Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

The free escape continuum of diffuse ions upstream of the Earth's quasi-parallel bow shock

The Earth's bow shock is very efficient in accelerating ions out of the incident solar wind distribution to high energies (≈ 200 keV/e). Fluxes of energetic ions accelerated at the quasi-parallel bow shock, also known as diffuse ions, are best represented by exponential spectra in energy/charge, which require additional assumptions to be incorporated into these model spectra. One of these assumptions is a so-called "free escape boundary" along the interplanetary magnetic field into the upstream direction. Locations along the IBEX orbit are ideally suited for in situ measurements to investigate the existence of an upstream free escape boundary for bow shock accelerated ions. In this study we use 2 years of ion measurements from the background monitor on the IBEX spacecraft, supported by ACE solar wind observations. The IBEX Background Monitor is sensitive to protons > 14 keV, which includes the energy of the maximum flux for diffuse ions. With increasing distance from the bow shock along the interplanetary magnetic field, the count rates for diffuse ions stay constant for ions streaming away from the bow shock, while count rates for diffuse ions streaming toward the shock gradually decrease from a maximum value to ~1/e at distances of about 10 RE to 14 RE. These observations of a gradual decrease support the transition to a free escape continuum for ions of energy >14 keV at distances from 10 RE to 14 RE from the bow shock.

The quasi 16-day wave in mesospheric water vapor during boreal winter 2011/2012

This study investigates the characteristics of the quasi 16-day wave in the mesosphere during boreal winter 2011/2012 using observations of water vapor from ground-based microwave radiometers and satellite data. The ground-based microwave radiometers are located in Seoul (South Korea, 37° N), Bern (Switzerland, 47° N) and Sodankylä (Finland, 67° N). The quasi 16-day wave is observed in the mesosphere at all three locations, while the dominant period increases with latitude from 15 days at Seoul to 20 days at Sodankylä. The observed evolution of the quasi 16-day wave confirms that the wave activity is strongly decreased during a sudden stratospheric warming that occurred in mid-January 2012. Using satellite data from the Microwave Limb Sounder on the Aura satellite, we examine the zonal characteristics of the quasi 16-day wave and conclude that the observed waves above the mid-latitudinal stations Seoul and Bern are eastward-propagating s=−1 planetary waves with periods of 15 to 16 days, while the observed oscillation above the polar station Sodankylä is a standing oscillation with a period of approximately 20 days. The strongest relative wave amplitudes in water vapor during the investigated time period are approximately 15%. The wave activity varies strongly along a latitude circle. The activity of the quasi 16-day wave in mesospheric water vapor during boreal winter 2011/2012 is strongest over Northern Europe, the North Atlantic ocean and North-West Canada. The region of highest wave activity seems to be related to the position of the polar vortex. We conclude that the classic approach to characterize planetary waves zonally averaged along a latitude circle is not sufficient to explain the local observations because of the strong longitudinal dependence of the wave activity.

The quasi 16-day wave in mesospheric water vapor during boreal winter 2011/2012

This study investigates the characteristics of the quasi 16-day wave in the mesosphere during boreal winter 2011/2012 using observations of water vapor from ground-based microwave radiometers and satellite data. The ground-based microwave radiometers are located in Seoul (South Korea, 37° N), Bern (Switzerland, 47° N) and Sodankylä (Finland, 67° N). The quasi 16-day wave is observed in the mesosphere at all three locations, while the dominant period increases with latitude from 15 days at Seoul to 20 days at Sodankylä. The observed evolution of the quasi 16-day wave confirms that the wave activity is strongly decreased during a sudden stratospheric warming that occurred in mid-January 2012. Using satellite data from the Microwave Limb Sounder on the Aura satellite, we examine the zonal characteristics of the quasi 16-day wave and conclude that the observed waves above the midlatitudinal stations Seoul and Bern are eastward-propagating s = −1 planetary waves with periods of 15 to 16 days, while the observed oscillation above the polar station Sodankylä is a standing wave with a period of approximately 20 days. The strongest relative wave amplitudes in water vapor during the investigated time period are approximately 15%. The wave activity varies strongly along a latitude circle. The activity of the quasi 16-day wave in mesospheric water vapor during boreal winter 2011/2012 is strongest over northern Europe, the North Atlantic Ocean and northwestern Canada. The region of highest wave activity seems to be related to the position of the polar vortex. We conclude that the classic approach to characterize planetary waves zonally averaged along a latitude circle is not sufficient to explain the local observations because of the strong longitudinal dependence of the wave activity.

Quasi-Self-Dual Exponential Lévy Processes

The important application of semistatic hedging in financial markets naturally leads to the notion of quasi--self-dual processes. The focus of our study is to give new characterizations of quasi--self-duality. We analyze quasi--self-dual Lévy driven markets which do not admit arbitrage opportunities and derive a set of equivalent conditions for the stochastic logarithm of quasi--self-dual martingale models. Since for nonvanishing order parameter two martingale properties have to be satisfied simultaneously, there is a nontrivial relation between the order and shift parameter representing carrying costs in financial applications. This leads to an equation containing an integral term which has to be inverted in applications. We first discuss several important properties of this equation and, for some well-known Lévy-driven models, we derive a family of closed-form inversion formulae.