Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Asymptotic theory for a moving droplet driven by a wettability gradient

An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.Comment: 8 fig

Impacts of nano-clay particles and heat-treating on out-of-phase thermo-mechanical fatigue characteristics in piston aluminum-silicon alloys

Abstract. In this article, the effect of nano-clay particles and heat-treating on thermo-mechanical fatigue (TMF) behaviors and failures of piston aluminum-silicon (AlSi) alloys was investigated. For this purpose, thermo-mechanical fatigue tests were conducted under out-of-phase (OP) loading conditions. Two loading conditions were checked based on different maximum temperatures (250, 300, and 350 °C) and various thermo-mechanical loading factors (100, 125, and 150%). The minimum temperature was constant in all tests at 50 °C under a heating/cooling rate of 10 °C/s and a dwell time of 5 s. Results showed that the nano-composites had a longer fatigue lifetime, at least 2 times higher, compared to the Al alloy, when the maximum temperature was 250 °C and the thermo-mechanical loading factor was 100%. However, no effective change was seen for the stress value and the plastic strain. At higher maximum temperatures, the change in the material behavior was lower. The fracture analysis by scanning electron microscopy (SEM) demonstrated that both materials had a brittle behavior due to cleavage and quasi-cleavage marks. The damage mechanism was also due to the Si-rich phase and intermetallics, respectively for the crack propagation and the micro-crack initiation

Submarine mass wasting and associated tsunami risk offshore western Thailand, Andaman Sea, Indian Ocean

2-D seismic data from the top and the western slope of Mergui Ridge in water depths between 300 and 2200 m off the Thai west coast have been investigated in order to identify mass transport deposits (MTDs) and evaluate the tsunamigenic potential of submarine landslides in this outer shelf area. Based on our newly collected data, 17 mass transport deposits have been identified. Minimum volumes of individual MTDs range between 0.3 km3 and 14 km3. Landslide deposits have been identified in three different settings: (i) stacked MTDs within disturbed and faulted basin sediments at the transition of the East Andaman Basin to the Mergui Ridge; (ii) MTDs within a pile of drift sediments at the basin-ridge transition; and (iii) MTDs near the edge of/on top of Mergui Ridge in relatively shallow water depths ( 1000 m) and/or comprise small volumes suggesting a small tsunami potential. Moreover, the recurrence rates of failure events seem to be low. Some MTDs with tsunami potential, however, have been identified on top of Mergui Ridge. Mass-wasting events that may occur in the future at similar locations may trigger tsunamis if they comprise sufficient volumes. Landslide tsunamis, emerging from slope failures in the working area and affecting western Thailand coastal areas therefore cannot be excluded, though the probability is very small compared to the probability of earthquake-triggered tsunamis, arising from the Sunda Trench

Mapping of bioavailable strontium isotope ratios in France for archaeological provenance studies

Strontium isotope ratios (⁸⁷Sr/⁸⁶Sr) of archaeological samples (teeth and bones) can be used to track mobility and migration across geologically distinct landscapes. However, traditional interpolation algorithms and classification approaches used to generate Sr isoscapes are often limited in predicting multiscale ⁸⁷Sr/⁸⁶Sr patterning. Here we investigate the suitability of plant samples and soil leachates from the IRHUM database (www.irhumdatabase.com) to create a bioavailable ⁸⁷Sr/⁸⁶Sr map using a novel geostatistical framework. First, we generated an ⁸⁷Sr/⁸⁶Sr map by classifying ⁸⁷Sr/⁸⁶Sr values into five geologically-representative isotope groups using cluster analysis. The isotope groups were then used as a covariate in kriging to integrate prior geological knowledge of Sr cycling with the information contained in the bioavailable dataset and enhance ⁸⁷Sr/⁸⁶Sr predictions. Our approach couples the strengths of classification and geostatistical methods to generate more accurate ⁸⁷Sr/⁸⁶Sr predictions (Root Mean Squared Error = 0.0029) with an estimate of spatial uncertainty based on lithology and sample density. This bioavailable Sr isoscape is applicable for provenance studies in France, and the method is transferable to other areas with high sampling density. While our method is a step forward in generating accurate ⁸⁷Sr/⁸⁶Sr isoscapes, the remaining uncertainty also demonstrates that fine-modelling of ⁸⁷Sr/⁸⁶Sr variability is challenging and requires more than geological maps for accurately predicting ⁸⁷Sr/⁸⁶Sr variations across the landscape. Future efforts should focus on increasing sampling density and developing predictive models to further quantify and predict the processes that lead to ⁸⁷Sr/⁸⁶Sr variability.Funding was provided by ARC DP110101415 (Grün, Spriggs, Armstrong, Maureille and Falguères) Understanding the migrations of prehistoric populations through direct dating and isotopic tracking of their mobility patterns. Part of this research was supported by the Australian French Association for Science & Technology through the ACT Science Fellowship program (2013) to M. Willme

