The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimila... more The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations, population dynamics, etc. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualises the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations, or an interconnected network with associated long-range correlations. The model predictions are as follows: (i) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (ii) Fractals signify quantumlike chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (ii) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organisation of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.
Meteorological parameters, such as temperature, rainfall, pressure etc., exhibit selfsimilar spac... more Meteorological parameters, such as temperature, rainfall, pressure etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. The author has developed a general systems theory which predicts universal inverse powerlaw form incorporating the golden mean for the fractal fluctuations of all size scales, i.e., small, large and extreme values. The model predicted distribution is in close agreement with observed fractal fluctuations in the historic month-wise temperature (maximum and minimum) and rainfall in the UK region. The present study suggests that fractal fluctuations result from the superimposition of an eddy continuum fluctuations. The observed extreme values result from superimposition of maxima (or minima) of dominant eddies (waves) in the eddy continuum.
In an attempt to establish a relationship between surface potential gradient and rainfall in the ... more In an attempt to establish a relationship between surface potential gradient and rainfall in the monsoon rains measurements were made of these two parameters at three stations in the regions of the Western Ghats. The study indicates that while a definite conclusion in this regard is not possible, potential gradient and rainfall appear to be interdependent.
The fractal dimension of winter monsoon (October-: December) clouds over the Indian region during... more The fractal dimension of winter monsoon (October-: December) clouds over the Indian region during the 3 years 1985 to 1987 were determined from INSAT-I B cloud pictures using Lovejoy’s (1982) relationship P ~ÖAD  where , P, A and D are respectively the perimeter, area and the fractal dimension of the cloud.             The cloud study clearly indicates self-similar fractal structure to clouds of all sizes up to .the available maximum areal extent of about 5 x 106 sq km. The mean value of the fractal dimension of cloud perimeter is found to be equal to 1.30. Â
Abstract:- Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law ... more Abstract:- Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse power-law form of the power spectra of fractal space-time fluctuations is generic to the dynamical systems in nature and is identified as self-organized criticality. In this study it is shown that the power spectra of the frequency distributions of bases A, C, G, T in the Human chromosome 1 DNA exhibit self-organized criticality. DNA is a quasicrystal possessing maximum packing efficiency in a hierarchy of spirals or loops. Self-organized criticality implies that non-coding introns may not be redundant, but serve to organize the effective functioning of the coding exons in the DNA molecule as a complete unit.
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as at... more 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.
Power spectra of human DNA base C+G frequency distribution in all available contiguous sections e... more Power spectra of human DNA base C+G frequency distribution in all available contiguous sections exhibit the universal inverse power law form of the statistical normal distribution for the 24 chromosomes. Inverse power law form for power spectra of space-time fluctuations is generic to dynamical systems in nature and indicate long-range space-time correlations. A recently developed general systems theory predicts the observed non-local connections as intrinsic to quantumlike chaos governing space-time fluctuations of dynamical systems. The model predicts the following. (1) The quasiperiodic Penrose tiling pattern for the nested coiled structure of the DNA molecule in the chromosome resulting in maximum packing efficiency. (2) The DNA molecule functions as a unified whole fuzzy logic network with ordered two-way signal transmission between the coding and non-coding regions. Recent studies indicate influence of non-coding regions on functions of coding regions in the DNA molecule.
Cantorian Fractal Spacetime, Quantum-like Chaos and Scale Relativity in Atmospheric Flows
Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. The... more Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. The macroscale atmospheric flow structure behaves as a unified whole quantum system, where, the superimposition of a continuum of eddies results in the observed global weather patterns with long-range spatiotemporal correlations such as that of the widely investigated El Nino phenomenon. Large eddies are visualised as envelopes enclosing smaller eddies, thereby generating a hierarchy of eddy circulations, originating initially from a fixed primary small scale energising perturbation, e.g. the frictional upward momentum flux at the boundary layer of the earth's surface. In this paper it is shown that the relative motion concepts of Einstein's special and general theories of relativity are applicable to eddy circulations originating from a constant primary perturbation.
