Analytical non-perturbative study of thethree-dimensional nonlinear stochastic partialdifferential equation
with additive thermal noise, analogous to thatproposed by V.N.Nikolaevskii [1]-[5] to describelongitudinal
seismic waves, is presented. Theequation has a threshold of short-wave instability and symmetry, providing
long wave dynamics.New mechanism of quantum chaos generating in nonlineardynamical systemswith
infinite number of degrees of freedom is proposed. The hypothesis is said,that physical turbulence could be
identifiedwith quantum chaos of considered type. It is shown that the additive thermal noise destabilizes
dramatically the ground state of theNikolaevskii system thus causing it to make a direct transition from a
spatially uniform to a turbulent state.
NEW SCENARIO FOR TRANSITION TO SLOW 3-D TURBULENCE PART I.SLOW 1-D TURBULENCE...ijrap
This document analyzes the 3D and 1D stochastic Nikolaevskii systems, which model turbulence. It introduces the 3D and 1D stochastic partial differential equations that were obtained by adding small white noise to the original non-stochastic Nikolaevskii systems. The key findings are: 1) Numerical integration of the 1D system is actually solving the stochastic model due to inherent computational noise. 2) Even small noise can significantly impact turbulent modes and change system behavior dramatically. 3) Developed turbulence in physical systems may be characterized as quantum chaos driven by thermal fluctuations based on modeling of the stochastic systems.
Projective and hybrid projective synchronization of 4-D hyperchaotic system v...TELKOMNIKA JOURNAL
Nonlinear control strategy was established to realize the Projective Synchronization (PS) and Hybrid Projective Synchronization (HPS) for 4-D hyperchaotic system at different scaling matrices. This strategy, which is able to achieve projective and hybrid projective synchronization by more precise and adaptable method to provide a novel control scheme. On First stage, three scaling matrices were given in order to achieving various projective synchronization phenomena. While the HPS was implemented at specific scaling matrix in the second stage. Ultimately, the precision of controllers were compared and analyzed theoretically and numerically. The long-range precision of the proposed controllers are confirmed by third stage.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
I have used "Exact Exponential Algorithms" book by 'Fedor V. Fomin and Dieter Kratsch' to prepare this presentation. It will be helpful in understanding split and list technique in breaking and solving hard problems in exponential time.
This document provides an overview of particle filtering and sampling algorithms. It discusses key concepts like Bayesian estimation, Monte Carlo integration methods, the particle filter, and sampling algorithms. The particle filter approximates probabilities with weighted samples to estimate states in nonlinear, non-Gaussian systems. It performs recursive Bayesian filtering by predicting particle states and updating their weights based on new observations. While powerful, particle filters have high computational complexity and it can be difficult to determine the optimal number of particles.
Chaos Suppression and Stabilization of Generalized Liu Chaotic Control Systemijtsrd
In this paper, the concept of generalized stabilization for nonlinear systems is introduced and the stabilization of the generalized Liu chaotic control system is explored. Based on the time-domain approach with differential inequalities, a suitable control is presented such that the generalized stabilization for a class of Liu chaotic system can be achieved. Meanwhile, not only the guaranteed exponential convergence rate can be arbitrarily pre-specified but also the critical time can be correctly estimated. Finally, some numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained results. Yeong-Jeu Sun | Jer-Guang Hsieh "Chaos Suppression and Stabilization of Generalized Liu Chaotic Control System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: http://www.ijtsrd.com/papers/ijtsrd20195.pdf
http://www.ijtsrd.com/engineering/electrical-engineering/20195/chaos-suppression-and-stabilization-of-generalized-liu-chaotic-control-system/yeong-jeu-sun
SCHRODINGER'S CAT PARADOX RESOLUTION USING GRW COLLAPSE MODELijrap
This document discusses a possible resolution to Schrodinger's cat paradox using the GRW collapse model. It proposes that:
1) The wavefunctions of the nucleus, detection apparatus, and cat would each undergo a spontaneous localization ("collapse") according to the GRW model, resulting in definite states for each.
2) These collapsed states would accurately reflect the actual decayed/undecayed, triggered/untriggered, alive/dead states of the nucleus, apparatus, and cat respectively, even though they evolved unitarily according to the Schrodinger equation.
3) This resolves the paradox of the cat being in a superposition of alive and dead states, since the GRW col
A one parameter Poisson-Mishra distribution has been obtained by compounding Poisson distribution with Mishra distribution of B.K.Sah(2015). The first four moments about origin have been obtained. The maximum likelihood method and the method of moments have been discussed for estimating its parameter. The distribution has been fitted to some data-sets to test its goodness of fit. It has been found that this distribution gives better fit to all the discrete data sets which are used by Sankaran (1970) and others to test goodness of fit of Poisson-Lindley distribution.
NEW SCENARIO FOR TRANSITION TO SLOW 3-D TURBULENCE PART I.SLOW 1-D TURBULENCE...ijrap
This document analyzes the 3D and 1D stochastic Nikolaevskii systems, which model turbulence. It introduces the 3D and 1D stochastic partial differential equations that were obtained by adding small white noise to the original non-stochastic Nikolaevskii systems. The key findings are: 1) Numerical integration of the 1D system is actually solving the stochastic model due to inherent computational noise. 2) Even small noise can significantly impact turbulent modes and change system behavior dramatically. 3) Developed turbulence in physical systems may be characterized as quantum chaos driven by thermal fluctuations based on modeling of the stochastic systems.
Projective and hybrid projective synchronization of 4-D hyperchaotic system v...TELKOMNIKA JOURNAL
Nonlinear control strategy was established to realize the Projective Synchronization (PS) and Hybrid Projective Synchronization (HPS) for 4-D hyperchaotic system at different scaling matrices. This strategy, which is able to achieve projective and hybrid projective synchronization by more precise and adaptable method to provide a novel control scheme. On First stage, three scaling matrices were given in order to achieving various projective synchronization phenomena. While the HPS was implemented at specific scaling matrix in the second stage. Ultimately, the precision of controllers were compared and analyzed theoretically and numerically. The long-range precision of the proposed controllers are confirmed by third stage.
New approach for wolfe’s modified simplex method to solve quadratic programmi...eSAT Journals
Abstract
In this paper, an alternative method for Wolfe’s modified simplex method is introduced. This method is easy to solve quadratic programming problem (QPP) concern with non-linear programming problem (NLPP). In linear programming models, the characteristic assumption is the linearity of the objective function and constraints. Although this assumption holds in numerous practical situations, yet we come across many situations where the objective function and some or all of the constraints are non-linear functions. The non-linearity of the functions makes the solution of the problem much more involved as compared to LPPs and there is no single algorithm like the simplex method, which can be employed to solve efficiently all NPPs.
Keywords: Quadratic programming problem, New approach, Modified simplex method, and Optimal solution.
I have used "Exact Exponential Algorithms" book by 'Fedor V. Fomin and Dieter Kratsch' to prepare this presentation. It will be helpful in understanding split and list technique in breaking and solving hard problems in exponential time.
This document provides an overview of particle filtering and sampling algorithms. It discusses key concepts like Bayesian estimation, Monte Carlo integration methods, the particle filter, and sampling algorithms. The particle filter approximates probabilities with weighted samples to estimate states in nonlinear, non-Gaussian systems. It performs recursive Bayesian filtering by predicting particle states and updating their weights based on new observations. While powerful, particle filters have high computational complexity and it can be difficult to determine the optimal number of particles.
Chaos Suppression and Stabilization of Generalized Liu Chaotic Control Systemijtsrd
In this paper, the concept of generalized stabilization for nonlinear systems is introduced and the stabilization of the generalized Liu chaotic control system is explored. Based on the time-domain approach with differential inequalities, a suitable control is presented such that the generalized stabilization for a class of Liu chaotic system can be achieved. Meanwhile, not only the guaranteed exponential convergence rate can be arbitrarily pre-specified but also the critical time can be correctly estimated. Finally, some numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained results. Yeong-Jeu Sun | Jer-Guang Hsieh "Chaos Suppression and Stabilization of Generalized Liu Chaotic Control System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: http://www.ijtsrd.com/papers/ijtsrd20195.pdf
http://www.ijtsrd.com/engineering/electrical-engineering/20195/chaos-suppression-and-stabilization-of-generalized-liu-chaotic-control-system/yeong-jeu-sun
SCHRODINGER'S CAT PARADOX RESOLUTION USING GRW COLLAPSE MODELijrap
This document discusses a possible resolution to Schrodinger's cat paradox using the GRW collapse model. It proposes that:
1) The wavefunctions of the nucleus, detection apparatus, and cat would each undergo a spontaneous localization ("collapse") according to the GRW model, resulting in definite states for each.
2) These collapsed states would accurately reflect the actual decayed/undecayed, triggered/untriggered, alive/dead states of the nucleus, apparatus, and cat respectively, even though they evolved unitarily according to the Schrodinger equation.
3) This resolves the paradox of the cat being in a superposition of alive and dead states, since the GRW col
A one parameter Poisson-Mishra distribution has been obtained by compounding Poisson distribution with Mishra distribution of B.K.Sah(2015). The first four moments about origin have been obtained. The maximum likelihood method and the method of moments have been discussed for estimating its parameter. The distribution has been fitted to some data-sets to test its goodness of fit. It has been found that this distribution gives better fit to all the discrete data sets which are used by Sankaran (1970) and others to test goodness of fit of Poisson-Lindley distribution.
This document summarizes a study that analyzes magnetohydrodynamic (MHD) flow of Newtonian and non-Newtonian nanofluids passing over a magnetic sphere. Nanofluids containing alumina or copper nanoparticles in water or oil bases were examined. Governing equations for continuity, momentum, and energy were derived and non-dimensionalized. The equations were transformed into similarity equations using a stream function and solved numerically. Results showed that increasing the magnetic parameter decreases velocity and temperature. Newtonian nanofluid velocity and temperature were higher than non-Newtonian. Copper-water nanofluid also had higher values than alumina-water.
