Energy Statistics in Open Harmonic Networks

We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full large deviation principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. (Phys. Rev. Lett. 110:180601, 2013).     

Experimental Investigation of the Biofunctional Properties of Nickel–Titanium Alloys Depending on the Type of Production

Nickel–titanium alloys used in dentistry have a variety of mechanical, chemical, and biofunctional properties that are dependent on the manufacturing process. The aim of this study was to compare the mechanical and biofunctional performances of a nickel–titanium alloy produced by the continuous casting method (NiTi-2) with commercial nitinol (NiTi-1) manufactured by the classical process, i.e., from remelting in a vacuum furnace with electro-resistive heating and final casting into ingots. The chemical composition of the tested samples was analyzed using an energy dispersive X-ray analysis (EDX) and X-ray fluorescence (XRF). Electron backscatter diffraction (EBSD) quantitative microstructural analysis was performed to determine phase distribution in the samples. As part of the mechanical properties, the hardness on the surface of samples was measured with the static Vickers method. The release of metal ions (Ni, Ti) in artificial saliva (pH 6.5) and lactic acid (pH 2.3) was measured using a static immersion test. Finally, the resulting corrosion layer was revealed by means of a scanning electron microscope (SEM), which allows the detection and direct measurement of the formatted oxide layer thickness. To assess the biocompatibility of the tested nickel–titanium alloy samples, an MTT test of fibroblast cellular proliferation on direct contact with the samples was performed. The obtained data were analyzed with the IBM SPSS Statistics v22 software. EDX and XRF analyses showed a higher presence of Ni in the NiTi-2 sample. The EBSD analysis detected an additional NiTi₂-cubic phase in the NiTi-2 microstructure. Additionally, in the NiTi-2 higher hardness was measured. An immersion test performed in artificial saliva after 7 days did not induce significant ion release in either group of samples (NiTi-1 and NiTi-2). The acidic environment significantly increased the release of toxic ions in both types of samples. However, Ni ion release was two times lower, and Ti ion release was three times lower from NiTi-2 than from NiTi-1. Comparison of the cells’ mitochondrial activity between the NiTi-1 and NiTi-2 groups did not show a statistically significant difference. In conclusion, we obtained an alloy of small diameter with an appropriate microstructure and better response compared to classic NiTi material. Thus, it appears from the present study that the continuous cast technology offers new possibilities for the production of NiTi material for usage in dentistry.     

Infinite partitions of random graphs

We determine the set of canonical equivalence relations on [G]ⁿ, where G is a random graph, extending the result of Erd?s and Rado for the integers to random graphs.