IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document compares the statistical properties of solar flares and earthquakes by analyzing event energy distributions, time series, and interevent times from solar flare and earthquake catalogs. It finds that the two phenomena exhibit different scaling statistics, and the same phenomenon observed in different periods or locations cannot be uniformly scaled to a single distribution. This suggests an apparent complexity in impulsive energy release processes that does not follow a common behavior attributable to a universal physical mechanism.
Computation of Lyapunov Exponent for Characterizing the Dynamics of Earthquakeijrap
Earthquakes forecasting and prediction is a global challenge, several precursors and methods of
earthquake prediction have been proposed, but lack consistency and are not reliable for prediction hence
occurrence of earthquakes is sometimes assumed to be random. This study was designed to investigate and
characterise the occurrence of earthquakes using chaos theory. The Lyapunov Exponent and its spectrum
were obtained from earthquake data using modified two dimensional system method from Sprott’s
procedures. The results show that the values of the Lyapunov exponent were positive but the magnitude
varies for all regions considered and the Lyapunov exponent spectrum exhibit an asymptotic behaviour in
all the regions.This study showed that although seismicity exhibit apparent randomness but earthquake
occurrence is not stochastic but a non-linear deterministic dynamical process.
This document discusses the statistical distributions of earthquake recurrence times and introduces a technique to analyze sequences of microearthquakes (microrepeaters). It specifically:
1) Discusses commonly used distributions like Weibull and log-normal to model recurrence times and introduces a rescaling technique to combine multiple microrepeater sequences to establish larger data sets.
2) Applies this technique to analyze recurrence times of microrepeater sequences from California and Japan.
3) Finds that when sequences are sufficiently stationary, the recurrence times can be well fitted by Weibull or log-normal distributions, demonstrating these distributions may also apply to characteristic earthquakes on major faults.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the
temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and
temperature field are studied in detail with the aid of graphs.
Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical
gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on
their motion in the Minkowski space on the world lines is determined. The expression for the field intensity
and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates
and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.
Nonclassical Properties of Even and Odd Semi-Coherent StatesIOSRJAP
Even and odd semi-coherent states have been introduced. Some of the nonclasscial properties of the states are studied in terms of the quadrature squeezing as well as sub-Poissonian photon statistics. The Husimi– Kano Q-function and the phase distribution in the framework of Pegg and Barnett formalism, are also discussed.
Non-Darcy Convective Heat and Mass Transfer Flow in a Vertical Channel with C...IJERA Editor
In this paper, We made an attempt to study thermo-diffusion and dissipation effect on non-Darcy convective
heat and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with Radiation and
heat sources. The governing equations of flow, heat and mass transfer are solved by using regular perturbation
method with δ, the porosity parameter as a perturbation parameter. The velocity, temperature, concentration,
shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document compares the statistical properties of solar flares and earthquakes by analyzing event energy distributions, time series, and interevent times from solar flare and earthquake catalogs. It finds that the two phenomena exhibit different scaling statistics, and the same phenomenon observed in different periods or locations cannot be uniformly scaled to a single distribution. This suggests an apparent complexity in impulsive energy release processes that does not follow a common behavior attributable to a universal physical mechanism.
Computation of Lyapunov Exponent for Characterizing the Dynamics of Earthquakeijrap
Earthquakes forecasting and prediction is a global challenge, several precursors and methods of
earthquake prediction have been proposed, but lack consistency and are not reliable for prediction hence
occurrence of earthquakes is sometimes assumed to be random. This study was designed to investigate and
characterise the occurrence of earthquakes using chaos theory. The Lyapunov Exponent and its spectrum
were obtained from earthquake data using modified two dimensional system method from Sprott’s
procedures. The results show that the values of the Lyapunov exponent were positive but the magnitude
varies for all regions considered and the Lyapunov exponent spectrum exhibit an asymptotic behaviour in
all the regions.This study showed that although seismicity exhibit apparent randomness but earthquake
occurrence is not stochastic but a non-linear deterministic dynamical process.
This document discusses the statistical distributions of earthquake recurrence times and introduces a technique to analyze sequences of microearthquakes (microrepeaters). It specifically:
1) Discusses commonly used distributions like Weibull and log-normal to model recurrence times and introduces a rescaling technique to combine multiple microrepeater sequences to establish larger data sets.
2) Applies this technique to analyze recurrence times of microrepeater sequences from California and Japan.
3) Finds that when sequences are sufficiently stationary, the recurrence times can be well fitted by Weibull or log-normal distributions, demonstrating these distributions may also apply to characteristic earthquakes on major faults.
Effects of Hall and thermal on MHD Stokes’ second problem for unsteady second...IJERA Editor
In this paper, we investigated the combined effects of Hall and thermal on MHD Stokes’ second problem for
unsteady second grade fluid flow through porous medium. The expressions for the velocity field and the
temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and
temperature field are studied in detail with the aid of graphs.
Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical
gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on
their motion in the Minkowski space on the world lines is determined. The expression for the field intensity
and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates
and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.
Nonclassical Properties of Even and Odd Semi-Coherent StatesIOSRJAP
Even and odd semi-coherent states have been introduced. Some of the nonclasscial properties of the states are studied in terms of the quadrature squeezing as well as sub-Poissonian photon statistics. The Husimi– Kano Q-function and the phase distribution in the framework of Pegg and Barnett formalism, are also discussed.
Non-Darcy Convective Heat and Mass Transfer Flow in a Vertical Channel with C...IJERA Editor
In this paper, We made an attempt to study thermo-diffusion and dissipation effect on non-Darcy convective
heat and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with Radiation and
heat sources. The governing equations of flow, heat and mass transfer are solved by using regular perturbation
method with δ, the porosity parameter as a perturbation parameter. The velocity, temperature, concentration,
shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.
Validity Of Principle Of Exchange Of Stabilities Of Rivilin- Ericksen Fluid...IRJET Journal
This document presents research on establishing the validity of the Principle of Exchange of Stabilities (PES) for thermal convection of a Rivlin-Ericksen fluid layer in porous medium heated from below with variable gravity. The fluid layer contains suspended particles and is subjected to rotation. The linearized stability equations are formulated using an operator method. It is established that PES is valid for this problem under sufficient conditions, when the gravity field g(z) is nonnegative throughout the fluid layer. This is done by analyzing the resolvent of the linearized stability operator as a composition of integral operators and applying the method of positive operators to show the system has a single greatest eigenvalue.