Analysis of convection diffusion problems at various peclet numbers using fin...Alexander Decker
This document summarizes research analyzing convection-diffusion problems at various Peclet numbers using finite volume and finite difference schemes. It introduces convection-diffusion equations, defines Peclet number, and describes how central differencing and upwind differencing schemes were used to discretize and solve sample convection-diffusion problems numerically. The results show that central differencing leads to inaccurate solutions at high Peclet numbers, while upwind differencing satisfies consistency criteria by accounting for flow direction.
Quadratic programming (Tool of optimization)VARUN KUMAR
This document provides an overview of quadratic programming, including:
1. It defines quadratic programming as a special case of nonlinear programming where the objective function is quadratic and all constraints are linear.
2. It presents the general mathematical formulation of a quadratic programming problem and provides an example problem.
3. It discusses solutions to quadratic programs using the graphical method and the Karush-Kuhn-Tucker (KKT) conditions.
1) The document discusses model theory and similarity conditions for physical models. It defines geometric, kinematic, and dynamic similarity between models and prototypes.
2) For dynamic similarity, the Froude and Reynolds numbers must be equal between corresponding points on the model and prototype. This requires a relationship between velocity and geometric length scales.
3) For Froude models, which are used for open channel flow, the velocity scale is the square root of the length scale. Examples are provided to demonstrate calculating discharge, velocity, and force values between models and prototypes.
Iterative methods for the solution of saddle point problemIAEME Publication
This document summarizes an iterative method for solving saddle point problems that arise in mixed finite element approximations of Stokes fluid flow problems. It presents classical solution methods like primal-dual conjugate gradient algorithms. It then proposes a general primal-dual algorithm that combines these classical methods to solve the coupled primal and dual problems simultaneously. The algorithm defines descent directions as solutions to preconditioned residual equations to minimize both the primal and dual residuals at each iteration.
Mixed Spectra for Stable Signals from Discrete Observationssipij
This paper concerns the continuous-time stable alpha symmetric processes which are inivitable in the modeling of certain signals with indefinitely increasing variance. Particularly the case where the spectral measurement is mixed: sum of a continuous measurement and a discrete measurement. Our goal is to estimate the spectral density of the continuous part by observing the signal in a discrete way. For that, we propose a method which consists in sampling the signal at periodic instants. We use Jackson's polynomial kernel to build a periodogram which we then smooth by two spectral windows taking into account the width of the interval where the spectral density is non-zero. Thus, we bypass the phenomenon of aliasing often encountered in the case of estimation from discrete observations of a continuous time process.
Slow steady motion of a thermo viscous fluid between two parallel plates with...eSAT Journals
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
Principal component analysis (PCA) is a technique used to reduce the dimensionality of large data sets by transforming correlated variables into a smaller number of uncorrelated variables called principal components. PCA identifies patterns in data and expresses the data in such a way as to highlight their similarities and differences. The main goals of PCA are data reduction and interpretation. It works by identifying the directions (principal components) along which the variation in the data is maximized.
Bound- State Solution of Schrodinger Equation with Hulthen Plus Generalized E...ijrap
- The document discusses using the Nikiforov-Uvarov method to find bound state solutions to the Schrodinger equation with Hulthen plus generalized exponential Coulomb potential.
- The method is applied to obtain the energy eigenvalues and total wave function for the potential.
- A C++ algorithm is used to numerically calculate the energy values for different quantum states and screening parameter values.
Application of Residue Inversion Formula for Laplace Transform to Initial Val...iosrjce
This document discusses using the residue inversion formula of the Laplace transform to solve initial value problems of linear ordinary differential equations. Specifically:
1) It reviews the traditional algebraic method of using partial fractions and Laplace transform tables to find the inverse Laplace transform.
2) It introduces the residue inversion formula, which allows directly calculating the inverse Laplace transform by finding the residues of isolated singularities.
3) It provides an example problem solved using both the traditional partial fractions method and the residue inversion formula, showing they produce the same result but the latter is more direct and efficient.
4) It concludes the residue inversion approach is faster, more precise and avoids needing to resolve partial fractions or use tables, making it advantageous for
The inverse scattering series for tasks associated with primaries: direct non...Arthur Weglein
The inverse scattering series for tasks associated with primaries: direct non-linear inversion of 1D elastic media. In this paper, research on direct inversion for two pa-
rameter acoustic media (Zhang and Weglein, 2005) is
extended to the three parameter elastic case. We present
the first set of direct non-linear inversion equations for
1D elastic media (i.e., depth varying P-velocity, shear
velocity and density). The terms for moving mislocated
reflectors are shown to be separable from amplitude
correction terms. Although in principle this direct
inversion approach requires all four components of elastic
data, synthetic tests indicate that consistent value-added
results may be achieved given only ˆDPP measurements.
We can reasonably infer that further value would derive
from actually measuring ˆDPP , ˆD PS, ˆDSP and ˆDSS as
the method requires. The method is direct with neither
a model matching nor cost function minimization.
Exponential State Observer Design for a Class of Uncertain Chaotic and Non-Ch...ijtsrd
The document presents an exponential state observer design for uncertain chaotic and non-chaotic systems. It introduces a class of uncertain nonlinear systems and explores the state observation problem for such systems. Using an approach with integral and differential equalities, an exponential state observer is established that guarantees global exponential stability of the error system. Numerical simulations exhibit the feasibility and effectiveness of the observer design.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document summarizes research on using an affine combination of two time-varying least mean square (TVLMS) adaptive filters for applications such as echo cancellation and system identification. The affine combination aims to obtain faster convergence and lower steady-state error compared to individual TVLMS filters. Simulation results show the affine combination of TVLMS filters achieves mean square error of 0.0055 after 1000 iterations for noise cancellation, outperforming standard LMS, affine LMS, and RLS algorithms. The affine combination also performs well for system identification applications, identifying an unknown FIR filter model with low error. The approach provides dependent estimates of an unknown system response from each filter, and finds an optimal affine combining coefficient to minimize mean square error
This document summarizes a study on the effect of parameters of a geometric multigrid method on CPU time for solving one-dimensional problems related to heat transfer and fluid flow. The parameters studied include coarsening ratio of grids, number of inner iterations, number of grid levels, and tolerances. Finite difference methods were used to discretize partial differential equations for problems involving Poisson, advection-diffusion, and heat transfer equations. Comparisons were made between multigrid and single grid methods like Gauss-Seidel and TDMA. Results confirmed some literature findings and presented some new results on the effect of parameters on CPU time.
Some new exact Solutions for the nonlinear schrödinger equationinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
NEW SCENARIO FOR TRANSITION TO SLOW 3-D TURBULENCE PART I.SLOW 1-D TURBULENCE...ijrap
Analyticalnon-perturbative study of thethree-dimensional nonlinear stochastic partialdifferential equation
with additive thermal noise, analogous to thatproposed by V.N.Nikolaevskii [1]-[5] to describelongitudinal
seismic waves, ispresented. Theequation has a threshold of short-waveinstability and symmetry, providing
longwavedynamics.New mechanism of quantum chaos generating in nonlineardynamical systemswith
infinite number of degrees of freedom is proposed. The hypothesis is said,that physical turbulence could be
identifiedwith quantum chaos of considered type. It is shown that the additive thermal noise destabilizes
dramatically the ground state of theNikolaevskii system thus causing it to make a direct transition from a
spatially uniform to a turbulent state
This document summarizes Emmy Noether's method for obtaining the infinitesimal point symmetries of Lagrangians using the Noether current. It presents Noether's theorem in the Lanczos approach to construct the first integral associated with each symmetry. Several examples of Lagrangians are analyzed using this method, including those studied by Rothe, Henneaux, and Torres del Castillo. For each Lagrangian, the Noether current is derived and the resulting Killing equations are solved to obtain the point symmetries and associated first integrals.
Simple Exponential Observer Design for the Generalized Liu Chaotic Systemijtsrd
In this paper, the generalized Liu chaotic system is firstly introduced and the state observation problem of such a system is investigated. Based on the time-domain approach with differential and integral equalities, a novel state observer for the generalized Liu chaotic system is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential convergence rate can be precisely calculated. Finally, numerical simulations are presented to exhibit the effectiveness and feasibility of the obtained results. Yeong-Jeu Sun"Simple Exponential Observer Design for the Generalized Liu Chaotic System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd7126.pdf http://www.ijtsrd.com/engineering/engineering-maths/7126/simple-exponential-observer-design-for-the-generalized-liu-chaotic-system/yeong-jeu-sun
This document discusses strategies for parallelizing spectral methods. Spectral methods are global in nature due to their use of global basis functions, making them challenging to parallelize on fine-grained architectures. However, the document finds that spectral methods can be effectively parallelized. The main computational steps in spectral methods are the calculation of differential operators on functions and solving linear systems, both of which can exploit parallelism. Domain decomposition techniques may also help parallelize computations over non-Cartesian domains.