The frequency distribution of DNA bases A, C, G, T exhibit fractal fluctuations ubiquitous to dyn... more The frequency distribution of DNA bases A, C, G, T exhibit fractal fluctuations ubiquitous to dynamical systems in nature. The power spectra of fractal fluctuations exhibit inverse power law form signifying long-range correlations between local (small-scale) and global (large-scale) perturbations. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts that 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. The model predicted distribution is very close to statistical normal distribution for fluctuations within two standard deviations from the mean and exhibits a fat long tail. In this paper it is shown that DNA base CG frequency distribution in Takifugu rubripes (Puffer fish) Genome Release 4 exhibit universal inverse power law form consistent wit...
Universal Spectrum for Natural Variability of Climate: Implications for Climate Change
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging fro... more The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity. Self-similarity or scale invariance implies long-range spatiotemporal correlations and is manifested in atmospheric flows as the fractal geometry to spatial pattern concomitant with inverse power-law form for power spectra of temporal fluctuations. Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard meteorological theory cannot explain satisfactorily the observed self-organized criticality. Numerical models for simulation and prediction of atmospheric flows are subject to deterministic chaos and give unrealistic solutions. Deterministic chaos is a direct consequence of round-off error growth in iterative computations. Round-off error of finite precision...
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales in... more 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.
Journal of Advanced Mathematics and Applications, 2012
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space... more Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mmsec to climate scales of thousands of kilometers -years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long -range correlations identified as self -organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the selfsimilar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and incorporate basic physical concepts of nonlinear dynamics and chaos into classical meteorological theory for more realistic simulation and prediction of weather and climate. A review of nonlinear dynamics and chaos in meteorology and atmospheric physics is summarized in this paper.
Atmospheric flows exhibit self-similar fractal space-time fluctuations on all space-time scales i... more Atmospheric flows exhibit self-similar fractal space-time fluctuations on all space-time scales in association with inverse power law distribution for power spectra of meteorological parameters such as wind, temperature, etc., and thus implies long-range correlations, identified as self-organized criticality generic to dynamical systems in nature. A general systems theory based on classical statistical physical concepts developed by the author visualizes the fractal fluctuations to result from the coexistence of eddy fluctuations in an eddy continuum, the larger scale eddies being the integrated mean of enclosed smaller scale eddies. The model satisfies the maximum entropy principle and predicts that the probability distributions of component eddy amplitudes and the corresponding variances (power spectra) are quantified by the same universal inverse power law distribution which is a function of the golden mean. Atmospheric particulates are held in suspension by the vertical velocity distribution (spectrum). The atmospheric particulate size spectrum is derived in terms of the model predicted universal inverse power law characterizing atmospheric eddy spectrum. Model predicted spectrum is in agreement with the following four experimentally determined data sets: (i) CIRPAS mission TARFOX_WALLOPS_SMPS aerosol size distributions (ii) CIRPAS mission ARM-IOP (Ponca City, OK) aerosol size distributions (iii) SAFARI 2000 CV-580 (CARG Aerosol and Cloud Data) cloud drop size distributions and (iv) TWP-ICE (Darwin, Australia) rain drop size distributions.
Abstract~Geostrophic balance over the Arabian Sea and Bay of Bengal regions has been studied usin... more Abstract~Geostrophic balance over the Arabian Sea and Bay of Bengal regions has been studied using the wind data obtained from the AVRO (HS-748) aircraft during the FGGE-MONEX-79. In the Arabian Sea and the Bay of Bengal regions, the observed wind south of 20~ was found to be sub-geostrophic. In the Arabian Sea region the departure at 1500 m was 75-95~ and at 3050 m it was 60-65~. In the Bay of Bengal region the departure was 85-95~o. In a few cases north of 20~ the observed winds at 3050 m were found to be super-geostrophic in the regions of enhanced monsoon activity, cyclonic circulation reaching up to 6000 m and in the region of monsoon trough.