Machiwal, D. y Jha, MK (2012). Modelado estocástico de series de tiempo. En A...SandroSnchezZamora
This document provides an overview of stochastic modelling and different stochastic processes that are commonly used, including:
- Purely random (white noise) processes where data points are independent and identically distributed
- Autoregressive (AR) processes where each data point is modeled as a linear combination of previous data points plus noise
- Moving average (MA) processes where each data point is modeled as a linear combination of previous noise terms plus a constant
- Autoregressive moving average (ARMA) processes which combine AR and MA processes
- Autoregressive integrated moving average (ARIMA) processes which explicitly include differencing to make time series stationary
The use of Cellular Automata is extended in various disciplines for the modeling of complex system procedures. Their inherent simplicity and their natural parallelism make them a very efficient tool for the simulation of large scale physical phenomena. We explore the framework of Cellular Automata to develop a physically based model for the spatial and temporal prediction of shallow landslides. Particular weight is given to the modeling of hydrological processes in order to investigate the hydrological triggering mechanisms and the importance of continuous modeling of water balance to detect timing and location of soil slips occurrences. Specifically, the 3D flow of water and the resulting water balance in the unsaturated and saturated zone is modeled taking into account important phenomena such as hydraulic hysteresis and evapotranspiration. In this poster the hydrological component of the model will be presented and tested against well established benchmark experiments [Vauclin et al, 1975; Vauclin et al, 1979]. Furthermore, we investigate the applicability of incorporating it in a hydrological catchment model for the prediction (temporal and spatial) of rainfall-triggered shallow landslides.
Disc dark matter_in_the_galaxy_and_potential_cycles_of_extraterrestrial_impac...Sérgio Sacani
This document discusses potential periodic cycles of extraterrestrial impacts, mass extinctions, and geological events on Earth. It proposes that:
1) Mass extinctions and impact cratering may exhibit cycles of around 26-30 million years that could be linked to the Sun's vertical oscillations through the Galactic plane around every 30-42 million years.
2) Near the Galactic plane, comets in the Oort Cloud could be perturbed by Galactic tidal forces and a possible thin dark matter disc, producing periodic comet showers and impacts on Earth linked to extinction events.
3) Records of geological events like tectonism and volcanism also show a potential cycle of around 30 million years that could be linked to the
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail.
This document proposes a modification to the Gutenberg-Richter law to describe the cumulative distribution of earthquake magnitudes using concepts from nonextensive statistical mechanics. It introduces a new "q-stretched exponential" form for the modified Gutenberg-Richter law and fits this form to seismic data from California and Iran. The empirical data fits extremely well with the proposed modification over the entire range of magnitudes. Nonextensive statistical mechanics is applied to derive a q-exponential distribution for the surface size of fragments produced during earthquakes. A new hypothetical relationship is also proposed between the surface size of fragments and the released energy.
This document discusses the distribution of slip along earthquake faults based on analyses of five major earthquake slip models. It finds that the distribution follows a piecewise Gutenberg-Richter law, with different b-values above and below a transition point. For smaller slips, b is near 1, while for larger slips b is greater than 1. It analyzes the slip distributions using rank-ordering analysis to overcome data limitations. This verifies the existence of power laws with different scaling constants in the two slip regimes identified.
This document discusses methods for calculating the standard error of the b-value parameter in the Gutenberg-Richter magnitude-frequency relationship. It presents two key formulas:
1) For large samples where b can be treated as constant over time, the standard error of b is given by σ(b) = 2.30b2/√n, where n is the sample size and σ2(M) is the sample variance of magnitudes.
2) When b varies slowly over time, its standard error has two components - the time-averaged variance of b at different times, plus the variance of the mean b averaged over the entire time period.
The document also provides tables to determine confidence intervals for
Comparison of the FE/FE and FV/FE treatment of fluid-structure interactionIJERA Editor
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Five-Dimensional Cosmological Model with Time-Dependent G and Lamda for Const...IOSR Journals
In this paper we have consider five-dimensional cosmological model in presence of perfect fluid
source with time dependent G and .The Einstein field equations are solvable with the help of constant
deceleration parameter. Physical and kinematical properties of this model are investigated. It has been shown
that the solutions are comparable with recent observations. The behavior of gravitational constant,
cosmological constant, density, critical density and pressure is discussed for dust, radiation dominated and stiff matter of the Universe. It is also examined the behavior of gravitational constant and cosmological constant for expansion law and exponential law for stiff matter
Using resonant ultrasound spectroscopy (RUS), the author will determine the complete elastic constant matrices of two thermoelectric single crystal samples, Ce.75Fe3CoSb12 and CeFe4Sb12. RUS involves measuring the resonant frequencies of a sample's vibrations, which depend on the sample's elastic constants, shape, orientation, and density. The author aims to obtain the elastic moduli from a single RUS spectrum for each sample. Understanding the elastic properties may help identify better thermoelectric materials by correlating low elastic stiffness with low thermal conductivity and higher thermoelectric efficiency. The author will compute the resonant frequencies using the samples' properties and compare to measurements.
A Markov Chain Approach on Daily Rainfall Occurrenceijtsrd
Markov modeling is one of the tools that can be used to help planners for assess precipitation. The first order Markov chain model was used to predict daily precipitation intervals using transition probability matrices. The demand for precipitation is increasing, not only for data invention, but also to provide useful information in numerous applications, including water properties organization and the hydrological and agricultural subdivisions. In this study, the objective is to predict the probability of future precipitation of the city of Pyin Oo Lwin using the Markov chain model. The system was developed on the basis of the Markov method to forecast the occurrence of precipitation. The results show that models can forecast the state of a given day by 74 on average. Phyu Thwe | Ei Khaing Win | Hnin Pwint Myu Wai "A Markov Chain Approach on Daily Rainfall Occurrence" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd28075.pdf Paper URL: https://www.ijtsrd.com/computer-science/data-miining/28075/a-markov-chain-approach-on-daily-rainfall-occurrence/phyu-thwe
1) The document discusses the maximum likelihood estimator of b-value for mainshocks versus all events.
