Signatures of quantum-like chaos in Dow Jones Index

Dow Jones Index time series exhibit irregular or fractal fluctuations on all time scales from days, months to years. The apparently irregular (nonlinear) fluctuations are selfsimilar as exhibited in inverse power law form for power spectra of temporal fluctuations. Inverse power law form for power spectra of fractal fluctuations in space or time is generic to all dynamical systems in nature and is identified as self-organized criticality. Selfsimilarity implies long-range space-time correlations or non-local connections. It is important to quantify the total pattern of fractal fluctuations for predictability studies, e.g., weather and climate prediction, stock market trends, etc. The author has developed a general systems theory for universal quantification of the observed inverse power law spectra in dynamical systems. The model predictions are as follows. (1) The power spectra of fractal fluctuations follow the universal and unique inverse power law form of the statistical normal distribution. (2) The nonlocal connections or long-range correlations in space or time exhibited by the fractal fluctuations are signatures of quantum-like chaos in dynamical systems. (3) The apparently irregular geometry of the fractal fluctuations forms the component parts of a unified whole precise geometrical pattern of the logarithmic spiral with quasiperiodic Penrose tiling pattern for the internal structure. Conventional power spectral analyses will resolve the logarithmic spiral pattern as an eddy continuum with progressive increase in eddy phase angle. (4) Continuous periodogram power spectral analyses of normalised daily, monthly and annual Dow Jones Index for the past 100-years show that the power spectra follow the universal inverse power law form of the statistical normal distribution in agreement with model prediction. The fractal fluctuations of the non-stationary Dow Jones Index time series therefore exhibit signature of quantum-like chaos on all time scales from days to years

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

This paper proposes 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. Global gridded time series data sets of monthly mean temperatures for the period 1880-2007/2008 are analysed to show that data sets and 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

Universal spectrum for DNA base C+G frequency distribution in human chromosomes 1 to 24

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

Fractal fluctuations and statistical normal distribution

Dynamical systems in nature exhibit self-similar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of self-organized criticality is not yet identified. The Gaussian probability distribution used widely for analysis and description of large data sets underestimates the probabilities of occurrence of extreme events such as stock market crashes, earthquakes, heavy rainfall, etc. The assumptions underlying the normal distribution such as fixed mean and standard deviation, independence of data, are not valid for real world fractal data sets exhibiting a scale-free power law distribution with fat tails. A general systems theory for fractals visualizes the emergence of successively larger scale fluctuations to result from the space-time integration of enclosed smaller scale fluctuations. The model predicts a universal inverse power law incorporating the golden mean for fractal fluctuations and for the corresponding power spectra, i.e., the variance spectrum represents the probabilities, a signature of quantum systems. Fractal fluctuations therefore exhibit quantum-like chaos. The model predicted inverse power law is very close to the Gaussian distribution for small-scale fluctuations, but exhibits a fat long tail for large-scale fluctuations. Extensive data sets of Dow Jones index, human DNA, Takifugu rubripes (Puffer fish) DNA are analyzed to show that the space/time data sets are close to the model predicted power law distribution

Universal spectrum for atmospheric aerosol size distribution: Comparison with PCASP-B observations of VOCALS 2008

Atmospheric flows exhibit scale-free fractal fluctuations. A general systems theory based on classical statistical physical concepts 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 predicts (i) the eddy energy (variance) spectrum and corresponding eddy amplitude probability distribution are quantified by the same universal inverse power law distribution incorporating the golden mean. (ii) The steady state ordered hierarchical growth of atmospheric eddy continuum is associated with maximum entropy production. (iii) atmospheric particulate size spectrum is derived in terms of the model predicted universal inverse power law for atmospheric eddy energy spectrum. Model predictions are in agreement with observations. Universal inverse power law for power spectra of fractal fluctuations rules out linear secular trends in meteorological parameters. Global warming related climate change, if any, will be manifested as intensification of fluctuations of all scales manifested immediately in high frequency fluctuations. The universal aerosol size spectrum presented in this paper may be computed for any location with two measured parameters, namely, the mean volume radius and the total number concentration and may be incorporated in climate models for computation of radiation budget of earth-atmosphere system

