Stability of Transonic Characteristic Discontinuities in Two-Dimensional Steady Compressible Euler Flows

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence subsonic). We proved that such a transonic characteristic discontinuity is structurally stable under small perturbations of the upstream supersonic flow in $BV$. The existence of a weak entropy solution and Lipschitz continuous free boundary (i.e. characteristic discontinuity) is established. To achieve this, the problem is formulated as a free boundary problem for a nonstrictly hyperbolic system of conservation laws; and the free boundary problem is then solved by analyzing nonlinear wave interactions and employing the front tracking method.Comment: 26 pages, 3 figure

Data-Based Model Refinement Using Retrospective Cost Optimization

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83642/1/AIAA-2010-7889-194.pd

Management of Radiation Induced, Bilateral Primary THA Loosening with an Aseptic Paprosky Type IIB Acetabular Defect and a Contralateral Septic Type IIIB Acetabular Defect: A Case Report and Review of Literature

INTRODUCTION: Primary THA in an irradiated hip poses risk for early loosening and inadequate ingrowth. Adverse effects such as decreased vascularity and increased infection risk pose a threat. CASE PRESENTATION: Our patient was a case of post-irradiation (for cervical cancer) bilateral THA loosening causing aseptic acetabular loosening on one side and catastrophic septic loosening with a Paprosky type IIIB acetabular defect with pelvic discontinuity on the contralateral side. DISCUSSION: There have been various studies documenting deleterious effects of irradiation on osseoin-tegration and provide a challenge for long-term implant stability in THA patients. CONCLUSION: A meticulous treatment protocol with contemporary implant technology and staged bilateral stepwise management can lead to satisfactory clinical outcomes.This case report highlights on such specific nuances and principles