Spatio-Temporal Characterization with Wavelet Coherence: Anexus between Envir...ijsc
Identifying spatio-temporal synchrony in a complex, interacting and oscillatory coupled-system is a challenge. In particular, the characterization of statistical relationships between environmental or biophysical variables with the multivariate data of pandemic is a difficult process because of the intrinsic variability and non-stationary nature of the time-series in space and time. This paper presents a methodology to address these issues by examining the bivariate relationship between Covid-19 and temperature time-series in the time-localized frequency domain by using Singular Value Decomposition (SVD) and continuous cross-wavelet analysis. First, the dominant spatio-temporal trends are derived by using the eigen decomposition of SVD. The Covid-19 incidence data and the temperature data of the corresponding period are transformed into significant eigen-state vectors for each spatial unit. The Morlet Wavelet transformation is performed to analyse and compare the frequency structure of the dominant trends derived by the SVD. The result provides cross-wavelet transform and wavelet coherence measures in the ranges of time period for the corresponding spatial units. Additionally, wavelet power spectrum and paired wavelet coherence statistics and phase difference are estimated. The result suggests statistically significant coherency at various frequencies providing insight into spatio-temporal dynamics. Moreover, it provides information about the complex conjugate dynamic relationships in terms phases and phase
differences.
THE RESEARCH OF QUANTUM PHASE ESTIMATION ALGORITHMIJCSEA Journal
This document discusses phase estimation in quantum computing. It begins by introducing quantum Fourier transforms and how they are important for algorithms like Shor's algorithm. It then describes the phase estimation algorithm in detail, including how it uses two registers to estimate the phase of a quantum state and how the inverse quantum Fourier transform improves this estimate. Simulation results are presented that show the probability distribution of the estimated phase converging to the true value and how the probability of success increases with more qubits while computational costs rise polynomially. The paper concludes that the optimal number of qubits balances high success probability and low costs for phase estimation.
This document summarizes a study that analyzes magnetohydrodynamic (MHD) flow of Newtonian and non-Newtonian nanofluids passing over a magnetic sphere. Nanofluids containing alumina or copper nanoparticles in water or oil bases were examined. Governing equations for continuity, momentum, and energy were derived and non-dimensionalized. The equations were transformed into similarity equations using a stream function and solved numerically. Results showed that increasing the magnetic parameter decreases velocity and temperature. Newtonian nanofluid velocity and temperature were higher than non-Newtonian. Copper-water nanofluid also had higher values than alumina-water.
Analysis of convection diffusion problems at various peclet numbers using fin...Alexander Decker
This document summarizes research analyzing convection-diffusion problems at various Peclet numbers using finite volume and finite difference schemes. It introduces convection-diffusion equations, defines Peclet number, and describes how central differencing and upwind differencing schemes were used to discretize and solve sample convection-diffusion problems numerically. The results show that central differencing leads to inaccurate solutions at high Peclet numbers, while upwind differencing satisfies consistency criteria by accounting for flow direction.
Quadratic programming (Tool of optimization)VARUN KUMAR
This document provides an overview of quadratic programming, including:
1. It defines quadratic programming as a special case of nonlinear programming where the objective function is quadratic and all constraints are linear.
2. It presents the general mathematical formulation of a quadratic programming problem and provides an example problem.
3. It discusses solutions to quadratic programs using the graphical method and the Karush-Kuhn-Tucker (KKT) conditions.
1) The document discusses model theory and similarity conditions for physical models. It defines geometric, kinematic, and dynamic similarity between models and prototypes.
2) For dynamic similarity, the Froude and Reynolds numbers must be equal between corresponding points on the model and prototype. This requires a relationship between velocity and geometric length scales.
3) For Froude models, which are used for open channel flow, the velocity scale is the square root of the length scale. Examples are provided to demonstrate calculating discharge, velocity, and force values between models and prototypes.
Iterative methods for the solution of saddle point problemIAEME Publication
This document summarizes an iterative method for solving saddle point problems that arise in mixed finite element approximations of Stokes fluid flow problems. It presents classical solution methods like primal-dual conjugate gradient algorithms. It then proposes a general primal-dual algorithm that combines these classical methods to solve the coupled primal and dual problems simultaneously. The algorithm defines descent directions as solutions to preconditioned residual equations to minimize both the primal and dual residuals at each iteration.
Mixed Spectra for Stable Signals from Discrete Observationssipij
This paper concerns the continuous-time stable alpha symmetric processes which are inivitable in the modeling of certain signals with indefinitely increasing variance. Particularly the case where the spectral measurement is mixed: sum of a continuous measurement and a discrete measurement. Our goal is to estimate the spectral density of the continuous part by observing the signal in a discrete way. For that, we propose a method which consists in sampling the signal at periodic instants. We use Jackson's polynomial kernel to build a periodogram which we then smooth by two spectral windows taking into account the width of the interval where the spectral density is non-zero. Thus, we bypass the phenomenon of aliasing often encountered in the case of estimation from discrete observations of a continuous time process.
Slow steady motion of a thermo viscous fluid between two parallel plates with...eSAT Journals
Abstract
In this paper, the slow steady motion of a second order thermo-viscous fluid between two parallel plates is examined. The closed form
solutions of the velocity and temperature distributions are obtained when thermo-stress coefficient is far less compared to strain
thermal conductivity coefficient and coefficient of cross viscosity for the following two cases: (i) when the upper plate is in relative
motion and (ii) when the upper plate is thermally insulated. The heat transfer coefficient on the upper plate , The mean Bulk
temperature and the transverse force perpendicular to the flow direction are also calculated. It is observed that forces are generated
in transverse directions which are special feature of these types of fluids. The effect of various flow parameters on the flow field have
been discussed with the help of graphical illustrations.
Keywords: Thermo-viscous fluids, Strain thermal conductivity coefficient and Thermo stress Coefficient.
Principal component analysis (PCA) is a technique used to reduce the dimensionality of large data sets by transforming correlated variables into a smaller number of uncorrelated variables called principal components. PCA identifies patterns in data and expresses the data in such a way as to highlight their similarities and differences. The main goals of PCA are data reduction and interpretation. It works by identifying the directions (principal components) along which the variation in the data is maximized.
Bound- State Solution of Schrodinger Equation with Hulthen Plus Generalized E...ijrap
- The document discusses using the Nikiforov-Uvarov method to find bound state solutions to the Schrodinger equation with Hulthen plus generalized exponential Coulomb potential.
- The method is applied to obtain the energy eigenvalues and total wave function for the potential.
- A C++ algorithm is used to numerically calculate the energy values for different quantum states and screening parameter values.
Application of Residue Inversion Formula for Laplace Transform to Initial Val...iosrjce
This document discusses using the residue inversion formula of the Laplace transform to solve initial value problems of linear ordinary differential equations. Specifically:
1) It reviews the traditional algebraic method of using partial fractions and Laplace transform tables to find the inverse Laplace transform.
2) It introduces the residue inversion formula, which allows directly calculating the inverse Laplace transform by finding the residues of isolated singularities.
3) It provides an example problem solved using both the traditional partial fractions method and the residue inversion formula, showing they produce the same result but the latter is more direct and efficient.
4) It concludes the residue inversion approach is faster, more precise and avoids needing to resolve partial fractions or use tables, making it advantageous for
The inverse scattering series for tasks associated with primaries: direct non...Arthur Weglein
The inverse scattering series for tasks associated with primaries: direct non-linear inversion of 1D elastic media. In this paper, research on direct inversion for two pa-
rameter acoustic media (Zhang and Weglein, 2005) is
extended to the three parameter elastic case. We present
the first set of direct non-linear inversion equations for
1D elastic media (i.e., depth varying P-velocity, shear
velocity and density). The terms for moving mislocated
reflectors are shown to be separable from amplitude
correction terms. Although in principle this direct
inversion approach requires all four components of elastic
data, synthetic tests indicate that consistent value-added
results may be achieved given only ˆDPP measurements.
We can reasonably infer that further value would derive
from actually measuring ˆDPP , ˆD PS, ˆDSP and ˆDSS as
the method requires. The method is direct with neither
a model matching nor cost function minimization.
Exponential State Observer Design for a Class of Uncertain Chaotic and Non-Ch...ijtsrd
The document presents an exponential state observer design for uncertain chaotic and non-chaotic systems. It introduces a class of uncertain nonlinear systems and explores the state observation problem for such systems. Using an approach with integral and differential equalities, an exponential state observer is established that guarantees global exponential stability of the error system. Numerical simulations exhibit the feasibility and effectiveness of the observer design.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document summarizes research on using an affine combination of two time-varying least mean square (TVLMS) adaptive filters for applications such as echo cancellation and system identification. The affine combination aims to obtain faster convergence and lower steady-state error compared to individual TVLMS filters. Simulation results show the affine combination of TVLMS filters achieves mean square error of 0.0055 after 1000 iterations for noise cancellation, outperforming standard LMS, affine LMS, and RLS algorithms. The affine combination also performs well for system identification applications, identifying an unknown FIR filter model with low error. The approach provides dependent estimates of an unknown system response from each filter, and finds an optimal affine combining coefficient to minimize mean square error
This document summarizes a study on the effect of parameters of a geometric multigrid method on CPU time for solving one-dimensional problems related to heat transfer and fluid flow. The parameters studied include coarsening ratio of grids, number of inner iterations, number of grid levels, and tolerances. Finite difference methods were used to discretize partial differential equations for problems involving Poisson, advection-diffusion, and heat transfer equations. Comparisons were made between multigrid and single grid methods like Gauss-Seidel and TDMA. Results confirmed some literature findings and presented some new results on the effect of parameters on CPU time.
