Improving the worthiness of the Elder problem as a benchmark for buoyancy driven convection models

An important trapping mechanism associated with the geosequestration of CO~2~ is that of dissolution into the formation water. Although supercritical CO~2~ is significantly less dense than water, experimental data reported in the literature show that the density of an aqueous solution of CO~2~ could be slightly greater. Under normal situations, the transfer of gas to solution is largely controlled by the relatively slow process of molecular diffusion. However, the presence of variable densities can trigger off gravity instabilities leading to much larger-scale convection processes. Such processes can potentially enhance rates of dissolution by an order of magnitude. Consequently there is a need for future performance assessment models to incorporate buoyancy driven convection (BDC). A major issue associated with BDC models is that of grid convergence when benchmarking to the Elder problem. The Elder problem originates from a heat convection experiment whereby a rectangular Hele-Shaw cell was heated over the central half of its base. A quarter of the way through the experiment, Elder (1967) observed six plumes, with four narrow plumes in the center and two larger plumes at the edges. As the experiment progressed, only four plumes remained. The issue is that depending on the grid resolution used when seeking to model this problem, modelers have found that different schemes yield steady states with either one, two or three plumes. The aim of this paper is to clarify and circumvent the issue of multiple steady state solutions in the Elder problem using a pseudospectral method

Optimal surface coating distribution on a femoral endoprosthesis

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1994.Includes bibliographical references (leaves 112-117).by Craig A. Simmons.M.S

Animal Models of Calcific Aortic Valve Disease

Calcific aortic valve disease (CAVD), once thought to be a degenerative disease, is now recognized to be an active pathobiological process, with chronic inflammation emerging as a predominant, and possibly driving, factor. However, many details of the pathobiological mechanisms of CAVD remain to be described, and new approaches to treat CAVD need to be identified. Animal models are emerging as vital tools to this end, facilitated by the advent of new models and improved understanding of the utility of existing models. In this paper, we summarize and critically appraise current small and large animal models of CAVD, discuss the utility of animal models for priority CAVD research areas, and provide recommendations for future animal model studies of CAVD

Study of the influence of actin-binding proteins using linear analyses of cell deformability

The actin cytoskeleton plays a key role in the deformability of the cell and in mechanosensing. Here we analyze the contributions of three major actin cross-linking proteins, myosin II, a-actinin and filamin, to cell deformability, by using micropipette aspiration of Dictyostelium cells. We examine the applicability of three simple mechanical models: for small deformation, linear viscoelasticity and drop of liquid with a tense cortex; and for large deformation, a Newtonian viscous fluid. For these models, we have derived linearized equations and we provide a novel, straightforward methodology to analyze the experiments. This methodology allowed us to differentiate the effects of the cross-linking proteins in the different regimes of deformation. Our results confirm some previous observations and suggest important relations between the molecular characteristics of the actin-binding proteins and the cell behavior: the effect of myosin is explained in terms of the relation between the lifetime of the bond to actin and the resistive force; the presence of a-actinin obstructs the deformation of the cytoskeleton, presumably mainly due to the higher molecular stiffness and to the lower dissociation rate constants; and filamin contributes critically to the global connectivity of the network, possibly by rapidly turning over crosslinks during the remodeling of the cytoskeletal network, thanks to the higher rate constants, flexibility and larger size. The results suggest a sophisticated relationship between the expression levels of actinbinding proteins, deformability and mechanosensing

