Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

An anisotropic elastic-viscoplastic damage model for bone tissue

A new anisotropic elastic-viscoplastic damage constitutive model for bone is proposed using an eccentric elliptical yield criterion and nonlinear isotropic hardening. A micromechanics-based multiscale homogenization scheme proposed by Reisinger et al. is used to obtain the effective elastic properties of lamellar bone. The dissipative process in bone is modeled as viscoplastic deformation coupled to damage. The model is based on an orthotropic ecuntric elliptical criterion in stress space. In order to simplify material identification, an eccentric elliptical isotropic yield surface was defined in strain space, which is transformed to a stress-based criterion by means of the damaged compliance tensor. Viscoplasticity is implemented by means of the continuous Perzyna formulation. Damage is modeled by a scalar function of the accumulated plastic strain D(κ) , reducing all element s of the stiffness matrix. A polynomial flow rule is proposed in order to capture the rate-dependent post-yield behavior of lamellar bone. A numerical algorithm to perform the back projection on the rate-dependent yield surface has been developed and implemented in the commercial finite element solver Abaqus/Standard as a user subroutine UMAT. A consistent tangent operator has been derived and implemented in order to ensure quadratic convergence. Correct implementation of the algorithm, convergence, and accuracy of the tangent operator was tested by means of strain- and stress-based single element tests. A finite element simulation of nano- indentation in lamellar bone was finally performed in order to show the abilities of the newly developed constitutive model.

Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R2 = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.

How fluids bend: the elastic expansion for higher-dimensional black holes

Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.

SOLAR RADIATION PRESSURE AND LOCAL INTERSTELLAR MEDIUM FLOW PARAMETERS FROM INTERSTELLAR BOUNDARY EXPLORER LOW ENERGY HYDROGEN MEASUREMENTS

Neutral hydrogen atoms that travel into the heliosphere from the local interstellar medium (LISM) experience strong effects due to charge exchange and radiation pressure from resonant absorption and re-emission of Lyα. The radiation pressure roughly compensates for the solar gravity. As a result, interstellar hydrogen atoms move along trajectories that are quite different than those of heavier interstellar species such as helium and oxygen, which experience relatively weak radiation pressure. Charge exchange leads to the loss of primary neutrals from the LISM and the addition of new secondary neutrals from the heliosheath. IBEX observations show clear effects of radiation pressure in a large longitudinal shift in the peak of interstellar hydrogen compared with that of interstellar helium. Here, we compare results from the Lee et al. interstellar neutral model with IBEX-Lo hydrogen observations to describe the distribution of hydrogen near 1 AU and provide new estimates of the solar radiation pressure. We find over the period analyzed from 2009 to 2011 that radiation pressure divided by the gravitational force (μ) has increased slightly from μ = 0.94 ± 0.04 in 2009 to μ = 1.01 ± 0.05 in 2011. We have also derived the speed, temperature, source longitude, and latitude of the neutral H atoms and find that these parameters are roughly consistent with those of interstellar He, particularly when considering the filtration effects that act on H in the outer heliosheath. Thus, our analysis shows that over the period from 2009 to 2011, we observe signatures of neutral H consistent with the primary distribution of atoms from the LISM and a radiation pressure that increases in the early rise of solar activity.

Lunar energetic neutral atom (ENA) spectra measured by the interstellar boundary explorer (IBEX)

The solar wind continuously flows out from the Sun, filling interplanetary space and directly interacting with the surfaces of small planetary bodies and other objects throughout the solar system. A significant fraction of these ions backscatter from the surface as energetic neutral atoms (ENAs). The first observations of these ENA emissions from the Moon were recently reported from the Interstellar Boundary Explorer (IBEX). These observations yielded a lunar ENA albedo of ˜10% and showed that the Moon reflects ˜150 metric tons of neutral hydrogen per year. More recently, a survey of the first 2.5 years of IBEX observations of lunar ENAs was conducted for times when the Moon was in the solar wind. Here, we present the first IBEX ENA observations when the Moon is inside the terrestrial magnetosheath and compare them with observations when the Moon is in the solar wind. Our analysis shows that: (1) the ENA intensities are on average higher when the Moon is in the magnetosheath, (2) the energy spectra are similar above ~0.6* solar wind energy but below there are large differences of the order of a factor of 10, (3) the energy spectra resemble a power law with a "hump" at ˜0.6 * solar wind energy, and (4) this "hump" is broader when the Moon is in the magnetosheath. We explore potential scenarios to explain the differences, namely the effects of the topography of the lunar surface and the consequences of a very different Mach number in the solar wind versus in the magnetosheath.

Morphology–elasticity relationships using decreasing fabric information of human trabecular bone from three major anatomical locations

With improving clinical CT scanning technology, the accuracy of CT-based finite element (FE) models of the human skeleton may be ameliorated by an enhanced description of apparent level bone mechanical properties. Micro-finite element (μFE) modeling can be used to study the apparent elastic behavior of human cancellous bone. In this study, samples from the femur, radius and vertebral body were investigated to evaluate the predictive power of morphology–elasticity relationships and to compare them across different anatomical regions. μFE models of 701 trabecular bone cubes with a side length of 5.3 mm were analyzed using kinematic boundary conditions. Based on the FE results, four morphology–elasticity models using bone volume fraction as well as full, limited or no fabric information were calibrated for each anatomical region. The 5 parameter Zysset–Curnier model using full fabric information showed excellent predictive power with coefficients of determination ( r2adj ) of 0.98, 0.95 and 0.94 of the femur, radius and vertebra data, respectively, with mean total norm errors between 14 and 20%. A constant orthotropy model and a constant transverse isotropy model, where the elastic anisotropy is defined by the model parameters, yielded coefficients of determination between 0.90 and 0.98 with total norm errors between 16 and 25%. Neglecting fabric information and using an isotropic model led to r2adj between 0.73 and 0.92 with total norm errors between 38 and 49%. A comparison of the model regressions revealed minor but significant (p<0.01) differences for the fabric–elasticity model parameters calibrated for the different anatomical regions. The proposed models and identified parameters can be used in future studies to compute the apparent elastic properties of human cancellous bone for homogenized FE models.

