Cross-Correlations in the Brownian Motion of Colloidal Nanoparticles

2020 ◽  
Vol 65 (1-2) ◽  
pp. 27-34
Author(s):  
Sz. Kelemen ◽  
◽  
L. Varga ◽  
Z. Néda ◽  
◽  
...  
Keyword(s):  
Brownian Motion ◽  
Power Law ◽  
Cross Correlation ◽  
Colloidal Particles ◽  
Pearson Correlation ◽  
Transverse Component ◽  
Collective Effects ◽  
Colloidal Nanoparticles ◽  
Diffusive Motion ◽  
Cross Correlations

"The two-body cross-correlation for the diffusive motion of colloidal nano-spheres is experimentally investigated. Polystyrene nano-spheres were used in a very low concentration suspension in order to minimize the three- or more body collective effects. Beside the generally used longitudinal and transverse component correlations we investigate also the Pearson correlation in the magnitude of the displacements. In agreement with previous studies we find that the longitudinal and transverse component correlations decay as a function of the inter-particle distance following a power-law trend with an exponent around -2. The Pearson correlation in the magnitude of the displacements decay also as a power-law with an exponent around -1. Keywords: colloidal particles, Brownian motion, cross-correlation. "

MODELING CROSS-CORRELATIONS OF TRAFFIC FLOW

2010 ◽  
Vol 20 (10) ◽  
pp. 3323-3328 ◽  
Author(s):  
PENGJIAN SHANG ◽  
KEQIANG DONG ◽  
SANTI KAMAE
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Power Law ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Fluctuation Analysis ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Large Increment ◽  
Active Research

The study of diverse natural and nonstationary signals has recently become an area of active research for physicists. This is because these signals exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails and fractality. The focus of the present paper is on the intriguing power-law autocorrelations and cross-correlations in traffic series. Detrended Cross-Correlation Analysis (DCCA) is used to study the traffic flow fluctuations. It is demonstrated that the time series, observed on the Anhua-Bridge highway in the Beijing Third Ring Road (BTRR), may exhibit power-law cross-correlations when they come from two adjacent sections or lanes. This indicates that a large increment in one traffic variable is more likely to be followed by large increment in the other traffic variable. However, for traffic time series derived from nonadjacent sections or lanes, we find that even though they are power-law autocorrelated, there is no cross-correlation between them with a unique exponent. Our results show that DCCA techniques based on Detrended Fluctuation Analysis (DFA) can be used to analyze and interpret the traffic flow.

scholarly journals Dynamic Cross-Correlations between Participants’ Attentions to P2P Lending and Offline Loan in the Private Lending Market

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yingxiu Zhao ◽  
Wei Zhang ◽  
Xiangyu Kong
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Cross Correlation ◽  
Granger Causality Test ◽  
Short Term ◽  
Causality Test ◽  
Cross Correlation Analysis ◽  
Private Lending ◽  
P2p Lending ◽  
Cross Correlations

In this paper, we examine the dynamic cross-correlations between participants’ attentions to the P2P lending and offline loan (lending) with the method of multifractal detrended cross-correlation analysis (MF-DCCA). The empirical result mainly shows that (1) the power-law cross-correlation exists between participants’ attentions to the P2P lending and offline loan and is persistent, (2) the cross-correlation is more stable in the short term, and (3) the relation subjected to a small fluctuation is more cross-correlated than that under larger ones. Furthermore, we carry out the robustness test to verify the result. The Granger causality test indicates that participants’ attentions to P2P lending and offline loan Granger cause each other in the short term.

EFFECT OF LINEAR AND NONLINEAR FILTERS ON MULTIFRACTAL DETRENDED CROSS-CORRELATION ANALYSIS

Fractals ◽  
2011 ◽  
Vol 19 (04) ◽  
pp. 443-453 ◽  
Author(s):  
JIE SONG ◽  
PENGJIAN SHANG
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Cross Correlation ◽  
Influence Factors ◽  
Nonlinear Filters ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Linear And Nonlinear ◽  
The Cross ◽  
Correlation Properties

