The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation

The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest is \begin{equation*} u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients $\lambda=\lambda(t)$ and $\rho=\rho(t)$ are shape functions and $\omega=\omega(t)$ is an oscillating function. If $\omega(t)\equiv1$ and $\rho(t)u_t$ is an "effective" dissipation term, then $L^2-L^2$ energy estimates are proved in [2]. In contrast, the main goal of the present paper is to generalize the previous results to coefficients including an oscillating function in the time-dependent coefficients. We will explain how the interplay between the shape functions and oscillating behavior of the coefficient will influence energy estimates.Comment: 37 pages, 2 figure

Multivalent 1,2,3‐Triazole‐Linked Carbohydrate Mimetics by Huisgen–Meldal‐Sharpless Cycloadditions of an Azidopyran

Starting from an enantiopure 3‐azido‐substituted pyran derivative and various oligo‐alkynes a series of multivalent 1,2,3‐triazole‐linked carbohydrate mimetics was synthesized. The copper‐catalyzed Huisgen–Meldal‐Sharpless cycloaddition (CuAAC) served as key coupling reaction. Cu/C in the presence of triethylamine proved to be a good catalytic system in most cases. Tri‐, tetra‐, hexa‐, and octavalent compounds with typical rigid or flexible core units were prepared. The most complex compound contains a C60‐fullerene center leading to a dodecavalent carbohydrate mimetic. Only a few of the multivalent target compounds could be converted into pure O‐sulfated derivatives that are required for their evaluation as L‐ and P‐selectin ligands. Nevertheless, preliminary experiments suggest that the dodecavalent C60‐derived compound may be a promising ligand of these biologically important proteins with IC50 values in the low nanomolar range

Lazy Abstraction-Based Controller Synthesis

We present lazy abstraction-based controller synthesis (ABCS) for continuous-time nonlinear dynamical systems against reach-avoid and safety specifications. State-of-the-art multi-layered ABCS pre-computes multiple finite-state abstractions of varying granularity and applies reactive synthesis to the coarsest abstraction whenever feasible, but adaptively considers finer abstractions when necessary. Lazy ABCS improves this technique by constructing abstractions on demand. Our insight is that the abstract transition relation only needs to be locally computed for a small set of frontier states at the precision currently required by the synthesis algorithm. We show that lazy ABCS can significantly outperform previous multi-layered ABCS algorithms: on standard benchmarks, lazy ABCS is more than 4 times faster

A moving boundary model motivated by electric breakdown: II. Initial value problem

An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be formulated as a Laplacian growth model regularized by a 'kinetic undercooling' boundary condition. Using this model we study both the linearized and the full nonlinear evolution of small perturbations of a uniformly translating circle. Within the linear approximation analytical and numerical results show that perturbations are advected to the back of the circle, where they decay. An initially analytic interface stays analytic for all finite times, but singularities from outside the physical region approach the interface for $t\to\infty$, which results in some anomalous relaxation at the back of the circle. For the nonlinear evolution numerical results indicate that the circle is the asymptotic attractor for small perturbations, but larger perturbations may lead to branching. We also present results for more general initial shapes, which demonstrate that regularization by kinetic undercooling cannot guarantee smooth interfaces globally in time.Comment: 44 pages, 18 figures, paper submitted to Physica

Global generalized solutions for Maxwell-alpha and Euler-alpha equations

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit

Spinal cord from body donors is suitable for multicolor immunofluorescence

Immunohistochemistry is a powerful tool for studying neuronal tissue from humans at the molecular level. Obtaining fresh neuronal tissue from human organ donors is difficult and sometimes impossible. In anatomical body donations, neuronal tissue is dedicated to research purposes and because of its easier availability, it may be an alternative source for research. In this study, we harvested spinal cord from a single organ donor 2 h (h) postmortem and spinal cord from body donors 24, 48, and 72 h postmortem and tested how long after death, valid multi-color immunofluorescence or horseradish peroxidase (HRP) immunohistochemistry is possible. We used general and specific neuronal markers and glial markers for immunolabeling experiments. Here we showed that it is possible to visualize molecularly different neuronal elements with high precision in the body donor spinal cord 24 h postmortem and the quality of the image data was comparable to those from the fresh organ donor spinal cord. High-contrast multicolor images of the 24-h spinal cords allowed accurate automated quantification of different neuronal elements in the same sample. Although there was antibody-specific signal reduction over postmortem intervals, the signal quality for most antibodies was acceptable at 48 h but no longer at 72 h postmortem. In conclusion, our study has defined a postmortem time window of more than 24 h during which valid immunohistochemical information can be obtained from the body donor spinal cord. Due to the easier availability, neuronal tissue from body donors is an alternative source for basic and clinical research

The role of structured reporting and structured operation planning in functional endoscopic sinus surgery

Computed tomography (CT) scans represent the gold standard in the planning of functional endoscopic sinus surgeries (FESS). Yet, radiologists and otolaryngologists have different perspectives on these scans. In general, residents often struggle with aspects involved in both reporting and operation planning. The aim of this study was to compare the completeness of structured reports (SR) of preoperative CT images and structured operation planning (SOP) to conventional reports (CR) and conventional operation planning (COP) to potentially improve future treatment decisions on an individual level. In total, 30 preoperative CT scans obtained for surgical planning of patients scheduled for FESS were evaluated using SR and CR by radiology residents. Subsequently, otolaryngology residents performed a COP using free texts and a SOP using a specific template. All radiology reports and operation plannings were evaluated by two experienced FESS surgeons regarding their completeness for surgical planning. User satisfaction of otolaryngology residents was assessed by using visual analogue scales. Overall radiology report completeness was significantly higher using SRs regarding surgically important structures compared to CRs (84.4 vs. 22.0%, p<0.001). SOPs produced significantly higher completeness ratings (97% vs. 39.4%, p<0.001) regarding pathologies and anatomical variances. Moreover, time efficiency was not significantly impaired by implementation of SR (148 s vs. 160 s, p = 0.61) and user satisfaction was significantly higher for SOP (VAS 8.1 vs. 4.1, p<0.001). Implementation of SR and SOP results in a significantly increased completeness of radiology reports and operation planning for FESS. Consequently, the combination of both facilitates surgical planning and may decrease potential risks during FESS