Mixed framework for Darcy-Stokes mixtures

textWe consider the system of equations arising from mantle dynamics introduced by McKenzie (J. Petrology, 1985). In this multi-phase model, the fluid melt velocity obeys Darcy's law while the deformable "solid" matrix is governed by a highly viscous Stokes equation. The system is then coupled through mass conservation and compaction relations. Together these equations form a coupled Darcy-Stokes system on a continuous single-domain mixture of fluid and matrix. The porosity φ, representing the relative volume of fluid melt to the bulk volume, is assumed to be much smaller than one. When coupled with solute transport and thermal evolution in a time-dependent problem, the model transitions dynamically from a non-porous single phase solid to a two-phase porous medium. Such mixture models have an advantage for numerical approximation since the free boundary between the one and two-phase regions need not be determined explicitly. The equations of mantle dynamics apply to a wide range of applications in deep earth physics such as mid-ocean ridges, subduction zones, and hot-spot volcanism, as well as to glacier dynamics and other two-phase flows in porous media. Mid-ocean ridges form when viscous corner flow of the solid mantle focuses fluid toward a central ridge. Melt is believed to migrate upward until it reaches the lithospheric "tent" where it then moves toward the ridge in a high porosity band. Simulation of this physical phenomenon required confidence in numerical methods to handle highly heterogeneous porosity as well as the single-phase to two-phase transition. In this work we present a standard mixed finite element method for the equations of mantle dynamics and investigate its limitations for vanishing porosity. While stable and optimally convergent for porosity bounded away from zero, the stability estimates we obtain suggest, and numerical results show, the method becomes unstable as porosity approaches zero. Moreover, the fluid pressure is no longer a physical variable when the fluid phase disappears and thus is not a good variable for numerical methods. Inspired by the stability estimates of the standard method, we develop a novel stable mixed method with uniqueness and existence of solutions by studying a linear degenerate elliptic sub-problem akin to the Darcy part of the full model: [mathematical equation], where a and b satisfy a(0)=b(0)=0 and are otherwise positive, and the porosity φ ≥ 0 may be zero on a set of positive measure. Using scaled variables and mild assumptions on the regularity of φ, we develop a practical mass-conservative method based on lowest order Raviart-Thomas finite elements. Finally, we adapt the numerical method for the sub-problem to the full system of equations. We show optimal convergence for sufficiently smooth solutions for a compacting column and mid-ocean ridge-like corner flow examples, and investigate accuracy and stability for less regular problemsComputational Science, Engineering, and Mathematic

Huntington’s Disease: Assessing The Needs of Patients and Caregivers in Vermont

Introduction: Huntington’s disease (HD) is an inherited neurological disorder that causes a progressive decline in motor, cognitive and psychiatric function. • HD affects 30,000 people in the USA. In Vermont it is estimated that 69 individuals have HD and 420 people are at risk for developing the disease. • Crescent Manor Care Centers is currently the only long term care facility in Vermont that houses Huntington’s patients. Patients receive care specific to HD including PT, OT, Speech Therapy and community activities. Currently, 13 of 40 beds are occupied. • There is one HD support group in the state located in South Burlington which meets once a month. Due to the low population of HD patients in the state, there is no single state government agency responsible for managing the care of HD patients.https://scholarworks.uvm.edu/comphp_gallery/1077/thumbnail.jp

Acute upper airway failure and mediastinal emphysema following a wire-guided percutaneous cricothyrotomy in a patient with severe maxillofacial trauma

Contains fulltext : 69538.pdf (publisher's version ) (Open Access)BACKGROUND: In the presence of severe maxillofacial trauma, management of the airway is important because this condition poses a significant threat to airway patency. That securing the airway is not always straightforward is described and illustrated in this paper. CASE: We present the case of a 23-year-old patient who sustained severe maxillofacial injury for which airway control was necessary. A wire-guided percutaneous dilation cricothyrotomy was performed, which was most probably the cause of an acute loss of airway patency. The literature regarding the role of percutaneous techniques in an elective and emergency setting is reviewed

Signal enhancement in protein NMR using the spin-noise tuning optimum

We have assessed the potential of an alternative probe tuning strategy based on the spin-noise response for application in common high-resolution multi-dimensional biomolecular NMR experiments with water signal suppression on aqueous and salty samples. The method requires the adjustment of the optimal tuning condition, which may be offset by several 100 kHz from the conventional tuning settings using the noise response of the water protons as an indicator. Although the radio frequency-pulse durations are typically longer under such conditions, signal-to-noise gains of up to 22% were achieved. At salt concentrations up to 100 mM a substantial sensitivity gain was observed