose a generalization of the discrete Klein-Gordon models free of the
Peierls-Nabarro barrier derived in Nonlinearity {\bf 12}, 1373 (1999) and Phys.
Rev. E {\bf 72}, 035602(R) (2005), such that they support not only kinks but a
one-parameter set of exact static solutions. These solutions can be obtained
iteratively from a two-point nonlinear map whose role is played by the
discretized first integral of the static Klein-Gordon field, as suggested in J.
Phys. A {\bf 38}, 7617 (2005). We then discuss some discrete models
free of the Peierls-Nabarro barrier and identify for them the full space of
available static solutions, including those derived recently in Phys. Rev. E
{\bf 72} 036605 (2005) but not limited to them. These findings are also
relevant to standing wave solutions of discrete nonlinear Schr{\"o}dinger
models. We also study stability of the obtained solutions. As an interesting
aside, we derive the list of solutions to the continuum equation that
fill the entire two-dimensional space of parameters obtained as the continuum
limit of the corresponding space of the discrete models.Comment: Accepted for publication in PRE; the M/S has been revised in line
with the referee repor
Nonlinear Lattices Generated from Harmonic Lattices with Geometric Constraints
Geometrical constraints imposed on higher dimensional harmonic lattices
generally lead to nonlinear dynamical lattice models. Helical lattices obtained
by such a procedure are shown to be described by sine- plus linear-lattice
equations. The interplay between sinusoidal and quadratic potential terms in
such models is shown to yield localized nonlinear modes identified as intrinsic
resonant modes
Lattice solitons in quasicondensates
We analyze finite temperature effects in the generation of bright solitons in
condensates in optical lattices. We show that even in the presence of strong
phase fluctuations solitonic structures with well defined phase profile can be
created. We propose a novel family of variational functions which describe well
the properties of these solitons and account for the non-linear effects in the
band structure. We discuss also the mobility and collisions of these localized
wave packets.Comment: 4 pages, 2 figure
Discrete Nonlinear Schrodinger Equations Free of the Peierls-Nabarro Potential
We derive a class of discrete nonlinear Schr{\"o}dinger (DNLS) equations for
general polynomial nonlinearity whose stationary solutions can be found from a
reduced two-point algebraic problem. It is demonstrated that the derived class
of discretizations contains subclasses conserving classical norm or a modified
norm and classical momentum. These equations are interesting from the physical
standpoint since they support stationary discrete solitons free of the
Peierls-Nabarro potential. As a consequence, even in highly-discrete regimes,
solitons are not trapped by the lattice and they can be accelerated by even
weak external fields. Focusing on the cubic nonlinearity we then consider a
small perturbation around stationary soliton solutions and, solving
corresponding eigenvalue problem, we (i) demonstrate that solitons are stable;
(ii) show that they have two additional zero-frequency modes responsible for
their effective translational invariance; (iii) derive semi-analytical
solutions for discrete solitons moving at slow speed. To highlight the unusual
properties of solitons in the new discrete models we compare them with that of
the classical DNLS equation giving several numerical examples.Comment: Misprints noticed in the journal publication are corrected [in Eq.
(1) and Eq. (34)
Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry
Ultra-pure conductors may exhibit hydrodynamic transport where the collective
motion of charge carriers resembles the flow of a viscous fluid. In a confined
geometry (e.g., in ultra-high quality nanostructures) the electronic fluid
assumes a Poiseuille-like flow. Applying an external magnetic field tends to
diminish viscous effects leading to large negative magnetoresistance. In
two-component systems near charge neutrality the hydrodynamic flow of charge
carriers is strongly affected by the mutual friction between the two
constituents. At low fields, the magnetoresistance is negative, however at high
fields the interplay between electron-hole scattering, recombination, and
viscosity results in a dramatic change of the flow profile: the
magnetoresistance changes its sign and eventually becomes linear in very high
fields. This novel non-monotonic magnetoresistance can be used as a fingerprint
to detect viscous flow in two-component conducting systems.Comment: 10 pages, 8 figure
Counterflows in viscous electron-hole fluid
In ultra-pure conductors, collective motion of charge carriers at relatively
high temperatures may become hydrodynamic such that electronic transport may be
described similarly to a viscous flow. In confined geometries (e.g., in
ultra-high quality nanostructures), the resulting flow is Poiseuille-like. When
subjected to a strong external magnetic field, the electric current in
semimetals is pushed out of the bulk of the sample towards the edges. Moreover,
we show that the interplay between viscosity and fast recombination leads to
the appearance of counterflows. The edge currents possess a non-trivial spatial
profile and consist of two stripe-like regions: the outer stripe carrying most
of the current in the direction of the external electric field and the inner
stripe with the counterflow.Comment: 10 pages, 5 figure
A study of the influence of soft particle size and concentration on strength and strain properties of ceramic composites
In the paper a theoretical study of the influence of particle distribution of soft inclusions-agglomerates in a ceramic composite sample on its strength and deformation characteristics was carried out. A movable cellular automaton method was used to simulate a uniaxial compression test of two-dimensional rectangle composite samples. It was found that the average size of inclusions agglomerate-while maintaining the volume fraction of the particles of the soft phase has little effect on the strength and deformation properties of the simulated samples. The simulation results can help to understand the mechanical properties of such objects within any generalized model
Magnetoresistance of compensated semimetals in confined geometries
Two-component conductors -- e.g., semi-metals and narrow band semiconductors
-- often exhibit unusually strong magnetoresistance in a wide temperature
range. Suppression of the Hall voltage near charge neutrality in such systems
gives rise to a strong quasiparticle drift in the direction perpendicular to
the electric current and magnetic field. This drift is responsible for a strong
geometrical increase of resistance even in weak magnetic fields. Combining the
Boltzmann kinetic equation with sample electrostatics, we develop a microscopic
theory of magnetotransport in two and three spatial dimensions. The compensated
Hall effect in confined geometry is always accompanied by electron-hole
recombination near the sample edges and at large-scale inhomogeneities. As the
result, classical edge currents may dominate the resistance in the vicinity of
charge compensation. The effect leads to linear magnetoresistance in two
dimensions in a broad range of parameters. In three dimensions, the
magnetoresistance is normally quadratic in the field, with the linear regime
restricted to rectangular samples with magnetic field directed perpendicular to
the sample surface. Finally, we discuss the effects of heat flow and
temperature inhomogeneities on the magnetoresistance.Comment: 22 pages, 7 figures, published versio
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