Mixing-cell boundary conditions and apparent mass balance errors for advective-dispersive solute transport

In many field or laboratory situations, well-mixed reservoirs like, for instance, injection or detection wells and gas distribution or sampling chambers define boundaries of transport domains. Exchange of solutes or gases across such boundaries can occur through advective or diffusive processes. First we analyzed situations, where the inlet region consists of a well-mixed reservoir, in a systematic way by interpreting them in terms of injection type. Second, we discussed the mass balance errors that seem to appear in case of resident injections. Mixing cells (MC) can be coupled mathematically in different ways to a domain where advective-dispersive transport occurs: by assuming a continuous solute flux at the interface (flux injection, MC-FI), or by assuming a continuous resident concentration (resident injection). In the latter case, the flux leaving the mixing cell can be defined in two ways: either as the value when the interface is approached from the mixing-cell side (MC-RT -), or as the value when it is approached from the column side (MC-RT +). Solutions of these injection types with constant or-in one case-distance-dependent transport parameters were compared to each other as well as to a solution of a two-layer system, where the first layer was characterized by a large dispersion coefficient. These solutions differ mainly at small Peclet numbers. For most real situations, the model for resident injection MC-RI + is considered to be relevant. This type of injection was modeled with a constant or with an exponentially varying dispersion coefficient within the porous medium. A constant dispersion coefficient will be appropriate for gases because of the Eulerian nature of the usually dominating gaseous diffusion coefficient, whereas the asymptotically growing dispersion coefficient will be more appropriate for solutes due to the Lagrangian nature of mechanical dispersion, which evolves only with the fluid flow. Assuming a continuous resident concentration at the interface between a mixing cell and a column, as in case of the MC-RI + model, entails a flux discontinuity. This flux discontinuity arises inherently from the definition of a mixing cell: the mixing process is included in the balance equation, but does not appear in the description of the flux through the mixing cell. There, only convection appears because of the homogeneous concentration within the mixing cell. Thus, the solute flux through a mixing cell in close contact with a transport domain is generally underestimated. This leads to (apparent) mass balance errors, which are often reported for similar situations and erroneously used to judge the validity of such models. Finally, the mixing cell model MC-RI + defines a universal basis regarding the type of solute injection at a boundary. Depending on the mixing cell parameters, it represents, in its limits, flux as well as resident injections. (C) 1998 Elsevier Science B.V. All rights reserved.

Elastic Uplift in Southeast Greenland Due to Rapid Ice Mass Loss

The rapid unloading of ice from the southeastern sector of the Greenland ice sheet between 2001 and 2006 caused an elastic uplift of similar to 35 mm at a GPS site in Kulusuk. Most of the uplift results from ice dynamic-induced volume losses on two nearby outlet glaciers. Volume loss from Helheim Glacier, calculated from sequential digital elevation models, contributes about similar to 16 mm of the observed uplift, with an additional similar to 5 mm from volume loss of Kangerdlugssuaq Glacier. The remaining uplift signal is attributed to significant melt-induced ice volume loss from the ice sheet margin along the southeast coast between 62 degrees N and 66 degrees N.

Improved Localization of Implanted Subdural Electrode Contacts on MRI Using an Elastic Image Fusion Algorithm in Invasive EEG Recording

BACKGROUND: Accurate projection of implanted subdural electrode contacts in presurgical evaluation of pharmacoresistant epilepsy cases by invasive EEG is highly relevant. Linear fusion of CT and MRI images may display the contacts in the wrong position due to brain shift effects. OBJECTIVE: A retrospective study in five patients with pharmacoresistant epilepsy was performed to evaluate whether an elastic image fusion algorithm can provide a more accurate projection of the electrode contacts on the pre-implantation MRI as compared to linear fusion. METHODS: An automated elastic image fusion algorithm (AEF), a guided elastic image fusion algorithm (GEF), and a standard linear fusion algorithm (LF) were used on preoperative MRI and post-implantation CT scans. Vertical correction of virtual contact positions, total virtual contact shift, corrections of midline shift and brain shifts due to pneumencephalus were measured. RESULTS: Both AEF and GEF worked well with all 5 cases. An average midline shift of 1.7mm (SD 1.25) was corrected to 0.4mm (SD 0.8) after AEF and to 0.0mm (SD 0) after GEF. Median virtual distances between contacts and cortical surface were corrected by a significant amount, from 2.3mm after LF to 0.0mm after AEF and GEF (p<.001). Mean total relative corrections of 3.1 mm (SD 1.85) after AEF and 3.0mm (SD 1.77) after GEF were achieved. The tested version of GEF did not achieve a satisfying virtual correction of pneumencephalus. CONCLUSION: The technique provided a clear improvement in fusion of pre- and post-implantation scans, although the accuracy is difficult to evaluate.