2) It shows that mainshocks do not entirely satisfy the Gutenberg-Richter law since their magnitude distribution depends on factors other than b-value alone.
3) Analyzing earthquake data from southern California, it demonstrates that the commonly used maximum likelihood estimator produces a statistically insignificant difference between b-values for mainshocks and all events when a more appropriate estimator is used that accounts for the non-exponential distribution of mainshock magnitudes.
This document summarizes a study that analyzes earthquake statistics in a mean-field model of a heterogeneous fault zone. The model examines the interplay between disorder, dynamical effects, and driving mechanisms. It finds a two-parameter phase diagram depending on the amplitude of dynamical weakening effects and the normal distance of driving forces from the fault. Small weakening effects and driving forces produce Gutenberg-Richter type power law distributions, while large weakening effects and driving forces lead to characteristic earthquakes that rupture the entire fault. For some parameters, the behavior can switch between these two phases, resembling observations of real faults.
This document discusses using geometric approaches to analyze differential equations. It examines four different differential equations: 1) the damped, forced oscillator equation, 2) the damped, forced pendulum equation, 3) the damped, forced Duffing oscillator equation, and 4) the extended Lorenz-Maxwell-Bloch equation. For each equation, it applies Melnikov's method to show the existence of different types of homoclinic or heteroclinic orbits in the Poincare map. It then asserts properties of the invariant sets that result from these orbits based on homoclinic bifurcation theorems.
The document compares 11 time series models for fitting daily stock return data from the KLCI before and after the 1997 Asian financial crisis using two methods: 1) ranking models based on log likelihood, SBC, and AIC values, and 2) principal component analysis of these criteria. For the pre-crisis period, both methods identify GARCH(1,2) as the best fitting model and ARCH(1) as the worst, but disagree on intermediate models. PCA avoids information loss from ranking and better classifies models by performance level.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
1) The study investigated the effect of short coir fiber reinforcement on the flexural properties of polymer composites at varying fiber weight percentages (5-25%) and thicknesses (3-5mm).
2) Testing found that flexural strength and elongation increased with fiber content up to 20% reinforcement, but then decreased at 25%. The 20% reinforced 4mm thick composite exhibited the highest flexural strength and elongation.
3) Increasing fiber content improved bonding between the coir and polymer matrix, while higher contents led to more porosity and weaker properties. Coir was shown to be an effective and lightweight reinforcement for polymer composites.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Validity Of Principle Of Exchange Of Stabilities Of Rivilin- Ericksen Fluid...IRJET Journal
This document presents research on establishing the validity of the Principle of Exchange of Stabilities (PES) for thermal convection of a Rivlin-Ericksen fluid layer in porous medium heated from below with variable gravity. The fluid layer contains suspended particles and is subjected to rotation. The linearized stability equations are formulated using an operator method. It is established that PES is valid for this problem under sufficient conditions, when the gravity field g(z) is nonnegative throughout the fluid layer. This is done by analyzing the resolvent of the linearized stability operator as a composition of integral operators and applying the method of positive operators to show the system has a single greatest eigenvalue.
Machiwal, D. y Jha, MK (2012). Modelado estocástico de series de tiempo. En A...SandroSnchezZamora
This document provides an overview of stochastic modelling and different stochastic processes that are commonly used, including:
- Purely random (white noise) processes where data points are independent and identically distributed
- Autoregressive (AR) processes where each data point is modeled as a linear combination of previous data points plus noise
- Moving average (MA) processes where each data point is modeled as a linear combination of previous noise terms plus a constant
- Autoregressive moving average (ARMA) processes which combine AR and MA processes
- Autoregressive integrated moving average (ARIMA) processes which explicitly include differencing to make time series stationary
The use of Cellular Automata is extended in various disciplines for the modeling of complex system procedures. Their inherent simplicity and their natural parallelism make them a very efficient tool for the simulation of large scale physical phenomena. We explore the framework of Cellular Automata to develop a physically based model for the spatial and temporal prediction of shallow landslides. Particular weight is given to the modeling of hydrological processes in order to investigate the hydrological triggering mechanisms and the importance of continuous modeling of water balance to detect timing and location of soil slips occurrences. Specifically, the 3D flow of water and the resulting water balance in the unsaturated and saturated zone is modeled taking into account important phenomena such as hydraulic hysteresis and evapotranspiration. In this poster the hydrological component of the model will be presented and tested against well established benchmark experiments [Vauclin et al, 1975; Vauclin et al, 1979]. Furthermore, we investigate the applicability of incorporating it in a hydrological catchment model for the prediction (temporal and spatial) of rainfall-triggered shallow landslides.
Disc dark matter_in_the_galaxy_and_potential_cycles_of_extraterrestrial_impac...Sérgio Sacani
This document discusses potential periodic cycles of extraterrestrial impacts, mass extinctions, and geological events on Earth. It proposes that:
1) Mass extinctions and impact cratering may exhibit cycles of around 26-30 million years that could be linked to the Sun's vertical oscillations through the Galactic plane around every 30-42 million years.
2) Near the Galactic plane, comets in the Oort Cloud could be perturbed by Galactic tidal forces and a possible thin dark matter disc, producing periodic comet showers and impacts on Earth linked to extinction events.
3) Records of geological events like tectonism and volcanism also show a potential cycle of around 30 million years that could be linked to the
Thermal Effects in Stokes’ Second Problem for Unsteady Second Grade Fluid Flo...IOSR Journals
In this paper, we investigated the effects of magnetic field and thermal in Stokes’ second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail.
This document proposes a modification to the Gutenberg-Richter law to describe the cumulative distribution of earthquake magnitudes using concepts from nonextensive statistical mechanics. It introduces a new "q-stretched exponential" form for the modified Gutenberg-Richter law and fits this form to seismic data from California and Iran. The empirical data fits extremely well with the proposed modification over the entire range of magnitudes. Nonextensive statistical mechanics is applied to derive a q-exponential distribution for the surface size of fragments produced during earthquakes. A new hypothetical relationship is also proposed between the surface size of fragments and the released energy.
This document discusses the distribution of slip along earthquake faults based on analyses of five major earthquake slip models. It finds that the distribution follows a piecewise Gutenberg-Richter law, with different b-values above and below a transition point. For smaller slips, b is near 1, while for larger slips b is greater than 1. It analyzes the slip distributions using rank-ordering analysis to overcome data limitations. This verifies the existence of power laws with different scaling constants in the two slip regimes identified.
