266 research outputs found
The Natural Logarithm on Time Scales
We define an appropriate logarithm function on time scales and present its
main properties. This gives answer to a question posed by M. Bohner in [J.
Difference Equ. Appl. {\bf 11} (2005), no. 15, 1305--1306].Comment: 6 page
Control of light transmission through opaque scattering media in space and time
We report the first experimental demonstration of combined spatial and
temporal control of light trajectories through opaque media. This control is
achieved by solely manipulating spatial degrees of freedom of the incident
wavefront. As an application, we demonstrate that the present approach is
capable to form bandwidth-limited ultrashort pulses from the otherwise randomly
transmitted light with a controllable interaction time of the pulses with the
medium. Our approach provides a new tool for fundamental studies of light
propagation in complex media and has potential for applications for coherent
control, sensing and imaging in nano- and biophotonics
Delta-Nabla Optimal Control Problems
We present a unified treatment to control problems on an arbitrary time scale
by introducing the study of forward-backward optimal control problems.
Necessary optimality conditions for delta-nabla isoperimetric problems are
proved, and previous results in the literature obtained as particular cases. As
an application of the results of the paper we give necessary and sufficient
Pareto optimality conditions for delta-nabla bi-objective optimal control
problems.Comment: Preprint version of an article submitted 28-Nov-2009; revised
02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration
and Contro
R-matrix approach to integrable systems on time scales
A general unifying framework for integrable soliton-like systems on time
scales is introduced. The -matrix formalism is applied to the algebra of
-differential operators in terms of which one can construct infinite
hierarchy of commuting vector fields. The theory is illustrated by two
infinite-field integrable hierarchies on time scales which are difference
counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer
soliton systems are constructed as related finite-field restrictions.Comment: 21 page
Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study
Covariant vectors, Lyapunov vectors, or Oseledets vectors are increasingly
being used for a variety of model analyses in areas such as partial
differential equations, nonautonomous differentiable dynamical systems, and
random dynamical systems. These vectors identify spatially varying directions
of specific asymptotic growth rates and obey equivariance principles. In recent
years new computational methods for approximating Oseledets vectors have been
developed, motivated by increasing model complexity and greater demands for
accuracy. In this numerical study we introduce two new approaches based on
singular value decomposition and exponential dichotomies and comparatively
review and improve two recent popular approaches of Ginelli et al. (2007) and
Wolfe and Samelson (2007). We compare the performance of the four approaches
via three case studies with very different dynamics in terms of symmetry,
spectral separation, and dimension. We also investigate which methods perform
well with limited data
On the critical level-curvature distribution
The parametric motion of energy levels for non-interacting electrons at the
Anderson localization critical point is studied by computing the energy
level-curvatures for a quasiperiodic ring with twisted boundary conditions. We
find a critical distribution which has the universal random matrix theory form
for large level-curvatures corresponding to
quantum diffusion, although overall it is close to approximate log-normal
statistics corresponding to localization. The obtained hybrid distribution
resembles the critical distribution of the disordered Anderson model and makes
a connection to recent experimental data.Comment: 4 pages, 3 figure
Correlation function of weakly interacting bosons in a disordered lattice
One of the most important issues in disordered systems is the interplay of
the disorder and repulsive interactions. Several recent experimental advances
on this topic have been made with ultracold atoms, in particular the
observation of Anderson localization, and the realization of the disordered
Bose-Hubbard model. There are however still questions as to how to
differentiate the complex insulating phases resulting from this interplay, and
how to measure the size of the superfluid fragments that these phases entail.
It has been suggested that the correlation function of such a system can give
new insights, but so far little experimental investigation has been performed.
Here, we show the first experimental analysis of the correlation function for a
weakly interacting, bosonic system in a quasiperiodic lattice. We observe an
increase in the correlation length as well as a change in shape of the
correlation function in the delocalization crossover from Anderson glass to
coherent, extended state. In between, the experiment indicates the formation of
progressively larger coherent fragments, consistent with a fragmented BEC, or
Bose glass.Comment: 16 pages, 8 figure
Effect of uniaxial stress on ferroelectric behavior of (Bi1/2Na1/2)TiO3-based lead-free piezoelectric ceramics
Prior studies have shown that a field-induced ferroelectricity in ceramics with general chemical formula (1-x-y) (Bi1/2 Na1/2) TiO3 -x BaTiO3 -y (K0.5 Na0.5) NbO3 and a very low remanent strain can produce very large piezoelectric strains. Here we show that both the longitudinal and transverse strains gradually change with applied electric fields even during the transition from the nonferroelectric to the ferroelectric state, in contrast to known Pb-containing antiferroelectrics. Hence, the volume change and, in turn, the phase transition can be affected using uniaxial compressive stresses, and the effect on ferroelectricity can thus be assessed. It is found that the 0.94 (Bi1/2 Na1/2) TiO3 -0.05 BaTiO3 -0.01 (K0.5 Na0.5) NbO3 ceramic (largely ferroelectric), with a rhombohedral R3c symmetry, displays large ferroelectric domains, significant ferroelastic deformation, and large remanent electrical polarizations even at a 250 MPa compressive stress. In comparison, the 0.91 (Bi1/2 Na1/2) TiO3 -0.07 BaTiO3 -0.02 (K0.5 Na0.5) NbO3 ceramic (largely nonferroelectric) possesses characteristics of a relaxor ferroelectric ceramic, including a pseudocubic structure, limited ferroelastic deformation, and low remanent polarization. The results are discussed with respect of the proposed antiferroelectric nature of the nonferroelectric state.open291
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