Radiation piezoelectric effect

Kikoin, I.K.; Kikoin, L.I.; Lasarev, S.D.

doi:10.1016/0375-9601(76)90349-2

“…Kinetic theory of ideal gases is a study of systems consisting of a great number of molecules, which are considered as bodies having a small size and mass [33] . Classical statistical methods of investigation [33][34][35][36][37][38][39][40] are employed to estimate average values of quantities characterizing aggregate molecular motion such as mean velocity, mean energy etc., which determine the macro-scale characteristics of gases.…”

Section: General Systems Theory and Classical Statistical Physicsmentioning

confidence: 99%

“…Classical statistical methods of investigation [33][34][35][36][37][38][39][40] are employed to estimate average values of quantities characterizing aggregate molecular motion such as mean velocity, mean energy etc., which determine the macro-scale characteristics of gases. The mean properties of ideal gases are calculated with the following assumptions.…”

Section: General Systems Theory and Classical Statistical Physicsmentioning

confidence: 99%

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Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies

Selvam

¹

2011

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Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is not completely understood. It is important to quantify the physics underlying the irregular fractal fluctuations for prediction of space-time evolution of dynamical systems. A general systems theory for fractals visualising the emergence of successively larger scale fluctuations resulting from the space-time integration of enclosed smaller scale fluctuations is proposed. The theoretical model predictions are: (i) The probability distribution and the power spectrum for fractal fluctuations is the same inverse power law function incorporating the golden mean. (ii) The predicted distribution is close to the Gaussian distribution for small-scale fluctuations but exhibits fat long tail for large-scale fluctuations with higher probability of occurrence than predicted by Gaussian distribution. (iii) Since the power spectrum (variance, i.e., square of eddy amplitude) also represents the probability densities as in the case of quantum systems such as the electron or photon, fractal fluctuations exhibit quantumlike chaos. (iv) The fine structure constant for spectrum of fractal fluctuations is a function of the golden mean and is analogous to atomic spectra equal to about 1/137. Global gridded time series data sets of monthly mean temperatures for the period 1880 -2007/2008 were analysed. The data sets and the corresponding power spectra exhibit distributions close to the model predicted inverse power law distribution. The model predicted and observed universal spectrum for interannual variability rules out linear secular trends in global monthly mean temperatures. Global warming results in intensification of fluctuations of all scales and manifested immediately in high frequency fluctuations.Key words Fractals and statistical normal distribution, power law distributions, longrange correlations and fat tail distributions, golden mean and fractal fluctuations

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“…In classical statistical physics kinetic theory of ideal gases is a study of systems consisting of a great number of molecules, which are considered as bodies having a small size and mass [33] ( Kikoin and Kikoin, 1978). Classical statistical methods of investigation [33][34][35][36][37][38][39][40] ( Kikoin and Kikoin, 1978;Dennery, 1972;Yavorsky and Detlaf, 1975;Rosser, 1985;Guenault, 1988;Gupta, 1990;Dorlas, 1999;Chandrasekhar, 2000) are employed to estimate average values of quantities characterizing aggregate molecular motion such as mean velocity, mean energy etc., which determine the macro-scale characteristics of gases.…”

Section: General Systems Theory and Classical Statistical Physicsmentioning

confidence: 99%

“…Classical statistical methods of investigation [33][34][35][36][37][38][39][40] ( Kikoin and Kikoin, 1978;Dennery, 1972;Yavorsky and Detlaf, 1975;Rosser, 1985;Guenault, 1988;Gupta, 1990;Dorlas, 1999;Chandrasekhar, 2000) are employed to estimate average values of quantities characterizing aggregate molecular motion such as mean velocity, mean energy etc., which determine the macro-scale characteristics of gases. The mean properties of ideal gases are calculated with the following assumptions.…”

Section: General Systems Theory and Classical Statistical Physicsmentioning

confidence: 99%

Universal Inverse Power-Law Distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter-Annual Variability of Indian and USA Region Rainfall

Selvam

¹

2016

Pure Appl. Geophys.

