Quadratic interaction functional for general systems of conservation laws

For the Glimm scheme approximation u_\e to the solution of the system of conservation laws in one space dimension \begin{equation*} u_t + f(u)_x = 0, \qquad u(0,x) = u_0(x) \in \R^n, \end{equation*} with initial data $u_0$ with small total variation, we prove a quadratic (w.r.t. \TV(u_0)) interaction estimate, which has been used in the literature for stability and convergence results. No assumptions on the structure of the flux $f$ are made (apart smoothness), and this estimate is the natural extension of the Glimm type interaction estimate for genuinely nonlinear systems. More precisely we obtain the following results: \begin{itemize} \item a new analysis of the interaction estimates of simple waves; \item a Lagrangian representation of the derivative of the solution, i.e. a map $\mathtt x(t,w)$ which follows the trajectory of each wave $w$ from its creation to its cancellation; \item the introduction of the characteristic interval and partition for couples of waves, representing the common history of the two waves; \item a new functional $\mathfrak Q$ controlling the variation in speed of the waves w.r.t. time. \end{itemize} This last functional is the natural extension of the Glimm functional for genuinely nonlinear systems. The main result is that the distribution $D_{tt} \mathtt x(t,w)$ is a measure with total mass \leq \const \TV(u_0)^2

Emission Fourier transform spectroscopy for remote sensingof the Earth's atmosphere

Fourier transform emission spectroscopy can make an important contribution in the observation of the Earth's atmosphere and in the investigation of atmospheric physics and chemistry. In this paper, we report the measurement performances and the result obtained by a Fourier transform spectrometer, named SAFIRE-A (Spectroscopy of the Atmosphere using Far Infrared Emission - Airborne), operating in the far infrared spectral region from limb sounding observation of the atmospheric emission from a high altitude aircraft. After a short review of the advantages of FTS emission limb sounding in comparison with competing techniques and observation geometries, a detailed description of the instrument is given with the result obtained during the APE-GAIA (Airborne Polar Experiment - Geophysica Aircraft In Antarctica) fi eld campaign carried out over the Antarctic Peninsula

Measurement of the water vapour vertical profile and of the Earth's outgoing far infrared flux

International audienceOur understanding of global warming depends on the accuracy with which the atmospheric components that modulate the Earth's radiation budget are known. Many uncertainties still exist on the radiative effect of water in the different spectral regions, among which the far infrared where few observations have been made. An assessment is shown of the atmospheric outgoing flux obtained from a balloon-borne platform with wideband spectrally resolved nadir measurements at the top-of-atmosphere over the full spectral range, including the far infrared, from 100 to 1400 cm?1, made by a Fourier transform spectrometer with uncooled detectors. From these measurements, we retrieve 15 pieces of information about water vapour and temperature profiles, and surface temperature, with a precision of 5% for the mean water vapour profile and a major improvement of the upper troposphere-lower stratosphere knowledge. The retrieved atmospheric state makes it possible to calculate the emitted radiance as a function of the zenith angle and to determine the outgoing radiation flux, proving that spectrally resolved observations can be used to derive accurate information on the integrated flux. While the retrieved temperature is in good agreement with ECMWF analysis, the retrieved water vapour profile differs significantly, and, depending on time and location, the derived flux differs in the far infrared (0?600 cm?1) from that derived from ECMWF by 2?3.5 W/m2±0.4 W/m2. The observed discrepancy is larger than current estimates of radiative forcing due to CO2 increases since pre-industrial time. The error with which the flux is determined is caused mainly by calibration uncertainties while detector noise has a negligible effect, proving that uncooled detectors are adequate for top of the atmosphere radiometry

Optical observations of "hot" novae returning to quiescence

We have monitored the return to quiescence of novae previously observed in outburst as supersoft X-ray sources, with optical photometry of the intermediate polar (IP) V4743 Sgr and candidate IP V2491 Cyg, and optical spectroscopy of these two and seven other systems. Our sample includes classical and recurrent novae, short period (few hours), intermediate period (1-2 days) and long period (symbiotic) binaries. The light curves of V4743 Sgr and V2491 Cyg present clear periodic modulations. For V4743 Sgr, the modulation occurs with the beat of the rotational and orbital periods. If the period measured for V2491 Cyg is also the beat of these two periods, the orbital one should be almost 17 hours. The recurrent nova T Pyx already shows fragmentation of the nebular shell less than 3 years after the outburst. While this nova still had strong [OIII] at this post-outburst epoch, these lines had already faded after 3 to 7 years in all the others. We did not find any difference in the ratio of equivalent widths of high ionization/excitation lines to that of the Hbeta line in novae with short and long orbital period, indicating that irradiation does not trigger high mass transfer rate from secondaries with small orbital separation. An important difference between the spectra of RS Oph and V3890 Sgr and those of many symbiotic persistent supersoft sources is the absence of forbidden coronal lines. With the X-rays turn-off, we interpret this as an indication that mass transfer in symbiotics recurrent novae is intermittent.Comment: In press in Monthly Notices of the Royal Astronomical Societ

Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

Seismic assessment of masonry cross vaults through numerical nonlinear static and dynamic analysis

Masonry vaults represent a pleasant typology of structural horizontal element in traditional architecture and historical buildings, widespread on a large scale along all the European countries, even those characterized by a high level of seismicity. However, they are some of the most vulnerable structural elements particularly under dynamic actions. Therefore, the assessment of their structural safety and the determination of their stress field is a very important task for preservation of historic buildings. Vaults have been studied from an architectural and structural point of view as sequences of arches, and thus extending the use of bidimensional tools of analysis. This assumption can be reliable for the analysis of barrel vaults, but it is not always the most appropriate solution for investigating more complex vaulted systems with a not negligible three-dimensional behavior. The paper presents on the analysis of a particular groin vault, typically found in monumental buildings which will be successively tested during an experimental dynamic campaign on the shake table. Among all the failure mechanisms of this type of vault, the shear failure is one of the most frequently recorded during post-earthquake surveys. The activation of the shear response is caused by asymmetric boundary conditions and difference in stiffness between two sides of the vault, as it occurs in groin vaults covering churches aisles characterized by the presence of a perimeter wall on one side and two columns on the other side. The main aim of the paper is to investigate the seismic response of a brick groin vault simulating the boundary conditions and loadings of an aisle in a three naves church prototype. Static and dynamic nonlinear numerical analyses were performed using a finite element model. The boundary conditions simulate from one side the presence of a perimeter wall and from the other side the two columns between the main and the lateral nave. The role of the infill and- (undefined

Laboratory Test Campaign Aimed at the Analysis of an Uncommon Wear Phenomenon in a Marble Quarry

The use of ornamental stones has a historical value that makes them strategically precious in Italy; marble can offer high performance in architectural applications, even though the variability of the rock mass requires detailed studies to optimize the exploitation techniques and reduce waste. Italy is world famous for its marble, which is extracted mainly through chainsaw cutting machines, which are currently used intensively due to their high‐safety working conditions compared to alternative techniques and for their great versatility, especially in underground applications. Although this cutting technique is well‐rooted, an uncommon problem of tool wear was found in the quarry under study, which strongly affected productivity. A series of laboratory test were carried out to estimate the wear potential of the rock and the suitability of the tools. The Cerchar abrasivity test highlighted a mean wear potential for the marble of 2.77, while microhardness outcomes pointed out the presence of quartz veins in the tested material (values over 10000 MPa). Finally, additives typically used in the conditioning process of EPB machines in tunneling were tested with the purpose of reducing the extent of wear. A reduction of about 50% in the wear (in terms of weight lost) was obtained for a moisture content of 9%