Universal spectrum for interannual variability in COADS global air and sea-surface temperatures

Continuous periodogram spectral analyses of 28 years (1961-1988) of seasonal (September-November) mean COADS global surface (air and sea) temperature time-series show that the power spectra follow the universal inverse power law form of the statistical normal distribution. An inverse power law form for power spectra of temporal fluctuations implies long-range temperal correlation and is a signature of self-organized criticality. Universal quantification for self-organized criticality presented in this paper is consistent with a recently developed cell dynamical system model for atmospheric flows, which predicts such non-local connections as intrinsic to quantum-like mechanis governing flow dynamics. -from Author

A numerical technique for simulation of cloud seeding experiments

Two numerical cloud seeding experiments, using historic rainfall for the Deccan plateau region in Maharashtra state, were performed adopting different simulation techniques. The data used consisted of 1-day total rainfall for the 5-year period 1951-55. A double-area cross-over design with area randomisation was adopted. The first experiment, EXP-TR, was based on the simulation technique of Twomey and Robertson which involves about 100 hr of Robotron EC-1040 computer time. The second experiment, EXP-MMM was based on a different simulation technique proposed in the present study. The results of EXP-TR and EXP-MMM have shown close agreement. The numerical simulation technique of EXP-MMM is more promising for the following two reasons: (i) the computational time is reduced by about an order of magnitude without compromising the scientific value of the results, and (ii) a direct estimate of the lower limit of the double ratio value which can be detected at 5 level of significance is defined. The results of the two numerical experiments suggested that, for the Deccan plateau region, 15 and 20 increases in rainfall due to seeding could be detected with 80 or more probability in 5 years

Numercial simulation of cloud seeding experiments in Maharashtra state, India

Two numerical cloud seeding simulation experiments of 5-, 8- and 10-years duration, with a double area cross-over design and area randomization, were performed using historic rainfall data for the Deccan plateau region in Maharashtra state. The first numerical experiment (EXP-TR) used the simulation technique of Twomey and Roberstson (1973), second (EXP-MMM) used different simulation technique proposed in the present study. The results of the two numerical experiments have agreed closely. The EXP-MMM technique not only reduces computational time by an order of magnitude but also defines the exact lower limit for the double ration value which can be detected at 5 per cent level of significance. The results of the numerical experiments suggest that 15 and 20 percent increases in rainfall due to seeding in Maharashtra could be detected, with 80 percent or more probability, in 5 years. In a 10-year experiment the probabilities of detecting 5 and 10 percent increases in rainfall due to seeding are 27 and 65 percent, respectivel

Experimental investigation of the influence of electric field on the collision - coalescence of water drops

Laboratory experiments were conducted on the collision-coalescence of pairs of water drops of equal size, in two oil media (kerosene and mustard), with and without external vertical electric field (F). The radii of the water drops used were in the range 1.6 to 1.7 mm and the external electric field varied from 0 to 375 V cm-'. Collision frequencies were determined for various combinations of mean lateral (X)a nd mean vertical (Z) separations of the drop pairs as fixed combinations of X and Z could not be reproduced in any given set of experiments due to the limitations of the mechanical set up of the apparatu

Dynamic responses of warm monsoon clouds to salt seeding

High resolution temperature measurements during single-level air- craft penetrations through warm monsoon clouds before and after salt seeding had a significant wave-length of about 2 km. The slope of the spectra relating to not-seeded traverses followed a -5/3 power law. The slope of the spectra relating to seeded traverses increased when liquid water content increased and rain formed. The temperature spectra of the seeded traverses showed a net energy gain in the larger wave-lengths ( >540 m) and a net energy loss in the shorter wavelengths. The net-energy gain could be due to condensation of water vapor on the salt parti- cles, the net energy loss to the decrease in the small scale turbulence resulting from the invigoration of the updraft. These features could be manifestations of the alteration of the dynamics of the cloud through salt seeding