A quantitative nonequilibrium phase transition theory for analyzing the turbulence development process

In this paper, a quantitative nonequilibrium multi-dimensional phase transition theory is proposed for describing the turbulence spectrum (energy E with wave number k and scaling index [Formula: see text]) of the turbulence development process by a fold catastrophe model. Each of the control variables in this catastrophe model is subtly expressed into a relative multi-parameter multiplication, and then the state variable can be quantitatively described by these parameters. By using this nonequilibrium phase transition theory, the quantitative relationship in the process of turbulence formation can be strictly derived through dimensionless analysis. Therefore, the turbulence development process can be described with respect to a scaling index [Formula: see text], in which there exists an energy containing range with −1.12 power law (E [Formula: see text] k[Formula: see text]) when [Formula: see text] varies from −2 to −1.2, and an inertial subrange with −1.69 power law (E [Formula: see text] k[Formula: see text]) that is almost identical with the famous Kolmogorov’s −5/3 power law when [Formula: see text] varies from −1.2 to −0.8, and then the dissipation range with −2.52 power law (E [Formula: see text] k[Formula: see text]) when [Formula: see text] varies from −0.8 to 0. Furthermore, this quantitative nonequilibrium phase transition theory has been verified by the corresponding theoretical comparison and experiment. This theory provides not only a new understanding of turbulence, but also a new perspective for other complex nonequilibrium phase transitions.

Application of an Improved Correlation Method in Electrostatic Gait Recognition of Hemiparetic Patients

Hemiparesis is one of the common sequelae of neurological diseases such as strokes, which can significantly change the gait behavior of patients and restrict their activities in daily life. The results of gait characteristic analysis can provide a reference for disease diagnosis and rehabilitation; however, gait correlation as a gait characteristic is less utilized currently. In this study, a new non-contact electrostatic field sensing method was used to obtain the electrostatic gait signals of hemiplegic patients and healthy control subjects, and an improved Detrended Cross-Correlation Analysis cross-correlation coefficient method was proposed to analyze the obtained electrostatic gait signals. The results show that the improved method can better obtain the dynamic changes of the scaling index under the multi-scale structure, which makes up for the shortcomings of the traditional Detrended Cross-Correlation Analysis cross-correlation coefficient method when calculating the electrostatic gait signal of the same kind of subjects, such as random and incomplete similarity in the trend of the scaling index spectrum change. At the same time, it can effectively quantify the correlation of electrostatic gait signals in subjects. The proposed method has the potential to be a powerful tool for extracting the gait correlation features and identifying the electrostatic gait of hemiplegic patients.

ALONG THE EVOLUTION PROCESS KLEIBER'S 3/4 LAW MAKES WAY FOR RUBNER'S SURFACE LAW: A FRACTAL APPROACH

Rubner 1880 surface law reveals that the basal metabolic rate scales with body mass raised to the power of 2/3, which is geometrically correct and biologically relevant. However, Kleiber 1932 scaling law experimentally found that the scaling index was 3/4 instead of 2/3. There is no theory that can explain the Kleiber's data, explanations in Science in 1997 and later in Nature in 2002 for 3/4 scaling law for all life were apparently wrong. Here we show that Rubner's surface law was approximately correct, and it requires modification due to the fact that a cell is porous. Using fractal theory, the scaling index is about 0.7, 0.73, and 0.83, respectively, for inactive, active and motion statuses, and Kleiber's exponent can be fully explained by Rubner's law.

Detrended fluctuation analysis in a simple spreadsheet as a tool for teaching fractal physiology

Fractal physiology demonstrated growing interest over the last decades among physiologists, neuroscientists, and clinicians. Many physiological systems coordinate themselves for reducing variability and maintain a steady state. When recorded over time, the output signal exhibits small fluctuations around a stable value. It is becoming increasingly clear that these fluctuations, in most free-running healthy systems, are not simply due to uncorrelated random errors and possess interesting properties, one of which is the property of fractal dynamics. Fractal dynamics model temporal processes in which similar patterns occur across multiple timescales of measurement. Smaller copies of a pattern are nested within larger copies of the pattern, a property termed scale invariance. It is an intriguing process that may deserve attention for implementing curricular development for students to reconsider homeostasis. Teaching fractal dynamics needs to make calculating resources available for students. The present paper offers a calculating resource that uses a basic formula and is executable in a simple spreadsheet. The spreadsheet allows computing detrended fluctuation analysis (DFA), the most frequently used method in the literature to quantify the fractal-scaling index of a physiological time series. DFA has been nicely described by the group at Harvard that designed it; the authors made the C language source available. Going further, it is suggested here that a guide to build DFA step by step in a spreadsheet has many advantages for teaching fractal physiology and beyond: 1) it promotes the DIY (do-it-yourself) in students and highlights scaling concepts; and 2) it makes DFA available for people not familiarized with executing code in C language.

Multi-frequency scatter-broadening evolution of pulsars

In this paper, we present our study on multi-frequency scatter-broadening observations of a large sample of pulsars, made using the Ooty Radio Telescope (ORT) and the Giant Metrewave Radio Telescope (GMRT). For each pulsar, the scatter-broadening time scales (τsc) have been estimated at different observing frequencies and the dependence of τsc with the observing frequency, i.e., the frequency scaling index (α) has been obtained. We report estimates of α for a set of 39 pulsars, of which 31 are completely new and provide the first-time measurement on about 50% of the sample. This enhanced sample suggests that almost 65% of the pulsars have an α much lower than the conventional value of 4.4 for a Kolmogorov type turbulence spectrum, and a considerably large scattering strength. An increase in scattering strength is observed with the distance to the pulsar in the Galaxy.

The Application of Detrended Fluctuation Analysis in Rice Blast in the Early Warning

In this paper, the 5-9 months of 2000-2011 temperature and humidity data, used the detrended fluctuation analysis, obtained how the two data series’ non-uniform scaling index changes with time. In order to comprehensive influence of temperature and relative humidity of the two meteorological factors, the temperature and humidity coefficient is introduced. We also proposed a new non-uniform scaling index taking into account the information of temperature and relative humidity, and discusses the possible correlation between temperature and humidity and rice blast. The preliminary results show, A long-range power-law correlation can be found in the time series of temperature and humidity. About 5-15 days before the occurrence of rice blast will appear anomalies of non-uniform scaling index. It reflects the rice blast made a difference of statistical significance to the characteristic of nonlinear system internal of temperature and humidity coefficient. It can predict the occurrence and prevalence of rice blast according to the abnormal changes of temperature and humidity coefficient scaling exponent.