On moments-preserving cosine families and semigroups in C[0,1]C[0,1]

We use the newly developed Kelvin's method of images \cite{kosinusy,kelvin} to show existence of a unique cosine family generated by a restriction of the Laplace operator in $C[0,1]$, that preserves the first two moments. We characterize the domain of its generator by specifying its boundary conditions. Also, we show that it enjoys inherent symmetry properties, and in particular that it leaves the subspaces of odd and even functions invariant. Furthermore, we provide information on long-time behavior of the related semigroup.Comment: 20 pages, 2 figure

An averaging principle for fast diffusions in domains separated by semi-permeable membranes

We prove an averaging principle which asserts convergence of diffusion processes on domains separated by semi-permeable membranes, when diffusion coefficients tend to infinity while the flux through the membranes remains constant. In the limit, points in each domain are lumped into a single state of a limit Markov chain. The limit chain's intensities are proportional to the membranes' permeability and inversely proportional to the domains' sizes. Analytically, the limit is an example of a singular perturbation in which boundary and transmission conditions play a crucial role. This averaging principle is strongly motivated by recent signaling pathways models of mathematical biology, which are discussed towards the end of the paper.Comment: 34 pages, 6 figures; revised version of the article which was restructured and now contains a section explaining the general idea and the used mathematical tools to make the article more accessible to a broader audience. The main results are unchange

Long-term monitoring of SO2 quiescent degassing from Nyiragongo’s lava lake

The activity of open-vent volcanoes with an active lava-lake, such as Nyiragongo, is characterized by persistent degassing, thus continuous monitoring of the rate, volume and fate of their gas emissions is of great importance to understand their geophysical state and their potential impact. We report results of SO2 emission measurements from Nyiragongo conducted between 2004 and 2012 with a network of ground-based scanning-DOAS (Differential Optical Absorption Spectroscopy) remote sensors. The mean SO2 emission rate is found to be 13 ± 9 kg s−1, similar to that observed in 1959. Daily emission rate has a distribution close to log-normal and presents large inter-day variability, reflecting the dynamics of percolation of magma batches of heterogeneous size distribution and changes in the effective permeability of the lava lake. The degassed S content is found to be between 1000 and 2000 ppm from these measurements and the reported magma flow rates sustaining the lava lake. The inter-annual trend and plume height statistics indicate stability of a quiescently degassing lava lake during the period of study

Investigation of chlorine radical chemistry in the Eyjafjallajkull volcanic plume using observed depletions in non-methane hydrocarbons

As part of the effort to understand volcanic plume composition and chemistry during the eruption of the Icelandic volcano Eyjafjallajkull, the CARIBIC atmospheric observatory was deployed for three special science flights aboard a Lufthansa passenger aircraft. Measurements made during these flights included the collection of whole air samples, which were analyzed for non-methane hydrocarbons (NMHCs). Hydrocarbon concentrations in plume samples were found to be reduced to levels below background, with relative depletions characteristic of reaction with chlorine radicals (Cl). Recent observations of halogen oxides in volcanic plumes provide evidence for halogen radical chemistry, but quantitative data for free halogen radical concentrations in volcanic plumes were absent. Here we present the first observation-based calculations of Cl radical concentrations in volcanic plumes, estimated from observed NMHC depletions. Inferred Cl concentrations were between 1.3 × 10 and 6.6 × 10 Cl cm. The relationship between NMHC variability and local lifetimes was used to investigate the ratio between OH and Cl within the plume, with [OH]/[Cl] estimated to be ∼37. Copyright 2011 by the American Geophysical Union

From snapping out Brownian motions to Walsh's spider processes on star-like graphs

By analyzing matrices involved, we prove that a snapping-out Brownian motion with large permeability coefficients is a good approximation of Walsh's spider process on the star-like graph $K_{1,k}$. Thus, the latter process can be seen as a Brownian motion perturbed by a trace of semi-permeable membrane at the graph's center

On shape preserving semigroups

Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of shape preserving semigroups is preserved by perturbations and taking limits. These results are applied to partial delay differential equations.Comment: referees comments incorporated. To appear in Archiv der Mathematik (Basel