On continuity of the Álvarez class under deformation

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Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

Random mating with a finite number of matings.

Random mating is the null model central to population genetics. One assumption behind random mating is that individuals mate an infinite number of times. This is obviously unrealistic. Here we show that when each female mates a finite number of times, the effective size of the population is substantially decreased.

Analyzing complex rock slope deformation at Stampa, western Norway, by integrating geomorphology, kinematics and numerical modeling

The unstable rock slope, Stampa, above the village of Flåm, Norway, shows signs of both active and postglacial gravitational deformation over an area of 11 km2. Detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, as well as geomorphic analysis of high-resolution digital elevation models based on airborne and terrestrial laser scanning indicate that slope deformation is complex and spatially variable. Numerical modeling was used to investigate the influence of former rockslide activity and to better understand the failure mechanism. Field observations, kinematic analysis and numerical modeling indicate a strong structural control of the unstable area. Based on the integration of the above analyses, we propose that the failure mechanism is dominated by (1) a toppling component, (2) subsiding bilinear wedge failure and (3) planar sliding along the foliation at the toe of the unstable slope. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points have an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks with volumes smaller than 300,000 m3. Large fractures indicate deep-seated gravitational deformation of volumes reaching several 100 million m3, but the movement rates in these areas are below 2 mm/year. Two different lobes of prehistoric rock slope failures were dated with terrestrial cosmogenic nuclides. While the northern lobe gave an average age of 4,300 years BP, the southern one resulted in two different ages (2,400 and 12,000 years BP), which represent most likely multiple rockfall events. This reflects the currently observable deformation style with unstable blocks in the northern part in between Joasete and Furekamben and no distinct blocks but a high rockfall activity around Ramnanosi in the south. With a relative susceptibility analysis it is concluded that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes > 100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A larger collapse involving several million m3 is presently considered of very low likelihood.

An introductory review on gravitational-deformation induced structures, fabrics and modeling

Recent studies have pointed out a similarity between tectonics and slope tectonic-induced structures. Numerous studies have demonstrated that structures and fabrics previously interpreted as of purely geodynamical origin are instead the result of large slope deformation, and this led in the past to erroneous interpretations. Nevertheless, their limit seems not clearly defined, but it is somehow transitional. Some studies point out continuity between failures developing at surface with upper crust movements. In this contribution, the main studies which examine the link between rock structures and slope movements are reviewed. The aspects regarding model and scale of observation are discussed together with the role of pre-existing weaknesses in the rock mass. As slope failures can develop through progressive failure, structures and their changes in time and space can be recognized. Furthermore, recognition of the origin of these structures can help in avoiding misinterpretations of regional geology. This also suggests the importance of integrating different slope movement classifications based on distribution and pattern of deformation and the application of structural geology techniques. A structural geology approach in the landslide community is a tool that can greatly support the hazard quantification and related risks, because most of the physical parameters, which are used for landslide modeling, are derived from geotechnical tests or the emerging geophysical approaches.

Detailed assessment of the deep-seated gravitational deformation at Stampa above Flåm, Norway

The unstable rock slope above the village of Flåm shows signs of active and postglacial gravitational deformation over an area of 11 km2. We performed detailed structural field mapping, annual differential Global Navigation Satellite System (GNSS) surveys, and generated a detailed topographic model based on airborne and terrestrial laser scanning. Kinematic analyses of the structural data indicates that deformation is complex and varies over the slope. Both sliding and toppling are locally feasible. Using differential GNSS, 18 points were measured annually over a period of up to 6 years. Two of these points show an average yearly movement of around 10 mm/year. They are located at the frontal cliff on almost completely detached blocks. Large fractures indicate deep-seated gravitational deformation of volumes up to 80 million m3, but the movement rates in these areas are below 2 mm/year. Based upon these combined observations, we interpret that small collapses of blocks along the frontal cliff will be more frequent. Larger collapses of free-standing blocks along the cliff with volumes >100,000 m3, thus large enough to reach the fjord, cannot be ruled out. A large collapse involving more than 10 million m3, however, is of very low likelihood at present.

Development and experimental validation of a finite element model of total ankle replacement.

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

The Tertiary structural and thermal evolution of the central Alps - Compressional and extensional structures in an orogenic belt

The Western Alpine Are has been created during the Cretaceous and the Tertiary orogenies. The interference patterns of the Tertiary structures suggest their formation during continental collision of the European and the Adriatic Plates, with an accompanying anticlockwise rotation of the Adriatic indenter. Extensional structures are mainly related to ductile deformation by simple shear. These structures developed at a deep tectonic level, in granitic crustal rocks, at depths in excess of 10 km. In the early Palaeogene period of the Tertiary Orogeny, the main Tertiary nappe emplacement resulted from a NW-thrusting of the Austroalpine, Penninic and Helvetic nappes. Heating of the deep zone of the Upper Cretaceous and Tertiary nappe stack by geothermal heat flow is responsible for the Tertiary regional metamorphism, reaching amphibolite-facies conditions in the Lepontine Gneiss Dome (geothermal gradient 25 degrees C/ km). The Tertiary thrusting occurred mainly during prograde metamorphic conditions with creation of a penetrative NW-SE-oriented stretching lineation, X(1) (finite extension), parallel to the direction of simple shear. Earliest cooling after the culmination of the Tertiary metamorphism, some 38 Ma ago, is recorded by the cooling curves of the Monte Rosa and Mischabel nappes to the west and the Suretta Nappe to the east of the Lepontine Gneiss Dome. The onset of dextral transpression, with a strong extension parallel to the mountain belt, and the oldest S-vergent `'backfolding'' took place some 35 to 30 Ma ago during retrograde amphibolite-facies conditions and before the intrusion of the Oligocene dikes north of the Periadriatic Line. The main updoming of the Lepontine Gneiss Dome started some 32-30 Ma ago with the intrusion of the Bergell tonalites and granodiorites, concomitant with S-vergent backfolding and backthrusting and dextral strike-slip movements along the Tonale and Canavese Lines (Argand's Insubric phase). Subsequently, the center of main updoming migrated slowly to the west, reaching the Simplon region some 20 Ma ago. This was contemporaneous with the westward migration of the Adriatic indenter. Between 20 Ma and the present, the Western Aar Massif-Toce culmination was the center of strong uplift. The youngest S-vergent backfolds, the Glishorn anticline and the Berisal syncline fold the 12 Ma Rb/Sr biotite isochron and are cut by the 11 Ma old Rhone-Simplon Line. The discrete Rhone-Simplon Line represents a late retrograde manifestation in the preexisting ductile Simplon Shear Zone. This fault zone is still active today. The Oligocene-Neogene dextral transpression and extension in the Simplon area were concurrent with thrusting to the northwest of the Helvetic nappes, the Prealpes (35-15 Ma) and with the Jura thin-skinned thrust (11-3 Ma). It was also contemporaneous with thrusting to the south of the Bergamasc (> 35-5 Ma) and Milan thrusts (16-5 Ma).

Folner sequences and finite operators

This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators.