Wave equation with concentrated nonlinearities

In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of \CO^n and a discrete set Y\subset\RE^3 with $n$ elements, we define a nonlinear operator $\Delta_{V,Y}$ on L^2(\RE^3) which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean matrix. We then consider the nonlinear wave equation $\ddot \phi=\Delta_{V,Y}\phi$ and study the corresponding Cauchy problem, giving an existence and uniqueness result in the case $V$ is Lipschitz. The solution of such a problem is explicitly expressed in terms of the solutions of two Cauchy problem: one relative to a free wave equation and the other relative to an inhomogeneous ordinary differential equation with delay and principal part $\dot\zeta+V(\zeta)$. Main properties of the solution are given and, when $Y$ is a singleton, the mechanism and details of blow-up are studied.Comment: Revised version. To appear in Journal of Physics A: Mathematical and General, special issue on Singular Interactions in Quantum Mechanics: Solvable Model

Quantification of Evaporation and Drainage Processes in Unsaturated Porous Media Using Magnetic Resonance Imaging

The water loss in packed beds was studied spatially and time‐resolved via magnetic resonance imaging on the pore scale. The packed beds were measured under water‐saturated and unsaturated conditions, while the magnetic resonance method allowed a quantitative differentiation between air, liquid, and solid phases exploring the native contrast of the named phases without additional contrast agents. Beside a qualitative image comparison, subsequent quantitative image processing allowed for a detailed spatially resolved determination of water distribution, the differentiation between water transport processes, and the quantification of liquid clusters in 3‐D. Results are presented for two packed beds that show significant differences in their evaporation and drainage dynamics, which are mainly determined by the physical properties of the packed beds. The water loss of the packed bed of 2–4mmquartz particles reached a level below interpretability after 18.2 hr; meanwhile, a successive decrease of the largest liquid cluster volume from 82.5 to 0.7 mm$^{3}$ was observed. The water content of the packed bed of 2 mm glass spheres was still observable after 70.9 hr. During the experiment, no significant changes in the structure of the liquid clusters were measured. The current work displays the applicability of magnetic resonance imaging for porescale investigations without the addition of contrast agents

Valorization of organic carbon in primary sludge via semi-continuous dark fermentation: First step to establish a wastewater biorefinery

In this study, lab-scale, bench-scale, and pilot-scale experiments were carried out to optimize short-chain fatty acids production from primary sludge. Batch tests showed the requirement of short retention times and semi-continuous operation mode showed a plateau of maximum daily productivity at 36-hours hydraulic retention time with minimal methanation. Optimization from pH 5 to pH 10 at 36 h-hydraulic retention time under long-term semi-continuous operating mode revealed that production of short-chain fatty acids was pH dependent and highest yields could be achieved at pH 7 by establishing optimum redox conditions for fermentation. Pilot-scale experiments at 32 °C showed that daily productivity (3.1 g∙L$_{reactor}$$^{-1}$∙d$_{HRT}$$^{-1}$) and yields (150 mg∙g$_{VS}$$^{-1}$; OLR = 21 g$_{VS}$∙L$_{reactor}$$^{-1}$∙d$_{HRT}$$^{-1}$; pH 7) of short-chain fatty acids could be significantly improved, specifically for acetic and propionic acids. From these results, a robust dark fermentation step for recovery of valuable products from the solids treatment step in a biorefinery can be achieved

Efficacious enrichment of butyrate-oxidizing exoelectrogens upgrades energy recovery in relevant bioelectrochemical systems

Energy recovery via bioelectrochemical systems (BESs) while treating organic wastes has proven to be a promising technology. Organic waste hydrolysates are appealing feedstocks for BESs due to their richness in short-chain fatty acids rather than complex organics. However, butyrate, among the abundant acids in hydrolysates, has been found to particularly hinder the efficiency of BESs. The lack of efficient anodic butyrate-oxidizers appears to be critical; therefore, this study targeted the enrichment of an anodic community to enhance butyrate oxidation efficiency in BESs. We initially tested three different inoculum sources using butyrate as the sole electron donor. Then, through successive transfers of a bioanode piece to fresh anodes, significant improvement in coulombic efficiency (CE) from 9.4 % to 78.6 % was achieved over six transfers. The enriched bioanode was dominated by the bacterial genera Geobacter (72 %) and Sporomusa (16 %), which correlated positively with CE development over transfers. The metagenomic/transcriptomic analyses confirmed the key role of Geobacter in the anodic oxidation of butyrate, while Sporomusa likely displayed a syntrophic interaction, assimilating acetate from CO$^2$ and excess H$_2$. The enriched culture was further bioaugmented with Geobacter sulfurreducens and tested with real butyrate-containing hydrolysate, in which CE and maximum current density of 86.9 % and ∼3.5 A/m$^2$ were achieved, respectively. Overall, the enriched butyrate-oxidizing culture, bioaugmented with G. sulfurreducens, proves efficient for BESs treating butyrate-rich waste-streams

Separation of Short-Chain Fatty Acids from Primary Sludge into a Particle-Free Permeate by Coupling Chamber Filter-Press and Cross-Flow Microfiltration: Optimization, Semi-Continuous Operation, and Evaluation