Some new exact Solutions for the nonlinear schrödinger equationinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
NEW SCENARIO FOR TRANSITION TO SLOW 3-D TURBULENCE PART I.SLOW 1-D TURBULENCE...ijrap
Analyticalnon-perturbative study of thethree-dimensional nonlinear stochastic partialdifferential equation
with additive thermal noise, analogous to thatproposed by V.N.Nikolaevskii [1]-[5] to describelongitudinal
seismic waves, ispresented. Theequation has a threshold of short-waveinstability and symmetry, providing
longwavedynamics.New mechanism of quantum chaos generating in nonlineardynamical systemswith
infinite number of degrees of freedom is proposed. The hypothesis is said,that physical turbulence could be
identifiedwith quantum chaos of considered type. It is shown that the additive thermal noise destabilizes
dramatically the ground state of theNikolaevskii system thus causing it to make a direct transition from a
spatially uniform to a turbulent state
This document summarizes Emmy Noether's method for obtaining the infinitesimal point symmetries of Lagrangians using the Noether current. It presents Noether's theorem in the Lanczos approach to construct the first integral associated with each symmetry. Several examples of Lagrangians are analyzed using this method, including those studied by Rothe, Henneaux, and Torres del Castillo. For each Lagrangian, the Noether current is derived and the resulting Killing equations are solved to obtain the point symmetries and associated first integrals.
Simple Exponential Observer Design for the Generalized Liu Chaotic Systemijtsrd
In this paper, the generalized Liu chaotic system is firstly introduced and the state observation problem of such a system is investigated. Based on the time-domain approach with differential and integral equalities, a novel state observer for the generalized Liu chaotic system is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential convergence rate can be precisely calculated. Finally, numerical simulations are presented to exhibit the effectiveness and feasibility of the obtained results. Yeong-Jeu Sun"Simple Exponential Observer Design for the Generalized Liu Chaotic System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd7126.pdf http://www.ijtsrd.com/engineering/engineering-maths/7126/simple-exponential-observer-design-for-the-generalized-liu-chaotic-system/yeong-jeu-sun
This document discusses strategies for parallelizing spectral methods. Spectral methods are global in nature due to their use of global basis functions, making them challenging to parallelize on fine-grained architectures. However, the document finds that spectral methods can be effectively parallelized. The main computational steps in spectral methods are the calculation of differential operators on functions and solving linear systems, both of which can exploit parallelism. Domain decomposition techniques may also help parallelize computations over non-Cartesian domains.
Spatio-Temporal Characterization with Wavelet Coherence: Anexus between Envir...ijsc
Identifying spatio-temporal synchrony in a complex, interacting and oscillatory coupled-system is a challenge. In particular, the characterization of statistical relationships between environmental or biophysical variables with the multivariate data of pandemic is a difficult process because of the intrinsic variability and non-stationary nature of the time-series in space and time. This paper presents a methodology to address these issues by examining the bivariate relationship between Covid-19 and temperature time-series in the time-localized frequency domain by using Singular Value Decomposition (SVD) and continuous cross-wavelet analysis. First, the dominant spatio-temporal trends are derived by using the eigen decomposition of SVD. The Covid-19 incidence data and the temperature data of the corresponding period are transformed into significant eigen-state vectors for each spatial unit. The Morlet Wavelet transformation is performed to analyse and compare the frequency structure of the dominant trends derived by the SVD. The result provides cross-wavelet transform and wavelet coherence measures in the ranges of time period for the corresponding spatial units. Additionally, wavelet power spectrum and paired wavelet coherence statistics and phase difference are estimated. The result suggests statistically significant coherency at various frequencies providing insight into spatio-temporal dynamics. Moreover, it provides information about the complex conjugate dynamic relationships in terms phases and phase
differences.
THE RESEARCH OF QUANTUM PHASE ESTIMATION ALGORITHMIJCSEA Journal
This document discusses phase estimation in quantum computing. It begins by introducing quantum Fourier transforms and how they are important for algorithms like Shor's algorithm. It then describes the phase estimation algorithm in detail, including how it uses two registers to estimate the phase of a quantum state and how the inverse quantum Fourier transform improves this estimate. Simulation results are presented that show the probability distribution of the estimated phase converging to the true value and how the probability of success increases with more qubits while computational costs rise polynomially. The paper concludes that the optimal number of qubits balances high success probability and low costs for phase estimation.
A Stochastic Limit Approach To The SAT ProblemValerie Felton
This document proposes using quantum adaptive stochastic systems to solve NP-complete problems like SAT in polynomial time. It summarizes the SAT problem, discusses existing quantum algorithms for it, and introduces the concept of using channels instead of just unitary operators to model more realistic quantum computations. It argues that combining a quantum SAT algorithm with a stochastic limit approach using channels could provide a method to distinguish computation results that existing algorithms cannot, potentially solving NP-complete problems efficiently.
This document describes numerical simulations of subsonic and supersonic flow through a choked nozzle using various schemes to solve the quasi-1D Euler equations. The author compares the steady state solutions from the Jameson-Schmidt-Turkel (JST) scheme (3, 4, and 5 stages), first-order Steger flux-vector splitting, and an analytic solution. The JST scheme converges quickly but is overly diffusive, while Steger converges slower but is less diffuse and more accurate near shocks. Higher-order JST stages and adjusting diffusion coefficients improve accuracy versus the analytic solution.
Foundation and Synchronization of the Dynamic Output Dual Systemsijtsrd
In this paper, the synchronization problem of the dynamic output dual systems is firstly introduced and investigated. Based on the time domain approach, the state variables synchronization of such dual systems can be verified. Meanwhile, the guaranteed exponential convergence rate can be accurately estimated. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the obtained result. Yeong-Jeu Sun "Foundation and Synchronization of the Dynamic Output Dual Systems" 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/ijtsrd29256.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/29256/foundation-and-synchronization-of-the-dynamic-output-dual-systems/yeong-jeu-sun
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcscpconf
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with the accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcsandit
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the
stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with
accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
An Exponential Observer Design for a Class of Chaotic Systems with Exponentia...ijtsrd
In this paper, a class of generalized chaotic systems with exponential nonlinearity is studied and the state observation problem of such systems is explored. Using differential inequality with time domain analysis, a practical state observer for such generalized chaotic systems is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to demonstrate the validity, effectiveness, and correctness of the obtained result. Yeong-Jeu Sun "An Exponential Observer Design for a Class of Chaotic Systems with Exponential Nonlinearity" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38233.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/38233/an-exponential-observer-design-for-a-class-of-chaotic-systems-with-exponential-nonlinearity/yeongjeu-sun
This work proposes a technique called pseudo-source injection to reduce pseudo-shear artifacts in finite-difference modeling of acoustic wave propagation in transversely isotropic media. The technique derives pseudo-sources from the pseudo-differential operator governing wave propagation and injects them into the coupled finite-difference equations at each time step. This projects the solution onto the shear-free solution space, resulting in significantly fewer pseudo-shear artifacts compared to other kinematically accurate finite-difference methods. Numerical examples modeling wave propagation through models with gradients and inclusions demonstrate the absence of pseudo-shear artifacts when using the proposed pseudo-source technique.
Development, Optimization, and Analysis of Cellular Automaton Algorithms to S...IRJET Journal
This document summarizes research on using cellular automaton algorithms to solve stochastic partial differential equations (SPDEs). It proposes a finite-difference method to approximate an SPDE modeling a random walk with angular diffusion. A Monte Carlo algorithm is also developed for comparison. Analysis finds a moderate correlation between the two methods, suggesting the finite-difference approach is reasonably accurate. It also identifies an inverse-square relationship between variables, linking to a foundational stochastic analysis concept. The research concludes the finite-difference method shows promise for approximating SPDEs while considering boundary conditions.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
FITTED OPERATOR FINITE DIFFERENCE METHOD FOR SINGULARLY PERTURBED PARABOLIC C...ieijjournal
In this paper, we study the numerical solution of singularly perturbed parabolic convection-diffusion type
with boundary layers at the right side. To solve this problem, the backward-Euler with Richardson
extrapolation method is applied on the time direction and the fitted operator finite difference method on the
spatial direction is used, on the uniform grids. The stability and consistency of the method were established
very well to guarantee the convergence of the method. Numerical experimentation is carried out on model
examples, and the results are presented both in tables and graphs. Further, the present method gives a more
accurate solution than some existing methods reported in the literature.
This document provides information about a computational stochastic processes course, including lecture details, prerequisites, syllabus, and examples. The key points are:
- Lectures will cover Monte Carlo simulation, stochastic differential equations, Markov chain Monte Carlo methods, and inference for stochastic processes.
- Prerequisites include probability, stochastic processes, and programming.
- Assessments will include a coursework and exam. The coursework will involve computational problems in Python, Julia, R, or similar languages.
- Motivating examples discussed include using Monte Carlo methods to evaluate high-dimensional integrals and simulating Langevin dynamics in statistical physics.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
Stochastic Analysis of Van der Pol OscillatorModel Using Wiener HermiteExpans...IJERA Editor
We study a model related to Van der Poloscillatorunder an external stochastic excitation described by white
noise process. This study is limited to find the Gaussian behavior of the stochastic solution processes related to
the model. Under the application ofWiener-Hermite expansion, a deterministic system is generated to describe
the Gaussian solution parameters (Mean and Variance).The deterministic system solution is approximated by
applying the multi-stepdifferential transformedmethodand the results are compared with NDSolveMathematica
10 package. Some case studies are considered to illustrate some comparisons for the obtained results related to
the Gaussian behavior parameters.
Stochastic Analysis of Van der Pol OscillatorModel Using Wiener HermiteExpans...IJERA Editor
We study a model related to Van der Poloscillatorunder an external stochastic excitation described by white
noise process. This study is limited to find the Gaussian behavior of the stochastic solution processes related to
the model. Under the application ofWiener-Hermite expansion, a deterministic system is generated to describe
the Gaussian solution parameters (Mean and Variance).The deterministic system solution is approximated by
applying the multi-stepdifferential transformedmethodand the results are compared with NDSolveMathematica
10 package. Some case studies are considered to illustrate some comparisons for the obtained results related to
the Gaussian behavior parameters.
