651 research outputs found
Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are
approximated by equations of the discrete nonlinear Schrodinger type. We show
how to justify this approximation by two methods, which have been very popular
in the recent literature. The first method relies on a priori energy estimates
and multi-scale decompositions. The second method is based on a resonant normal
form theorem. We show that although the two methods are different in the
implementation, they produce equivalent results as the end product. We also
discuss applications of the discrete nonlinear Schrodinger equation in the
context of existence and stability of breathers of the Klein--Gordon lattice
Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices
We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite
lattices. We also show that the breathers are well approximated by the ground
state of the nonlinear Schroedinger equation. The result is obtained by
exploiting the relation between the Klein Gordon lattice and the discrete Non
Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt
decomposition and continuum approximation techniques introduced in [7],
actually using its main result as an important lemma
FPU phenomenon for generic initial data
The well known FPU phenomenon (lack of attainment of equipartition of the
mode--energies at low energies, for some exceptional initial data) suggests
that the FPU model does not have the mixing property at low energies. We give
numerical indications that this is actually the case. This we show by computing
orbits for sets of initial data of full measure, sampled out from the
microcanonical ensemble by standard Montecarlo techniques. Mixing is tested by
looking at the decay of the autocorrelations of the mode--energies, and it is
found that the high--frequency modes have autocorrelations that tend instead to
positive values. Indications are given that such a nonmixing property survives
in the thermodynamic limit. It is left as an open problem whether mixing
obtains within time--scales much longer than the presently available ones
Tail resonances of FPU q-breathers and their impact on the pathway to equipartition
Upon initial excitation of a few normal modes the energy distribution among
all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits
exponential localization on large time scales. At the same time resonant
anomalies (peaks) are observed in its weakly excited tail for long times
preceding equipartition. We observe a similar resonant tail structure also for
exact time-periodic Lyapunov orbits, coined q-breathers due to their
exponential localization in modal space. We give a simple explanation for this
structure in terms of superharmonic resonances. The resonance analysis agrees
very well with numerical results and has predictive power. We extend a
previously developed perturbation method, based essentially on a
Poincare-Lindstedt scheme, in order to account for these resonances, and in
order to treat more general model cases, including truncated Toda potentials.
Our results give qualitative and semiquantitative account for the superharmonic
resonances of q-breathers and natural packets
The Impacts of Airport Centrality in the EU Network and Inter- Airport Competition on Airport Efficiency
In this paper we study the relationship between airport efficiency and two factors: an airport’s centrality in the EU network, and the intensity of competition from alternative airports in the same catchment area. We apply a two-stage econometric model based on the Simar & Wilson (2007) bootstrap procedure to a balanced sample of 57 European airports. We also design and compute our own measures of airport centrality and competition. The results show that efficiency is positively related to centrality in the European network, as measured by a weighted sum of minimal paths passing through the airport in question. The intensity of competition between airports also has a positive effect on efficiency. Our analysis suggests that air transportation policies should focus on increasing competition within important catchment areas (e.g., by investing in infrastructure facilitating access to alternative airports) and enhancing the connectivity of the EU network (e.g., by subsidizing new point-to-point connections between airports with capacity to spare).air transportation, efficiency, network centrality, inter – airports competition.
Hamiltonian lattice dynamics
Hamiltonian lattice dynamics is a very active and relevant field of research. In this Special Issue, by means of some recent results by leading experts in the field, we tried to illustrate how broad and rich it can be, and how it can be seen as excellent playground for Mathematics in Engineering
Giant g factor tuning of long-lived electron spins in Ge
Control of electron spin coherence via external fields is fundamental in
spintronics. Its implementation demands a host material that accommodates the
highly desirable but contrasting requirements of spin robustness to relaxation
mechanisms and sizeable coupling between spin and orbital motion of charge
carriers. Here we focus on Ge, which, by matching those criteria, is rapidly
emerging as a prominent candidate for shuttling spin quantum bits in the mature
framework of Si electronics. So far, however, the intrinsic spin-dependent
phenomena of free electrons in conventional Ge/Si heterojunctions have proved
to be elusive because of epitaxy constraints and an unfavourable band
alignment. We overcome such fundamental limitations by investigating a two
dimensional electron gas (2DEG) confined in quantum wells of pure Ge grown on
SiGe-buffered Si substrates. These epitaxial systems demonstrate exceptionally
long spin relaxation and coherence times, eventually unveiling the potential of
Ge in bridging the gap between spintronic concepts and semiconductor device
physics. In particular, by tuning spin-orbit interaction via quantum
confinement we demonstrate that the electron Land\'e g factor and its
anisotropy can be engineered in our scalable and CMOS-compatible architectures
over a range previously inaccessible for Si spintronics
On the nonexistence of degenerate phase-shift multibreathers in Klein-Gordon models with interactions beyond nearest neighbors
In this work, we study the existence of, low amplitude, phase-shift multibreathers for small values of the linear coupling in KleinGordon chains with interactions beyond the classical nearest-neighbor (NN) ones. In the proper parameter regimes, the considered lattices bear connections to models beyond one spatial dimension, namely the so-called zigzag lattice, as well as the two-dimensional square lattice or coupled chains. We examine initially the necessary persistence conditions of the system derived by the so-called Effective Hamiltonian Method, in order to seek for unperturbed solutions whose continuation is feasible. Although this approach provides useful insights, in the presence of degeneracy, it does not allow us to determine if they constitute true solutions of our system. In order to overcome this obstacle, we follow a different route. By means of a Lyapunov-Schmidt decomposition, we are able to establish that the bifurcation equation for our models can be considered, in the small energy and small coupling regime, as a perturbation of a corresponding, beyond nearest-neighbor, discrete nonlinear Schr\ua8odinger equation. There, nonexistence results of degenerate phase-shift discrete solitons can be demonstrated by an additional Lyapunov-Schmidt decomposition, and translated to our original problem on the Klein-Gordon system. In this way, among other results, we can prove nonexistence of four-sites vortex-like waveforms in the zigzag Klein-Gordon model. Finally, briefly considering a one-dimensional model bearing similarities to the square lattice, we conclude that the above strategy is not efficient for the proof of the existence or nonexistence of vortices due to the higher degeneracy of this configuration
- …