Characteristics of cloud drop spectra were studied using 400 samples obtained from 120 warm cumul... more Characteristics of cloud drop spectra were studied using 400 samples obtained from 120 warm cumulus clouds formed during the summer monsoon season. The total concentration of cloud drops (Nr) varied from 384 to 884 cm -3 and the maximum concentration was observed in the layer below the cloud-top. The width of the drop spectrum was broader in the cloud-base region and in the region below the cloud-top. The spectrum was multimodal at all levels except in the cloud-top region where it was unimodal. The concentration of drops with diameter greater than 50/lm (NL) varied from 0.0 to 0.674 cm-3. NL was larger in the cloud-base region. NL decreased with height up to the middle level and thereafter showed an increase. In the cloud-top region no large drops were present. The computed values of the liquid water varied between 0.132 and 0.536 g m -3 and the mean volume diameter (MVD) varied between 8.1 and 12.0 ,am. The LWC and MVD showed a decrease with height except in the middle region of the cloud where the values were higher than the adjacent levels. The dispersion of the cloud drops was lower (0.65) in the cloud-top region and higher (1.01) in the cloud-base region. The observed cloud microphysical characteristics were attributed to vertical mixing in clouds induced by the cloud-top gravity oscillations (buoyancy oscillations) generated by the intensification of turbulent eddies due to the buoyant production of energy by the microscale-fractional-condensation (MFC) in turbulent eddies.
Fractal Nature of TOGA Surface Pressure Time Series
The variability of temporal (or spatial) fluctuations of any variable is represented in conventio... more The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with increase in time(or space) resolution and for uncorrelated fluctuations dealt with in traditional statistics, is given as a linear function of Relative Dispersion at the smallest resolution and the ratio of the time resolutions.However, it is now established that temporal (or spatial) fluctuations of dynamical systems exhibit selfsimilarity or long-range correlations and traditional statistical concepts are not valid. In this paper, it is shown that resolution dependent variance is described by the fractal dimension .
Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form freque... more Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse power-law form of the power spectra of fractal space-time fluctuations is generic to the dynamical systems in nature and is identified as self-organized criticality. In this study it is shown that the power spectra of the frequency distributions of bases C+G in the Human chromosome X DNA exhibit self-organized criticality. DNA is a quasicrystal possessing maximum packing efficiency in a hierarchy of spirals or loops. Self-organized criticality implies that non-coding introns may not be redundant, but serve to organize the effective functioning of the coding exons in the DNA molecule as a complete unit.
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimila... more The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows, stock market fluctuations, population dynamics, etc. The physics of long-range correlations exhibited by fractals is not yet identified. A recently developed general systems theory visualises the eddy continuum underlying fractals to result from the growth of large eddies as the integrated mean of enclosed small scale eddies, thereby generating a hierarchy of eddy circulations, or an interconnected network with associated long-range correlations. The model predictions are as follows: (i) The probability distribution and power spectrum of fractals follow the same inverse power law which is a function of the golden mean. The predicted inverse power law distribution is very close to the statistical normal distribution for fluctuations within two standard deviations from the mean of the distribution. (ii) Fractals signify quantumlike chaos since variance spectrum represents probability density distribution, a characteristic of quantum systems such as electron or photon. (ii) Fractal fluctuations of frequency distribution of prime numbers signify spontaneous organisation of underlying continuum number field into the ordered pattern of the quasiperiodic Penrose tiling pattern. The model predictions are in agreement with the probability distributions and power spectra for different sets of frequency of occurrence of prime numbers at unit number interval for successive 1000 numbers. Prime numbers in the first 10 million numbers were used for the study.