Similar to New Scenario for Transition to Slow 3-D Turbulence Part I.Slow 1-D Turbulence in Nikolaevskii System (20)
New Thermodynamics: A Superior Fit Revised Kinetic Theoryijrap
The accepted kinetic theory forms a basis for modern thermodynamics and is mathematically based upon equipartition and degrees of freedom. It remains plagued with the necessity of numerous degrees of freedom exceptions for it to explain both empirically determined heat capacities and adiabatic indexes. Furthermore, assuming kT/2 per degree of freedom is to accept that a gas molecule possesses a specified energy without providing any clarity concerning that energy’s origins. Energy without an origin contravenes the first law of thermodynamics. This author’s previously published superior fit kinetic theory will be clarified and elaborated upon. This includes showing that this revised kinetic theory is a superior fit to both known heat capacities and adiabatic indexes. Not only is it a superior fit that does not rely upon any exceptions, this author’s kinetic theory also provides insight into the actual sources of a gas molecule’s energy. Furthermore, clarity concerning the difference between isometric (isochoric) and isobaric heat capacities in terms of sensible work will be discussed, along withits likely empirical verification.
On the Unification of Physic and the Elimination of Unbound Quantitiesijrap
This paper supports Descartes' idea of a constant quantity of motion, modernized by Leibniz. Unlike Leibniz, the paper emphasizes that the idea is not realized by forms of energy, but by energy itself. It remains constant regardless of the form, type, or speed of motion, even that of light. Through force, energy is only transformed. Here it is proved that force is its derivative. It exists even at rest, representing the object's minimal energy state. With speed, we achieve its multiplication up to the maximum energy state, from which a maximum force is derived from the object. From this point, corresponding to Planck's Length, we find the value of the force wherever we want. Achieving this removes the differences between various natural forces. The new idea eliminates infinite magnitudes. The process allows the laws to transition from simple to complex forms and vice versa, through differentiation-integration. For this paper, this means achieving the Unification Theory.
Gravity Also Redshifts Light – the Missing Phenomenon That Could Resolve Most...ijrap
In this paper I discover that gravity also redshifts light like the velocity of its source does. When light travels towards a supermassive object, its waves (or photons) undergo continuous stretching, thereby shifting towards lower frequencies. Gravity redshifts light irrespective of whether its source is in motion or static with respect to its observer. An equation is derived for gravitational redshift, and a formula for combined redshift is presented by considering both the velocity, and gravity redshifts. Also explained is how frequencies of electromagnetic spectrum continuously downgrade as a light beam of mix frequencies passes towards a black hole. Further, a clear methodology is provided to figure out whether expansion of the universe is accelerating or decelerating, or alternatively, the universe is contracting.
In this paper I present a new theory that explains as to when and how dark energy is created as mass is destroyed. The theory extends Einstein’s mass energy equation to a more generic form in order to make it work even in high gravity conditions. It also explains why dark energy is created. Further, it is proved Einstein’s mass energy equation holds good only when the destroyed mass has no supermassive object in its close vicinity. The relationship between dark energy and dark matter is unveiled. An extended mathematical form of Einstein’s mass energy equation is derived, based on which the conditions leading to dark energy creation are explained. Three new physical parameters called dark energy discriminant, dark energy radius and dark energy boundary are introduced to facilitate easy understanding of the theory. It is explained in detail that an extremely superdense object has two dark energy boundaries, outer and inner. Mass destroyed only between these two boundaries creates dark energy. Dark energy space, the space between the two aforementioned boundaries, shrouds visible matter in obscurity from optical and electromagnetic telescopes. This theory identifies Gargantuan as a superdense black hole currently creating fresh dark energy, which could be the subject of interest for the astronomical research community having access to sophisticated telescopes, and working on dark energy. It also upholds dark energy and denies the existence of dark matter. Dark matter is nothing but the well-known visible matter positioned in dark energy space. An important relationship is derived between a photon’s frequency and its distance from a black hole to demonstrate the effect of gravity on light. Another important fact revealed by this theory is gravity stretches out light, thereby causing redshift, which is unaccounted in the computation of velocities of outer galaxies. Whether the universe is undergoing accelerated or decelerated expansion, or accelerated contraction can precisely be determined only after accounting for the redshift caused by gravity
International Journal on Soft Computing, Artificial Intelligence and Applicat...ijrap
International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI)
is an open access peer-reviewed journal that provides an excellent international forum for sharing
knowledge and results in theory, methodology and applications of Artificial Intelligence, Soft
Computing. The Journal looks for significant contributions to all major fields of the Artificial
Intelligence, Soft Computing in theoretical and practical aspects. The aim of the Journal is to
provide a platform to the researchers and practitioners from both academia as well as industry to
meet and share cutting-edge development in the field.
Authors are solicited to contribute to the journal by submitting articles that illustrate research
results, projects, surveying works and industrial experiences that describe significant advances in
the areas of Database management systems.
SOME THEORETICAL ASPECTS OF HYDROGEN DIFFUSION IN BCC METALS AT LOW TEMPERATURESijrap
Purpose of the work is to discuss some theoretical aspects of the diffusion of hydrogen atoms in the crystal
lattice of BCC metals at low temperatures using the methods of statistical thermodynamics. The values of
the statistical model calculations of H diffusion coefficients in α-Fe, V, Ta, Nb, K are in good agreement
with the experimental data. The statistical model can also explain deviations from the Arrhenius equation
at temperatures 300-100 K in α-Fe, V, Nb and K. It was suggested that thermally activated fast tunnelling
transition of hydrogen atoms through the potential barrier at a temperature below 300 K provides an
almost free movement of H atoms in the α-Fe and V lattice at these temperatures. The results show that
quantum-statistical effects play a decisive role in the H diffusion in BCC metals at low temperatures. Using
the statistical model allows for the prediction of the diffusion coefficient for H in BCC metals at low
temperatures, where it’s necessary to consider quantum effects.
MASSIVE PHOTON HYPOTHESIS OPENS DOORS TO NEW FIELDS OF RESEARCHijrap
1) A massive photon hypothesis is proposed, where the photon mass is directly calculated from kinetic gas theory to be 1.25605 x 10-39 kg.
2) This photon mass explains various experiments like light deflection near the Sun and the gravitational redshift.
3) The photon gas is found to behave as a perfect blackbody and ideal gas, with photons having 6 degrees of freedom.
4) The thermal de Broglie wavelength of this photon gas is calculated to be 1.75967 x 10-3 m, matching the wavelength of the cosmic microwave background radiation.
5) This links the CMB radiation to being continuously generated by the photon gas permeating space, rather than being a relic of
PHENOMENOLOGICAL METHOD REGARDING A THIRD THEORY OF PHYSICS “THE EVENT:THE TH...ijrap
The quest for a third theory uniting macro-cosmos (relativity) and micro-cosmos (quantum mechanics) has coexisted with the denial of feminine/subjective polarity to masculine/objective. The dismissal of electromagnetism as the tension of opposites in quest of inner/outer unity is sourced in the denial of the feminine qualia -- the negative force field attributed to dark energy/dark matter. However, a conversion philosophy sourced in the hieros gamos and signified by the Mobius strip has formulated an integral consciousness methodology producing quantum objects by means of embracing the shadow haunting contemporary physics. This Self-reflecting process integrating subject/object comprises an ontology of kairos as the “quantum leap.” An interdisciplinary quest to create a phenomenological narrative is disclosed via a holistic apparatus of hermeneutics manifesting image/text of a contemporary grail journey. Reflected in this Third space is the sacred reality of autonomous number unifying polarities of feminine/subjective (quality) and objective/masculine (quantity) as new measurement apparatus for the quantum wave collapse.
3rd International Conference on Integrating Technology in Education (ITE 2022)ijrap
3rd International Conference on Integrating Technology in Education (ITE 2022) This forum also aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals.
A SPECIAL RELATIONSHIP BETWEEN MATTER, ENERGY, INFORMATION, AND CONSCIOUSNESSijrap
This paper discusses the advantages of describing the universe, or nature, in terms of information and consciousness. Some problems encountered by theoretical physicists in the quest for the theory of everything stem from the limitations of trying to understand everything in terms of matter and energy only. However, if everything, including matter, energy, life, and mental processes, is described in terms of information and consciousness, much progress can be made in the search for the ultimate theory of the universe. As brilliant and successful as physics and chemistry have been over the last two centuries, it is important that nature is not viewed solely in terms of matter and energy. Two additional components are needed to unlock her secrets. While extensive writing exists that describes the connection between matter and energy and their physical basis, little work has been done to learn the special relationship between matter, energy, information, and consciousness.
This paper discusses the advantages of describing the universe, or nature, in terms of information and consciousness. Some problems encountered by theoretical physicists in the quest for the theory of everything stem from the limitations of trying to understand everything in terms of matter and energy only. However, if everything, including matter, energy, life, and mental processes, is described in terms of information and consciousness, much progress can be made in the search for the ultimate theory of the universe. As brilliant and successful as physics and chemistry have been over the last two centuries, it is important that nature is not viewed solely in terms of matter and energy. Two additional components are needed to unlock her secrets. While extensive writing exists that describes the connection between matter and energy and their physical basis, little work has been done to learn the special relationship between matter, energy, information, and
consciousness.
