Modelling the trajectory of the corpses of mountaineers who disappeared in 1926 on Aletschgletscher, Switzerland

In this paper we reconstruct the space–time trajectory beneath the surface of Aletschgletscher, Switzerland, of the corpses of three mountaineers that disappeared in March 1926 and reappeared at the glacier surface in June 2012. Our method integrates the time-dependent velocity field of an existing full-Stokes glacier model, starting at the point where the corpses were found at the glacier surface. Our main result is that we were able to localize the immersion location where the brothers presumably died. As a second result, the upstream end point of the computed trajectory emerges very close to the glacier surface in 1926, giving a new and global validation of the glacier model in space and time. Testing the sensitivity of the immersion location obtained with respect to the model and other uncertainties indicates an area of 0.6% of the entire glacier area where the accident could have occurred. Our result suggests that death was not caused by an avalanche or a fall into a crevasse; instead, it is likely that the mountaineers became disoriented in prolonged severe weather conditions and froze to death

Analysis and finite element approximation of a nonlinear stationary stokes problem arising in glaciology

The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms (including Newton's method) are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies

An adaptive Newton multigrid method for a model of marine ice sheets

In this paper, we consider a model for the time evolution of three-dimensional marine ice sheets. This model combines the Shallow Ice Approximation (SIA) for the ice deformation, the Shallow Shelf Approximation (SSA) for the basal sliding, and the mass conservation principle. At each time step, we solve a scalar p-Laplace minimization-type problem with obstacle (SIA), a vectorial p-Laplace minimization-type problem (SSA) and a transport equation (mass conservation). The two minimization problems are solved using a truncated nonsmooth Newton multigrid method while the transport equation is solved using a vertex-centred finite volume method. Our approach is combined to an heuristic mesh adaptive refinement procedure to face the large gradients of the solution that are expected between the ice sheet and the ice shelf. As applications, we present some simulations of the Marine Ice Sheet Model Intercomparison Project MISMIP (2D and 3D) and validate our results against an analytic solution (2D) and other participant model results (3D). Further numerical results show that the convergence of our Newton multigrid method is insensitive to local refinements making our overall adaptive strategy fully efficient

Numerical analysis and simulation of the dynamics of mountain glaciers

In this chapter, we analyze and approximate a nonlinear stationary Stokes problem that describes the motion of glacier ice. The existence and uniqueness of solutions are proved and an a priori error estimate for the finite element approximation is found. In a second time, we combine the Stokes problem with a transport equation for the volume fraction of ice, which describes the time evolution of a glacier. The accumulation due to snow precipitation and melting are accounted for in the source term of the transport equation. A decoupling algorithm allows the diffusion and the advection problems to be solved using a two-grids method. As an illustration, we simulate the evolution of Aletsch glacier, Switzerland, over the 21st century by using realistic climatic conditions

A nonsmooth Newton multigrid method for a hybrid, shallow model of marine ice sheets

The time evolution of ice sheets and ice shelves is model by combining a shallow lubrication approximation for shear deformation with the shallow shelf approximation for basal sliding, along with the mass conservation principle. At each time step two p-Laplace problems and one transport problem are solved. Both p-Laplace problems are formulated as minimisation problems. They are approximated by a finite element truncated nonsmooth Newton multigrid method. As an illustration, we compute the steady state shape of an idealized ice sheet/shelf system

A coupled thermal-analytical and mechanical approach to investigate the behavior of bonded anchors cured at sub-zero temperatures