This document discusses methods for calculating the standard error of the b-value parameter in the Gutenberg-Richter magnitude-frequency relationship. It presents two key formulas:
1) For large samples where b can be treated as constant over time, the standard error of b is given by σ(b) = 2.30b2/√n, where n is the sample size and σ2(M) is the sample variance of magnitudes.
2) When b varies slowly over time, its standard error has two components - the time-averaged variance of b at different times, plus the variance of the mean b averaged over the entire time period.
The document also provides tables to determine confidence intervals for
Comparison of the FE/FE and FV/FE treatment of fluid-structure interactionIJERA Editor
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Five-Dimensional Cosmological Model with Time-Dependent G and Lamda for Const...IOSR Journals
In this paper we have consider five-dimensional cosmological model in presence of perfect fluid
source with time dependent G and .The Einstein field equations are solvable with the help of constant
deceleration parameter. Physical and kinematical properties of this model are investigated. It has been shown
that the solutions are comparable with recent observations. The behavior of gravitational constant,
cosmological constant, density, critical density and pressure is discussed for dust, radiation dominated and stiff matter of the Universe. It is also examined the behavior of gravitational constant and cosmological constant for expansion law and exponential law for stiff matter
Using resonant ultrasound spectroscopy (RUS), the author will determine the complete elastic constant matrices of two thermoelectric single crystal samples, Ce.75Fe3CoSb12 and CeFe4Sb12. RUS involves measuring the resonant frequencies of a sample's vibrations, which depend on the sample's elastic constants, shape, orientation, and density. The author aims to obtain the elastic moduli from a single RUS spectrum for each sample. Understanding the elastic properties may help identify better thermoelectric materials by correlating low elastic stiffness with low thermal conductivity and higher thermoelectric efficiency. The author will compute the resonant frequencies using the samples' properties and compare to measurements.
A Markov Chain Approach on Daily Rainfall Occurrenceijtsrd
Markov modeling is one of the tools that can be used to help planners for assess precipitation. The first order Markov chain model was used to predict daily precipitation intervals using transition probability matrices. The demand for precipitation is increasing, not only for data invention, but also to provide useful information in numerous applications, including water properties organization and the hydrological and agricultural subdivisions. In this study, the objective is to predict the probability of future precipitation of the city of Pyin Oo Lwin using the Markov chain model. The system was developed on the basis of the Markov method to forecast the occurrence of precipitation. The results show that models can forecast the state of a given day by 74 on average. Phyu Thwe | Ei Khaing Win | Hnin Pwint Myu Wai "A Markov Chain Approach on Daily Rainfall Occurrence" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd28075.pdf Paper URL: https://www.ijtsrd.com/computer-science/data-miining/28075/a-markov-chain-approach-on-daily-rainfall-occurrence/phyu-thwe
1) The document discusses the maximum likelihood estimator of b-value for mainshocks versus all events.
2) It shows that mainshocks do not entirely satisfy the Gutenberg-Richter law since their magnitude distribution depends on factors other than b-value alone.
3) Analyzing earthquake data from southern California, it demonstrates that the commonly used maximum likelihood estimator produces a statistically insignificant difference between b-values for mainshocks and all events when a more appropriate estimator is used that accounts for the non-exponential distribution of mainshock magnitudes.
This document summarizes a study that analyzes earthquake statistics in a mean-field model of a heterogeneous fault zone. The model examines the interplay between disorder, dynamical effects, and driving mechanisms. It finds a two-parameter phase diagram depending on the amplitude of dynamical weakening effects and the normal distance of driving forces from the fault. Small weakening effects and driving forces produce Gutenberg-Richter type power law distributions, while large weakening effects and driving forces lead to characteristic earthquakes that rupture the entire fault. For some parameters, the behavior can switch between these two phases, resembling observations of real faults.
This document discusses using geometric approaches to analyze differential equations. It examines four different differential equations: 1) the damped, forced oscillator equation, 2) the damped, forced pendulum equation, 3) the damped, forced Duffing oscillator equation, and 4) the extended Lorenz-Maxwell-Bloch equation. For each equation, it applies Melnikov's method to show the existence of different types of homoclinic or heteroclinic orbits in the Poincare map. It then asserts properties of the invariant sets that result from these orbits based on homoclinic bifurcation theorems.
The document compares 11 time series models for fitting daily stock return data from the KLCI before and after the 1997 Asian financial crisis using two methods: 1) ranking models based on log likelihood, SBC, and AIC values, and 2) principal component analysis of these criteria. For the pre-crisis period, both methods identify GARCH(1,2) as the best fitting model and ARCH(1) as the worst, but disagree on intermediate models. PCA avoids information loss from ranking and better classifies models by performance level.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
1) The study investigated the effect of short coir fiber reinforcement on the flexural properties of polymer composites at varying fiber weight percentages (5-25%) and thicknesses (3-5mm).
2) Testing found that flexural strength and elongation increased with fiber content up to 20% reinforcement, but then decreased at 25%. The 20% reinforced 4mm thick composite exhibited the highest flexural strength and elongation.
3) Increasing fiber content improved bonding between the coir and polymer matrix, while higher contents led to more porosity and weaker properties. Coir was shown to be an effective and lightweight reinforcement for polymer composites.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
3 d modeling and dynamic charectarization of steam turbine packet blade and c...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Performance of energy balanced territorial predator scent marking algorithm b...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
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IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Analytical review of loss reduction techniques in indian power distribution s...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Exposure to elevated temperatures and cooled under different regimes – a stud...eSAT Publishing House
This study examined the effects of elevated temperatures and different cooling regimes on blended concrete. Concrete cubes containing 30% ground granulated blast furnace slag were subjected to temperatures from 150°C to 550°C and cooled via furnace cooling, air cooling, or sudden water cooling. Weight loss and residual compressive and split tensile strengths were then tested. Results showed that weight and strengths decreased significantly with higher temperatures and depended strongly on the cooling method, with furnace cooling producing the best retention of properties. Furnace and air cooling resulted in gradual heat loss while sudden cooling induced thermal shock. This research provides information about fire-damaged concrete structures and their residual performance.