THE CONCEPT OF SPACE AND TIME: AN AFRICAN PERSPECTIVEijrap
Understanding the concept of space and time is critical, essential, and fundamental in searching for theall-encompassing theory or the theory of everything (ToE). Some physicists argue that time exists, whileothers posit that time is only a social or mental construct. The author presents an African thought systemon space and time conception, focusing on the African (Bantu) view of space and time. The author arguesthat before the advent of the Western linear view of space and time, Africans had their own visionregarding these two concepts. Their conception of time appears to be holistic, highly philosophical, non-linear, and thought-provoking. The author hopes that exploring these two concepts from an African perspective will provide a new and more in-depth insight into reality's nature. A scientific investigation of space and time from an African-centered perspective is a worthy and necessary endeavor in the quest forthe ToE
Learning to Pronounce as Measuring Cross Lingual Joint Orthography Phonology ...ijrap
Machine learning models allow us to compare languages by showing how hard a task in each language might be to learn and perform well on. Following this line of investigation, we explore what makes a language “hard to pronounce” by modelling the task of grapheme-to-phoneme (g2p) transliteration. By training a character-level transformer model on this task across 22 languages and measuring the model’s proficiency against its grapheme and phoneme inventories, we show that certain characteristics emerge that separate easier and harder languages with respect to learning to pronounce. Namely the complexity of a language's pronunciation from its orthography is due to the expressive or simplicity of its grapheme-to phoneme mapping. Further discussion illustrates how future studies should consider relative data sparsity per language to design fairer cross-lingual comparison tasks.
THE CONCEPT OF SPACE AND TIME: AN AFRICAN PERSPECTIVEijrap
Understanding the concept of space and time is critical, essential, and fundamental in searching for the all-encompassing theory or the theory of everything (ToE). Some physicists argue that time exists, while others posit that time is only a social or mental construct. The author presents an African thought system on space and time conception, focusing on the African (Bantu) view of space and time. The author argues
that before the advent of the Western linear view of space and time, Africans had their own vision
regarding these two concepts. Their conception of time appears to be holistic, highly philosophical, nonlinear, and thought-provoking. The author hopes that exploring these two concepts from an African
perspective will provide a new and more in-depth insight into reality's nature. A scientific investigation of space and time from an African-centered perspective is a worthy and necessary endeavor in the quest for the ToE.
International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
The Concept of Space and Time: An African Perspectiveijrap
Understanding the concept of space and time is critical, essential, and fundamental in searching for the all-encompassing theory or the theory of everything (ToE). Some physicists argue that time exists, while others posit that time is only a social or mental construct. The author presents an African thought system on space and time conception, focusing on the African (Bantu) view of space and time. The author argues that before the advent of the Western linear view of space and time, Africans had their own vision regarding these two concepts. Their conception of time appears to be holistic, highly philosophical, nonlinear, and thought-provoking. The author hopes that exploring these two concepts from an African perspective will provide a new and more in-depth insight into reality's nature. A scientific investigation of space and time from an African-centered perspective is a worthy and necessary endeavor in the quest for the ToE.
The majority of physicists take it for granted that the universe is made up of matter. In turn, matter is composed of atoms; atoms are made up of particles such as electrons, protons, neutrons, etc. Also, protons
and neutrons are composed of quarks, etc. Furthermore, that everything in nature is governed by the known laws of physics and chemistry. The author only partially shares this view. He argues that many phenomena in the universe may depend on rules or factors as yet incorporated by the physical sciences.
The last few years have led him to reflect on the many unsolved physics problems, such as the quest for the theory of everything (ToE), the arrow of time, the interpretation of quantum mechanics, the fine-tuned
universe, etc. to mention just a few. The author posits that a field carries information, performs various mathematical and computational operations, and behaves as an intelligent entity embedded with consciousness.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
The International Journal of Recent Advances in Physics (IJRAP) is a peer-reviewed open access journal that addresses impacts and challenges in the field of physics. It covers theoretical and practical results across many areas of physics including advanced functional materials, applied optics, condensed matter physics, nuclear physics, quantum physics, and more. Authors are invited to submit papers by email before October 30, 2021. Notifications of acceptance will be provided by November 25, 2021.
Call For Papers - International Journal of Recent advances in Physics (IJRAP)ijrap
International Journal of Recent advances in Physics (IJRAP) is a peer-reviewed, open access journal, addresses the impacts and challenges of Physics. The journal documents practical and theoretical results which make a fundamental contribution for the development of Physics.
Mechanisms and Applications of Antiviral Neutralizing Antibodies - Creative B...Creative-Biolabs
Neutralizing antibodies, pivotal in immune defense, specifically bind and inhibit viral pathogens, thereby playing a crucial role in protecting against and mitigating infectious diseases. In this slide, we will introduce what antibodies and neutralizing antibodies are, the production and regulation of neutralizing antibodies, their mechanisms of action, classification and applications, as well as the challenges they face.
Compositions of iron-meteorite parent bodies constrainthe structure of the pr...Sérgio Sacani
Magmatic iron-meteorite parent bodies are the earliest planetesimals in the Solar System,and they preserve information about conditions and planet-forming processes in thesolar nebula. In this study, we include comprehensive elemental compositions andfractional-crystallization modeling for iron meteorites from the cores of five differenti-ated asteroids from the inner Solar System. Together with previous results of metalliccores from the outer Solar System, we conclude that asteroidal cores from the outerSolar System have smaller sizes, elevated siderophile-element abundances, and simplercrystallization processes than those from the inner Solar System. These differences arerelated to the formation locations of the parent asteroids because the solar protoplane-tary disk varied in redox conditions, elemental distributions, and dynamics at differentheliocentric distances. Using highly siderophile-element data from iron meteorites, wereconstruct the distribution of calcium-aluminum-rich inclusions (CAIs) across theprotoplanetary disk within the first million years of Solar-System history. CAIs, the firstsolids to condense in the Solar System, formed close to the Sun. They were, however,concentrated within the outer disk and depleted within the inner disk. Future modelsof the structure and evolution of the protoplanetary disk should account for this dis-tribution pattern of CAIs.
BIRDS DIVERSITY OF SOOTEA BISWANATH ASSAM.ppt.pptxgoluk9330
Ahota Beel, nestled in Sootea Biswanath Assam , is celebrated for its extraordinary diversity of bird species. This wetland sanctuary supports a myriad of avian residents and migrants alike. Visitors can admire the elegant flights of migratory species such as the Northern Pintail and Eurasian Wigeon, alongside resident birds including the Asian Openbill and Pheasant-tailed Jacana. With its tranquil scenery and varied habitats, Ahota Beel offers a perfect haven for birdwatchers to appreciate and study the vibrant birdlife that thrives in this natural refuge.
JAMES WEBB STUDY THE MASSIVE BLACK HOLE SEEDSSérgio Sacani
The pathway(s) to seeding the massive black holes (MBHs) that exist at the heart of galaxies in the present and distant Universe remains an unsolved problem. Here we categorise, describe and quantitatively discuss the formation pathways of both light and heavy seeds. We emphasise that the most recent computational models suggest that rather than a bimodal-like mass spectrum between light and heavy seeds with light at one end and heavy at the other that instead a continuum exists. Light seeds being more ubiquitous and the heavier seeds becoming less and less abundant due the rarer environmental conditions required for their formation. We therefore examine the different mechanisms that give rise to different seed mass spectrums. We show how and why the mechanisms that produce the heaviest seeds are also among the rarest events in the Universe and are hence extremely unlikely to be the seeds for the vast majority of the MBH population. We quantify, within the limits of the current large uncertainties in the seeding processes, the expected number densities of the seed mass spectrum. We argue that light seeds must be at least 103 to 105 times more numerous than heavy seeds to explain the MBH population as a whole. Based on our current understanding of the seed population this makes heavy seeds (Mseed > 103 M⊙) a significantly more likely pathway given that heavy seeds have an abundance pattern than is close to and likely in excess of 10−4 compared to light seeds. Finally, we examine the current state-of-the-art in numerical calculations and recent observations and plot a path forward for near-future advances in both domains.
Microbial interaction
Microorganisms interacts with each other and can be physically associated with another organisms in a variety of ways.
One organism can be located on the surface of another organism as an ectobiont or located within another organism as endobiont.
Microbial interaction may be positive such as mutualism, proto-cooperation, commensalism or may be negative such as parasitism, predation or competition
Types of microbial interaction
Positive interaction: mutualism, proto-cooperation, commensalism
Negative interaction: Ammensalism (antagonism), parasitism, predation, competition
I. Mutualism:
It is defined as the relationship in which each organism in interaction gets benefits from association. It is an obligatory relationship in which mutualist and host are metabolically dependent on each other.
Mutualistic relationship is very specific where one member of association cannot be replaced by another species.
Mutualism require close physical contact between interacting organisms.
Relationship of mutualism allows organisms to exist in habitat that could not occupied by either species alone.
Mutualistic relationship between organisms allows them to act as a single organism.
Examples of mutualism:
i. Lichens:
Lichens are excellent example of mutualism.
They are the association of specific fungi and certain genus of algae. In lichen, fungal partner is called mycobiont and algal partner is called
II. Syntrophism:
It is an association in which the growth of one organism either depends on or improved by the substrate provided by another organism.
In syntrophism both organism in association gets benefits.
Compound A
Utilized by population 1
Compound B
Utilized by population 2
Compound C
utilized by both Population 1+2
Products
In this theoretical example of syntrophism, population 1 is able to utilize and metabolize compound A, forming compound B but cannot metabolize beyond compound B without co-operation of population 2. Population 2is unable to utilize compound A but it can metabolize compound B forming compound C. Then both population 1 and 2 are able to carry out metabolic reaction which leads to formation of end product that neither population could produce alone.
Examples of syntrophism:
i. Methanogenic ecosystem in sludge digester
Methane produced by methanogenic bacteria depends upon interspecies hydrogen transfer by other fermentative bacteria.
Anaerobic fermentative bacteria generate CO2 and H2 utilizing carbohydrates which is then utilized by methanogenic bacteria (Methanobacter) to produce methane.
ii. Lactobacillus arobinosus and Enterococcus faecalis:
In the minimal media, Lactobacillus arobinosus and Enterococcus faecalis are able to grow together but not alone.