Meteorological parameters, such as temperature, rainfall, pressure etc., exhibit selfsimilar spac... more Meteorological parameters, such as temperature, rainfall, pressure etc., exhibit selfsimilar space-time fractal fluctuations generic to dynamical systems in nature such as fluid flows, spread of forest fires, earthquakes, etc. The power spectra of fractal fluctuations display inverse power-law form signifying long-range correlations. The author has developed a general systems theory which predicts universal inverse powerlaw form incorporating the golden mean for the fractal fluctuations of all size scales, i.e., small, large and extreme values. The model predicted distribution is in close agreement with observed fractal fluctuations in the historic month-wise temperature (maximum and minimum) and rainfall in the UK region. The present study suggests that fractal fluctuations result from the superimposition of an eddy continuum fluctuations. The observed extreme values result from superimposition of maxima (or minima) of dominant eddies (waves) in the eddy continuum.
In an attempt to establish a relationship between surface potential gradient and rainfall in the ... more In an attempt to establish a relationship between surface potential gradient and rainfall in the monsoon rains measurements were made of these two parameters at three stations in the regions of the Western Ghats. The study indicates that while a definite conclusion in this regard is not possible, potential gradient and rainfall appear to be interdependent.
The fractal dimension of winter monsoon (October-: December) clouds over the Indian region during... more The fractal dimension of winter monsoon (October-: December) clouds over the Indian region during the 3 years 1985 to 1987 were determined from INSAT-I B cloud pictures using Lovejoy’s (1982) relationship P ~ÖAD  where , P, A and D are respectively the perimeter, area and the fractal dimension of the cloud.             The cloud study clearly indicates self-similar fractal structure to clouds of all sizes up to .the available maximum areal extent of about 5 x 106 sq km. The mean value of the fractal dimension of cloud perimeter is found to be equal to 1.30. Â
Abstract:- Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law ... more Abstract:- Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse power-law form of the power spectra of fractal space-time fluctuations is generic to the dynamical systems in nature and is identified as self-organized criticality. In this study it is shown that the power spectra of the frequency distributions of bases A, C, G, T in the Human chromosome 1 DNA exhibit self-organized criticality. DNA is a quasicrystal possessing maximum packing efficiency in a hierarchy of spirals or loops. Self-organized criticality implies that non-coding introns may not be redundant, but serve to organize the effective functioning of the coding exons in the DNA molecule as a complete unit.
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as at... more 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.
Power spectra of human DNA base C+G frequency distribution in all available contiguous sections e... more Power spectra of human DNA base C+G frequency distribution in all available contiguous sections exhibit the universal inverse power law form of the statistical normal distribution for the 24 chromosomes. Inverse power law form for power spectra of space-time fluctuations is generic to dynamical systems in nature and indicate long-range space-time correlations. A recently developed general systems theory predicts the observed non-local connections as intrinsic to quantumlike chaos governing space-time fluctuations of dynamical systems. The model predicts the following. (1) The quasiperiodic Penrose tiling pattern for the nested coiled structure of the DNA molecule in the chromosome resulting in maximum packing efficiency. (2) The DNA molecule functions as a unified whole fuzzy logic network with ordered two-way signal transmission between the coding and non-coding regions. Recent studies indicate influence of non-coding regions on functions of coding regions in the DNA molecule.
Cantorian Fractal Spacetime, Quantum-like Chaos and Scale Relativity in Atmospheric Flows
Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. The... more Cantorian fractal spacetime fluctuations characterize quantumlike chaos in atmospheric flows. The macroscale atmospheric flow structure behaves as a unified whole quantum system, where, the superimposition of a continuum of eddies results in the observed global weather patterns with long-range spatiotemporal correlations such as that of the widely investigated El Nino phenomenon. Large eddies are visualised as envelopes enclosing smaller eddies, thereby generating a hierarchy of eddy circulations, originating initially from a fixed primary small scale energising perturbation, e.g. the frictional upward momentum flux at the boundary layer of the earth's surface. In this paper it is shown that the relative motion concepts of Einstein's special and general theories of relativity are applicable to eddy circulations originating from a constant primary perturbation.