In post-installed connection in reinforced concrete structures, bonded anchors are commonly adopted when elevated mechanical performances are required. Such performances may be significantly impaired by adverse service conditions, above all temperature variations with respect to room ambient one. It is also generally acknowledged that the curing temperature may impact on the anchor performances, to the extent that all the main existing qualification procedures assess the anchor behavior when cured at different temperatures, in particular below zero Celsius degree. However, among the few investigations focusing on the impact of a low curing temperature on the long term behavior of an anchor, a low effort exists in addressing the relationship between the anchor mechanical behavior and the thermal properties of the bonding agent. The paper proposes a coupled thermal-analytical and mechanical approach to detect potential critical issues in the long term mechanical behavior of the anchor as a function of the adhesive behavior, as investigated by thermal or thermo-mechanical analyses. To the scope, a wide investigation on two adhesives is carried out comprising MDSC, DMA, pull-out and sustained load tests. On the basis of the obtained results, it is concluded that some thresholds in the variations of degree of conversion and phase transition temperatures may indicate a negligible impact of a low curing temperature on the anchor mechanical behavior, but also that existing qualification procedures are not able to capture the anchor behavior, when cured at low temperatures and subjected, during its service life, to temperatures higher than room ambient one

Subglacial hydrology from high-resolution ice-flow simulations of the Rhine Glacier during the Last Glacial Maximum: a proxy for glacial erosion

At the Last Glacial Maximum (LGM), the Rhine Glacier complex (Rhine and Linth glaciers) formed large piedmont lobes extending north into the Swiss and German Alpine forelands. Numerous overdeepened valleys there were formed by repeated glaciations. A characteristic of these overdeepened valleys is their location close to the LGM ice margin, away from the Alps. Numerical models of ice flow of the Rhine Glacier indicate a poor fit between the sliding distance, a proxy for glacial erosion, and the location of these overdeepenings. Calculations of the hydraulic potential based on the computed time-dependent ice surface elevations of the Rhine Glacier lobe obtained from a high-resolution thermo-mechanically coupled Stokes flow model are used to estimate the location of subglacial water drainage routes. Results indicate that the subglacial water discharge is high and focused along glacial valleys and overdeepenings when water pressure is equal to the ice overburden pressure. These conditions are necessary for subglacial water to remove basal sediments, expose fresh bedrock, and favor further erosion by quarrying and abrasion. Knowledge of the location of paleo-subglacial water drainage routes may be useful to understand patterns of subglacial erosion beneath paleo-ice masses that do not otherwise relate to the sliding of ice. Comparison of the erosion pattern from subglacial meltwater with those from quarrying and abrasion shows the importance of subglacial water flow in the formation of distal overdeepenings in the Swiss lowlands.</p

Photo-fragmentation spectroscopy of benzylium and 1-phenylethyl cations

The electronic spectra of cold benzylium (C6H5-CH2+) and 1-phenylethyl (C6H5-CH-CH3+)cations have been recorded via photofragment spectroscopy. Benzylium and 1-phenylethyl cations produced from electrosprayed benzylamine and phenylethylamine solutions, respectively, were stored in a cryogenically cooled quadrupole ion trap and photodissociated by an OPO laser, scanned in parts of the UV and visible regions (600-225 nm). The electronic states and active vibrational modes of the benzylium and 1-phenylethyl cations as well as those of their tropylium or methyl tropylium isomers have been calculated with ab initio methods for comparison with the spectra observed. Sharp vibrational progressions are observed in the visible region while the absorption features are much broader in the UV. The visible spectrum of the benzylium cation is similar to that obtained in an argon tagging experiment [V. Dryza, N. Chalyavi, J.A. Sanelli, and E.J. Bieske, J. Chem. Phys. 137, 204304 (2012)], with an additional splitting assigned to Fermi resonances. The visible spectrum of the 1-phenylethyl cation also shows vibrational progressions. For both cations, the second electronic transition is observed in the UV, around 33 000 cm-1 (4.1 eV), and shows a broadened vibrational progression. In both cases the S2 optimized geometry is non planar. The third electronic transition observed around 40 000 cm-1 (5.0 eV) is even broader with no apparent vibrational structures, which is indicative of either a fast non-radiative process or a very large change in geometry between the excited and the ground states. The oscillator strengths calculated for tropylium and methyl tropylium are weak. Therefore, these isomeric structures are most likely not responsible for these absorption features. Finally, the fragmentation pattern changes in the second and third electronic states: C2H2 loss becomes predominant at higher excitation energies, for both cations