The fluctuation spectroscopy based on the scaling properties of beta-distribution: Analysis of triple pendulum data

© 2014 Elsevier Ltd. All rights reserved. A new method of consideration and reduced analysis of long-time series is suggested. The method is based on the scaling (fractal) properties of the beta-distribution function that allows finding the stable parameters and reducing the long-time series containing 5 × 105-106 data points to analysis of 10-20 stable parameters. The new procedure of clusterization with the usage of the generalized Pearson correlation function allows to take into account the influence of external factor and combine/separate different parameters into a cluster with respect to the influence of the qualitative external parameter considered. The method is rather flexible and can be applied to wide set of large data. As an example the triple pendulum data are considered. This method opens new possibilities in creation of the reduced database (specific fingerprints) of different long-time series for their comparison and subsequent analysis

Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

In this paper we apply a new method of analysis of random behavior of chaotic systems based on the Prony decomposition. The generalized Prony spectrum (GPS) is used for quantitative description of a wide class of random functions when information about their probability distribution function is absent. The scaling properties of the random functions that keep their invariant properties on some range of scales help to fit the compressed function based on the Prony's decomposition. In paper [1] the first author (RRN) found the physical interpretation of this decomposition that includes the conventional Fourier decomposition as a partial case. It has been proved also that the GPS can be used for detection of quasi-periodic processes that are appeared usually in the repeated or similar measurements. A triple physical pendulum is used as a chaotic system to obtain a chaotic behavior of displacement angles with one, two and three positive Lyapunov's exponents (LEs). The chaotic behavior of these angles can be expressed in the form of amplitude-frequency response (AFR) that is extracted from the corresponding GPS and can serve as a specific "fingerprint" characterizing the random behavior of the triple-pendulum system studied. This new quantitative presentation of random data opens additional possibilities in classification of chaotic responses and random behaviors of different complex systems. © 2014 Versita Warsaw and Springer-Verlag Wien

Foam-Mat Freeze-Drying of Blueberry Juice by Using Trehalose-β-Lactoglobulin and Trehalose-Bovine Serum Albumin as Matrices

This study aimed to evaluate the effect of pure protein compounds and trehalose incorporated into blueberry juice for foam-mat freeze-drying on the foam and powder properties. Foam-mat freeze-drying (FMFD) of blueberry juice was tested at − 55 °C for 24 h. Matrices used were trehalose + β-lactoglobulin (T3BL1) and trehalose + bovine serum albumin (T3A1) and compared with maltodextrin + whey protein isolate (M3W1). Physicochemical properties of foam and powder, e.g., foam stability, foam density, moisture, rehydration time, color, particle morphology, total phenolic, and anthocyanins (total and individuals), were investigated. T3BL1 and T3A1 had more stable foam than M3W1. However, overrun of T3BL1 and T3A1 foamed were inferior to the M3W1 sample. The M3W1 sample recovered 79% powder (dry weight) and was superior to others. Rehydration time of powdered T3BL1 and T3A1, with bulk densities of 0.55–0.60 g cm−3, was the fastest (34–36 s). The blueberry powders of M3W1 showed more irregular particle size and shape, while the samples with trehalose and pure proteins generated particles of more uniform size with obvious pores. T3BL1 and T3A1 showed less redness (a*) values than the M3W1 product. All samples were considered pure red due to hue values < 90. M3W1 was superior in total phenolic content (TPC) and total monomeric anthocyanins (TMA) compared with both samples made with trehalose + β-lactoglobulin and trehalose+bovine serum albumin. Delphinidin-3-glucoside (Del3Gl) concentration was found to be higher in M3W1. Also, M3W1 had higher cyanidin-3-glucoside (Cyn3Gl) and malvidin-3-glucoside (Mal3Gl) concentration. M3W1 also prevented the degradation of these bioactive compounds better than the other FMFD samples. The use of pure proteins and trehalose as matrices in the FMFD process had little advantage compared with maltodextrin/whey protein isolate. Thus, maltodextrin/whey protein isolate seems an ideal matrix for the manufacture of FMFD blueberry

A smooth model of the resultant friction force on a plane contact area

A class of smooth approximations of the total friction force occurring on a plane finite contact surface is presented. It is assumed that the classical Coulomb friction law is valid on any infinitesimal element of the contact region. The models describe the stick phase, the fully developed sliding and the transition between these two modes. They take into account different values of static and dynamic friction coefficients. The models are applied in simulation of a dynamical system performing translational and rotational stick-slip oscillations, and then they are verified by comparison with the corresponding results in which an event-driven discontinuous model of friction is used

Celtic Stone Dynamics Revisited Using Dry Friction and Rolling Resistance

The integral model of dry friction components is built with assumption of classical Coulomb friction law and with specially developed model of normal stress distribution coupled with rolling resistance for elliptic contact shape. In order to avoid a necessity of numerical integration over the contact area at each the numerical simulation step, few versions of approximate model are developed and then tested numerically. In the numerical experiments the simulation results of the Celtic stone with the friction forces modelled by the use of approximants of different complexity (from no coupling between friction force and torque to the second order Padé approximation) are compared to results obtained from model with friction approximated in the form of piecewise polynomial functions (based on the Taylor series with hertzian stress distribution). The coefficients of the corresponding approximate models are found by the use of optimization methods, like as in identification process using the real experiment data