Effects of Interplanetary Dust on the LISA drag-free Constellation

The analysis of non-radiative sources of static or time-dependent gravitational fields in the Solar System is crucial to accurately estimate the free-fall orbits of the LISA space mission. In particular, we take into account the gravitational effects of Interplanetary Dust (ID) on the spacecraft trajectories. The perturbing gravitational field has been calculated for some ID density distributions that fit the observed zodiacal light. Then we integrated the Gauss planetary equations to get the deviations from the LISA keplerian orbits around the Sun. This analysis can be eventually extended to Local Dark Matter (LDM), as gravitational fields are expected to be similar for ID and LDM distributions. Under some strong assumptions on the displacement noise at very low frequency, the Doppler data collected during the whole LISA mission could provide upper limits on ID and LDM densities.Comment: 11 pages, 6 figures, to be published on the special issue of "Celestial Mechanics and Dynamical Astronomy" on the CELMEC V conferenc

The Scientific Case for Brain Simulators

A key element of the European Union’s Human Brain Project (HBP) and other large-scale brain research projects is the simulation of large-scale model networks of neurons. Here, we argue why such simulations will likely be indispensable for bridging the scales between the neuron and system levels in the brain, and why a set of brain simulators based on neuron models at different levels of biological detail should therefore be developed. To allow for systematic refinement of candidate network models by comparison with experiments, the simulations should be multimodal in the sense that they should predict not only action potentials, but also electric, magnetic, and optical signals measured at the population and system levels

Organics in comet 67P – a first comparative analysis of mass spectra from ROSINA–DFMS, COSAC and Ptolemy

The ESA Rosetta spacecraft followed comet 67P at a close distance for more than 2 yr. In addition, it deployed the lander Philae on to the surface of the comet. The (surface) composition of the comet is of great interest to understand the origin and evolution of comets. By combining measurements made on the comet itself and in the coma, we probe the nature of this surface material and compare it to remote sensing observations. We compare data from the double focusing mass spectrometer (DFMS) of the ROSINA experiment on ESA's Rosetta mission and previously published data from the two mass spectrometers COSAC (COmetary Sampling And Composition) and Ptolemy on the lander. The mass spectra of all three instruments show very similar patterns of mainly CHO-bearing molecules that sublimate at temperatures of 275 K. The DFMS data also show a great variety of CH-, CHN-, CHS-, CHO2- and CHNO-bearing saturated and unsaturated species. Methyl isocyanate, propanal and glycol aldehyde suggested by the earlier analysis of the measured COSAC spectrum could not be confirmed. The presence of polyoxymethylene in the Ptolemy spectrum was found to be unlikely. However, the signature of the aromatic compound toluene was identified in DFMS and Ptolemy data. Comparison with remote sensing instruments confirms the complex nature of the organics on the surface of 67P, which is much more diverse than anticipated