The frequency distribution of DNA bases A, C, G, T exhibit fractal fluctuations ubiquitous to dyn... more The frequency distribution of DNA bases A, C, G, T exhibit fractal fluctuations ubiquitous to dynamical systems in nature. The power spectra of fractal fluctuations exhibit inverse power law form signifying long-range correlations between local (small-scale) and global (large-scale) perturbations. The author has developed a general systems theory based on classical statistical physics for fractal fluctuations which predicts that 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. The model predicted distribution is very close to statistical normal distribution for fluctuations within two standard deviations from the mean and exhibits a fat long tail. In this paper it is shown that DNA base CG frequency distribution in Takifugu rubripes (Puffer fish) Genome Release 4 exhibit universal inverse power law form consistent wit...
Universal Spectrum for Natural Variability of Climate: Implications for Climate Change
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging fro... more The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity. Self-similarity or scale invariance implies long-range spatiotemporal correlations and is manifested in atmospheric flows as the fractal geometry to spatial pattern concomitant with inverse power-law form for power spectra of temporal fluctuations. Long-range spatiotemporal correlations are ubiquitous to dynamical systems in nature and are identified as signatures of self-organized criticality. Standard meteorological theory cannot explain satisfactorily the observed self-organized criticality. Numerical models for simulation and prediction of atmospheric flows are subject to deterministic chaos and give unrealistic solutions. Deterministic chaos is a direct consequence of round-off error growth in iterative computations. Round-off error of finite precision...
Dynamical systems in nature exhibit self-similar fractal space-time fluctuations on all scales in... more 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.
Journal of Advanced Mathematics and Applications, 2012
Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space... more Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mmsec to climate scales of thousands of kilometers -years and may be visualized as a nested continuum of weather cycles or periodicities, the smaller cycles existing as intrinsic fine structure of the larger cycles. The power spectra of fractal fluctuations exhibit inverse power law form signifying long -range correlations identified as self -organized criticality and are ubiquitous to dynamical systems in nature and is manifested as sensitive dependence on initial condition or 'deterministic chaos' in finite precision computer realizations of nonlinear mathematical models of real world dynamical systems such as atmospheric flows. Though the selfsimilar nature of atmospheric flows have been widely documented and discussed during the last three to four decades, the exact physical mechanism is not yet identified. There now exists an urgent need to develop and incorporate basic physical concepts of nonlinear dynamics and chaos into classical meteorological theory for more realistic simulation and prediction of weather and climate. A review of nonlinear dynamics and chaos in meteorology and atmospheric physics is summarized in this paper.
Atmospheric flows exhibit self-similar fractal space-time fluctuations on all space-time scales i... more Atmospheric flows exhibit self-similar fractal space-time fluctuations on all space-time scales in association with inverse power law distribution for power spectra of meteorological parameters such as wind, temperature, etc., and thus implies long-range correlations, identified as self-organized criticality generic to dynamical systems in nature. A general systems theory based on classical statistical physical concepts developed by the author visualizes the fractal fluctuations to result from the coexistence of eddy fluctuations in an eddy continuum, the larger scale eddies being the integrated mean of enclosed smaller scale eddies. The model satisfies the maximum entropy principle and predicts that the probability distributions of component eddy amplitudes and the corresponding variances (power spectra) are quantified by the same universal inverse power law distribution which is a function of the golden mean. Atmospheric particulates are held in suspension by the vertical velocity distribution (spectrum). The atmospheric particulate size spectrum is derived in terms of the model predicted universal inverse power law characterizing atmospheric eddy spectrum. Model predicted spectrum is in agreement with the following four experimentally determined data sets: (i) CIRPAS mission TARFOX_WALLOPS_SMPS aerosol size distributions (ii) CIRPAS mission ARM-IOP (Ponca City, OK) aerosol size distributions (iii) SAFARI 2000 CV-580 (CARG Aerosol and Cloud Data) cloud drop size distributions and (iv) TWP-ICE (Darwin, Australia) rain drop size distributions.
