THE SOLAR-TERRESTRIAL RELATIONSHIP USING FRACTAL DIMENSION

Sun is the main source of energy for the earth and other planets. Its activity in one or other way influences the terrestrial climate. Particularly, the solar activity manifested in the form of sunspots is found to be much more influential on the earth’s climate and on its magnetosphere. Links of the variability in terrestrial climate and sunspot cycles and associated magnetic cycles have been the concern of many recent studies. These two time series data sunspots and K-index are distributed into 22-year cycles, according to the magnetic field of the sun in which polarity reverses after 11-years. The fractal dimension of each sunspot cycle from 1 to 24 is calculated and found to be quasi-regular (persistent, [Formula: see text]). To understand the regular effects of the dynamics of sunspot cycles on the earth’s climate and magnetosphere, the sunspot cycles and K-index cycles (22 years each) from 1932 to 2014 are observed and discussed comparatively in the perspective of fractal dimension and Hurst exponent.

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Solitary potential structures observed in the magnetosheath by the Cluster spacecraft

Nonlinear Processes in Geophysics ◽

10.5194/npg-10-3-2003 ◽

2003 ◽

Vol 10 (1/2) ◽

pp. 3-11 ◽

Cited By ~ 67

Author(s):

J. S. Pickett ◽

J. D. Menietti ◽

D. A. Gurnett ◽

B. Tsurutani ◽

P. M. Kintner ◽

...

Keyword(s):

Magnetic Field ◽

Time Series Data ◽

Broad Band ◽

Low Frequency ◽

Bow Shock ◽

Local Magnetic Field ◽

Series Data ◽

The Individual ◽

Almost All ◽

The Magnetic Field

Abstract. Bipolar pulses of ~ 25-100 µs in duration have been observed in the wave electric field data obtained by the Wideband plasma wave instrument on the Cluster spacecraft in the dayside magnetosheath. These pulses are similar in almost all respects to those observed on several spacecraft over the last few years. They represent solitary potential structures, and in this case, electron phase space holes. When the time series data containing the bipolar pulses on Cluster are transformed to the frequency domain by a windowed FFT, the pulses appear as typical broad-band features, extending from the low-frequency cutoff of the bandpass filter, ~ 1 kHz, up to as great as 20-40 kHz in some cases, with decreasing intensity as the frequency increases. The upper frequency cutoff of the broad band is an indication of the individual pulse durations (1/f). The solitary potential structures are detected when the local magnetic field is contained primarily in the spin plane, indicating that they propagate along the magnetic field. Their frequency extent and intensity seem to increase as the angle between the directions of the magnetic field and the plasma flow decreases from 90°. Of major significance is the finding that the overall profile of the broad-band features observed simultaneously by two Cluster spacecraft, separated by a distance of over 750 km, are strikingly similar in terms of onset times, frequency extent, intensity, and termination. This implies that the generation region of the solitary potential structures observed in the magnetosheath near the bow shock is very large and may be located at or near the bow shock, or be connected with the bow shock in some way.

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FRACTAL ANALYSIS OF DIFFERENT EASTERN AND WESTERN MUSICAL INSTRUMENTS

Fractals ◽

10.1142/s0218348x06003192 ◽

2006 ◽

Vol 14 (03) ◽

pp. 165-170 ◽

Cited By ~ 7

Author(s):

ATIN DAS ◽

PRITHA DAS

Keyword(s):

Time Series ◽

Spectral Analysis ◽

Fractal Dimension ◽

Time Series Data ◽

Musical Instruments ◽

Series Data ◽

Data Sets ◽

Different Types ◽

Frequency Regime ◽

Musical Sounds

In this paper, we attempt musical analysis by measuring fractal dimension (D) of musical pieces played by several musical instruments. We collected solo performances of popular instruments of Western and Eastern origin as samples. We attempted usual spectral analysis of the selected clips to observe peaks of fundamental and harmonics in frequency regime. After appropriate processing, we converted them into time series data sets and computed their fractal dimension. Based on our results, we conclude that instrumental musical sounds may have higher Ds than those computed from vocal performances of different types of Indian songs.