Polarimetry of the Type Ia Supernova SN 1996X

We present broad-band and spectropolarimetry of the Type Ia SN 1996X obtained on April 14, 1996 (UT), and broad-band polarimetry of SN 1996X on May 22,1996, when the supernova was about a week before and 4 weeks after optical maximum, respectively. The Stokes parameters derived from the broad-band polarimetry are consistent with zero polarization. The spectropolarimetry, however, shows broad spectral features which are due intrinsically to an asymmetric SN atmosphere. The spectral features in the flux spectrum and the polarization spectrum show correlations in the wavelength range from 4900 AA up to 5500 AA. The degree of this intrinsic component is low (<0.3 %). Theoretical polarization spectra have been calculated. It is shown that the polarization spectra are governed by line blending. Consequently, for similar geometrical distortions, the residual polarization is smaller by about a factor of 2 to 3 compared to the less blended Type II atmosphere, making it intrinsically harder to detect asphericities in SNIa. Comparison with theoretical model polarization spectra shows a resemblance to the observations. Taken literally, this implies an asphericity of about 11 % in the chemical distribution in the region of partial burning. This may not imperil the use of Type Ia supernovae as standard candles for distance determination, but nontheless poses a source of uncertainty. SN 1996X is the first Type Ia supernova for which spectropolarimetry revealed a polarized component intrinsic to the supernova and the first Type Ia with spectropolarimetry well prior to optical maximum.Comment: 7 pages, 5 figures, macros 'aas2pp4.sty,psfig.tex'. LaTeX Style. Astrophysical Journal Letters, submitted September 199

COMPARISON OF ANALYTICAL AND FINITE ELEMENT IMPLEMENTATION OF EXPONENTIAL CONSTITUTIVE MODELS FOR VALVE TISSUE UNDER MICROPIPETTE ASPIRATION SBC2010-19245

INTROUDUCTION Micropipette aspiration (MA) has been widely used to measure the biomechanical properties of cells and biomaterials The goal of this study was to determine whether aortic valve tissue material parameters estimated by the easily-implemented analytical approach [3] differ from those obtained by finite element (FE) analysis aortic valve tissue under MA. To do so, we implemented an exponential hyperelastic constitutive model in the FE model and used an inverse FE approach to predict material parameters METHODS AND MATERIALS Material models To fit the MA experimental measurements of the embryonic atrioventricular cushions, Butcher et al. implemented an exponential constitutive model [2] where W is the strain energy, C and α are material constants and E is the Green&apos;s finite strain with the 2 nd Piola-Kirchoff stress (S) being calculated by S = ∂W/∂E. To relate the stress and strain in the constitutive model to experimental measurements, Butcher et al. directly assigned the measured aspiration length (L) to pipette radius (a) ratio as the Green&apos;s strain, and the measured aspiration pressure ΔP as the Lagrangian stress T, which is calculated by T = λS with the stretch ratio in the aspiration direction (λ) given by λ = (E + 1) 0.5 To account for the multicomponent stress-strain field in the valve tissue during MA process, we implemented an incompressible isotropic exponential constitutive model. The strain energy density function of this model is expressed as where W is the strain energy, C and α are material constants and I 1 is the first strain invariant, defined as I 1 = with λ 1 , λ 2 and λ 3 being the principal stretches. This isotropic exponential constitutiv

Spectropolarimetry of Supernovae

Overwhelming evidence has accumulated in recent years that supernova explosions are intrinsically 3-dimensional phenomena with significant departures from spherical symmetry. We review the evidence derived from spectropolarimetry that has established several key results: virtually all supernovae are significantly aspherical near maximum light; core-collapse supernovae behave differently than thermonuclear (Type Ia) supernovae; the asphericity of core-collapse supernovae is stronger in the inner layers showing that the explosion process itself is strongly aspherical; core-collapse supernovae tend to establish a preferred direction of asymmetry; the asphericity is stronger in the outer layers of thermonuclear supernovae providing constraints on the burning process. We emphasize the utility of the Q/U plane as a diagnostic tool and revisit SN 1987A and SN 1993J in a contemporary context. An axially-symmetric geometry can explain many basic features of core-collapse supernovae, but significant departures from axial symmetry are needed to explain most events. We introduce a spectropolarimetry type to classify the range of behavior observed in polarized supernovae. Understanding asymmetries in supernovae is important for phenomena as diverse as the origins of gamma-ray bursts and the cosmological applications of Type Ia supernovae in studies of the dark energy content of the universe.Comment: Draft of Annual Review article prior to final copy editing; 85 pages, 13 figures, 1 tabl