The synergistic relationship between E. faecalis and L. arobinosus occurs in which E. faecalis require folic acid
Dr. Firoozeh Kashani-Sabet is an innovator in Middle Eastern Studies and approaches her work, particularly focused on Iran, with a depth and commitment that has resulted in multiple book publications. She is notable for her work with the University of Pennsylvania, where she serves as the Walter H. Annenberg Professor of History.
TOPIC OF DISCUSSION: CENTRIFUGATION SLIDESHARE.pptxshubhijain836
Centrifugation is a powerful technique used in laboratories to separate components of a heterogeneous mixture based on their density. This process utilizes centrifugal force to rapidly spin samples, causing denser particles to migrate outward more quickly than lighter ones. As a result, distinct layers form within the sample tube, allowing for easy isolation and purification of target substances.
New Scenario for Transition to Slow 3-D Turbulence Part I.Slow 1-D Turbulence in Nikolaevskii System
1. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
DOI : 10.14810/ijrap.2015.4102 21
NEW SCENARIO FOR TRANSITION TO SLOW
3-D TURBULENCE PART I.SLOW 1-D
TURBULENCE IN NIKOLAEVSKII SYSTEM.
J. Foukzon
Israel Institute of Technology,Haifa, Israel
Abstract:
Analyticalnon-perturbative study of thethree-dimensional nonlinear stochastic partialdifferential equation
with additive thermal noise, analogous to thatproposed by V.N.Nikolaevskii [1]-[5] to describelongitudinal
seismic waves, ispresented. Theequation has a threshold of short-waveinstability and symmetry, providing
longwavedynamics.New mechanism of quantum chaos generating in nonlineardynamical systemswith
infinite number of degrees of freedom is proposed. The hypothesis is said,that physical turbulence could be
identifiedwith quantum chaos of considered type. It is shown that the additive thermal noise destabilizes
dramatically the ground state of theNikolaevskii system thus causing it to make a direct transition from a
spatially uniform to a turbulent state.
Keywords:
3D turbulence, chaos, quantum chaos,additive thermal noise,Nikolaevskii system.
1.Introduction
In the present work a non-perturbative analyticalapproach to the studying of problemof quantum chaos in
dynamical systems withinfinite number of degrees of freedom isproposed.Statistical descriptions of
dynamical chaos and investigations of noise effects on chaoticregimes arestudied.Proposed approach also
allows estimate the influence of additive (thermal)fluctuations on the processes of formation ofdeveloped
turbulence modes in essentially nonlinearprocesses like electro-convection andother. A principal rolethe
influence ofthermalfluctuations on thedynamics of some types of dissipative systems inthe approximate
environs of derivation rapid of ashort-wave instability was ascertained. Impotentphysicalresults follows
from Theorem 2, is illustrated by example of 3D stochastic model system:
,
,
14. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
22
which was obtained from thenon-stochastic3.Nikolaevskiimodel:
!/$,%,0
41. = 0.(1.7)
Systematic study of a different type of chaos at onset ‘‘soft-mode turbulence’’based onnumerical
integration of the simplest 1DNikolaevskii model (1.7)has been executed by many authors [2]-[7].There is
an erroneous belief that such numerical integration gives a powerful analysisismeans of the processes of
turbulence conception, based on the classical theory ofchaos of the finite-dimensional classical systems
[8]-[11].
Remark1.1.However, as it well known, such approximations correct only in a phase ofturbulence
conception, when relatively small number of the degrees of freedom excites. In general case, when a very
large number of the degrees of freedom excites, well known phenomena of thenumerically induced chaos,
can to spoils in the uncontrollable wayany numerical integration[12]-[15]
Remark1.2.Other non trivial problem stays from noise roundoff error in computer computation using
floatingpoint arithmetic [16]-[20].In any computer simulation the numerical solution is fraught with
truncation by roundoff errors introduced by finite-precision calculation of trajectories of dynamical systems,
where roundoff errors or other noise can introduce new behavior and this problem is a very more
pronounced in the case of chaotic dynamical systems, because the trajectories of such systems
exhibitextensivedependence on initial conditions. As a result, a small random truncation or roundoff error,
made computational error at any step of computation will tend to be large magnified by future
computationalof the system[17].
Remark1.3.As it well known, if the digitized or rounded quantity is allowed to occupy the nearest of a
large number of levels whose smallest separation is 56, then, provided that the
original quantity is large compared to 56 and is reasonably well behaved, theeffect of the quantization or
rounding may betreated as additive random noise [18].Bennett has shown that such additive noise is nearly
white, withmean squared value of 56
/12[19].However the complete uniform white-noise model to be valid
in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices
of realization of the system in the state space satisfy certain nonresonance conditions and the
finite-dimensional distributions of the input signal are absolutely continuous[19].
The method deprived of these essential lacks in general case has been offered by the author in papers
42. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
23
[23]-[27].
Remark1.4.Thus from consideration above it is clear thatnumerical integration procedure ofthe1D
Nikolaevskii model (1.6)-(1.7) executed in papers [2]-[7]in fact dealing withstochastic model
(1.4)-(1.5).There is an erroneous the point of view,that a white noise with enough small intensity does not
bringanysignificant contributions in turbulent modes, see for example [3]. By this wrong assumptions the
results of the numerical integration procedure ofthe1D Nikolaevskii model (1.6)-(1.7) were mistakenly
considered and interpretedas a veryexact modeling the slow turbulence within purely non stochastic
Nikolaevskii model (1.6)-(1.7).Accordingly wrongconclusionsabout that temperature noisesdoes not
influence slowturbulence have been proposed in [3].However in [27] has shown non-perturbativelythat that
a white noise with enough small intensity can to bring significant contributions in turbulent modes and
even to change this modes dramatically.
At the present time it is generally recognized thatturbulence in its developed phase has essentiallysingular
spatially-temporal structure. Such asingular conduct is impossible to describeadequately by the means of
some model system of equations of a finite dimensionality. In thispoint a classical theory of chaos is able
todescribe only small part of turbulencephenomenon in liquid and another analogous sof dynamical
systems. The results of non-perturbative modeling ofsuper-chaotic modes, obtained in the present paper
allow us to put out a quite probablehypothesis: developed turbulence in the realphysical systems with
infinite number of degreesof freedom is a quantum super-chaos, at that the quantitative characteristics of
this super-chaos, iscompletely determined by non-perturbativecontribution of additive (thermal)
fluctuations inthe corresponding classical system dynamics [18]-[20].
2.Main Theoretical Results
We study the stochastic 7-dimensionaldifferential equation analogous proposed byNikolaevskii [1] to
describe longitudinal seismicwaves:
!/4$,%,0,8
52. !$!$'…!$?!%
, 0 +, , = 1, … , 7.(2.2)
The main difficulty with the stochasticNikolaevskii equationis that the solutions do not take values in an
function space but in generalized functionspace. Thus it is necessary to give meaning to the non-linear
terms $B
,
, , 9
53. , , = 1, … , 7 because the usual product makes no sense for arbitrary distributions.
We deal with product of distributions via regularizations, i.e., we approximate the distributions by
appropriate way and pass to the limit.In this paper we use the approximation of the distributions by
approach of Colombeaugeneralized functions [28].
Notation 2.1.We denote byCℝ=
× ℝE
54. the space of the infinitely differentiable functionswith compact
supportin ℝ=
× ℝEandbyC′ℝ=
× ℝE
85. = 0almost surely for 9 ∈ Ω.
However in this paper we use the solutionsofstochastic Nikolaevskii equation only in the sense of
Colombeaugeneralized functions [30].
Remark2.1.Note that from Definition 2.2it is clear that any strong generalized solution,
, , 9
90. one can todefine appropriate generalized solutionof the Eq.(2.1)-(2.2) even if a strong
generalized solutionof the Eq.(2.1)-(2.2) does not exist.
Definition 2.3.Assumethata strong generalized solution of the Eq.(2.1)-(2.2) does not exist.We shall say
that:
(I)Colombeaugeneralized stochastic process a,
, , T, 9
91. b
[
is a weak generalized solution (WGS) of
the Eq.(2.1)-(2.2) orColombeausolutionof the Eq.(2.1)-(2.2) iffor all L ∈ Cℝ=
× ℝE
115. = 0almost surely for 9 ∈ Ω.
Notation 2.2.[30]. Thealgebra of moderate element we denote byℰeℝ=.The Colombeau algebra of the
Colombeau generalized functionwe denote by fℝ=
172. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
26
Definition 2.7.Smoothedwith respect to ℝ=
white noise j[,
213. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
27
Proof.The proof based on Strong large deviations principles(SLDP-Theorem) for Colombeau-Ito’ssolution
of the Colombeau-Ito’s SDE, see [26],theorem 6.BySLDP-Theorem one obtain directlythe differential
master equation (see [26],Eq.(90)) for Colombeau-Ito’s SDE(2.5)-(2.7):
_ ag[,ŒŒ,
,
225. = −›. (2.14)
From Eq.(2.5)-Eq.(2.7) and Eq.(2.13)-Eq.(2.14) by SLDP-Theorem (see see[26], inequality(89)) we obtain
the inequality
liminf[→6 1¡[,ŒŒ,
, , , 9
244. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
28
In the limit ™ → ∞ fromthe inequality we obtain the inequality
|[,
, , , 9
252. (2.22)
In the limit ™ → ∞ from Eq.(2.13)-Eq.(2.14) for any fixed T ≠ 0, T ≪ 1, we obtain the differential master
equationforColombeau-Ito’s SPDE (2.3)-(2.4)
_jg[,
, , ›
261. . (2.25)
In the limit T → 0from differential equation (2.23)-(2.24)we obtain the differential equation (2.8)-(2.9)and
it is easy to see that
lim[→6g[,
, , ›
274. = 0 (2.30),
We will call asthe differential master equation.
275. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
29
Definition 2.8.(TheTranscendental Master Equation)Thetranscendental equation
ℜj,
, , ›,
,
276. k = 0, (2.31)
wewill call asthe transcendentalmaster equation.
Remark2.2.We note that concrete structure of the Nikolaevskii chaos is determined by the
solutions›,
,
278. which is the main constructive object, determining
thecharacteristics of quantum chaos in the corresponding model of Euclidian quantum fieldtheory.
3.Criterion of the existence quantum chaos in Euclidian quantum
N-model.
Definition3.1.Let ,
, , 9
279. be the solution of the Eq.(2.1). Assume that for almost all points,
280. ∈
ℝ=
× ℝE(in the sense of Lebesgue–measureonℝ=
× ℝE), there exist a function ,
283. b
¨ = 0. (3.1)
Then we will say that afunction ,
284. is a quasi-determined solution (QD-solution of the Eq.(2.).
Definition3.2. Assume that there exist a setℌ ⊂ ℝ=
× ℝEthat is positive
Lebesgue–measure, i.e.,tℌ
290. £does not exist.
Then we will say thatEuclidian quantum N-model has thequasi-determined Euclidian quantum chaos
(QD-quantum chaos).
Definition3.3.For each point,
300. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
Pic.3.1.Evolution of
at point
Pic.3.2.The spatial structure of
instant
Theorem3.1.Assume that,
301. such that 7 ∈ ³, + ∈ ℝE, , = 1, …
QD-chaotic solutions.
Definition3.5.For each point ,
(i) E,
,
323. =
Then we will say that Euclidian quantum N
width at point ∈ ℝ=
.
Pic.3.3.TheQD-quantum chaos of the asymptotically infinite width at point
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
is called lower bound of the QD-quantum chaosat point ,
326. * ∞.(3.5)
Then we will say thatEuclidian quantum N-model has QD-quantum chaos of the asymptotically
327. = ∞. (3.6)
Then we will say that Euclidian quantum N-model has QD-quantum chaos of the asymptotically
quantum chaos of the asymptotically infinite width at point = 3. = 0.1
10
, ´ = 1.
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
31
328. .
quantum chaos of the asymptotically
quantum chaos of the asymptotically infinite
1, = 10, s =
329. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
32
Pic.3.4.The fine structure of the QD-quantum chaos of the asymptotically infinite width at point =
3, = 0, = 10, s = 10µ
, ´ = 1,
∈ 10µ
, 10µ
+ 10ƒ, › ∈ −0.676,0.676.
Definition3.10. For each point ,
330. ∈ ℝ=
× ℝE we define the functions such that:
(i) ℜ
±E,
,
340. .(3.7)
Proof. Immediately follows by Theorem2.1 and Definitions 3.5, 3.10.
Theorem3.3. (Criterion of QD-quantum chaos in Euclidian quantum N-model)
Assume that
mes,
342. 0° 0.(3.8)
Then Euclidian quantum N-model has QD-quantum chaos.
Proof. Immediately follows bytheinequality(3.7)and Definition3.2.
4. Quasi-determined quantum chaos and physical turbulencenature.
In generally accepted at the present time hypothesiswhatphysical turbulencein the dynamical systems with
an infinite number of degrees of freedom really is, thephysical turbulence is associated with a
strangeattractors, on which the phase trajectories of dynamical system reveal the knownproperties of
stochasticity: a very high dependence on the initial conditions, whichis associated with exponential
dispersion of the initially close trajectories and bringsto their non-reproduction; everywhere the density on
the attractor almost of all thetrajectories a very fast decreaseoflocal auto-correlation function[2]-[9]
Φx, τ
352. .
In contrast with canonical numerical simulation, by using Theorem2.1 it is possible to study
non-perturbativelythe influence of thermal additive fluctuationson classical dynamics, which in the
consideredcase is described by equation (4.1).
The physicalnature of quasi-determined chaosis simple andmathematically is associated
withdiscontinuously of the trajectories of the stochastic process,
, , 9
353. on parameter .
In order to obtain thecharacteristics of this turbulence, which is a very similarlytolocal auto-correlation
function (3.1) we define bellowsomeappropriatefunctions.
354. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
33
Definition 4.1.The numbering function™
,
419. Q
The result of calculation using transcendental
is presented by Pic.4.1 and Pic.4.2.
Pic.4.1.Evolution of QD-chaotic solution
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
, , ›
429. Q ∙ s ∙ ƒ
∙ ´ƒ
›
0.(4.15)
transcendental master equation (4.15) the corresponding function
is presented by Pic.4.1 and Pic.4.2.
chaotic solutionO
±10
,
,
430. in time
∈ 0, 10, ∆
0.1,
s 10
, 1, , ∆› 0.01
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
34
master equation (4.15) the corresponding function O
±,
,
432. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
Pic.4.2.The spatial structure ofQD
The result of calculation using master equation(4.
presented by Pic.4.3 and Pic.4.4
Pic.4.3.The
EuclidianquantumN-model
Pic.4.4.The development
Euclidian quantum N-model at point
Let us calculate now corresponding
of calculation using Eq.(4.7)-Eq.(4.7)
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
QD-chaoticsolutionO
±,
,
433. at instant
10
, 0, ´
1, ∆ 0.1, ∆› 0.01.
calculation using master equation(4.13) the correspondingfunction
4.
Thedevelopment of temporal chaotic regime of1D
model at point 1,
∈ 0, 10. 10ƒÍ
, s 10
, 1,
The developmentof temporal chaotic regimeof 1D
model at point 1,
∈ 0, 10, 10ƒÍ
, s 5 ∙ 10Ï
, 1
correspondingnormalized local auto-correlation functionΦ¿
Eq.(4.7) is presented by Pic.4.5 and Pic.4.6.
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
35
= 1, s 10
,
unction O
Ð,
,
436. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
Pic.4.5. Normalized local auto
∈
Pic.4.6.Normalized local auto
∈ 0
Inpaper [7]the mechanism of the onset of chaos and its relationship to the characteristics of the spiral
attractors are demonstrated for inhomogeneous media that can be modeled by the Ginzburg
equation(4.14). Numerical data are compared with experimental results.
!Ñ$,%
439. 1 |Ò
Ò
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
Normalized local auto-correlation function Φ¿1, ¹
440. ∈ 0,50, 10ƒÍ
, s 10
, 1, ´ 1.
Normalized local auto-correlation functionΦ¿1, ¹
441. .
0,100, 10ƒÍ
, s 5 ∙ 10Ï
, 1, ´ 1.
the mechanism of the onset of chaos and its relationship to the characteristics of the spiral
attractors are demonstrated for inhomogeneous media that can be modeled by the Ginzburg
. Numerical data are compared with experimental results.
,
447. 0, ∈ 0, Ô, Ô 50.
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
36
the mechanism of the onset of chaos and its relationship to the characteristics of the spiral
attractors are demonstrated for inhomogeneous media that can be modeled by the Ginzburg– Landau
448. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
Pic.4.7. Normalized local auto
However as pointed out above (see
for stochastic model
!Ñ$,%
451. 1 |Ò
Ò
5.The order of the phase transition
turbulent state at instant
In order to obtain the character of the phase transition
a spatially uniform to a turbulent state
Oj,
, , ›,
,
452. k 0. (5.1)
Bydifferentiation the Eq.(5.1) one obtain
Oj$,%,0,œ$,%,0
456. k
!0
b ∙ a
!Oj
Let us consider now 1DEuclidian quantum N
transcendental master equation Eq.(4.13)
›one obtain
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
Normalized local auto-correlation functionΦ¿25, ¹
457. [7].
However as pointed out above (see Remark1.1-1.4 ) such numerical simulation in factgives
,
464. 0, ∈ 0, Ô, Ô 50.
phase transitionfrom a spatially uniformstate
at instant Ö × Ø.
In order to obtain the character of the phase transition (first-order or second-order on parameter
a spatially uniform to a turbulent stateat instant
× 0one can to use the master equation () of the form
one obtain
k $,%,0
467. k
!œ
b
ƒ
.(5.3)
Euclidian quantum N-model given byEq. (4.9)-Eq. (4.10). From corresponding
transcendental master equation Eq.(4.13)by differentiation the equation Eq.(4.13)with respect to
International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
37
givesnumerical data
state to a
on parameters , ´) from
one can to use the master equation () of the form
Eq. (4.10). From corresponding
with respect to variable
468. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
38
Oj,
, , ›,
,
550. at instant
= 0.
Therefore the system causing it to make a direct transitionfrom a spatially uniformstate≈6, 0,
551. = 0
to a turbulent statein an analogous fashion to the second-order phase transition inquasi-equilibrium
systems.
6.Chaotic regime generatedby periodical multi-modes external
perturbation.
Assume nowthat external periodical force
571. at instant
= 5 ∙ 10
,
∈ 1.4 ∙ 10
, 2.5 ∙ 10, ç = 1, — = 100, = −1, ´ = 1, s = 10
, = 1,
∆ = 0.1, ∆› = 0.01.
7.Conclusion
A non-perturbative analytical approach to the studying of problemof quantum chaos in dynamical systems
withinfinite number of degrees of freedom isproposed and developed successfully.It is shown that the
additive thermal noise destabilizes dramatically the ground state of the system thus causing it to make a
direct transition from a spatially uniform to a turbulent state.
572. International Journal of Recent advances in Physics (IJRAP) Vol.4, No.1, February 2015
41
8.Acknowledgments
A reviewer provided important clarifications.
References
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New Mexico, SS 9A, Special Session on Mathematical Methods in Turbulence.
http://www.ams.org/meetings/sectional/1000-76-7.pdf
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