Structure, microstructure and dielectric study of (ba0.6 sr0.4)(zr0.6ti0.4)o3...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Secure and efficient handover authentication and detection of spoofing attackeSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
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It has been already revealed that the daily Solar Irradiance Data during the time period from October, 1984 to October, 2003 obtained by Earth Radiation Budget Satellite (ERBS) exhibits an Anti-persistent trend having multi-periodic phenomena. The solar irradiance time series data being a complex non linear signal in this paper we have tried to detect the irregularity and multifractality in the signal using continuous wavelet transform modulus maxima(WTMM) algorithm. Singularity spectrum of the signal has been obtained to measure the degree of multifractality of the Solar Irradiance signal.
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The Equation Based on the Rotational and Orbital Motion of the PlanetsIJERA Editor
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Arch-like loop structures filled with million Kelvin hot plasma form the building blocks of the quiet-Sun corona.
Both high-resolution observations and magnetoconvection simulations show the ubiquitous presence of magnetic
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This document summarizes Colin D'Elia's senior project applying Suzuki's fourth-order symplectic integration scheme to numerically integrate a simplified solar system model over 165 million years. Key findings include:
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The Sun’s differential rotation is controlled by high- latitude baroclinicall...Sérgio Sacani
Rapidly rotating fluids have a rotation profile that depends only on the distance from the rotation axis, in accor-dance with the Taylor- Proudman theorem. Although the Sun was expected to be such a body, helioseismology showed that the rotation rate in the convection zone is closer to constant on radii. It has been postulated that this deviation is due to the poles being warmer than the equator by a few degrees. Using numerical simulations, we show that the pole- to-equator temperature difference cannot exceed 7 kelvin as a result of the back- reaction of the high- latitude baroclinically unstable inertial modes. The observed amplitudes of the modes further indicate that this maximum temperature difference is reached in the Sun. We conclude that the Sun’s latitudinal differential rotation reaches its maximum allowed value
A Fuzzy Inventory Model with Perishable and Aging ItemsIJERA Editor
A parametric multi-period inventory model for perishable items considered in this paper. Each item in the stock perishes in a given period of time with some uncertainty. A model derived for recursive unnormalized conditional distributions of {} given the information accumulated about the inventory level- surviving items processes.
A Fuzzy Inventory Model with Perishable and Aging ItemsIJERA Editor
A parametric multi-period inventory model for perishable items considered in this paper. Each item in the stock
perishes in a given period of time with some uncertainty. A model derived for recursive unnormalized
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IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Long term modulation of cosmic ray intensity in statistical relation with cor...Alexander Decker
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Application of stochastic modeling in geomagnetism
1. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 811
APPLICATION OF STOCHASTIC MODELING IN GEOMAGNETISM
N. Gururajan1
, V. Kayalvizhi Prabhakaran2
1
Retd. Director, 2
Dept. of Mathematics, Kanchi Mamunivar Centre for Post Graduate Studies, Pondicherry-8
vgngpondy@yahoo.com, kayaldew@yahoo.co.in
Abstract
The objective of the present study is the identification of the characteristics of monthly Sq variations for geomagnetic components D,
H and Z for a time series at four Indian geomagnetic observatories, namely, Alibag (ALB), Hyderabad (HYD), Pondicherry (PON)
and Visakhapatnam (VIZ). To study the behavior of Sq monthly variation, a two state Markov chain model is employed. With the help
of Markov transition probabilities, one can guess the behavior of a time series data.
Index Terms: Geomagnetic field – Geomagnetic Sq variation– Stochastic process – Markov chain model – Bernoulli
trials
-----------------------------------------------------------------------***-----------------------------------------------------------------------
1. INTRODUCTION
Significant contribution to research in geomagnetism started
from India as back as in 19th century with the pioneering work
of Brown and Chambers and Moos. The geographical location
of India plays a pivotal role with the latitudinal coverage
existing from equator to the focus of the low latitude Sq
current system.
Variations in the natural magnetic field are measured at the
Earth's surface and elsewhere in the Earth's magnetosphere (
for example, at the geostationary orbit ). These are field
changes with periodicities from about 0.3 second to hundreds
of years. (These boundaries are set to distinguish geomagnetic
variations from the quasipermanent field and higher -
frequency waves). Many of these observed variations from-
very short periods (seconds, minutes, hours) to daily, seasonal,
semiannual, solar-cycle (11-years), and secular (60–80 years)
periods - arise from sources that either are external to the
Earth (but superposed upon the larger, mainly dipolar field) or
internal to the Earth (the magnetic-dipole and higher -
harmonic trends and variations on the scales of hundreds and
even thousands of years). The daily and seasonal motions of
the atmosphere at ionospheric altitudes cause field variations
that are smooth in form and relatively predictable, given the
time and location of the observation. During occasions of high
solar–terrestrial disturbance activity that give rise to aurorae
(northern and southern lights) at high latitudes, very large
geomagnetic variations occur that even mask the quiet daily
changes. These geomagnetic variations are so spectacular in
size and global extent that they have been named geomagnetic
storms and sub storms, with the latter generally limited to the
Polar Regions.
Solar-terrestrial-physics associated studies were mainly
utilizing long series of geomagnetic field observations at the
Indian Observatories and also worldwide network of
geomagnetic data. The Geomagnetic Observatory data were
also used for studies on Interplanetary Magnetic Field (IMF)
associations, Solar flare effects etc. The continuously recorded
data from the Institute gives an opportunity to decipher the
long-term secular changes as well as the daily variations of the
magnetic components that is basically the reflection of the
ionospheric and magnetospheric changes occurring over the
region. Thus, the variations in the geomagnetic field can be
used as a diagnostic tool for understanding the internal
structure of the Earth as well as the dynamics of the upper
atmosphere and magnetosphere.
A stochastic process is the mathematical abstraction of an
empirical process whose development is governed by
probabilistic laws. Markov chain is a class of stochastic
process which has got certain applications. Feller (1968)
applied stochastic processes in several situations. Lawless
(1982) established Markov and statistical models for life time
applications. Anderson (1976) used Box-Jenkins approach to
study stochastic models. Chatfield (1977) developed some
stochastic models for forecasting, such as, queuing models,
renewal process, etc. Recently researchers developed
switching models to analyze the behavior of time series.