Abstract~Geostrophic balance over the Arabian Sea and Bay of Bengal regions has been studied usin... more Abstract~Geostrophic balance over the Arabian Sea and Bay of Bengal regions has been studied using the wind data obtained from the AVRO (HS-748) aircraft during the FGGE-MONEX-79. In the Arabian Sea and the Bay of Bengal regions, the observed wind south of 20~ was found to be sub-geostrophic. In the Arabian Sea region the departure at 1500 m was 75-95~ and at 3050 m it was 60-65~. In the Bay of Bengal region the departure was 85-95~o. In a few cases north of 20~ the observed winds at 3050 m were found to be super-geostrophic in the regions of enhanced monsoon activity, cyclonic circulation reaching up to 6000 m and in the region of monsoon trough.
Characteristics of cloud drop spectra were studied using 400 samples obtained from 120 warm cumul... more Characteristics of cloud drop spectra were studied using 400 samples obtained from 120 warm cumulus clouds formed during the summer monsoon season. The total concentration of cloud drops (Nr) varied from 384 to 884 cm -3 and the maximum concentration was observed in the layer below the cloud-top. The width of the drop spectrum was broader in the cloud-base region and in the region below the cloud-top. The spectrum was multimodal at all levels except in the cloud-top region where it was unimodal. The concentration of drops with diameter greater than 50/lm (NL) varied from 0.0 to 0.674 cm-3. NL was larger in the cloud-base region. NL decreased with height up to the middle level and thereafter showed an increase. In the cloud-top region no large drops were present. The computed values of the liquid water varied between 0.132 and 0.536 g m -3 and the mean volume diameter (MVD) varied between 8.1 and 12.0 ,am. The LWC and MVD showed a decrease with height except in the middle region of the cloud where the values were higher than the adjacent levels. The dispersion of the cloud drops was lower (0.65) in the cloud-top region and higher (1.01) in the cloud-base region. The observed cloud microphysical characteristics were attributed to vertical mixing in clouds induced by the cloud-top gravity oscillations (buoyancy oscillations) generated by the intensification of turbulent eddies due to the buoyant production of energy by the microscale-fractional-condensation (MFC) in turbulent eddies.
Fractal Nature of TOGA Surface Pressure Time Series
The variability of temporal (or spatial) fluctuations of any variable is represented in conventio... more The variability of temporal (or spatial) fluctuations of any variable is represented in conventional statistical theory by the relative dispersion equal to the standard deviation divided by the mean . The Relative Dispersion decreases with increase in time(or space) resolution and for uncorrelated fluctuations dealt with in traditional statistics, is given as a linear function of Relative Dispersion at the smallest resolution and the ratio of the time resolutions.However, it is now established that temporal (or spatial) fluctuations of dynamical systems exhibit selfsimilarity or long-range correlations and traditional statistical concepts are not valid. In this paper, it is shown that resolution dependent variance is described by the fractal dimension .
Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form freque... more Recent studies of DNA sequence of letters A, C, G and T exhibit the inverse power law form frequency spectrum. Inverse power-law form of the power spectra of fractal space-time fluctuations is generic to the dynamical systems in nature and is identified as self-organized criticality. In this study it is shown that the power spectra of the frequency distributions of bases C+G in the Human chromosome X DNA exhibit self-organized criticality. DNA is a quasicrystal possessing maximum packing efficiency in a hierarchy of spirals or loops. Self-organized criticality implies that non-coding introns may not be redundant, but serve to organize the effective functioning of the coding exons in the DNA molecule as a complete unit.
Uploads
Papers by A.M. Selvam