363 research outputs found

### Origin of Multikinks in Dispersive Nonlinear Systems

We develop {\em the first analytical theory of multikinks} for strongly {\em
dispersive nonlinear systems}, considering the examples of the weakly discrete
sine-Gordon model and the generalized Frenkel-Kontorova model with a piecewise
parabolic potential. We reveal that there are no $2\pi$-kinks for this model,
but there exist {\em discrete sets} of $2\pi N$-kinks for all N>1. We also show
their bifurcation structure in driven damped systems.Comment: 4 pages 5 figures. To appear in Phys Rev

### Lubricated friction between incommensurate substrates

This paper is part of a study of the frictional dynamics of a confined solid
lubricant film - modelled as a one-dimensional chain of interacting particles
confined between two ideally incommensurate substrates, one of which is driven
relative to the other through an attached spring moving at constant velocity.
This model system is characterized by three inherent length scales; depending
on the precise choice of incommensurability among them it displays a strikingly
different tribological behavior. Contrary to two length-scale systems such as
the standard Frenkel-Kontorova (FK) model, for large chain stiffness one finds
that here the most favorable (lowest friction) sliding regime is achieved by
chain-substrate incommensurabilities belonging to the class of non-quadratic
irrational numbers (e.g., the spiral mean). The well-known golden mean
(quadratic) incommensurability which slides best in the standard FK model shows
instead higher kinetic-friction values. The underlying reason lies in the
pinning properties of the lattice of solitons formed by the chain with the
substrate having the closest periodicity, with the other slider.Comment: 14 pagine latex - elsart, including 4 figures, submitted to Tribology
Internationa

### 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.

### A truth-based epistemological framework for supporting teachers in integrating indigenous knowledge into science teaching

Integrating indigenous knowledge (IK) into school science teaching is one way of maximising the sociocultural
relevance of science education for enhanced learners’ performance. The epistemological
differences however between the nature of science (NOS) and nature of indigenous knowledge (NOIK)
constitute a major challenge for an inclusive IK-science curriculum integration. This article is about the
application of a truth-based epistemological framework designed to support teachers to make decisions
on how specific pieces of indigenous knowledge (local traditional practices and technologies) may be
included in science lessons. First, an attempt was made to develop a truth-based epistemological
framework for identifying epistemology(ies) of indigenous knowledge and practices. Second a group of
science teachers used the truth-based epistemological framework to examine ways in which some
specified IK practices that comprised a coherent set of knowledge themes on health, agriculture and
technology could be integrated into the school science curriculum in a valid and legitimate way. The IK
practices used in the study were systematically identified and documented by means of personal
observations and interviews of key informants in a rural community in Zimbabwe. The main findings of
the study showed that the truth-based epistemological framework was useful in providing an
epistemological basis for including some IK practices in science teaching and learning. As a tool for
pedagogy the framework enabled the science teachers to reconsider and change their valuing of
Indigenous knowledge Systems (IKS), more specifically in ways in which local knowledge can validly be
incorporated into school science teaching.http://www.tandfonline.com/loi/rmse202017-10-31hb2017Science, Mathematics and Technology Educatio

### Two-color nonlinear localized photonic modes

We analyze second-harmonic generation (SHG) at a thin effectively quadratic
nonlinear interface between two linear optical media. We predict multistability
of SHG for both plane and localized waves, and also describe two-color
localized photonic modes composed of a fundamental wave and its second harmonic
coupled together by parametric interaction at the interface.Comment: 4 pages, 5 figures (updated references

### Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas

We study analytically and numerically the one-dimensional quantum
Frenkel-Kontorova chain in the regime when the classical model is located in
the pinned phase characterized by the gaped phonon excitations and devil's
staircase. By extensive quantum Monte Carlo simulations we show that for the
effective Planck constant $\hbar$ smaller than the critical value $\hbar_c$ the
quantum chain is in the pinned instanton glass phase. In this phase the
elementary excitations have two branches: phonons, separated from zero energy
by a finite gap, and instantons which have an exponentially small excitation
energy. At $\hbar=\hbar_c$ the quantum phase transition takes place and for
$\hbar>\hbar_c$ the pinned instanton glass is transformed into the sliding
phonon gas with gapless phonon excitations. This transition is accompanied by
the divergence of the spatial correlation length and appearence of sliding
modes at $\hbar>\hbar_c$.Comment: revtex 16 pages, 18 figure

### Effects of disorder on the wave front depinning transition in spatially discrete systems

Pinning and depinning of wave fronts are ubiquitous features of spatially
discrete systems describing a host of phenomena in physics, biology, etc. A
large class of discrete systems is described by overdamped chains of nonlinear
oscillators with nearest-neighbor coupling and subject to random external
forces. The presence of weak randomness shrinks the pinning interval and it
changes the critical exponent of the wave front depinning transition from 1/2
to 3/2. This effect is derived by means of a recent asymptotic theory of the
depinning transition, extended to discrete drift-diffusion models of transport
in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.

### Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

We study topological solitary waves (kinks and antikinks) in a nonlinear
one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse
type. This chain is used to describe the collective proton dynamics in
quasi-one-dimensional networks of hydrogen bonds, where the on-site potential
plays role of the proton potential in the hydrogen bond. The system supports a
rich variety of stationary kink solutions with different symmetry properties.
We study the stability and bifurcation structure of all these stationary kink
states. An exactly solvable model with a piecewise ``parabola-constant''
approximation of the double-Morse potential is suggested and studied
analytically. The dependence of the Peierls-Nabarro potential on the system
parameters is studied. Discrete travelling-wave solutions of a narrow permanent
profile are shown to exist, depending on the anharmonicity of the Morse
potential and the cooperativity of the hydrogen bond (the coupling constant of
the interaction between nearest-neighbor protons).Comment: 12 pages, 20 figure

### 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
$F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate,
for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and
for $|F| > F_{cs}$ (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.

### Stability of mode-locked kinks in the ac driven and damped sine-Gordon lattice

Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice
that is driven by the oscillating force is studied. The investigation is
focused mostly on the properties of the mode-locked states in the {\it
overband} case, when the driving frequency lies above the linear band. With the
help of Floquet theory it is demonstrated that the destabilizing of the
mode-locked state happens either through the Hopf bifurcation or through the
tangential bifurcation. It is also observed that in the overband case the
standing mode-locked kink state maintains its stability for the bias amplitudes
that are by the order of magnitude larger than the amplitudes in the
low-frequency case.Comment: To appear in Springer Series on Wave Phenomena, special volume
devoted to the LENCOS'12 conference; 6 figure

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