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seyd ghasem enayati
2017-01-01
Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.
Eshkuvatov, Z K; Zulkarnain, F S; Nik Long, N M A; Muminov, Z
2016-01-01
Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm convergence are obtained in Hilbert space. Comparisons between modified HPM, standard HPM, Bernstein polynomials approach Mandal and Bhattacharya (Appl Math Comput 190:1707-1716, 2007), Chebyshev expansion method Mahiub et al. (Int J Pure Appl Math 69(3):265-274, 2011) and reproducing kernel Chen and Zhou (Appl Math Lett 24:636-641, 2011) are made by solving five examples. Theoretical and practical examples revealed that the modified HPM dominates the standard HPM and others. Finally, it is found that the modified HPM is exact, if the solution of the problem is a product of weights and polynomial functions. For rational solution the absolute error decreases very fast by increasing the number of collocation points.
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Norhasimah Mahiddin
2014-01-01
Full Text Available The modified decomposition method (MDM and homotopy perturbation method (HPM are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.
Beyond perturbation introduction to the homotopy analysis method
Liao, Shijun
2003-01-01
Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity.This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra''s population model, Von Kármán swirling viscous flow, and nonlinear progressive waves in deep water.Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be ...
Approximate solution fuzzy pantograph equation by using homotopy perturbation method
Jameel, A. F.; Saaban, A.; Ahadkulov, H.; Alipiah, F. M.
2017-09-01
In this paper, Homotopy Perturbation Method (HPM) is modified and formulated to find the approximate solution for its employment to solve (FDDEs) involving a fuzzy pantograph equation. The solution that can be obtained by using HPM is in the form of infinite series that converge to the actual solution of the FDDE and this is one of the benefits of this method In addition, it can be used for solving high order fuzzy delay differential equations directly without reduction to a first order system. Moreover, the accuracy of HPM can be detected without needing the exact solution. The HPM is studied for fuzzy initial value problems involving pantograph equation. Using the properties of fuzzy set theory, we reformulate the standard approximate method of HPM and obtain the approximate solutions. The effectiveness of the proposed method is demonstrated for third order fuzzy pantograph equation.
Application of New Variational Homotopy Perturbation Method For ...
African Journals Online (AJOL)
This paper discusses the application of the New Variational Homotopy Perturbation Method (NVHPM) for solving integro-differential equations. The advantage of the new Scheme is that it does not require discretization, linearization or any restrictive assumption of any form be fore it is applied. Several test problems are ...
DEFF Research Database (Denmark)
Farrokhzad, F.; Mowlaee, P.; Barari, Amin
2011-01-01
The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation......., and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...
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Anant Kant Shukla
2014-11-01
Full Text Available We obtain approximate analytical solutions of two mathematical models of the dynamics of tobacco use and relapse including peer pressure using the homotopy perturbation method (HPM and the homotopy analysis method (HAM. To enlarge the domain of convergence we apply the Padé approximation to the HPM and HAM series solutions. We show graphically that the results obtained by both methods are very accurate in comparison with the numerical solution for a period of 30 years.
International Nuclear Information System (INIS)
Dehghan, Mehdi; Shakeri, Fatemeh
2007-01-01
In this work, the solution of an inverse problem concerning a diffusion equation with source control parameters is presented. The homotopy perturbation method is employed to solve this equation. This method changes a difficult problem into a simple problem which can be easily solved. In this procedure, according to the homotopy technique, a homotopy with an embedding parameter p element of [0,1] is constructed, and this parameter is considered a 'small parameter', so the method is called the homotopy perturbation method, which can take full advantage of the traditional perturbation method and homotopy technique. The approximations obtained by the proposed method are uniformly valid not only for small parameters, but also for very large parameters. The fact that this technique, in contrast to the traditional perturbation methods, does not require a small parameter in the system, leads to wide applications in nonlinear equations
Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method
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Seval Pinarbasi
2012-01-01
Full Text Available The design of slender beams, that is, beams with large laterally unsupported lengths, is commonly controlled by stability limit states. Beam buckling, also called “lateral torsional buckling,” is different from column buckling in that a beam not only displaces laterally but also twists about its axis during buckling. The coupling between twist and lateral displacement makes stability analysis of beams more complex than that of columns. For this reason, most of the analytical studies in the literature on beam stability are concentrated on simple cases: uniform beams with ideal boundary conditions and simple loadings. This paper shows that complex beam stability problems, such as lateral torsional buckling of rectangular beams with variable cross-sections, can successfully be solved using homotopy perturbation method (HPM.
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
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Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
International Nuclear Information System (INIS)
Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.
2008-01-01
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient
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Muhammad Aslam Noor
2008-01-01
Full Text Available We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method (VHPM. We use this method for solving higher dimensional initial boundary value problems with variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these problems. The proposed scheme finds the solution without any discritization, transformation, or restrictive assumptions and avoids the round-off errors. Several examples are given to check the reliability and efficiency of the proposed technique.
The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Momani, S.
2009-01-01
In this paper, a new reliable algorithm based on an adaptation of the standard homotopy-perturbation method (HPM) is presented. The HPM is treated as an algorithm in a sequence of intervals (i.e. time step) for finding accurate approximate solutions to the famous Lorenz system. Numerical comparisons between the multistage homotopy-perturbation method (MHPM) and the classical fourth-order Runge-Kutta (RK4) method reveal that the new technique is a promising tool for the nonlinear systems of ODEs.