Milkovitch (1977) compared semi-Markov and Markov
models in forecasting. Colin (1968) estimated Markov
transition probabilities for certain data.
With the help of Markov transition probabilities, one can
guess the behavior of a time series data. Kaplan (1975) has
studied the ergodicity of a Markov chain.
2. OBJECTIVE:
The objective of the present study is the identification of the
characteristics of monthly Sq variations for geomagnetic
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components D, H and Z for a time series at four Indian
geomagnetic observatories, namely, Alibag (ALB), Hyderabad
(HYD), Pondicherry (PON) and Visakhapatnam (VIZ).
2.1 DATA USED:
This research work is based on the data of Indian geomagnetic
observatories only. Data for monthly variations of the
geomagnetic components D, H and Z, from January 1995 to
December 1997, for Alibag, Hyderabad, Pondicherry and
Visakhapatnam observatories have been obtained from the
volumes of Indian Magnetic data.
The monthly Sq variations for geomagnetic components D, H
and Z for a time series of 36 months from January 1995 to
December 1997 at four Indian geomagnetic observatories,
namely, Alibag (ALB), Hyderabad (HYD), Pondicherry
(PON) and Visakhapatnam (VIZ) is considered.
3. APPLICATION OF STOCHASTIC MODELING
TO GEOMAGNETIC Sq VARIATION:
A TWO STATE MARKOV CHAIN MODEL:
A Markov chain is considered which has two states namely 0
and 1.
3.1 BERNOULLI TRIAL:
A Bernoulli trial is an experiment with only two possible
outcomes namely success and failure which are denoted
respectively by S and F. Example of such an experiment is
testing the quality of a finished product and determining
whether it is defective (F) or non – defective (S). One may
denote S and F respectively by 1, 0.[5]. The probability
distribution of the random variable in this case according to
Bernoulli trial is provided below.
3.2 PROBABILITY DISTRIBUTION
Random
Variable x
0 1
Probability
p(x)
1-p p Total
= 1
Bernoulli trial involves two states. One of the states is
considered as success and denoted by 1. The other state is
considered as failure and denoted by 0.
3.3 DEPENDENT BERNOULLI TRIALS:
In the dependent Bernoulli trials, the probability of success or
failure at each trial depends on the outcome of the previous
trial.
3.3.1 TRANSITION PROBABILITIES FOR
DEPENDENT BERNOULLI TRIALS:
Consider dependent Bernoulli trials. If the nth trial results in
failure then the probability of failure at the (n+1)th trial is
taken as (1- α) while the probability of success at the (n+1)th
trial is assumed to be α. Similarly if the result in nth trial is
success, then the probabilities of success and failure at the
(n+1)th trial are taken as (1-ß) and ß respectively. i.e., if the
system is in state 0 at time n, then the probability of being in
state 0 at time (n+1) is taken as (1- α) and the probability of
being in state 1 at time (n+1) is taken as α. Similarly if the
system is in state 1 at time n, then the probability of being in
state 1 at time (n+1) is taken as (1- ß) and the probability of
being in state 0 at time (n+1) is taken as ß. These probabilities
are called transition probabilities.
They can be written in the form of a matrix as follows.
(n+1)th trial
nth trial state 0 state 1
P = state 0 (1- α) α ( 1 )
state 1 ß (1- ß)
The matrix provided by equation (1) is called the matrix of
transition probabilities. The element in (i,j)th position of the
matrix denotes the conditional probability of a transition state j
at time (n+1), given that the system was in state i at time n.
n – STEP TRANSITION PROBABILITIES:
It is assumed that the initial probabilities for the system to be
in state 0 or 1 are given by the row vector p(0) = ( p0(0) ,
p1(1) ). Let the row vector p(n) = ( p0(n) , p1(n) ) denote the
probabilities for the system to be in state 0 or 1 at time n. The
latter is referred to as the vector of the nth step transition
probabilities.
RECURRENCE RELATION
A relation of the form
f(n+1) = k f(n)
For n= 1, 2, 3……, where k is a constant is called recurrence
relation. This relation provides the link between f(n+1) and
f(n). Using this relation, one can find the value of ‘f’ at the
stage (n+1) by means of the value of ‘f’ at the stage ‘n’.
Consider the event of the system being in state 0 at time n.
This event can occur in two mutually exclusive ways: either
state 0 was occupied at time (n-1) and no transition out of state
0 occurred at time n. The probability for this to happen is p(n-
1) (1- α); alternatively state 1 was occupied at time (n-1) and a
transition from state 1 to state 0 occurred at time n; this has the
probability p(n-1) ß. These possibilities can be represented in
the form of a recurrence relation as follows:
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p0(n) = p0(n-1) (1- α) + p1(n-1) ß
p1(n) = p0(n-1)α + p1(n-1)(1-ß) (2)
The equation ( 2 ) determines a dynamical system. This
system is discrete in nature. The equation ( 2 ) can be rewritten
in the form of a matrix equation as follows:
p0(n) 1- α ß p0(n-1)
= (3)
p1(n) α 1- ß p1(n-1)
Equation (3) provides an expression for the matrix P(n) in
terms of the matrices P and P(n-1) . By referring to the
equations (1) and (3), it is seen that
P(n)=PP(n-1) (4)
Equation (4) shows how P(n) can be defined recursively.
On iteration, one gets
P(n-1) = PP (n-2)
From this, it follows that
P(n) = PP (n-2) = P2 P(n-2)
By successive application of the process of iteration, P(n) can
be expressed in terms of P(0) as follows.
P(n) = P(n) P(0) (5)
STATE OCCUPATION PROBABILITIES:
Given the initial probability matrix P(0) and the matrix of
transition probability P, one can find the state occupation
probabilities at any time n using the equation (5). Denote the
(i,j)th element of P(n) by Pij(n) . The following two cases
arise.
CASE (i): If the system is initially in state 0, then one has
p(0) = { 1,0}
And , p(n) = { p00(n), p01(n) }
CASE (ii): If the system is initially in state 1, then one has
p(0) = { 0, 1 } and p(n) = { p10(n), p11(n) }
i.e., pij(n) = probability { state j at time n / state i at time 0 }
The quantities pij(n) provide the n – step transition
probabilities.