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Sonification of Astronomical Data

Proceedings of the International Astronomical Union ◽

10.1017/s1743921312000440 ◽

2011 ◽

Vol 7 (S285) ◽

pp. 133-136 ◽

Cited By ~ 5

Author(s):

Wanda L. Diaz-Merced ◽

Robert M. Candey ◽

Nancy Brickhouse ◽

Matthew Schneps ◽

John C. Mannone ◽

...

Keyword(s):

Solar Wind ◽

Time Series Data ◽

Solar Wind Plasma ◽

Series Data ◽

Astronomical Data ◽

X Ray ◽

The Earth ◽

Polar Type ◽

Mass Ejection ◽

The Impact

AbstractThis document presents Java-based software called xSonify that uses a sonification technique (the adaptation of sound to convey information) to promote discovery in astronomical data. The prototype is designed to analyze two-dimensional data, such as time-series data. We demonstrate the utility of the sonification technique with examples applied to X-ray astronomy and solar data. We have identified frequencies in the Chandra X-Ray observations of EX Hya, a cataclysmic variable of the intermediate polar type. In another example we study the impact of a major solar flare, with its associated coronal mass ejection (CME), on the solar wind plasma (in particular the solar wind between the Sun and the Earth), and the Earth's magnetosphere.

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Potensi dan Tantangan Pengembangan Sektor Unggulan di Kalimantan Barat

Jurnal Ekonomi Bisnis dan Kewirausahaan ◽

10.26418/jebik.v5i2.17142 ◽

2016 ◽

Vol 5 (2) ◽

pp. 94

Author(s):

Dinarjad Achmad

Keyword(s):

Time Series ◽

Water Supply ◽

Time Series Data ◽

Water Area ◽

Primary Objective ◽

Series Data ◽

West Kalimantan ◽

The Earth ◽

Descriptive Method ◽

Land Water

The primary objective of this study was to analyze the potential and challenges of superior sectordevelopment in West Kalimantan. Superior sectors here interpreted as a sector that producesgoods that can be exported. Descriptive method and time series data for 7 years (2007- 2013) wasused as the tools and materials to perform the analysis.The results showed that the based on ofnatural resources (land, water area and the river, fill the earth) and geography, West Kalimantanhave a greater potential for superior sector development, but there are several challenges to thedevelopment potential of the superior sector, including: (1) resource human (HR) is still weak.(2) Infrastructure (electricity, gas and water supply, road and port export) are limited. (3)Marketing and networking is still weak

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Can the Artificial Heart Make the Circulation Become Fractal?

The International Journal of Artificial Organs ◽

10.1177/039139889501800403 ◽

1995 ◽

Vol 18 (4) ◽

pp. 190-196 ◽

Cited By ~ 10

Author(s):

T. Yambe ◽

S. Nanka ◽

S. Naganuma ◽

S. Kobayashi ◽

H. Akiho ◽

...

Keyword(s):

Blood Pressure ◽

Time Series ◽

Fractal Dimension ◽

Artificial Heart ◽

Time Series Data ◽

Series Data ◽

Hemodynamic Parameters ◽

Arterial Blood ◽

Dimension Analysis ◽

Fractal Dimension Analysis

In order to analyze the hemodynamic parameters in prosthetic circulation as an entity and not as decomposed parts, non linear mathematical analyzing techniques, including the fractal dimension analyzing theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted, as biventricular bypasses (BVB), in chronic animal experiments, using four healthy adult goats. For the comparison between the natural and prosthetic circulation in the same animals, the BVB type complete prosthetic circulation model with ventricular fibrillation, was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions, and calculated with a personal computer system. Using the non-linear mathematical technique, the arterial blood pressure waveform was embedded into the return map as the beat-to-beat time series data and fractal dimension analysis were performed to analyze the reconstructed attractor. By the use of the Box counting method, fractal dimension analysis of the hemodynamics was performed. Return map of the hemodynamics during natural and artificial circulation showed fractal characteristics, and fractal dimension analysis of the arterial blood pressure revealed the fact that lower dimensional fractal dynamics were evident during prosthetic circulation. Fractal time series data is suggested to have robustness and error resistance, thus our results suggest that the circulatory regulatory system with an artificial heart may have these desired characteristics.

