Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

In this article, we develop the a priori and a posteriori error analysis of hp-version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ ℝd, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm, which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp-adaptive refinement algorithm.

Optical properties of a nanomatch-like plasmonic structure

The optical properties of a match-like plasmonic nanostructure are numerically investigated using full-wave finite-difference time-domain analysis in conjunction with dispersive material models. This work is mainly motivated by the developed technique enabling reproducible fabrication of nanomatch structures as well as the growing applications that utilize the localized field enhancement in plasmonic nanostructures. Our research revealed that due to the pronounced field enhancement and larger resonance tunabilities, some nanomatch topologies show potentials for various applications in the field of, e.g., sensing as well as a novel scheme for highly reproducible tips in scanning near field optical microscopy, among others. Despite the additional degrees of freedom that are offered by the composite nature of the proposed nanomatch topology, the paper also reflects on a fundamental complication intrinsic to the material interfaces especially in the nanoscale: stoichiometric mixing. We conclude that the specificity in material modeling will become a significant issue in future research on functionalized composite nanostructures.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Bounding Standard Gaussian Tail Probabilities

We review various inequalities for Mills' ratio (1 - Φ)= Ø, where Ø and Φ denote the standard Gaussian density and distribution function, respectively. Elementary considerations involving finite continued fractions lead to a general approximation scheme which implies and refines several known bounds.

Extraordinary transmission through a single coaxial aperture in a thin metal film

We investigate experimentally the transmission properties of single sub-wavelength coaxial apertures in thin metal films (t = 110 nm). Enhanced transmission through a single sub-wavelength coaxial aperture illuminated with a strongly focused radially polarized light beam is reported. In our experiments we achieved up to four times enhanced transmission through a single coaxial aperture as compared to a (hollow) circular aperture with the same outer diameter.We attribute this enhancement of transmission to the excitation of a TEM-mode for illumination with radially polarized light inside the single coaxial aperture. A strong polarization contrast is observed between the transmission for radially and azimuthally polarized illumination. Furthermore, the observed transmission through a single coaxial aperture can be strongly reduced if surface plasmons are excited. The experimental results are in good agreement with finite difference time domain (FDTD) simulations.

Quantitative Myocardial Contrast Echocardiography during Pharmacological Stress for Diagnosis of Coronary Artery Disease: A Systematic Review and Meta-analysis of Diagnostic Accuracy Studies

AIMS: We conducted a meta-analysis to evaluate the accuracy of quantitative stress myocardial contrast echocardiography (MCE) in coronary artery disease (CAD). METHODS AND RESULTS: Database search was performed through January 2008. We included studies evaluating accuracy of quantitative stress MCE for detection of CAD compared with coronary angiography or single-photon emission computed tomography (SPECT) and measuring reserve parameters of A, beta, and Abeta. Data from studies were verified and supplemented by the authors of each study. Using random effects meta-analysis, we estimated weighted mean difference (WMD), likelihood ratios (LRs), diagnostic odds ratios (DORs), and summary area under curve (AUC), all with 95% confidence interval (CI). Of 1443 studies, 13 including 627 patients (age range, 38-75 years) and comparing MCE with angiography (n = 10), SPECT (n = 1), or both (n = 2) were eligible. WMD (95% CI) were significantly less in CAD group than no-CAD group: 0.12 (0.06-0.18) (P < 0.001), 1.38 (1.28-1.52) (P < 0.001), and 1.47 (1.18-1.76) (P < 0.001) for A, beta, and Abeta reserves, respectively. Pooled LRs for positive test were 1.33 (1.13-1.57), 3.76 (2.43-5.80), and 3.64 (2.87-4.78) and LRs for negative test were 0.68 (0.55-0.83), 0.30 (0.24-0.38), and 0.27 (0.22-0.34) for A, beta, and Abeta reserves, respectively. Pooled DORs were 2.09 (1.42-3.07), 15.11 (7.90-28.91), and 14.73 (9.61-22.57) and AUCs were 0.637 (0.594-0.677), 0.851 (0.828-0.872), and 0.859 (0.842-0.750) for A, beta, and Abeta reserves, respectively. CONCLUSION: Evidence supports the use of quantitative MCE as a non-invasive test for detection of CAD. Standardizing MCE quantification analysis and adherence to reporting standards for diagnostic tests could enhance the quality of evidence in this field.

Stent Thrombosis in Drug-Eluting or Bare-Metal Stents in Patients Receiving Dual Antiplatelet Therapy

OBJECTIVES This study sought to compare rates of stent thrombosis and major adverse cardiac and cerebrovascular events (MACCE) (composite of death, myocardial infarction, or stroke) after coronary stenting with drug-eluting stents (DES) versus bare-metal stents (BMS) in patients who participated in the DAPT (Dual Antiplatelet Therapy) study, an international multicenter randomized trial comparing 30 versus 12 months of dual antiplatelet therapy in subjects undergoing coronary stenting with either DES or BMS. BACKGROUND Despite antirestenotic efficacy of coronary DES compared with BMS, the relative risk of stent thrombosis and adverse cardiovascular events is unclear. Many clinicians perceive BMS to be associated with fewer adverse ischemic events and to require shorter-duration dual antiplatelet therapy than DES. METHODS Prospective propensity-matched analysis of subjects enrolled into a randomized trial of dual antiplatelet therapy duration was performed. DES- and BMS-treated subjects were propensity-score matched in a many-to-one fashion. The study design was observational for all subjects 0 to 12 months following stenting. A subset of eligible subjects without major ischemic or bleeding events were randomized at 12 months to continued thienopyridine versus placebo; all subjects were followed through 33 months. RESULTS Among 10,026 propensity-matched subjects, DES-treated subjects (n = 8,308) had a lower rate of stent thrombosis through 33 months compared with BMS-treated subjects (n = 1,718, 1.7% vs. 2.6%; weighted risk difference -1.1%, p = 0.01) and a noninferior rate of MACCE (11.4% vs. 13.2%, respectively, weighted risk difference -1.8%, p = 0.053, noninferiority p < 0.001). CONCLUSIONS DES-treated subjects have long-term rates of stent thrombosis that are lower than BMS-treated subjects. (The Dual Antiplatelet Therapy Study [DAPT study]; NCT00977938).