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

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

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

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

Static non-reciprocity in mechanical metamaterials

Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation associated with spatio-temporal variations. Here we show that it is possible to strongly break reciprocity in static systems, realizing mechanical metamaterials that, by combining large nonlinearities with suitable geometrical asymmetries, and possibly topological features, exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. In addition to extending non-reciprocity and isolation to statics, our work sheds new light on the understanding of energy propagation in non-linear materials with asymmetric crystalline structures and topological properties, opening avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.Comment: 19 pages, 3 figures, Supplementary information (11 pages and 5 figures

Resonant microwave dichroic surface

Dichroic surface has high stopband filter characteristics with a low stopband-to-passband frequency ratio. It utilizes two stagger-tuned, resonant artificial dielectric surfaces and is virtually polarization insensitive

Health in times of uncertainty in the eastern Mediterranean region, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

Background: The eastern Mediterranean region is comprised of 22 countries: Afghanistan, Bahrain, Djibouti, Egypt, Iran, Iraq, Jordan, Kuwait, Lebanon, Libya, Morocco, Oman, Pakistan, Palestine, Qatar, Saudi Arabia, Somalia, Sudan, Syria, Tunisia, the United Arab Emirates, and Yemen. Since our Global Burden of Disease Study 2010 (GBD 2010), the region has faced unrest as a result of revolutions, wars, and the so-called Arab uprisings. The objective of this study was to present the burden of diseases, injuries, and risk factors in the eastern Mediterranean region as of 2013. Methods: GBD 2013 includes an annual assessment covering 188 countries from 1990 to 2013. The study covers 306 diseases and injuries, 1233 sequelae, and 79 risk factors. Our GBD 2013 analyses included the addition of new data through updated systematic reviews and through the contribution of unpublished data sources from collaborators, an updated version of modelling software, and several improvements in our methods. In this systematic analysis, we use data from GBD 2013 to analyse the burden of disease and injuries in the eastern Mediterranean region specifically. Findings: The leading cause of death in the region in 2013 was ischaemic heart disease (90·3 deaths per 100 000 people), which increased by 17·2% since 1990. However, diarrhoeal diseases were the leading cause of death in Somalia (186·7 deaths per 100 000 people) in 2013, which decreased by 26·9% since 1990. The leading cause of disability-adjusted life-years (DALYs) was ischaemic heart disease for males and lower respiratory infection for females. High blood pressure was the leading risk factor for DALYs in 2013, with an increase of 83·3% since 1990. Risk factors for DALYs varied by country. In low-income countries, childhood wasting was the leading cause of DALYs in Afghanistan, Somalia, and Yemen, whereas unsafe sex was the leading cause in Djibouti. Non-communicable risk factors were the leading cause of DALYs in high-income and middle-income countries in the region. DALY risk factors varied by age, with child and maternal malnutrition affecting the younger age groups (aged 28 days to 4 years), whereas high bodyweight and systolic blood pressure affected older people (aged 60–80 years). The proportion of DALYs attributed to high body-mass index increased from 3·7% to 7·5% between 1990 and 2013. Burden of mental health problems and drug use increased. Most increases in DALYs, especially from non-communicable diseases, were due to population growth. The crises in Egypt, Yemen, Libya, and Syria have resulted in a reduction in life expectancy; life expectancy in Syria would have been 5 years higher than that recorded for females and 6 years higher for males had the crisis not occurred. Interpretation: Our study shows that the eastern Mediterranean region is going through a crucial health phase. The Arab uprisings and the wars that followed, coupled with ageing and population growth, will have a major impact on the region's health and resources. The region has historically seen improvements in life expectancy and other health indicators, even under stress. However, the current situation will cause deteriorating health conditions for many countries and for many years and will have an impact on the region and the rest of the world. Based on our findings, we call for increased investment in health in the region in addition to reducing the conflicts.Ali H Mokdad ... Azmeraw T Amare ... et al

Iron and bismuth bound human serum transferrin reveals a partially-opened conformation in the N-lobe

Human serum transferrin (hTF) binds Fe(III) tightly but reversibly, and delivers it to cells via a receptor-mediated endocytosis process. The metal-binding and release result in significant conformational changes of the protein. Here, we report the crystal structures of diferric-hTF (Fe N Fe C-hTF) and bismuth-bound hTF (Bi N Fe C-hTF) at 2.8 and 2.4 Å resolutions respectively. Notably, the N-lobes of both structures exhibit unique 'partially-opened' conformations between those of the apo-hTF and holo-hTF. Fe(III) and Bi(III) in the N-lobe coordinate to, besides anions, only two (Tyr95 and Tyr188) and one (Tyr188) tyrosine residues, respectively, in contrast to four residues in the holo-hTF. The C-lobe of both structures are fully closed with iron coordinating to four residues and a carbonate. The structures of hTF observed here represent key conformers captured in the dynamic nature of the transferrin family proteins and provide a structural basis for understanding the mechanism of metal uptake and release in transferrin families. © 2012 Macmillan Publishers Limited. All rights reserved.published_or_final_versio