This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resis...This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resist frame （MRF）, and validates the approach with shaking table tests. The time frequency feature （TFF） of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension （FD） is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1：8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.展开更多
In order to develop a new diagnostic method for partial epilepsy using fractaldimension measurement of theory of nonlinear dynamics, two kinds of EEG fractaldimensions (correlation dimension Dc and wave form dimension...In order to develop a new diagnostic method for partial epilepsy using fractaldimension measurement of theory of nonlinear dynamics, two kinds of EEG fractaldimensions (correlation dimension Dc and wave form dimension Dw) were calculatedand compared. It was observed that most of the EEG fractal dimension values of Dcand Dw at the epileptic electrodes were smaller than those at the non-epilepticelectrodes. The results showed that the fractal dimension could be a special parameterto diagnose epilepsy diseases and are worthy to study further.展开更多
A major concern in modern smart-phones and hand-held devices is a way of mitigating the time interval error (TIE) perceived at high-speed digital transits along the traces of the circuit-board (rigid and or flexible) ...A major concern in modern smart-phones and hand-held devices is a way of mitigating the time interval error (TIE) perceived at high-speed digital transits along the traces of the circuit-board (rigid and or flexible) used in baseband infrastructures. Indicated here is a way of adopting a planar fractal inductor configuration to improvise the necessary time-delay in the transits of digital signal phase jitter and reduce the TIE. This paper addresses systematic design considerations on fractal inductor geometry commensurate with practical aspects of its implementation as delaylines in the high-speed digital transports at the baseband operations of smart-phone infrastructures. Experimental results obtained from a test module are presented to illustrate the efficacy of the design and acceptable delay performance of the test structure commensurate with the digital transports of interest.展开更多
In the light of fractal geometry theory, the characteristics of coal's electric parameters (including dielectric constant, alternating conductivity, dielectric loss angle tangent and electric polarization constant...In the light of fractal geometry theory, the characteristics of coal's electric parameters (including dielectric constant, alternating conductivity, dielectric loss angle tangent and electric polarization constant) were studied by using literature data. The results are shown that the electrical properties of coal have fractal characteristic. The fractal dimensions of dielectric, alternating conductivity, dielectric loss angle tangent were obtained, and are relative to the content of pyrite sulfur, heat and ash content of coal.展开更多
The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three differen...The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods： the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.展开更多
Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the r...Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.展开更多
Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range ...Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.展开更多
At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynam...At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.展开更多
An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a...An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.展开更多
基金National Natural Science Foundation under Grant No.51161120359Ministry of Education under Grant No.20112302110050Special Fund for Earthquake Scientific Research in the Public Interest under Grant No.201308003
文摘This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resist frame （MRF）, and validates the approach with shaking table tests. The time frequency feature （TFF） of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension （FD） is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1：8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.
文摘In order to develop a new diagnostic method for partial epilepsy using fractaldimension measurement of theory of nonlinear dynamics, two kinds of EEG fractaldimensions (correlation dimension Dc and wave form dimension Dw) were calculatedand compared. It was observed that most of the EEG fractal dimension values of Dcand Dw at the epileptic electrodes were smaller than those at the non-epilepticelectrodes. The results showed that the fractal dimension could be a special parameterto diagnose epilepsy diseases and are worthy to study further.
文摘A major concern in modern smart-phones and hand-held devices is a way of mitigating the time interval error (TIE) perceived at high-speed digital transits along the traces of the circuit-board (rigid and or flexible) used in baseband infrastructures. Indicated here is a way of adopting a planar fractal inductor configuration to improvise the necessary time-delay in the transits of digital signal phase jitter and reduce the TIE. This paper addresses systematic design considerations on fractal inductor geometry commensurate with practical aspects of its implementation as delaylines in the high-speed digital transports at the baseband operations of smart-phone infrastructures. Experimental results obtained from a test module are presented to illustrate the efficacy of the design and acceptable delay performance of the test structure commensurate with the digital transports of interest.
基金Supported by Key Project of Chinese National Programs for Fundamental Research Development(973 Project 2005CB221502)
文摘In the light of fractal geometry theory, the characteristics of coal's electric parameters (including dielectric constant, alternating conductivity, dielectric loss angle tangent and electric polarization constant) were studied by using literature data. The results are shown that the electrical properties of coal have fractal characteristic. The fractal dimensions of dielectric, alternating conductivity, dielectric loss angle tangent were obtained, and are relative to the content of pyrite sulfur, heat and ash content of coal.
基金supported by the Eleventh Five-Year Key Technology R and D Program,China(Grant No.2006BAC02A15)the Colleges and Universities in Jiangsu Province Natural Science-Based Research Projects(Grant No.2006BAC02A15)+1 种基金the Jiangsu Province Post-Doctoral Fund Projects(Grant No.0801006C)the China Post-Doctoral Science Foundation(Grant No.20080441032)
文摘The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods： the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.
基金Project supported by NNSF of China (10371092)Foundation of Wuhan University
文摘Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.
基金Project supported by the National Natural Science Foundation of China (Grant No.11071282)the Chinese Program for New Century Excellent Talents in University (Grant No.NCET-08-06867)
文摘Multifractal detrended fluctuation analysis （MF-DFA） is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis （DFA）, which was developed for detecting the long-range correlation and the fractal properties in stationary and non-stationary time series. Although MF-DFA has become a widely used method, some relationships among the exponents established in the original paper seem to be incorrect under the general situation. In this paper, we theoretically and experimentally demonstrate the invalidity of the expression r（q） = qh（q） - 1 stipulating the relationship between the multifractal exponent T（q） and the generalized Hurst exponent h（q）. As a replacement, a general relationship is established on the basis of the universal multifractal formalism for the stationary series as .t-（q） = qh（q） - qH - 1, where H is the nonconservation parameter in the universal multifractal formalism. The singular spectra, a and f（a）, are also derived according to this new relationship.
文摘At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.
文摘An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.
