Parity-time (PT) symmetric periodic structures, near the spontaneous PT-symmetry breaking point, can act as unidirectional invisible media. In this regime, the reflection from one end is diminished ...while it is enhanced from the other. Furthermore, the transmission coefficient and phase are indistinguishable from those expected in the absence of a grating. The phenomenon is robust even in the presence of Kerr nonlinearities, and it can also effectively suppress optical bistabilities.
We prove a global estimate in the scale of Lorentz spaces for the gradient of weak solution to a general nonlinear obstacle problem of p(x)-growth. It is mainly assumed that the nonlinearity ...satisfies small BMO semi-norm in the spatial variable and the boundary of domain is flat in the Reifenberg sense, while the variable exponent p(x) is a strongly log-Hölder continuous function. Here, an essential ingredient of our main proof is to make use of a combination of the so-called large-M-inequality principle and the geometric argument.
Resummation of massive gravity de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J
Physical review letters,
06/2011, Letnik:
106, Številka:
23
Journal Article
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We construct four-dimensional covariant nonlinear theories of massive gravity which are ghost-free in the decoupling limit to all orders. These theories resum explicitly all the nonlinear terms of an ...effective field theory of massive gravity. We show that away from the decoupling limit the Hamiltonian constraint is maintained at least up to and including quartic order in nonlinearities, hence excluding the possibility of the Boulware-Deser ghost up to this order. We also show that the same remains true to all orders in a similar toy model.
The theory of nearly incompressible magnetohydrodynamics (NI MHD) was developed largely in the early 1990s, together with an important extension to inhomogeneous flows in 2010. Much of the focus in ...the earlier work was to understand the apparent incompressibility of the solar wind and other plasma environments, and the relationship of density fluctuations to apparently incompressible manifestations of turbulence in the solar wind and interstellar medium. Further important predictions about the "dimensionality" of solar wind turbulence and its relationship to the plasma beta were made and subsequently confirmed observationally. However, despite the initial success of NI MHD in describing fluctuations in the solar wind, a detailed application to solar wind turbulence has not been undertaken. Here, we use the equations of NI MHD to describe solar wind turbulence, rewriting the NI MHD system in terms of Elsässer variables. Distinct descriptions of 2D and slab turbulence emerge naturally from the Elsässer formulation, as do the nonlinear couplings between 2D and slab components. For plasma beta order 1 or less regions, predictions for 2D and slab spectra result from the NI MHD description, and predictions for the spectral characteristics of density fluctuations can be made. We conclude by presenting a NI MHD formulation describing the transport of majority 2D and minority slab turbulence throughout the solar wind. A preliminary comparison of theory and observations is presented.
Complex (dusty) plasmas are composed of a weakly ionized gas and charged microparticles and represent the plasma state of soft matter. Complex plasmas have several remarkable features: Dynamical time ...scales associated with microparticles are ''stretched'' to tens of milliseconds, yet the microparticles themselves can be easily visualized individually. Furthermore, since the background gas is dilute, the particle dynamics in strongly coupled complex plasmas is virtually undamped, which provides a direct analogy to regular liquids and solids in terms of the atomistic dynamics. Finally, complex plasmas can be easily manipulated in different ways--also at the level of individual particles. Altogether, this gives us a unique opportunity to go beyond the limits of continuous media and study--at the kinetic level--various generic processes occurring in liquids or solids, in regimes ranging from the onset of cooperative phenomena to large strongly coupled systems. In the first part of the review some of the basic and new physics are highlighted which complex plasmas enable us to study, and in the second (major) part strong coupling phenomena in an interdisciplinary context are examined. The connections with complex fluids are emphasized and a number of generic liquid and solid-state issues are addressed. In summary, application oriented research is discussed.
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of ...concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton–Krylov methods.
In this paper, the behavior of a Jarratt family of iterative methods applied to quadratic polynomials is studied. Some anomalies are found in this family be means of studying the dynamical behavior ...of this fourth-order family of methods. Parameter spaces are shown and the study of the stability of all the fixed points is presented. Dynamical planes for members with good and bad dynamical behavior are also provided.
We investigate the effect of nonlinearity on beam dynamics in parity-time (PT) symmetric potentials. We show that a novel class of one- and two-dimensional nonlinear self-trapped modes can exist in ...optical PT synthetic lattices. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow within these complex solitons is also examined.
ABSTRACT The observed relation between the soft X-ray and the optical-ultraviolet emission in active galactic nuclei (AGNs) is nonlinear and it is usually parametrized as a dependence between the ...logarithm of the monochromatic luminosity at 2500 and at 2 keV. Previous investigations have found that the dispersion of this relation is rather high (∼0.35-0.4 in log units), which may be caused by measurement uncertainties, variability, and intrinsic dispersion due to differences in the AGN physical properties (e.g., different accretion modes). We show that, once optically selected quasars with homogeneous SED and X-ray detection are selected, and dust reddened and/or gas obscured objects are not included, the measured dispersion drops to significantly lower values (i.e., ∼0.21-0.24 dex). We show that the residual dispersion is due to some extent to variability, and to remaining measurement uncertainties. Therefore, the real physical intrinsic dispersion should be dex. Such a tight relation, valid over four decades in luminosity, must be the manifestation of an intrinsic (and universal) physical relation between the disk, emitting the primary radiation, and the hot electron corona emitting X-rays.
A HUBBLE DIAGRAM FOR QUASARS Risaliti, G.; Lusso, E.
Astrophysical journal/The Astrophysical journal,
12/2015, Letnik:
815, Številka:
1
Journal Article
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ABSTRACT We present a new method to test the ΛCDM cosmological model and to estimate cosmological parameters based on the nonlinear relation between the ultraviolet and X-ray luminosities of quasars. ...We built a data set of 1138 quasars by merging several samples from the literature with X-ray measurements at 2 keV and SDSS photometry, which was used to estimate the extinction-corrected 2500 flux. We obtained three main results: (1) we checked the nonlinear relation between X-ray and UV luminosities in small redshift bins up to , confirming that the relation holds at all redshifts with the same slope; (2) we built a Hubble diagram for quasars up to , which is well matched to that of supernovae in the common z = 0-1.4 redshift interval and extends the test of the cosmological model up to ; and (3) we showed that this nonlinear relation is a powerful tool for estimating cosmological parameters. Using the present data and assuming a ΛCDM model, we obtain = 0.22 and = 0.92 ( = 0.28 0.04 and = 0.73 from a joint quasar-SNe fit). Much more precise measurements will be achieved with future surveys. A few thousand SDSS quasars already have serendipitous X-ray observations from Chandra or XMM-Newton, and at least 100,000 quasars with UV and X-ray data will be made available by the extended ROentgen Survey with an Imaging Telescope Array all-sky survey in a few years. The Euclid, Large Synoptic Survey Telescope, and Advanced Telescope for High ENergy Astrophysics surveys will further increase the sample size to at least several hundred thousand. Our simulations show that these samples will provide tight constraints on the cosmological parameters and will allow us to test for possible deviations from the standard model with higher precision than is possible today.
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