Linear and projective boundaries in HNN-extensions and distortion phenomena

Linear and projective boundaries of Cayley graphs were introduced in~\cite{kst} as quasi-isometry invariant boundaries of finitely generated groups. They consist of forward orbits $g^\infty=\{g^i: i\in \mathbb N\}$, or orbits $g^{\pm\infty}=\{g^i:i\in\mathbb Z\}$, respectively, of non-torsion elements~$g$ of the group $G$, where `sufficiently close' (forward) orbits become identified, together with a metric bounded by 1. We show that for all finitely generated groups, the distance between the antipodal points $g^\infty$ and $g^{-\infty}$ in the linear boundary is bounded from below by $\sqrt{1/2}$, and we give an example of a group which has two antipodal elements of distance at most $\sqrt{12/17}<1$. Our example is a derivation of the Baumslag-Gersten group. \newline We also exhibit a group with elements $g$ and $h$ such that $g^\infty = h^\infty$, but $g^{-\infty}\neq h^{-\infty}$. Furthermore, we introduce a notion of average-case-distortion---called growth---and compute explicit positive lower bounds for distances between points $g^\infty$ and $h^\infty$ which are limits of group elements $g$ and $h$ with different growth

Fractal diffusion in high temperature polymer electrolyte fuel cell membranes

© 2018 Author(s). The performance of fuel cells depends largely on the proton diffusion in the proton conducting membrane, the core of a fuel cell. High temperature polymer electrolyte fuel cells are based on a polymer membrane swollen with phosphoric acid as the electrolyte, where proton conduction takes place. We studied the proton diffusion in such membranes with neutron scattering techniques which are especially sensitive to the proton contribution. Time of flight spectroscopy and backscattering spectroscopy have been combined to cover a broad dynamic range. In order to selectively observe the diffusion of protons potentially contributing to the ion conductivity, two samples were prepared, where in one of the samples the phosphoric acid was used with hydrogen replaced by deuterium. The scattering data from the two samples were subtracted in a suitable way after measurement. Thereby subdiffusive behavior of the proton diffusion has been observed and interpreted in terms of a model of fractal diffusion. For this purpose, a scattering function for fractal diffusion has been developed. The fractal diffusion dimension dw and the Hausdorff dimension df have been determined on the length scales covered in the neutron scattering experiments

Wafer-sized multifunctional polyimine-based two-dimensional conjugated polymers with high mechanical stiffness

One of the key challenges in two-dimensional (2D) materials is to go beyond graphene, a prototype 2D polymer (2DP), and to synthesize its organic analogues with structural control at the atomic- or molecular-level. Here we show the successful preparation of porphyrin-containing monolayer and multilayer 2DPs through Schiff-base polycondensation reaction at an air-water and liquid-liquid interface, respectively. Both the monolayer and multilayer 2DPs have crystalline structures as indicated by selected area electron diffraction. The monolayer 2DP has a thickness of∼0.7 nm with a lateral size of 4-inch wafer, and it has a Young's modulus of 267±30 GPa. Notably, the monolayer 2DP functions as an active semiconducting layer in a thin film transistor, while the multilayer 2DP from cobalt-porphyrin monomer efficiently catalyses hydrogen generation from water. This work presents an advance in the synthesis of novel 2D materials for electronics and energy-related applications

Exciton spectroscopy and unidirectional transport in MoSe2-WSe2 lateral heterostructures encapsulated in hexagonal boron nitride

Chemical vapor deposition (CVD) allows lateral edge epitaxy of transition metal dichalcogenide heterostructures. Critical for carrier and exciton transport is the material quality and the nature of the lateral heterojunction. Important details of the optical properties were inaccessible in as-grown heterostructure samples due to large inhomogeneous broadening of the optical transitions. Here we perform optical spectroscopy of CVD grown MoSe$_2$-WSe$_2$ lateral heterostructures, encapsulated in hBN. Photoluminescence (PL), reflectance contrast and Raman spectroscopy reveal optical transition linewidths similar to high quality exfoliated monolayers, while PL imaging experiments uncover the effective excitonic diffusion length of both materials. The typical extent of the covalently bonded MoSe$_2$-WSe$_2$ heterojunctions is 3 nm measured by scanning transmission electron microscopy (STEM). Tip-enhanced, sub-wavelength optical spectroscopy mapping shows the high quality of the heterojunction which acts as an excitonic diode resulting in unidirectional exciton transfer from WSe$_2$ to MoSe$_2$

Cardiovascular Mortality Can Be Predicted by Heart Rate Turbulence in Hemodialysis Patients

Background: Excess mortality in hemodialysis patients is mostly of cardiovascular origin. We examined the association of heart rate turbulence (HRT), a marker of baroreflex sensitivity, with cardiovascular mortality in hemodialysis patients. Methods: A population of 290 prevalent hemodialysis patients was followed up for a median of 3 years. HRT categories 0 (both turbulence onset [TO] and slope [TS] normal), 1 (TO or TS abnormal), and 2 (both TO and TS abnormal) were obtained from 24 h Holter recordings. The primary end-point was cardiovascular mortality. Associations of HRT categories with the endpoints were analyzed by multivariable Cox regression models including HRT, age, albumin, and the improved Charlson Comorbidity Index for hemodialysis patients. Multivariable linear regression analysis identified factors associated with TO and TS. Results: During the follow-up period, 20 patients died from cardiovascular causes. In patients with HRT categories 0, 1 and 2, cardiovascular mortality was 1, 10, and 22%, respectively. HRT category 2 showed the strongest independent association with cardiovascular mortality with a hazard ratio of 19.3 (95% confidence interval: 3.69-92.03;P < 0.001). Age, calcium phosphate product, and smoking status were associated with TO and TS. Diabetes mellitus and diastolic blood pressure were only associated with TS. Conclusion: Independent of known risk factors, HRT assessment allows identification of hemodialysis patients with low, intermediate, and high risk of cardiovascular mortality. Future prospective studies are needed to translate risk prediction into risk reduction in hemodialysis patients