CHARACTERISTIC ROOTS OF THE MATRIX P:
Let I denote the identity matrix of order 2. The characteristic
polynomial of the matrix P is the determinant of the matrix P-
λI . On simplification, this polynomial is obtained as
λ2 + (α + ß - 2) λ + 1- α – ß
The characteristic equation of the matrix P is
λ2 + (α + ß - 2) λ + 1- α – ß = 0 ( 6 )
The roots of the equation (6) are called the characteristic roots
of the matrix P. The following two cases have to be
considered.
CASE (i): α + ß = 0
In this case, the equation ( 6 ) reduces to
λ2 - 2λ + 1 = 0
i.e., (λ - 1)2 = 0
Thus, the characteristic root in this case is 1, with a
multiplicity of two.
CASE (ii): α + ß 0
In this case, the roots of the equation ( 6 ) are given by
λ = (2- α - ß) ± (2- α - ß)2 – 4(1- α - ß ) (7)
2
The expression within the radical sign reduces to 2.
With the positive sign in equation (7), one obtains λ = 1.
Taking the negative sign in equation (7), λ is obtained as
. Thus, the characteristic roots of the matrix P
are obtained as
λ1 = 1
λ2 =
Since, α + ß 0, it follows that λ1 λ2
Thus in this case there are two distinct characteristic roots of
P.
THEOREM (Paria, 1992):
When an 2 X 2 matrix ‘a’, has distinct characteristic roots λ1
and λ2, there exists an invertible 2 X 2 matrix ‘b’ such that
λ1 0
a = b b-1 (8)
0 λ2
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EXPRESSION FOR Pn
:
Consider a matrix P with the property α + ß 0. By the above
theorem, there exists a matrix Q such that
λ1 0
P = Q Q-1 (9)
0 λ2
One obtains
1
Q = (10)
1 -
Its inverse is obtained as
Q-1 = 1 -1 (11)
From this, it follows that
1 0
P = Q Q-1 (12)
0
The quantities and being probabilities satisfy the
inequalities
0 1 and 0 1
So one obtains
0 2
Consequently one has
| λ2| = |1 - | = |1 – ( )| < 1
Thus if follows that
| λ2| < 1 (13)
Hence one obtains
1 1 0
Pn = (14)
1 - 0 (1 - n 1 -1
= + (1 - )n
-
(15)
With any initial probability vector P(o) one can use equation
(5) and (12) to find P(n). The first term in equation (15)
namely,
As a constant and the second term in equation (15) is
)n )n
)n )n
Because of the inequality (13), as n , it is observed that
(1 - )n 0
Therefore the second term in equation (15) tends to zero.
Consequently, if follows that
Pn
as n→
(16)
Denote by 0 and by 1 . Then it is seen that
0 1
Pn
(17)
n →
0 1
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In view of this fact, one has
limit Pn = 0 1 P0
n→ (18)
0 1
As a consequence of proceeding discussion, one is led to the
following result. Let { xt } be a given time series data,
following Bernoulli trails.
Let P be the 2 X 2 matrix of transition probability associated
with the series { xt }.
Suppose
1 -
P =
1 -
with + and | 1 – ( + | < 1
Then,
Limit Pn = 0 1 P(0)
n →
0 1
where,
0 = and 1 =
MARKOV CHAIN MODEL FOR Sq MONTHLY
VARIATION DATA:
To study the behaviour of Sq monthly variation data, a two
state Markov chain model is to be employed. It is assumed
that the probability of the reading, in a particular day
increasing or decreasing from the previous day depends on the
condition of previous days. The model has two conditional
probabilities as its parameters described below.
= prob (of being in state 1 today/previous day being
in state 0)
= prob (of being in state 0 today/previous day being
in state 1)
No other factor is taken into account to explain the occurrence
or non– occurrence of the change in the Sq monthly variation
data as described above.[9].
TRENDS IN A TIME SERIES:
There are two types of trends in a time series: positive trend
and negative trend. Positive trend means that the time series is
increasing, whereas negative trend implies that the time series
is decreasing. In a time series the number of periods in which
it is increasing or decreasing compared to the previous day is
taken into account.
The transition matrix for the occurrence of an increasing or a
decreasing trend in a time series data is given by:
0 1
0 1 -
A =
1 1 -
The n - step transition probabilities are given by the elements
of the matrix An where
An = + (1 - )n -
+ -
Substitute
0 = and 1 =
Then one has
lim An = 0 1
n → 0 1
APPLICATION OF STOCHASTIC MODELING
TO MONTHLY VARIATIONS OF THE
COMPONENTS D, H AND Z FOR THE YEARS
1995, 1996 AND 1997:
The question of transition probalility matrices for the
components D, H and Z at the four places ALB, HYD, PON
and VIZ is now taken up.
ASSUMPTION IN MODEL BUILDING:
While constructing a model, certain reasonable assumptions
have to be made. Some important aspects of the real life
situation have to be identified and incorporated in the model.
As regards to the data, during certain months, there is neither
an increase nor a decrease, compared with the previous month.
The number of such months for the 3 components is noted
below.
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FOR COMPONENT D:
Monthly
Variations
ALB HYD PON VIZ
No:of
Months
3 1 4 2
FOR COMPONENT H:
Monthly
Variations
ALB HYD PON VIZ
No:of
Months
3 0 1 2
FOR COMPONENT Z:
Monthly
Variations
ALB HYD PON VIZ
No:of
Months
0 2 2 4
Since this number is very less for each monthly variation data,
it is reasonable to restrict the attention to only those months
for which either positive signs or negative signs are noticed.
Thus a two state Markov model is assumed for the the
monthly Sq variations data.
VERIFICATION OF BERNOULLI TRIALS:
It has been verified that the Markov chains arising from ALB,
HYD, PON and VIZ series for the three components D, H and
Z follow Bernoulli trials. Because of the fulfillment of this
condition, one may go ahead with the construction of the
transition probalility matrix for each component in each place.
These matrices are determined in the sequel.
CALCULATION OF TRANSITION
PROBABILITY MATRIX FOR COMPONENT D :
The number of positive and negative signs are counted for the
four places ALB, HYD, PON and VIZ for the component D.