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EFFECT OF OUTLIERS ON THE FRACTAL DIMENSION ESTIMATION

Fractals ◽

10.1142/s0218348x11005324 ◽

2011 ◽

Vol 19 (02) ◽

pp. 233-241

Author(s):

SHAPOUR MOHAMMADI

Keyword(s):

Fractal Dimension ◽

Stock Prices ◽

Time Series Data ◽

Estimation Method ◽

Estimation Methods ◽

Series Data ◽

Data Series ◽

Box Dimension ◽

Dimension Estimation ◽

Stochastic Data

The effect of outliers on estimation of the fractal dimension of experimental chaotic and stock market stochastic data series is investigated. The results indicate that influential observations of a magnitude of mean ±5 standard deviations can lead to a distortion of fractal dimension estimations by as much as 40% for short (e.g. 500 observations) time series data. Moreover, the box dimension estimation method is more sensitive to outliers than information and correlation dimension estimation methods and the effect of outliers decreases as the number of observations increases. Application of outlier adjustment to the stock prices of 60 companies of the Dow Jones Industrial Index reveals that the effect of outliers is critical in estimating the fractal dimension. The fractal dimension has applications in risk analysis for financial markets that can be affected by outliers.

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A Novel Method for a COVID-19 Classification of Countries Based on an Intelligent Fuzzy Fractal Approach

Healthcare ◽

10.3390/healthcare9020196 ◽

2021 ◽

Vol 9 (2) ◽

pp. 196

Author(s):

Oscar Castillo ◽

Patricia Melin

Keyword(s):

Time Series ◽

Fuzzy Logic ◽

Fractal Dimension ◽

Fuzzy System ◽

Time Series Data ◽

Hybrid Approach ◽

Series Data ◽

Theoretical Concepts ◽

Fractal Approach

We outline in this article a hybrid intelligent fuzzy fractal approach for classification of countries based on a mixture of fractal theoretical concepts and fuzzy logic mathematical constructs. The mathematical definition of the fractal dimension provides a way to estimate the complexity of the non-linear dynamic behavior exhibited by the time series of the countries. Fuzzy logic offers a way to represent and handle the inherent uncertainty of the classification problem. The hybrid intelligent approach is composed of a fuzzy system formed by a set of fuzzy rules that uses the fractal dimensions of the data as inputs and produce as a final output the classification of countries. The hybrid approach calculations are based on the COVID-19 data of confirmed and death cases. The main contribution is the proposed hybrid approach composed of the fractal dimension definition and fuzzy logic concepts for achieving an accurate classification of countries based on the complexity of the COVID-19 time series data. Publicly available datasets of 11 countries have been the basis to construct the fuzzy system and 15 different countries were considered in the validation of the proposed classification approach. Simulation results show that a classification accuracy over 93% can be achieved, which can be considered good for this complex problem.

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The Long-term structural effect of Coronal index solar activity on the ENSO and QBO Time series data using Fractal Dimension

Punjab University Journal of Mathematics ◽

10.52280/pujm.2021.530205 ◽

2021 ◽

pp. 149-163

Author(s):

Muhammad Fahim Akhter

Keyword(s):

