Analysis of Heat And Mass Transfer and Deformation of Colloid Capillary-Porous Bodies Processes by Fractal Analysis and Discrete Nonlinear Dynamics Methods

Abstract

The fractal analysis of long-term series of parameters of colloidal capillary-porous bodies in conditions of heat and mass transfer to the environment and the resulting deformation process are presented. A fractal estimation of relevant statistical information on the moisture content, temperature and deformation of the above bodies is carried out. The algorithm for calculating the Hurst exponent is based on the R/S analysis. On the basis of the methodology for pre-predictive fractal analysis of time series (based on the sequential R/S analysis), the level of persistence is determined and the parameters (average values) of aperiodic cycles of time series are calculated. Based on smoothing of V-statistics using the ordinary moving averages and Kaufman’s adaptive moving average, the criterion for determining the average length of periodic and aperiodic cycles is proposed. The procedure of qualitative analysis of time series for which the hypothesis about the presence of a trend is not confirmed, using methods of nonlinear dynamics and chaos theory is also proposed. The real time series representative of the heat and mass transfer parameters (temperature, moisture content), stress and deformation in colloidal capillary-porous bodies (model of artistic paintings) involved in convective heat and mass transfer to their environment (premises where the museum exhibition is located) are examined; the latter also includes the artificial climate systems for museum premises and the museum visitors flow being present in this area at this time. Tuckens’s theorem is the support for such studies. The chaotic nature of the dynamical system under study, as prescribed by the time realizations, is determined with Liapunov exponent. The estimation of the persistence was evaluated using Hausdorff fractal dimension and fractal index. The visual estimation of time series was carried out using procedure for the reconstruction of phase trajectories. As a result of the phase area’s phase points analysis, a split attractor is discovered allowing to suppose its bifurcation.