In the case of Alibag(ALB),
Today t Total
- +
5 7 12
6 10 16
11 17 28
From this table, the transition probability matrix for ALB
series is obtained as
5/12 7/12
P =
6/16 10/16
In this case, = 7/12, ß = 6/16 and hence + ß 0. So there
are two distinct characteristic roots for the matrix P. It is
noticed that
| λ2| = |1 – ( )|
= 0.042 < 1
Hence the condition | λ2|< 1 is fulfilled.
Preceding the same way, the transition probability matrix for
HYD, PON and VIZ series is obtained as follows.
The transition probability matrix for HYD series:
5/14 9/14
P =
10/17 7/17
The transition probability matrix for PON series:
4/10 6/10
P =
6/16 10/16
The transition probability matrix for VIZ series:
6/15 9/15
P =
8/15 7/15
In all the cases, it is observed that + ß 0 and the condition |
λ2|<1 is fulfilled.
CALCULATION OF TRANSITION
PROBABILITY MATRIX FOR COMPONENT H:
The number of positive and negative signs is counted for the
four places ALB, HYD, PON and VIZ for the component H
and the results are presented as follows.
The transition probability matrix for ALB series is
8/15 7/15
P =
7/14 7/14
The transition probability matrix for HYD series is
8/16 8/16
P =
10/16 6/16
Previous day t-1
t- Total
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The transition probability matrix for PON series is
10/18 8/18
P =
8/14 6/14
The transition probability matrix for VIZ series is
9/17 8/17
P =
7/13 6/13
In all the cases, it is observed that + ß 0 and the condition
| λ2|<1 is fulfilled.
CALCULATION OF TRANSITION
PROBABILITY MATRIX FOR COMPONENT Z:
The numbers of positive and negative signs are counted at the
four places ALB, HYD, PON and VIZ for the component Z
and the results are presented as follows.
The transition probability matrix for ALB series is
10/20 10/20
P =
9/14 5/14
The transition probability matrix for HYD series is
5/13 8/13
P =
8/16 8/16
The transition probability matrix for PON series is
10/16 6/16
P =
8/14 6/14
The transition probability matrix for VIZ series is
6/13 7/13
P =
8/14 6/14
In all the cases, it is observed that + ß 0 and the condition
| λ2|<1 is fulfilled.
DETERMINATION OF TRENDS:
Let Pij denote the probability of transition from state i to state
j after ‘n’ months. For any positive integer n, the matrix Pn =
(Pij)n of the n – step transition probability can be obtained.
The limiting matrix Pn as n→ indicates that the probability
of finding an increasing trend is and of noticing a
decreasing trend is . The values of and ß for each place
are calculated for the 3 components D,H and Z. Using them,
the probabilities for increasing and decreasing trends are
determined. These results are provided in the following table.
LIMITING PROBABILITIES FOR THE 4 PLACES
ALB, HYD, PON AND VIZ:
CASE (i): FOR COMPONENT D:TABLE 3:
PLACE
ß
PROB.
INCRE-
ASING
TREND
FOR
DECRE-
ASING
TREND
ALB
0.583 0.375 0.6 0.4
HYD
0.643 0.588 0.5 0.5
PON
0.6 0.375 0.6 0.4
VIZ
0.6 0.533 0.5 0.5
CASE (ii): FOR COMPONENT H:TABLE 4:
PLACE
ß
PROB.
INCRE-
ASING
TREND
FOR
DECRE-
ASING
TREND
ALB
0.467 0.5 0.5 0.5
HYD
0.5 0.625 0.4 0.6
PON
0.444 0.571 0.4 0.6
IZ 0.471 0.538 0.5 0.5
CASE(iii): FOR COMPONENT Z:TABLE 5:
PLACE
ß
PROB.
INCRE-
ASING
TREND
FOR
DECRE-
ASING
TREND
ALB
0.5 0.643 0.4 0.6
HYD
0.615 0.5 0.6 0.4
PON
0.375 0.571 0.4 0.6
VIZ 0.538 0.571 0.5 0.5
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RESULT AND ANALYSIS
From case (i) it is seen that the monthly variations for
component D, at the places HYD and VIZ possess equal
chance to have increasing trend or decreasing trend in the
short run. In the case of ALB and PON, these probabilities
differ. For ALB the difference in probabilities is 0.2, which is
the same as the case of PON. From case (ii), it is observed that
the monthly variations for component H, at the places ALB
and VIZ possess equal chance to have increasing trend or
decreasing trend in the short run. In the case of HYD and PON
these probabilities differ. The difference in probabilities in the
2 places is 0.2. From case (iii), it is noticed that the monthly
variation for component Z at VIZ possess equal chance to
have increasing trend or decreasing trend in the short run,
whereas in the case of ALB, HYD and PON, the difference in
probabilities comes to 0.2.
CONCLUSION
The daily variation in the magnetic field at the Earth’s surface
during geomagnetic quiet periods (Sq) is known to be
associated with the dynamo currents driven by winds and tidal
motions in the E-region of the ionosphere known as
atmospheric dynamo. Besides the atmospheric dynamo, other
sources of electric field and currents at equatorial region
contribute to Sq variations on different components of
geomagnetic field observed at the ground level. Daily range of
the geomagnetic field is an important parameter measuring the
magnitude of diurnal variation. Being dependent on the daily
maximum and minimum field values, the parameter fluctuates
from day to day in accordance with the variability of both
these values. A continuous recording of any of the
components of the geomagnetic field typically exhibits two
types of variations: a smooth, regular variation, known as Sq,
the solar quiet day variation and a rapid irregular fluctuation.
The Sq variations are the most regular of all the geomagnetic
field variations. Here geomagnetic quiet day (Sq) variations
have been analyzed through the application of Graph
Theoretic Modeling.
The application of Stochastic Modeling for pattern recognition
and classification have been used for numerous applications in
astronomy, meteorology, cartography, satellite data analysis,
artificial intelligence etc., Here it is used to study the identical
pattern of geomagnetic variations at Indian observatories.
Generally, for a huge volume of data in a complicated analysis
this technique yields accurate results. As a result of this study,
it is expected that future usage of this technique may be
appropriate for exploring some new results in geomagnetism.
It is concluded that there seems to be good ground for
expecting a two state Markov chain model to describe the
increasing or decreasing trend in the series of monthly Sq
variations at the four observatories, in a short run.
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[4] Colin L., (1968), Estimating Markov transition
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