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Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales indicating long-range correlations and therefore the statistical normal distribution with implicit assumption of independence, fixed mean and standard deviation cannot be used for description and quantification of fractal data sets. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts the following. (i) The fractal fluctuations signify an underlying eddy continuum, the larger eddies being the integrated mean of enclosed smaller-scale fluctuations. (ii) The probability distribution of eddy amplitudes and the variance (square of eddy amplitude) spectrum of fractal fluctuations follow the universal Boltzmann inverse power law expressed as a function of the golden mean. (iii) Fractal fluctuations are signatures of quantum-like chaos since the additive amplitudes of eddies when squared represent probability densities analogous to the subatomic dynamics of quantum systems such as the photon or electron. (iv) The model predicted distribution is very close to statistical normal distribution for moderate events within two standard deviations from the mean but exhibits a fat long tail that are associated with hazardous extreme events. Continuous periodogram power spectral analyses of available GHCN annual total rainfall time series for the period 1900 to 2008 for Indian and USA stations show that the power spectra and the corresponding probability distributions follow model predicted universal inverse power law form signifying an eddy continuum structure underlying the observed inter-annual variability of rainfall. Global warming related atmospheric energy input will result in intensification of fluctuations of all scales and can be seen immediately in high frequency (shortterm) fluctuations such as devastating floods/droughts resulting from excess/deficit annual, quasi-biennial and other shorter period (years) rainfall cycles.

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Signatures of Universal Characteristics of Fractal Fluctuations in Global Mean Monthly Temperature Anomalies

Selvam¹

2017

Springer Atmospheric Sciences

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Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is not completely understood. It is important to quantify the physics underlying the irregular fractal fluctuations for prediction of space-time evolution of dynamical systems. A general systems theory for fractals visualising the emergence of successively larger scale fluctuations resulting from the space-time integration of enclosed smaller scale fluctuations is proposed. The theoretical model predictions are: (i) The probability distribution and the power spectrum for fractal fluctuations is the same inverse power law function incorporating the golden mean. (ii) The predicted distribution is close to the Gaussian distribution for small-scale fluctuations but exhibits fat long tail for large-scale fluctuations with higher probability of occurrence than predicted by Gaussian distribution. (iii) Since the power spectrum (variance, i.e., square of eddy amplitude) also represents the probability densities as in the case of quantum systems such as the electron or photon, fractal fluctuations exhibit quantumlike chaos. (iv) The fine structure constant for spectrum of fractal fluctuations is a function of the golden mean and is analogous to atomic spectra equal to about 1/137. Global gridded time series data sets of monthly mean temperatures for the period 1880 -2007/2008 were analysed. The data sets and the corresponding power spectra exhibit distributions close to the model predicted inverse power law distribution. The model predicted and observed universal spectrum for interannual variability rules out linear secular trends in global monthly mean temperatures. Global warming results in intensification of fluctuations of all scales and manifested immediately in high frequency fluctuations.Key words Fractals and statistical normal distribution, power law distributions, longrange correlations and fat tail distributions, golden mean and fractal fluctuations followed by decrease on all scales (space-time), for example in atmospheric flows, cycles of increase and decrease in meteorological parameters such as wind, temperature, etc. occur from the turbulence scale of millimeters-seconds to climate scales of thousands of kilometers-years. The power spectra of fractal fluctuations exhibit inverse power law of the form f - where f is the frequency and  is a constant. Inverse power law for power spectra indicate long-range space-time correlations or scale invariance for the scale range for which  is a constant, i.e., the amplitudes of the eddy fluctuations in this scale range are a function of the scale factor  alone. In general the value of  is different for different scale ranges indicating multifractal structure for the fluctuations. The long-range space-time correlations exhibited by dynamical systems are identified as self-organized criticality [2][3] . The physics of selforganized ...

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Radiation piezoelectric effect

Cited by 32 publications

References 0 publications

Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies

Signatures of universal characteristics of fractal fluctuations in global mean monthly temperature anomalies

Universal Inverse Power-Law Distribution for Fractal Fluctuations in Dynamical Systems: Applications for Predictability of Inter-Annual Variability of Indian and USA Region Rainfall

Signatures of Universal Characteristics of Fractal Fluctuations in Global Mean Monthly Temperature Anomalies

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