Short-chain fatty acids (SCFAs) are valuable metabolic intermediates that are produced during dark fermentation of sludge, which, when capitalized on, can be used as chemical precursors for biotechnological applications. However, high concentrations of solids with SCFAs in hydrolyzed sludge can be highly detrimental to downstream recovery processes. This pilot-scale study addresses this limitation and explores the recovery of SCFAs from primary sludge into a particle-free permeate through a combination of chamber filter-press (material: polyester; mesh size: 100 μm) and cross-flow microfiltration (material: α-Al$_2$O$_3$; pore size: 0.2 μm; cross-flow velocity: 3 m·s$^{−1}$; pressure = 2.2 bars). Firstly, primary sludge underwent dark fermentation yielding a hydrolyzate with a significant concentration of SCFAs along with total solids (TS) concentration in the range of 20 to 30 g·L$^{−1}$. The hydrolyzate was conditioned with hydroxypropyl trimethyl ammonium starch (HPAS), and then dewatered using a filter press, reducing TS by at least 60%, resulting in a filtrate with a suspended solids concentration ranging from 100 to 1300 mg·L$^{−1}$. Despite the lower suspended solids concentration, the microfiltration membrane underwent severe fouling due to HPAS’s electrostatic interaction. Two methods were optimized for microfiltration: (1) increased backwashing frequency to sustain a permeate flux of 20 L·m$^{−2}$·h$^{−1}$ (LMH), and (2) surface charge modification to maintain the flux between 70 and 80 LMH. With backwashing, microfiltration can filter around 900 L·m$_{eff}$$^{−2}$ (without chemical cleaning), with the flux between 50 and 60 LMH under semi-continuous operation. Evaluating the particle-free permeate obtained from the treatment chain, around 4 gC$_{SCFAs}$·capita$^{−1}$·d$^{−1}$ can be recovered from primary sludge with a purity of 0.85 to 0.97 C$_{SCFAs}$·DOC$^{−1}$

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Automated consumption and inventory control in cabinets using electronic labeling

Bacheloroppgave i data/informasjonsteknologi. Fakultet for ingeniør- og naturvitskap/ Institutt for datateknologi, elektroteknologi og realfag/ Høgskulen på Vestlandet, campus Bergen.DAT19

Visual mismatch negativity (vMMN): A review and meta-analysis of studies in psychiatric and neurological disorders

The visual mismatch negativity (vMMN) response is an event-related potential (ERP) component, which is automatically elicited by events that violate predictions based on prior events. VMMN experiments use visual stimulus repetition to induce predictions, and vMMN is obtained by subtracting the response to rare unpredicted stimuli from those to frequent stimuli. One increasingly popular interpretation of the mismatch response postulates that vMMN, similar to its auditory counterpart (aMMN), represents a prediction error response generated by cortical mechanisms forming probabilistic representations of sensory signals. Here we discuss the physiological and theoretical basis of vMMN and review thirty-three studies from the emerging field of its clinical applications, presenting a meta-analysis of findings in schizophrenia, mood disorders, substance abuse, neurodegenerative disorders, developmental disorders, deafness, panic disorder and hypertension. Furthermore, we include reports on aging and maturation as they bear upon many clinically relevant conditions. Surveying the literature we found that vMMN is altered in several clinical populations which is in line with aMMN findings. An important potential advantage of vMMN however is that it allows the investigation of deficits in predictive processing in cognitive domains which rely primarily on visual information; a principal sensory modality and thus of vital importance in environmental information processing and response, and a modality which arguably may be more sensitive to some pathological changes. However, due to the relative infancy of research in vMMN compared to aMMN in clinical populations its potential for clinical application is not yet fully appreciated. The aim of this review and meta-analysis therefore is to present, in a detailed systematic manner, the findings from clinically-based vMMN studies, to discuss their potential impact and application, to raise awareness of this measure and to improve our understanding of disease upon fundamental aspects of visual information processing

Domesticating the Exotic? An Online Survey of Attitudes towards the International Wildlife Pet Trade

There are a variety of perspectives on wildlife management and conservation, necessitating interdisciplinary research to develop better management strategies. We answered the call to action provided by Teel et al. (2018) to integrate social sciences into conservation and explored an important but understudied issue: views on the international pet-trade of exotic animals. Some pet owners advocate the pet trade as a means to promote conservation, where removing wild animals from their natural habitat could protect them from degraded environments. To gauge how prevalent this attitude is in a cross-national sample, we conducted an online survey that asked 882 participants worldwide to evaluate the pet trade and its relationship with biological conservation. Overall, our survey results showed regional patterns and indicated that younger respondents were more likely to consider international pet trade as a form of acceptable conservation practice compared to older respondents. Education also played a role in shaping views on the pet-trade and indicated that respondents with higher education degrees were less prone to accept pet trade as a substitute for conservation practices. Our research provides novel insights applicable to education programmes and international conservation efforts while highlighting variation in attitudes even among professionals with formal training in natural sciences and ecology