Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Interaction of various variants of the nanostructured surface of titanium with mscs isolated from adipose tissue

Titanium has been successfully used in dental implantology for a long time. Due to the osseointegration process, titanium implants are able to withstand the chewing load. This article is devoted to the study of surface treatment methods of titanium alloys and the study of their interaction with mesenchymal stem cells (MSCs). The surface microrelief can influence MSC differentiation in different ways, which subsequently gives it osteogenic potential. The paper proposes modes of surface modification of titanium alloys on Grade 4 and Grade 1 by chemical and electrochemical (anodizing) etching. The possibility of modifying the surface of titanium alloys using the synthesis of graphene layers has been proposed in this paper for the first time. The osteogenic potential of a particular surface was assessed by the number of mesenchymal stem cells cultured on them under identical conditions. © 2021 by the authors. Licensee MDPI, Basel, Switzerland