When probing the dynamical properties of complex systems, such as physical and physiological systems, the output signal may be not the expected one. It is often a linear or nonlinear filter (or a transformation) of the right one represented the properties we want to investigate. Besides, for a multiple-component system, it is necessary to consider the relations between different influence factors. Here, we investigate what effect kinds of linear and nonlinear filters have on the cross-correlation properties of monofractal series and binomial multifractal series relatively. We use the multifractal detrended cross-correlation analysis (MFDCCA) that has been known well for its accurate quantization of cross-correlations between two time series. We study the effect of five filters: (i) linear (yi = axi + b); (ii) polynomial [Formula: see text]; (iii) logarithmic (yi = log (xi + δ)); (iv) exponential (yi = exp (axi + b)); and (v) power-law (yi = (xi + a)b). We find that for both monofractal and multifractal signals, linear filters have no effect on the cross-correlation properties while the influence of polynomial, logarithmic and power-law filters mainly depends on (a) the strength of cross-correlations in the original series; (b) the parameter b of the polynomial filter; (c) the offset δ in the logarithmic filter; and (d) both the parameter a and b of the power-law filter. In addition, the parameter a and b of the exponential filter change the cross-correlation properties of monofractal signal, yet they have little influence on that of multifractal signal.

scholarly journals Detrended Multiple Cross-Correlation Coefficient applied to solar radiation, air temperature and relative humidity

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Andrea de Almeida Brito ◽  
Heráclio Alves de Araújo ◽  
Gilney Figueira Zebende
Keyword(s):  
Relative Humidity ◽  
Solar Radiation ◽  
Solar Energy ◽  
Correlation Coefficient ◽  
Air Temperature ◽  
Cross Correlation ◽  
Global Solar Radiation ◽  
Meteorological Variables ◽  
Hourly Data ◽  
Cross Correlations

AbstractDue to the importance of generating energy sustainably, with the Sun being a large solar power plant for the Earth, we study the cross-correlations between the main meteorological variables (global solar radiation, air temperature, and relative air humidity) from a global cross-correlation perspective to efficiently capture solar energy. This is done initially between pairs of these variables, with the Detrended Cross-Correlation Coefficient, ρDCCA, and subsequently with the recently developed Multiple Detrended Cross-Correlation Coefficient, $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2. We use the hourly data from three meteorological stations of the Brazilian Institute of Meteorology located in the state of Bahia (Brazil). Initially, with the original data, we set up a color map for each variable to show the time dynamics. After, ρDCCA was calculated, thus obtaining a positive value between the global solar radiation and air temperature, and a negative value between the global solar radiation and air relative humidity, for all time scales. Finally, for the first time, was applied $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}$$DMCx2 to analyze cross-correlations between three meteorological variables at the same time. On taking the global radiation as the dependent variable, and assuming that $${\boldsymbol{DM}}{{\boldsymbol{C}}}_{{\bf{x}}}^{{\bf{2}}}={\bf{1}}$$DMCx2=1 (which varies from 0 to 1) is the ideal value for the capture of solar energy, our analysis finds some patterns (differences) involving these meteorological stations with a high intensity of annual solar radiation.

POWER LAW AND STRETCHED EXPONENTIAL EFFECTS OF EXTREME EVENTS IN CHINESE STOCK MARKETS

2010 ◽  
Vol 09 (02) ◽  
pp. 203-217 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
YULEI PANG
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Extreme Events ◽  
Stock Markets ◽  
Cross Correlation ◽  
Extreme Values ◽  
Cumulative Distribution ◽  
Stretched Exponential ◽  
Cross Correlation Analysis ◽  
Chinese Stock Markets

This paper reports the statistics of extreme values and positions of extreme events in Chinese stock markets. An extreme event is defined as the event exceeding a certain threshold of normalized logarithmic return. Extreme values follow a piecewise function or a power law distribution determined by the threshold due to a crossover. Extreme positions are studied by return intervals of extreme events, and it is found that return intervals yield a stretched exponential function. According to correlation analysis, extreme values and return intervals are weakly correlated and the correlation decreases with increasing threshold. No long-term cross-correlation exists by using the detrended cross-correlation analysis (DCCA) method. We successfully introduce a modification specific to the correlation and derive the joint cumulative distribution of extreme values and return intervals at 95% confidence level.

scholarly journals Network Analysis of Cross-Correlations on Forex Market during Crises. Globalisation on Forex Market

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 352
Author(s):  
Janusz Miśkiewicz
Keyword(s):  
Time Series ◽  
Network Analysis ◽  
Exchange Rates ◽  
Power Law ◽  
Financial Crises ◽  
Classification Scheme ◽  
Significant Growth ◽  
Cross Correlations

Within the paper, the problem of globalisation during financial crises is analysed. The research is based on the Forex exchange rates. In the analysis, the power law classification scheme (PLCS) is used. The study shows that during crises cross-correlations increase resulting in significant growth of cliques, and also the ranks of nodes on the converging time series network are growing. This suggests that the crises expose the globalisation processes, which can be verified by the proposed analysis.

