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.

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.

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.

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.

Tracking the implicit self using event-related potentials

Negative biases in implicit self-evaluation are thought to be detrimental to subjective well-being and have been linked to various psychological disorders, including depression. An understanding of the neural processes underlying implicit self-evaluation in healthy subjects could provide a basis for the investigation of negative biases in depressed patients, the development of differential psychotherapeutic interventions, and the estimation of relapse risk in remitted patients. We thus studied the brain processes linked to implicit self-evaluation in 25 healthy subjects using event-related potential (ERP) recording during a self-relevant Implicit Association Test (sIAT). Consistent with a positive implicit self-evaluation in healthy subjects, they responded significantly faster to the congruent (self-positive mapping) than to the incongruent sIAT condition (self-negative mapping). Our main finding was a topographical ERP difference in a time window between 600 and 700 ms, whereas no significant differences between congruent and incongruent conditions were observed in earlier time windows. This suggests that biases in implicit self-evaluation are reflected only indirectly, in the additional recruitment of control processes needed to override the positive implicit self-evaluation of healthy subjects in the incongruent sIAT condition. Brain activations linked to these control processes can thus serve as an indirect measure for estimating biases in implicit self-evaluation. The sIAT paradigm, combined with ERP, could therefore permit the tracking of the neural processes underlying implicit self-evaluation in depressed patients during psychotherapy.

Unresolved Problems with the "I", the "A" and the "T": Logical and Psychometric Critique of the Implicit Association Test (IAT)

The Implicit Association Test (IAT) had already gained the status of a prominent assessment procedure before its psychometric properties and underlying task structure were understood. The present critique addresses five major problems that arise when the IAT is used for diagnostic inferences: (1) the asymmetry of causal and diagnostic inferences; (2) the viability of the underlying association model; (3) the lack of a testable model underlying IAT-based inferences; (4) the difficulties of interpreting difference scores; and (5) the susceptibility of the IAT to deliberate faking and strategic processing. Based on a theoretical reflection of these issues, and a comprehensive survey of published IAT studies, it is concluded that a number of uncontrolled factors can produce (or reduce) significant IAT scores independently of the personality attribute that is supposed to be captured by the IAT procedure.

Thermal 2-loop master spectral function at finite momentum

When considering NLO corrections to thermal particle production in the “relativistic” regime, in which the invariant mass squared of the produced particle is K2 ~ (πT)2, then the production rate can be expressed as a sum of a few universal “master” spectral functions. Taking the most complicated 2-loop master as an example, a general strategy for obtaining a convergent 2-dimensional integral representation is suggested. The analysis applies both to bosonic and fermionic statistics, and shows that for this master the non-relativistic approximation is only accurate for K2 ~(8πT)2, whereas the zero-momentum approximation works surprisingly well. Once the simpler masters have been similarly resolved, NLO results for quantities such as the right-handed neutrino production rate from a Standard Model plasma or the dilepton production rate from a QCD plasma can be assembled for K2 ~ (πT)2.

Precipitation isoscape of high reliefs: interpolation scheme designed and tested for monthly resolved precipitation oxygen isotope records of an Alpine domain

Stable oxygen isotope composition of atmospheric precipitation (δ18Op) was scrutinized from 39 stations distributed over Switzerland and its border zone. Monthly amount-weighted δ18Op values averaged over the 1995–2000 period showed the expected strong linear altitude dependence (−0.15 to −0.22‰ per 100 m) only during the summer season (May–September). Steeper gradients (~ −0.56 to −0.60‰ per 100 m) were observed for winter months over a low elevation belt, while hardly any altitudinal difference was seen for high elevation stations. This dichotomous pattern could be explained by the characteristically shallower vertical atmospheric mixing height during winter season and provides empirical evidence for recently simulated effects of stratified atmospheric flow on orographic precipitation isotopic ratios. This helps explain "anomalous" deflected altitudinal water isotope profiles reported from many other high relief regions. Grids and isotope distribution maps of the monthly δ18Op have been calculated over the study region for 1995–1996. The adopted interpolation method took into account both the variable mixing heights and the seasonal difference in the isotopic lapse rate and combined them with residual kriging. The presented data set allows a point estimation of δ18Op with monthly resolution. According to the test calculations executed on subsets, this biannual data set can be extended back to 1992 with maintained fidelity and, with a reduced station subset, even back to 1983 at the expense of faded reliability of the derived δ18Op estimates, mainly in the eastern part of Switzerland. Before 1983, reliable results can only be expected for the Swiss Plateau since important stations representing eastern and south-western Switzerland were not yet in operation.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Intracranial EEG correlates of implicit relational inference within the hippocampus

Drawing inferences from past experiences enables adaptive behavior in future situations. Inference has been shown to depend on hippocampal processes. Usually, inference is considered a deliberate and effortful mental act which happens during retrieval, and requires the focus of our awareness. Recent fMRI studies hint at the possibility that some forms of hippocampus-dependent inference can also occur during encoding and possibly also outside of awareness. Here, we sought to further explore the feasibility of hippocampal implicit inference, and specifically address the temporal evolution of implicit inference using intracranial EEG. Presurgical epilepsy patients with hippocampal depth electrodes viewed a sequence of word pairs, and judged the semantic fit between two words in each pair. Some of the word pairs entailed a common word (e.g.,‘winter - red’, ‘red - cat’) such that an indirect relation was established in following word pairs (e.g, ‘winter - cat’). The behavioral results suggested that drawing inference implicitly from past experience is feasible because indirect relations seemed to foster ‘fit’ judgments while the absence of indirect relations fostered 'do not fit' judgments, even though the participants were unaware of the indirect relations. A event-related potential (ERP) difference emerging 400 ms post-stimulus was evident in the hippocampus during encoding, suggesting that indirect relations were already established automatically during encoding of the overlapping word pairs. Further ERP differences emerged later post-stimulus (1500 ms), were modulated by the participants' responses and were evident during encoding and test. Furthermore, response-locked ERP effects were evident at test. These ERP effects could hence be a correlate of the interaction of implicit memory with decision-making. Together, the data map out a time-course in which the hippocampus automatically integrates memories from discrete but related episodes to implicitly influence future decision making.