Time Series ◽

Fractal Dimension ◽

Solar Activity ◽

Long Memory ◽

Time Series Data ◽

Southern Oscillation ◽

Research Work ◽

Inverse Correlation ◽

Series Data ◽

Quasi Biennial Oscillation

The study concentrated on the fractal dimension of solar activity and climatic parameters. We analyzed comparatively for each parameter numerically. All values are estimated by Box Counting technique of fractal dimension. According to the theme of study, we used a monthly dataset of Coronal Mass Ejection (Coronal Index (CI)), ElNino Southern Oscillation (ENSO) and Quasi-Biennial Oscillation (QBO) from 1954 to 2016. The time seriesof ENSO and QBO are distributed according to the CORONAL INDEX (CI) cycles (19, 20, 21, 22, 23, and 24) to understand their relationship in the perspective of persistence or anti-persistence.The fractal dimension(D) represents the complexity and Hurst exponent(H) indicates the long memory dependence of the selected time series, with scaling constant (a, c). The results obtained indicate the persistence (1 < D < 1.5) for CORONAL INDEX (CI) with distributed ENSO and QBO cycles. The fractional Brownian motion (fBm) is also found long memory dependence(1¿H¿ 0.5) and locally lowpass signal for all studied cycles observed.A linear relationship implies between Hurst coefficient and fractal dimension for a statistical assumption (H + D = 2).The fractal scaling instrument is established between the global indices (ENSO & QBO) and solar activity (particularly CORONAL INDEX (CI)) cycles,the inverse correlation with ENSO and direct with QBO are observed. The results obtained in this research work may help to describe the solar-terrestrial relationship

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The effect of source field polarization on estimates of the magnetotelluric impedance tensor

Geophysics ◽

10.1190/1.1441067 ◽

1980 ◽

Vol 45 (12) ◽

pp. 1803-1812 ◽

Cited By ~ 2

Author(s):

Barry R. Lienert

Keyword(s):

Time Series Data ◽

Noise Source ◽

Series Data ◽

Impedance Tensor ◽

Source Field ◽

Magnetic Source ◽

Polarization Characteristics ◽

The Magnetic Field ◽

East West ◽

Maximum Minimum

A technique is described which can be used to estimate magnetotelluric impedances using magnetic source fields having predetermined polarization characteristics. The technique involves digital filtering of the time‐series data, followed by estimates of the amplitudes and phases of single cycles, utilizing a simple “maximum/minimum” approach. The resulting impedance estimates are at least as consistent as estimates obtained using the more usual fast Fourier transform and bandwidth averaging technique. When magnetic source field amplitudes are subdivided into groups on the basis of their polarization directions, diagonal elements of the impedance tensors determined from individual groups show an upward bias. We interpret this as due to instability in solutions for the impedances which occurs when magnetic source fields are highly polarized. In addition, one of the tensor elements shows a consistent upward bias when the magnetic field is polarized predominantly in the east‐west direction. Since we observe this latter effect at three separate sites, we suggest that it may be due to either a noise source which is polarized in the east‐west direction, or to the assumption of vertical incidence not holding for horizontal magnetic source fields which are polarized in the east‐west sense.

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Earth’s albedo time series reveals low radiative energy input in December 2020

10.21203/rs.3.rs-677927/v1 ◽

2021 ◽

Author(s):

Antti Penttilä ◽

Karri Muinonen ◽

Olli Ihalainen ◽

Elizaveta Uvarova ◽

Mikko Vuori ◽

...

Keyword(s):

Time Series ◽

Time Series Data ◽

Radiative Energy ◽

Series Data ◽

Radiation Balance ◽

The Sun ◽

The Earth ◽

Important Input ◽

Low Earth Orbits ◽

Earth Orbits

Abstract The Earth’s spherical albedo describes the ratio of light reflected from the Earth to that incident from the Sun, an important input variable for the Earth’s radiation balance. The spherical albedo has been previously estimated from satellites in low-Earth orbits, and from light reflected from the Moon. However, neither of these methods can produce continuous time series of the entire planet. We developed a global method to derive the Earth’s spherical albedo using the images from the Earth Polychromatic Imaging Camera (EPIC) on board NOAA’s Deep Space Climate Observatory (DSCOVR). The satellite is located in the Lagrange 1 point between the Earth and the Sun and observes the complete illuminated part of the Earth at once. The method allows us to provide continuously updated spherical albedo time series data starting from 2015. This time series shows a systematic seasonal variation with the mean annual albedo estimated as 0.295±0.008 and an exceptional albedo maximum in 2020, attributed to unusually abundant cloudiness over the Southern Oceans.

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