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The supercritical Hopf bifurcation is one of the simplest ways in which a stationary state of a nonlinear system can undergo a transition to stable self-sustained oscillations. At the bifurcation point, a small-amplitude limit cycle is born, which already at onset displays a finite frequency. If we consider a reaction-diffusion system that undergoes a supercritical Hopf bifurcation, its dynamics is described by the complex Ginzburg-Landau equation (CGLE). Here, we study such a system in the parameter regime where the CGLE shows spatio-temporal chaos. We review a type of time-delay feedback methods which is suitable to suppress chaos and replace it by other spatio-temporal solutions such as uniform oscillations, plane waves, standing waves, and the stationary state.
In the present study, the charge distribution and the charge transport across the thickness of 2- and 3-dimensional polymer nanodielectrics was investigated. Chemically surface-treated polypropylene (PP) films and low-density polyethylene nanocomposite films with 3 wt % of magnesium oxide (LDPE/MgO) served as examples of 2-D and 3-D nanodielectrics, respectively. Surface charges were deposited onto the non-metallized surfaces of the one-side metallized polymer films and found to broaden and to thus enter the bulk of the films upon thermal stimulation at suitable elevated temperatures. The resulting space-charge profiles in the thickness direction were probed by means of Piezoelectrically-generated Pressure Steps (PPSs). It was observed that the chemical surface treatment of PP which led to the formation of nano-structures or the use of bulk nanoparticles from LDPE/MgO nanocomposites enhance charge trapping on or in the respective polymer films and also reduce charge transport inside the respective samples.
Dielectric materials for electro-active (electret) and/or electro-passive (insulation) applications
(2019)
Dielectric materials for electret applications usually have to contain a quasi-permanent space charge or dipole polarization that is stable over large temperature ranges and time periods. For electrical-insulation applications, on the other hand, a quasi-permanent space charge or dipole polarization is usually considered detrimental. In recent years, however, with the advent of high-voltage direct-current (HVDC) transmission and high-voltage capacitors for energy storage, new possibilities are being explored in the area of high-voltage dielectrics. Stable charge trapping (as e.g. found in nano-dielectrics) or large dipole polarizations (as e.g. found in relaxor ferroelectrics and high-permittivity dielectrics) are no longer considered to be necessarily detrimental in electrical-insulation materials. On the other hand, recent developments in electro-electrets (dielectric elastomers), i.e. very soft dielectrics with large actuation strains and high breakdown fields, and in ferroelectrets, i.e. polymers with electrically charged cavities, have resulted in new electret materials that may also be useful for HVDC insulation systems. Furthermore, 2-dimensional (nano-particles on surfaces or interfaces) and 3-dimensional (nano-particles in the bulk) nano-dielectrics have been found to provide very good charge-trapping properties that may not only be used for more stable electrets and ferroelectrets, but also for better HVDC electrical-insulation materials with the possibility to optimize charge-transport and field-gradient behavior. In view of these and other recent developments, a first attempt will be made to review a small selection of electro-active (i.e. electret) and electro-passive (i.e. insulation) dielectrics in direct comparison. Such a comparative approach may lead to synergies in materials concepts and research methods that will benefit both areas. Furthermore, electrets may be very useful for sensing and monitoring applications in electrical-insulation systems, while high-voltage technology is essential for more efficient charging and poling of electret materials.
Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems
(2019)
In this paper, we consider the linear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered in the reproducing kernel Hilbert space framework to reconstruct the estimator from the random noisy data. We discuss the rates of convergence for the regularized solution under the prior assumptions and link condition. For regression functions with smoothness given in terms of source conditions the error bound can explicitly be established.
In Memoriam Siegfried Bauer
(2019)
Siegfried Bauer, an internationally renowned, very creative applied physicist, who also was a prolific materials scientist and engineer, died on December 30, 2018, in Linz, Austria, after a one-year battle with cancer. He was full professor of soft-matter physics at the Johannes Kepler University Linz, Austria, and a scientific leader and innovator across the fields but mainly in the areas of electro-active materials (including electrets) and stretchable and imperceptible electronics.
We review the evidence for a putative early 21st-century divergence between global mean surface temperature (GMST) and Coupled Model Intercomparison Project Phase 5 (CMIP5) projections. We provide a systematic comparison between temperatures and projections using historical versions of GMST products and historical versions of model projections that existed at the times when claims about a divergence were made. The comparisons are conducted with a variety of statistical techniques that correct for problems in previous work, including using continuous trends and a Monte Carlo approach to simulate internal variability. The results show that there is no robust statistical evidence for a divergence between models and observations. The impression of a divergence early in the 21st century was caused by various biases in model interpretation and in the observations, and was unsupported by robust statistics.
Diffusion of cosmic rays (CRs) is the key process for understanding their propagation and acceleration. We employ the description of spatial separation of magnetic field lines in magnetohydrodynamic turbulence in Lazarian & Vishniac to quantify the divergence of the magnetic field on scales less than the injection scale of turbulence and show that this divergence induces superdiffusion of CR in the direction perpendicular to the mean magnetic field. The perpendicular displacement squared increases, not as the distance x along the magnetic field, which is the case for a regular diffusion, but as the x 3 for freely streaming CRs. The dependence changes to x 3/2 for the CRs propagating diffusively along the magnetic field. In the latter case, we show that it is important to distinguish the perpendicular displacement with respect to the mean field and to the local magnetic field. We consider how superdiffusion changes the acceleration of CRs in shocks and show how it decreases efficiency of the CRs acceleration in perpendicular shocks. We also demonstrate that in the case when the small-scale magnetic field is generated in the pre-shock region, an efficient acceleration can take place for the CRs streaming without collisions along the magnetic loops.