144 research outputs found
Impulse-induced localized nonlinear modes in an electrical lattice
Intrinsic localized modes, also called discrete breathers, can exist under
certain conditions in one-dimensional nonlinear electrical lattices driven by
external harmonic excitations. In this work, we have studied experimentally the
efectiveness of generic periodic excitations of variable waveform at generating
discrete breathers in such lattices. We have found that this generation
phenomenon is optimally controlled by the impulse transmitted by the external
excitation (time integral over two consecutive zerosComment: 5 pages, 8 figure
Speed-of-light pulses in a nonlinear Weyl equation
We introduce a prototypical nonlinear Weyl equation, motivated by recent
developments in massless Dirac fermions, topological semimetals and photonics.
We study the dynamics of its pulse solutions and find that a localized one-hump
initial condition splits into a localized two-hump pulse, while an associated
phase structure emerges in suitable components of the spinor field. For times
larger than a transient time this pulse moves with the speed of light (or
Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics
and maintaining its shape (both in two and three dimensions). We show that for
the considered nonlinearity, this pulse represents an exact solution of the
nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the
results to a broader class of nonlinearities and on their emerging potential
for observation in different areas of application.Comment: 7 pages, 6 figure
Effect of breather existence on reconstructive transformations in mica muscovite
The International Workshop on Complex Systems (5º. 2007. Sendai, Japan)Reconstructive transformations of layered silicates as mica muscovite take place at much lower temperatures than expected. A possible explanation is the existence of breathers within the potassium layer. Numerical analysis of a model shows the existence of many different types of breathers with different energies and existence ranges which spectrum coincides approximately with a statistical theory for them.Ministerio de Educacion y Ciencia, Spain, project FIS2004-0118
Discrete Breathers in Klein-Gordon Lattices: a Deflation-Based Approach
Deflation is an efficient numerical technique for identifying new branches of
steady state solutions to nonlinear partial differential equations. Here, we
demonstrate how to extend deflation to discover new periodic orbits in
nonlinear dynamical lattices. We employ our extension to identify discrete
breathers, which are generic exponentially localized, time-periodic solutions
of such lattices. We compare different approaches to using deflation for
periodic orbits, including ones based on a Fourier decomposition of the
solution, as well as ones based on the solution's energy density profile. We
demonstrate the ability of the method to obtain a wide variety of multibreather
solutions without prior knowledge about their spatial profile
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
Moving discrete breathers in a Klein–Gordon chain with an impurity
We analyse the influence of an impurity in the evolution of moving discrete breathers in a Klein–Gordon chain with non-weak nonlinearity. Three different types of behaviour can be observed when moving breathers interact with the impurity: they pass through the impurity continuing their direction of movement; they are reflected by the impurity; they are trapped by the impurity, giving rise to chaotic breathers, as their Fourier power spectra show. Resonance with a breather centred at the impurity site is conjectured to be a necessary condition for the appearance of the trapping phenomenon. This paper establishes a difference between the resonance condition of the non-weak nonlinearity approach and the resonance condition with the linear impurity mode in the case of weak nonlinearity.European Commission under the RTN project LOCNET, HPRN-CT-1999-0016
Moving breathers in bent DNA with realistic parameters
Recent papers have considered moving breathers (MBs) in DNA
models including long range
interaction due to the dipole moments of the hydrogen bonds.
We have recalculated the value of
the charge transfer when hydrogen bonds stretch using quant
um chemical methods which takes into
account the whole nucleoside pairs. We explore the conseque
nces of this value on the properties
of MBs, including the range of frequencies for which they exi
st and their effective masses. They
are able to travel through bending points with fairly large c
urvatures provided that their kinetic
energy is larger than a minimum energy which depends on the cu
rvature. These energies and the
corresponding velocities are also calculated in function o
f the curvatureMECD–FEDER project BMF2003- 03015/FIS
Numerical study of two-dimensional disordered Klein-Gordon lattices with cubic soft anharmonicity
Localized oscillations appear both in ordered nonlinear lattices (breathers) and in disordered linear lattices (Anderson modes). Numerical studies on a class of two-dimensional systems of the Klein-Gordon type show that there exist two different types of bifurcation in the path from nonlinearity-order to linearity-disorder: inverse pitchforks, with or without period doubling, and saddle-nodes. This was discovered for a one-dimensional system in a previous work of Archilla, MacKay and Marin. The appearance of a saddle-node bifurcation indicates that nonlinearity and disorder begin to interfere destructively and localization is not possible. In contrast, the appearance of a pitchfork bifurcation indicates that localization persists
Discrete breathers collisions in nonlinear Schrödinger and Klein-Gordon lattices
Collisions between moving localized modes (moving breathers) in non-
integrable lattices present a rich outcome. In this paper, some features of the
interaction of moving breathers in Discrete Nonlinear Schrödinger and Klein-
Gordon lattices, together with some plausible explanations, are exposed
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