Minimal surfaces from circle patterns: Geometry from combinatorics

We suggest a new definition for discrete minimal surfaces in terms of sphere packings with orthogonally intersecting circles. These discrete minimal surfaces can be constructed from Schramm's circle patterns. We present a variational principle which allows us to construct discrete analogues of some classical minimal surfaces. The data used for the construction are purely combinatorial--the combinatorics of the curvature line pattern. A Weierstrass-type representation and an associated family are derived. We show the convergence to continuous minimal surfaces.Comment: 30 pages, many figures, some in reduced resolution. v2: Extended introduction. Minor changes in presentation. v3: revision according to the referee's suggestions, improved & expanded exposition, references added, minor mistakes correcte

Nonlinear analysis of time series of vibration data from a friction brake: SSA, PCA, and MFDFA

We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake. SSA and PCA are used to study the long time-scale characteristics of the time series. MFDFA is applied for investigating all time scales up to the smallest recorded one. It turns out that the majority of the long time-scale dynamics, that is presumably dominated by the structural dynamics of the brake system, is dominated by very few active dimensions only and can well be understood in terms of low dimensional chaotic attractors. The multi-fractal analysis shows that the fast dynamical processes originating in the friction interface are in turn truly multi-scale in nature.Comment: 25 pages, 9 figure

ARCHETYPES OF DIGITAL BUSINESS MODELS IN LOGISTICS START-UPS

Our work develops an archetypical representation of current digital business models of Start-Ups in the logistics sector. In order to achieve our goal, we analyze the business models of 125 Start-Ups. We draw our sample from the Start-Up database AngelList and focus on platform-driven businesses. We chose Start-Ups as they often are at the forefront of innovation and thus have a high likelihood of operating digital business models. Following well-established methodological guidelines, we construct a taxonomy of digital business models in multiple iterations. We employ different algorithms for cluster analysis to find and generate clusters based on commonalities between the business models across the dimensions and characteristics of the taxonomy. Ultimately, we use the dominant features of the emerging patterns within the clusters to derive archetypes

A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure

Flow loop study of a cold and cohesive slurry. Pressure drop and formation of plugs

Slurries of cohesive particles constitute a significant risk during subsea petroleum production due to their potential to plug the flow. This article describes a flow loop study of a slurry consistent with 0.23-mm ice particles in decane. The experiments were conducted for the concentration of particles up to 20.3% vol. and Re 25000. The cohesion of ice was suggested by controlling the temperature of the slurry. The relative viscosity of the slurry was computed as a function of particle concentration using pressure drop measurements. The relative viscosity was 3.1 for the concentration of 20.3%. The Bingham-fluid model agreed with the empirical calculations within the discrepancy of 15.5%. Increased viscosity of slurry led to a higher pressure drop in the flow loop compared to the single-phase case. Pressure drops for 20.3% slurry flow were 5.2% and 44.4% higher than for pure decane at Reynolds numbers of 24778 and 4956, respectively. The test section of the loop was equipped with an orifice to induce the formation of plugs. The plugs were observed at particle concentrations below 7.0%. The article presents detailed experimental logs depicting the process of plug formation. The observed blocking cases partially agreed with flow maps from the literature. In addition, we note the applicability of the blockage risk evaluation technique from the Colorado School of Mines.publishedVersio

Long-term in vivo imaging of fibrillar tau in the retina of P301S transgenic mice.

Tauopathies are widespread neurodegenerative disorders characterised by the intracellular accumulation of hyperphosphorylated tau. Especially in Alzheimer's disease, pathological alterations in the retina are discussed as potential biomarkers to improve early diagnosis of the disease. Using mice expressing human mutant P301S tau, we demonstrate for the first time a straightforward optical approach for the in vivo detection of fibrillar tau in the retina. Longitudinal examinations of individual animals revealed the fate of single cells containing fibrillar tau and the progression of tau pathology over several months. This technique is most suitable to monitor therapeutic interventions aimed at reducing the accumulation of fibrillar tau. In order to evaluate if this approach can be translated to human diagnosis, we tried to detect fibrillar protein aggregates in the post-mortem retinas of patients that had suffered from Alzheimer's disease or Progressive Supranuclear Palsy. Even though we could detect hyperphosphorylated tau, we did not observe any fibrillar tau or Aß aggregates. In contradiction to previous studies, our observations do not support the notion that Aβ or tau in the retina are of diagnostic value in Alzheimer's disease

Resonant Biaxial Nanoprobe Utilized for Non-Contact Surface Measurements

In this work a non-contact biaxial nanoprobe for surface profile scans of macroscopic objects with 150 nm accuracy is presented. The biaxial nanoprobe oscillates in two directions to overcome the challenges of sticking in contact mode. Two electrostatic actuators drive the nanoprobe while two electrostatic sensors measure the position of the tip ball. The contact behavior between the tip ball and the specimen is determined by the contact stiffness and the contact damping. Dependent on the dominating effect the nanoprobeoperatesat semi- or non-contact mode, respectively. The aims of this paper are the investigation of the contact behavior, the proof of the independent evaluation of the two axes and the check if sticking is safely avoided

Real-time OCT feedback-controlled RPE photodisruption in ex vivo porcine eyes using 8 microsecond laser pulses

Selective retinal pigment epithelium (RPE) photodisruption requires reliable real-time feedback dosimetry (RFD) to prevent unwanted overexposure. In this study, optical coherence tomography (OCT) based RFD was investigated in ex vivo porcine eyes exposed to laser pulses of 8 µs duration (wavelength: 532 nm, exposure area: 90 × 90 µm2, radiant exposure: 247 to 1975 mJ/µm2). For RFD, fringe washouts in time-resolved OCT M-scans (central wavelength: 870 nm, scan rate: 85 kHz) were compared to an RPE cell viability assay. Statistical analysis revealed a moderate correlation between RPE lesion size and applied treatment energy, suggesting RFD adaptation to inter- and intraindividual RPE pigmentation and ocular transmission

Cohesive collisions of particles in liquid media studied by CFD-DEM, video tracking, and Positron Emission Particle Tracking

This paper investigates the cohesive collision of ice in an oil phase at temperatures ranging from −15.7 °C to −0.3 °C. The new information on the coefficient of restitution (COR) was obtained using three different velocity measurement methods: high-speed experimental video recording, Positron Emission Particle Tracking (PEPT), and numerical simulations. A new type of PEPT tracer was developed for the experiments. The COR values were in the interval 0.57...0.82, with a maximum at around −10 °C. The CFD-DEM coupled approach was applied to reproduce experiments with an ice particle drop and its collision with an inclined ice surface in a decane. The particle–wall interaction is modeled using commercial software, considering particle cohesion, particle size, and shape. CFD-DEM predicted the COR with an average deviation 10% from the experimental data. The numerical model’s results agree with the experiments, demonstrating that the CFD-DEM method is suitable for describing multiphase cohesive interactions