Remarks on the embedding of spaces of distributions into spaces of Colombeau generalized functions

We present some remarks about the embedding of spaces of Schwartz distributions into spaces of Colombeau generalized functions. We show that the various constructions of such embeddings existing in the literature lead in fact to the same one.Comment: 13 page

Generalized Integral Operators and Schwartz Kernel Theorem

In connection with the classical Schwartz kernel theorem, we show that in the framework of Colombeau generalized functions a large class of linear mappings admit integral kernels. To do this, we need to introduce news spaces of generalized functions with slow growth and the corresponding adapted linear mappings. Finally, we show that in some sense Schwartz' result is contained in our main theorem.Comment: 18 page

Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Is anthropogenic sea level fingerprint already detectable in the Pacific ocean ?

Sea level rates up to three times the global mean rate are being observed in the western tropical Pacific since 1993 by satellite altimetry. From recently published studies, it is not yet clear whether the sea level spatial trend patterns of the Pacific Ocean observed by satellite altimetry are mostly due to internal climate variability or if some anthropogenic fingerprint is already detectable. A number of recent studies have shown that the removal of the signal corresponding to the Pacific Decadal Oscillation (PDO)/Interdecadal Pacific Oscillation (IPO) from the observed altimetry sea level data over 1993–2010/2012 results in some significant residual trend pattern in the western tropical Pacific. It has thus been suggested that the PDO/IPO-related internal climate variability alone cannot account for all of the observed trend patterns in the western tropical Pacific and that the residual signal could be the fingerprint of the anthropogenic forcing. In this study, we investigate if there is any other internal climate variability signal still present in the residual trend pattern after the removal of IPO contribution from the altimetry-based sea level over 1993–2013. We show that subtraction of the IPO contribution to sea level trends through the method of linear regression does not totally remove the internal variability, leaving significant signal related to the non-linear response of sea level to El Niño Southern Oscillation (ENSO). In addition, by making use of 21 CMIP5 coupled climate models, we study the contribution of external forcing to the Pacific Ocean regional sea level variability over 1993–2013, and show that according to climate models, externally forced and thereby the anthropogenic sea level fingerprint on regional sea level trends in the tropical Pacific is still too small to be observable by satellite altimetry

Volcanic spreading forcing and feedback in geothermal reservoir development, Amiata Volcano, Italia

We made a stratigraphic, structural and morphologic study of Amiata Volcano in Italy. We find that the edifice is dissected by intersecting grabens that accommodate the collapse of the higher sectors of the volcano. In turn, a number of compressive structures and diapirs exist all around the margin of the volcano. These structures create an angular drainage pattern, with stream damming and captures, and a set of lakes within and around the volcano. We interpret these structures as the result of volcanic spreading of the edifice of Amiata onto its weak substratum, formed by the late Triassic evaporites (Anidriti of Burano) and the Middle-Jurassic to Early-Cretaceous clayey chaotic complexes (Ligurian Complex). Regional doming created a slope in the basement forcing the outward flow and spreading of the ductile layers below the volcano. We model the dynamics of spreading with a scaled lubrication approximation of the Navier Stokes equations, and numerically study a solution. In the model we include simple functions for volcanic deposition and surface erosion that change the topography over time. Scaling indicates that spreading at Amiata could still be active. The numerical solution shows that, as the central part of the edifice sinks into the weak basement, diapiric structures of the underlying formations form around the base of the volcano. Deposition of volcanic rocks within the volcano and surface erosion away from it both enhance spreading. In addition, a sloping basement may constitute a trigger for the formation of trains of adjacent diapirs. Finally, we observe that volcanic spreading has created ideal heat traps that constitute todays’ exploited geothermal fields at Amiata. Normal faults generated by volcanic spreading, volcanic conduits, and direct contact between volcanic rocks (which host an extensive fresh-water aquifer) and the rocks of the geothermal field, constitute ideal pathways for water recharge during vapour extraction for geothermal energy production. We think that volcanic spreading could maintain faults in a critically stressed state, facilitating the occurrence of triggered seismicity

Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma

We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.Comment: Accepted by PPC

Generalized Fourier Integral Operators on spaces of Colombeau type

Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data