Auto and Cross Correlation Measurements in a Turbine Cascade Using a Digital Correlator

1982 ◽  
Author(s):  
P. J. Bryanston-Cross ◽  
J. J. Camus
Keyword(s):  
Mach Number ◽  
High Speed ◽  
Cross Correlation ◽  
Turbine Blades ◽  
Image Plane ◽  
Strongly Correlated ◽  
Trailing Edge ◽  
Number Range ◽  
Cross Correlations ◽  
Digital Correlator

A simple technique has been developed which samples the dynamic image plane information of a schlieren system using a digital correlator. Measurements have been made in the passages and in the wakes of transonic turbine blades in a linear cascade. The wind tunnel runs continuously and has independently variable Reynolds and Mach number. As expected, strongly correlated vortices were found in the wake and trailing edge region at 50 KHz. Although these are strongly coherent we show that there is only limited cross-correlation from wake to wake over a Mach no. range M = 0.5 to 1.25 and variation of Reynolds number from 3 × 105 to 106. The trailing edge fluctuation cross correlations were extended both upstream and downstream and preliminary measurements indicate that this technique can be used to obtain information on wake velocity. The vortex frequency has also been measured over the same Mach number range for two different cascades. The results have been compared with high speed schlieren photographs.

Assessing Convergence in Predictions of Periodic-Unsteady Flowfields

2006 ◽  
Author(s):  
J. P. Clark ◽  
E. A. Grover
Keyword(s):  
Cross Correlation ◽  
Unsteady Flows ◽  
Digital Signal ◽  
Design Decisions ◽  
Time Resolved ◽  
Design Engineers ◽  
Cross Correlations ◽  
Parseval’S Theorem ◽  
Hot Streak

Predictions of time-resolved flowfields are now commonplace within the gas-turbine industry, and the results of such simulations are often used to make design decisions during the development of new products. Hence it is necessary for design engineers to have a robust method to determine the level of convergence in design predictions. Here we report on a method developed to determine the level of convergence in a predicted flowfield that is characterized by periodic-unsteadiness. The method relies on fundamental concepts from digital signal processing including the discrete Fourier transform, cross-correlation, and Parseval’s theorem. Often in predictions of vane-blade interaction in turbomachines, the period of the unsteady fluctuations is expected. In this method, the development of time-mean quantities. Fourier components (both magnitude and phase), cross-correlations, and integrated signal power are tracked at locations of interest from one period to the next as the solution progresses. Each of these separate quantities yields some relative measure of convergence that is subsequently processed to form a fuzzy set. Thus the overall level of convergence in the solution is given by the intersection of these sets. Examples of the application of this technique to several predictions of unsteady flows from two separate solvers are given. These include a prediction of hot-streak migration as well as more typical cases. It is shown that the method yields a robust determination of convergence. Also, the results of the technique can guide further analysis and/or post-processing of the flowfield. Finally, the method is useful for the detection of inherent unsteadiness in the flowfield, and as such it can be used to prevent design escapes.

scholarly journals Cross-Correlations in Meat Prices in Brazil: A Non-Linear Approach Using Different Time Scales

Economies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 133
Author(s):  
Derick Quintino ◽  
José Telo da Gama ◽  
Paulo Ferreira
Keyword(s):  
Time Scales ◽  
Cross Correlation ◽  
Positive Association ◽  
Recent Period ◽  
Linear Approach ◽  
Long Run ◽  
Short Run ◽  
Cross Correlations ◽  
Over Time ◽  
Different Time Scales

Brazil is one of the world’s largest producers and exporters of cattle, chicken and swine. Therefore, co-movements of Brazilian meat prices are important for both domestic and foreign stakeholders. We propose to analyse the cross-correlation between meat prices in Brazil, namely, cattle, swine and chicken, including also in the analysis information from some commodities, namely maize, soya beans, oil, and the Brazilian exchange rate. Our sample covers the recent period which coincided with extensive macroeconomic and institutional changes in Brazil, from 2011 to 2020, and is divided in two periods: (i) presidential pre-impeachment (P1), occurring in August 2016, and; (ii) post-impeachment (P2). Our results indicate that in P1, only the prices of swine and chicken showed a positive and strong correlation over time, and that cattle showed some positive correlation with chicken only in the short run. In P2, there was also a positive and consistent correlation between swine and chicken, and only a positive association with swine and cattle in the long run. For more spaced time scales (days), the changes in the degree of correlation were significant only in the long run for swine and cattle.

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