A Homotopy-Perturbation analysis of the non-linear contaminant ...
African Journals Online (AJOL)
In this research work, a Homotopy-perturbation analysis of a non –linear contaminant flow equation with an initial continuous point source is provided. The equation is characterized by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of ...
Analysis of Diffusion Problems using Homotopy Perturbation and Variational Iteration Methods
DEFF Research Database (Denmark)
Barari, Amin; Poor, A. Tahmasebi; Jorjani, A.
2010-01-01
In this paper, variational iteration method and homotopy perturbation method are applied to different forms of diffusion equation. The diffusion equations have found wide applications in heat transfer problems, theory of consolidation and many other problems in engineering. The methods proposed...
International Nuclear Information System (INIS)
Biazar, J.; Eslami, M.; Aminikhah, H.
2009-01-01
In this article, an application of He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the first kind. Some non-linear examples are prepared to illustrate the efficiency and simplicity of the method. Applying the method for linear systems is so easily that it does not worth to have any example.
International Nuclear Information System (INIS)
Biazar, J.; Ghazvini, H.
2009-01-01
In this paper, the He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the second kind. Some examples are presented to illustrate the ability of the method for linear and non-linear such systems. The results reveal that the method is very effective and simple.
Application of homotopy-perturbation method to nonlinear population dynamics models
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.
2007-01-01
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Fernandez, E; Neipp, C; Belendez, T
2008-01-01
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient
A discrete homotopy perturbation method for non-linear Schrodinger equation
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H. A. Wahab
2015-12-01
Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.
Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System
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M. S. H. Chowdhury
2012-01-01
Full Text Available Finding accurate solution of chaotic system by using efficient existing numerical methods is very hard for its complex dynamical behaviors. In this paper, the multistage homotopy-perturbation method (MHPM is applied to the Chaotic Genesio system. The MHPM is a simple reliable modification based on an adaptation of the standard homotopy-perturbation method (HPM. The HPM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the Chaotic Genesio system. Numerical comparisons between the MHPM and the classical fourth-order Runge-Kutta (RK4 solutions are made. The results reveal that the new technique is a promising tool for the nonlinear chaotic systems of ordinary differential equations.
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Jing Wang
2013-01-01
Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.
Approximate solution of generalized Ginzburg-Landau-Higgs system via homotopy perturbation method
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Lu Juhong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Dept. of Information Engineering, Coll. of Lishui Professional Tech., Zhejiang (China); Zheng Chunlong [School of Physics and Electromechanical Engineering, Shaoguan Univ., Guangdong (China); Shanghai Inst. of Applied Mathematics and Mechanics, Shanghai Univ., SH (China)
2010-04-15
Using the homotopy perturbation method, a class of nonlinear generalized Ginzburg-Landau-Higgs systems (GGLH) is considered. Firstly, by introducing a homotopic transformation, the nonlinear problem is changed into a system of linear equations. Secondly, by selecting a suitable initial approximation, the approximate solution with arbitrary degree accuracy to the generalized Ginzburg-Landau-Higgs system is derived. Finally, another type of homotopic transformation to the generalized Ginzburg-Landau-Higgs system reported in previous literature is briefly discussed. (orig.)
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
International Nuclear Information System (INIS)
Molabahrami, A.; Khani, F.; Hamedi-Nezhad, S.
2007-01-01
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple
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Abdoul R. Ghotbi
2008-01-01
Full Text Available Due to wide range of interest in use of bioeconomic models to gain insight into the scientific management of renewable resources like fisheries and forestry, homotopy perturbation method is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting. The results are compared with the results obtained by Adomian decomposition method. The results show that, in new model, there are less computations needed in comparison to Adomian decomposition method.
International Nuclear Information System (INIS)
Cuce, Erdem; Cuce, Pinar Mert
2015-01-01
Highlights: • Homotopy perturbation method has been applied to porous fins. • Dimensionless efficiency and effectiveness expressions have been firstly developed. • Effects of porous and convection parameters on thermal analysis have been clarified. • Ratio of porous fin to solid fin heat transfer rate has been given for various cases. • Reliability and practicality of homotopy perturbation method has been illustrated. - Abstract: In our previous works, thermal performance of straight fins with both constant and temperature-dependent thermal conductivity has been investigated in detail and dimensionless analytical expressions of fin efficiency and fin effectiveness have been developed for the first time in literature via homotopy perturbation method. In this study, previous works have been extended to porous fins. Governing equations have been formulated by performing Darcy’s model. Dimensionless temperature distribution along the length of porous fin has been determined as a function of porosity and convection parameters. The ratio of porous fin to solid fin heat transfer rate has also been evaluated as a function of thermo-geometric fin parameter. The results have been compared with those of finite difference method for a specific case and an excellent agreement has been observed. The expressions developed are beneficial for thermal engineers for preliminary assessment of thermophysical systems instead of consuming time in heat conduction problems governed by strongly nonlinear differential equations
DEFF Research Database (Denmark)
Reck, Kasper; Thomsen, Erik Vilain; