The Formation, Structure, and Stability of a Shear Layer in a Fluid with Temperature-Dependent Viscosity

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. However, experiments show that the flow of a fluid might form shear bands or shear layers, narrow bands in which the velocity of the fluid changes sharply. In general, adiabatic shear layers are observed not only in fluids but also in thermo-plastic materials subject to shear at a high-strain rate and in combustion. Therefore there is widespread interest in modeling the formation of shear layers. In this paper we investigate the basic system of conservation laws for a one-dimensional flow with temperature-dependent viscosity using a combination of analytical and numerical tools. We present results to substantiate the claim that the formation of shear layers is due to teh fact that viscosity decreases sufficiently quickly as temperature increases and analyze the structure and stability properties of the layers

Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence

Abstract. We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods. 1

Adaptive Finite Element Solution of Multiscale PDE-ODE Systems

We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of nonlinear ordinary differential equations. A motivating example is modeling the electrical activity of the heart taking into account the chemistry inside cells in the heart. Such multiscale models pose extremely computationally challenging problems due to the multiple scales in time and space that are involved. We describe a mathematically consistent approach to couple the microscale and macroscale models based on introducing an intermediate "coupling scale". Since the ordinary differential equations are defined on a much finer spatial scale than the finite element discretization for the partial differential equation, we introduce a Monte Carlo approach to sampling the fine scale ordinary differential equations. We derive goal-oriented a posteriori error estimates for quantities of interest computed from the solution of the multiscale model using adjoint problems and computable residuals. We distinguish the errors in time and space for the partial differential equation and the ordinary differential equations separately and include errors due to the transfer of the solutions between the equations. The estimate also includes terms reflecting the sampling of the microscale model. Based on the accurate error estimates, we devise an adaptive solution method using a "blockwise" approach. The method and estimates are illustrated using a realistic problem.Comment: 25 page

Analysis of Shear Layers in a Fluid with Temperature-Dependent Viscosity

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. Howerver, experiments show that the flow of a fluid in which viscosity decreases as temperature increases tends to form shear layers, narrow regions in which the velocity of the fluid changes sharply. In general, adiabatic shear layers are observed not only in fluids but also in thermo-plastic materials subject to shear at a high-strain rate and in combustion and there is widespread interest in modeling their formation. In this paper, we investigate a well-known model representing a basic system of conservation laws for a one-dimensional flow with temperature-dependent viscosity using a combination of analytical and numerical tools. We present results to substantiate the claim that the formation of shear layers can only occur in solutions of the model when the viscosity decreases sufficiently quickly as temperature increases and we further analyze the structure and stability properties of the layers

hp-adaptive Galerkin Time Stepping Methods for Nonlinear Initial Value Problems

This work is concerned with the derivation of an a posteriori error estimator for Galerkin approximations to nonlinear initial value problems with an emphasis on finite-time existence in the context of blow-up. The structure of the derived estimator leads naturally to the development of both h and hp versions of an adaptive algorithm designed to approximate the blow-up time. The adaptive algorithms are then applied in a series of numerical experiments, and the rate of convergence to the blow-up time is investigated

Risk Assessment and Comparative Effectiveness of Left Ventricular Assist Device and Medical Management in Ambulatory Heart Failure Patients The ROADMAP Study 2-Year Results

OBJECTIVES The authors sought to provide the pre-specified primary endpoint of the ROADMAP (Risk Assessment and Comparative Effectiveness of Left Ventricular Assist Device and Medical Management in Ambulatory Heart Failure Patients) trial at 2 years. BACKGROUND The ROADMAP trial was a prospective nonrandomized observational study of 200 patients (97 with a left ventricular assist device [LVAD], 103 on optimal medical management [OMM]) that showed that survival with improved functional status at 1 year was better with LVADs compared with OMM in a patient population of ambulatory New York Heart Association functional class IIIb/IV patients. METHODS The primary composite endpoint was survival on original therapy with improvement in 6-min walk distance \u3e= 75 m. RESULTS Patients receiving LVAD versus OMM had lower baseline health-related quality of life, reduced Seattle Heart Failure Model 1-year survival (78% vs. 84%; p = 0.012), and were predominantly INTERMACS (Interagency Registry for Mechanically Assisted Circulatory Support) profile 4 (65% vs. 34%; p \u3c 0.001) versus profiles 5 to 7. More LVAD patients met the primary endpoint at 2 years: 30% LVAD versus 12% OMM (odds ratio: 3.2 [95% confidence interval: 1.3 to 7.7]; p = 0.012). Survival as treated on original therapy at 2 years was greater for LVAD versus OMM (70 +/- 5% vs. 41 +/- 5%; p \u3c 0.001), but there was no difference in intent-to-treat survival (70 +/- 5% vs. 63 +/- 5%; p = 0.307). In the OMM arm, 23 of 103 (22%) received delayed LVADs (18 within 12 months; 5 from 12 to 24 months). LVAD adverse events declined after year 1 for bleeding (primarily gastrointestinal) and arrhythmias. CONCLUSIONS Survival on original therapy with improvement in 6-min walk distance was superior with LVAD compared with OMM at 2 years. Reduction in key adverse events beyond 1 year was observed in the LVAD group. The ROADMAP trial provides risk-benefit information to guide patient- and physician-shared decision making for elective LVAD therapy as a treatment for heart failure. (Risk Assessment and Comparative Effectiveness of Left Ventricular Assist Device and Medical Management in Ambulatory Heart Failure Patients [ROADMAP]; NCT01452802

Federal Control of Health and Safety Standards in Peacetime Private Atomic Energy Activities

This article is directed to the question of the power of Congress to provide for such regulation of those who handle radioactive materials in private industry and not to the policy question of whether Congress ought to attempt such regulation

Radiation Injuries and Statistics: The Need for a New Approach to Injury Litigation

The emphasis given by the mass media of communication to some of the dramatic problems arising from the use of nuclear energy unfortunately has diverted attention from some of the matters about which something can be done by lawyers, administrators, and legislators without the necessity of complicated international negotiations between various parties to the Cold War. The headlines leave the uninformed, and perhaps often also the informed, public with the impression that even for radiation injuries the important problems all deal with such questions as: (1) Will only a few or many millions of people survive an all-out nuclear war? (2) Will the fallout from nuclear weapons testing cause no, a few, or hundreds of thousands of cases of leukemia and similar diseases among the populations of the world

Introduction: Legislative, Administrative, and Judicial Nonscience

This symposium deals with the legal issues, or rather some of them, that are created by scientific research. Anyone remotely interested in scientific developments should be aware that even the existence of new scientific facts, let alone the application of such discoveries to everyday activities, gives rise to a host of human value judgments that should be faced and resolved by society. Although these problems are often left in purgatory forever, it is the legal system, broadly defined, that attempts to resolve the conflict of interests (or the balancing of values) when a decision is made. Making this type of balancing of values judgments is the overriding-or perhaps even sole-function of the legal system. This is true whether we act through administrative regulations, legislative enactments, or judicial decisions