The nonlinear heat equation on W-random graphs

For systems of coupled differential equations on a sequence of W-random graphs, we derive the continuum limit in the form of an evolution integral equation. We prove that solutions of the initial value problems (IVPs) for the discrete model converge to the solution of the IVP for its continuum limit. These results combined with the analysis of nonlocally coupled deterministic networks in [9] justify the continuum (thermodynamic) limit for a large class of coupled dynamical systems on convergent families of graphs

X-ray radiation of the jets and the supercritical accretion disk in SS 433

The observed X-ray luminosity of SS 433 is ~10^36 erg/s, it is known that all the radiation is formed in the famous SS 433 jets. The bolometric luminosity of SS 433 is ~10^40 erg/s, and originally the luminosity must be realized in X-rays. The original radiation is probably thermalized in the supercritical accretion disk wind, however the missing more than four orders of magnitude is surprising. We have analysed the XMM-Newton spectra of SS 433 using a model of adiabatically and radiatively cooling X-ray jets. The multi-temperature thermal jet model reproduces very well the strongest observed emission lines, but it can not reproduce the continuum radiation and some spectral features. We have found a notable contribution of ionized reflection to the spectrum in the energy range from 3 to 12 keV. The reflected spectrum is an evidence of the supercritical disk funnel, where the illuminating radiation comes from deeper funnel regions, to be further reflected in the outer visible funnel walls. The illuminating spectrum is similar to that observed in ULXs, its luminosity has to be no less than ~10^39 erg/s. A soft excess has been detected, that does not depend on the thermal jet model details. It may be represented as a BB with a temperature of ~0.1 keV and luminosity of ~3*10^37 erg/s. The soft spectral component has about the same parameters as those found in ULXs.Comment: 4 pages, 3 figures, Contribution to the IAU Symposium 275: Jets at all Scales. Buenos Aires, Argentina, September 13-17, 201

A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions

Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed

The Poincare map of randomly perturbed periodic motion

A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and analyze the Poincare map of the randomly perturbed periodic motion. We show that the time of the first exit from a small neighborhood of the fixed point of the map, which corresponds to the unperturbed periodic orbit, is well approximated by the geometric distribution. The parameter of the geometric distribution tends zero together with the noise intensity. Therefore, our result can be interpreted as an estimate of stability of periodic motion to random perturbations. In addition, we show that the geometric distribution of the first exit times translates into statistical properties of solutions of important differential equation models in applications. To this end, we demonstrate three examples from mathematical neuroscience featuring complex oscillatory patterns characterized by the geometric distribution. We show that in each of these models the statistical properties of emerging oscillations are fully explained by the general properties of randomly perturbed periodic motions identified in this paper

Role of gravity waves in vertical coupling during sudden stratospheric warmings

Gravity waves are primarily generated in the lower atmosphere, and can reach thermospheric heights in the course of their propagation. This paper reviews the recent progress in understanding the role of gravity waves in vertical coupling during sudden stratospheric warmings. Modeling of gravity wave effects is briefly reviewed, and the recent developments in the field are presented. Then, the impact of these waves on the general circulation of the upper atmosphere is outlined. Finally, the role of gravity waves in vertical coupling between the lower and the upper atmosphere is discussed in the context of sudden stratospheric warmings.Comment: Accepted for publication in Geoscience Letter

Influence of parameterized small-scale gravity waves on the migrating diurnal tide in Earth's thermosphere

Effects of subgrid-scale gravity waves (GWs) on the diurnal migrating tides are investigated from the mesosphere to the upper thermosphere for September equinox conditions, using a general circulation model coupled with the extended spectral nonlinear GW parameterization of Yi\u{g}it et al (2008). Simulations with GW effects cut-off above the turbopause and included in the entire thermosphere have been conducted. GWs appreciably impact the mean circulation and cool the thermosphere down by up to 12-18%. GWs significantly affect the winds modulated by the diurnal migrating tide, in particular in the low-latitude mesosphere and lower thermosphere and in the high-latitude thermosphere. These effects depend on the mutual correlation of the diurnal phases of the GW forcing and tides: GWs can either enhance or reduce the tidal amplitude. In the low-latitude MLT, the correlation between the direction of the deposited GW momentum and the tidal phase is positive due to propagation of a broad spectrum of GW harmonics through the alternating winds. In the Northern Hemisphere high-latitude thermosphere, GWs act against the tide due to an anti-correlation of tidal wind and GW momentum, while in the Southern high-latitudes they weakly enhance the tidal amplitude via a combination of a partial correlation of phases and GW-induced changes of the circulation. The variable nature of GW effects on the thermal tide can be captured in GCMs provided that a GW parameterization (1) considers a broad spectrum of harmonics, (2) properly describes their propagation, and (3) correctly accounts for the physics of wave breaking/saturation.Comment: Accepted for publication in Journal of Geophysical Research - Space Physic