A vegetation-focused soil-plant-atmospheric continuum model to study hydrodynamic soil-plant water relations

A novel simple soil-plant-atmospheric continuum model that emphasizes the vegetation's role in controlling water transfer (v-SPAC) has been developed in this study. The v-SPAC model aims to incorporate both plant and soil hydrological measurements into plant water transfer modeling. The model is different from previous SPAC models in which v-SPAC uses (1) a dynamic plant resistance system in the form of a vulnerability curve that can be easily obtained from sap flow and stem xylem water potential time series and (2) a plant capacitance parameter to buffer the effects of transpiration on root water uptake. The unique representation of root resistance and capacitance allows the model to embrace SPAC hydraulic pathway from bulk soil, to soil-root interface, to root xylem, and finally to stem xylem where the xylem water potential is measured. The v-SPAC model was tested on a native tree species in Australia, Eucalyptus crenulata saplings, with controlled drought treatment. To further validate the robustness of the v-SPAC model, it was compared against a soil-focused SPAC model, LEACHM. The v-SPAC model simulation results closely matched the observed sap flow and stem water potential time series, as well as the soil moisture variation of the experiment. The v-SPAC model was found to be more accurate in predicting measured data than the LEACHM model, underscoring the importance of incorporating root resistance into SPAC models and the benefit of integrating plant measurements to constrain SPAC modeling

Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate

The authors present inferences of diapycnal diffusivity from a compilation of over 5200 microstructure profiles. As microstructure observations are sparse, these are supplemented with indirect measurements of mixing obtained from (i) Thorpe-scale overturns from moored profilers, a finescale parameterization applied to (ii) shipboard observations of upper-ocean shear, (iii) strain as measured by profiling floats, and (iv) shear and strain from full-depth lowered acoustic Doppler current profilers (LADCP) and CTD profiles. Vertical profiles of the turbulent dissipation rate are bottom enhanced over rough topography and abrupt, isolated ridges. The geography of depth-integrated dissipation rate shows spatial variability related to internal wave generation, suggesting one direct energy pathway to turbulence. The global-averaged diapycnal diffusivity below 1000-m depth is O(10?4) m2 s?1 and above 1000-m depth is O(10?5) m2 s?1. The compiled microstructure observations sample a wide range of internal wave power inputs and topographic roughness, providing a dataset with which to estimate a representative global-averaged dissipation rate and diffusivity. However, there is strong regional variability in the ratio between local internal wave generation and local dissipation. In some regions, the depth-integrated dissipation rate is comparable to the estimated power input into the local internal wave field. In a few cases, more internal wave power is dissipated than locally generated, suggesting remote internal wave sources. However, at most locations the total power lost through turbulent dissipation is less than the input into the local internal wave field. This suggests dissipation elsewhere, such as continental margins

Numerical error in groundwater flow and solute transport simulation

Models of groundwater flow and solute transport may be affected by numerical error, leading to quantitative and qualitative changes in behavior. In this paper we compare and combine three methods of assessing the extent of numerical error: grid refinement, mathematical analysis, and benchmark test problems. In particular, we assess the popular solute transport code SUTRA [ Voss, 1984 ] as being a typical finite element code. Our numerical analysis suggests that SUTRA incorporates a numerical dispersion error and that its mass-lumped numerical scheme increases the numerical error. This is confirmed using a Gaussian test problem. A modified SUTRA code, in which the numerical dispersion is calculated and subtracted, produces better results. The much more challenging Elder problem [ Elder, 1967 ; Voss and Souza, 1987 ] is then considered. Calculation of its numerical dispersion coefficients and numerical stability show that the Elder problem is prone to error. We confirm that Elder problem results are extremely sensitive to the simulation method used.Juliette A. Woods, Michael D. Teubner, Craig T. Simmons and Kumar A. Naraya