A model of an electrochemical flow cell with porous layer

In this paper we discuss three different mathematical models for fluid-porous interfaces in a simple channel geometry that appears e.g. in thin-layer channel flow cells. Here the difficulties arise from the possibly different orders of the corresponding differential operators in the different domains. A finite volume discretization of this model allows to calculate the limiting current of the H_2 oxidation in a porous electrode with platinum catalyst particles

Mathematical modeling of channel-porous layer interfaces in PEM fuel cells

In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary. After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them. The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur. We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster

Synergistic multi-spectral CT reconstruction with directional total variation

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyse the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 2'.Peer reviewe

Diagnosis driven Anomaly Detection for CPS

In Cyber-Physical Systems (CPS) research, anomaly detection (detecting abnormal behavior) and diagnosis (identifying the underlying root cause) are often treated as distinct, isolated tasks. However, diagnosis algorithms require symptoms, i.e. temporally and spatially isolated anomalies, as input. Thus, anomaly detection and diagnosis must be developed together to provide a holistic solution for diagnosis in CPS. We therefore propose a method for utilizing deep learning-based anomaly detection to generate inputs for Consistency-Based Diagnosis (CBD). We evaluate our approach on a simulated and a real-world CPS dataset, where our model demonstrates strong performance relative to other state-of-the-art models

Lower alpha frequency of intraoperative frontal EEG is associated with postoperative delirium: A secondary propensity-matched analysis.

BACKGROUND Postoperative delirium (POD) is a serious complication of surgery, especially in the elderly patient population. It has been proposed that decreasing the amount of anesthetics by titrating to an EEG index will lower POD rate, but clear evidence is missing. A strong age-dependent negative correlation has been reported between the peak oscillatory frequency of alpha waves and end-tidal anesthetic concentration, with older patients generating slower alpha frequencies. We hypothesized, that slower alpha oscillations are associated with a higher rate of POD. METHOD Retrospective analysis of patients` data from a prospective observational study in cardiac surgical patients approved by the Bernese Ethics committee. Frontal EEG was recorded during Isoflurane effect-site concentrations of 0.7 to 0.8 and peak alpha frequency was measured at highest power between 6 and 17 Hz. Delirium was assessed by chart review. Demographic and clinical characteristics were compared between POD and non-POD groups. Selection bias was addressed using nearest neighbor propensity score matching (PSM) for best balance. This incorporated 18 variables, whereas patients with missing variable information or without an alpha oscillation were excluded. RESULT Of the 1072 patients in the original study, 828 were included, 73 with POD, 755 without. PSM allowed 328 patients into the final analysis, 67 with, 261 without POD. Before PSM, 8 variables were significantly different between POD and non-POD groups, none thereafter. Mean peak alpha frequency was significantly lower in the POD in contrast to non-POD group before and after matching (7.9 vs 8.9 Hz, 7.9 vs 8.8 Hz respectively, SD 1.3, p < 0.001). CONCLUSION Intraoperative slower frontal peak alpha frequency is independently associated with POD after cardiac surgery and may be a simple intraoperative neurophysiological marker of a vulnerable brain for POD. Further studies are needed to investigate if there is a causal link between alpha frequency and POD

From microtiter plates to droplets - there and back again

Droplet-based microfluidic screening techniques can benefit from interfacing established microtiter plate-based screening and sample management workflows. Interfacing tools are required both for loading preconfigured microtiter-plate (MTP)-based sample collections into droplets and for dispensing the used droplets samples back into MTPs for subsequent storage or further processing. Here, we present a collection of Digital Microfluidic Pipetting Tips (DMPTs) with integrated facilities for droplet generation and manipulation together with a robotic system for its operation. This combination serves as a bidirectional sampling interface for sample transfer from wells into droplets (w2d) and vice versa droplets into wells (d2w). The DMPT were designed to fit into 96-deep-well MTPs and prepared from glass by means of microsystems technology. The aspirated samples are converted into the channel-confined droplets’ sequences separated by an immiscible carrier medium. To comply with the demands of dose-response assays, up to three additional assay compound solutions can be added to the sample droplets. To enable different procedural assay protocols, four different DMPT variants were made. In this way, droplet series with gradually changing composition can be generated for, e.g., 2D screening purposes. The developed DMPT and their common fluidic connector are described here. To handle the opposite transfer d2w, a robotic transfer system was set up and is described briefly

Asymptotics of bordered Toeplitz determinants and next-to-diagonal Ising correlations

We prove the analogue of the strong Szeg{\H o} limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results to the formula of Au-Yang and Perk \cite{YP} for the next-to-diagonal correlations ⟨σ0,0σN−1,N⟩ in the anisotropic square lattice Ising model, we rigorously justify that the next-to-diagonal long-range order is the same as the diagonal and horizontal ones in the low temperature regime. The anisotropy-dependence of the subleading term in the asymptotics of the next-to-diagonal correlations is also established. We use Riemann-Hilbert and operator theory techniques, independently and in parallel, to prove these results

Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain

We study an asymptotic behavior of a special correlator known as the Emptiness Formation Probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length $n$ in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY Spin Chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviors for $n \to \infty$ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behavior holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behavior. We study this crossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due to arxiv space limitations. If You would like to see the pdf with good quality figures, please contact Fabio Franchini at "[email protected]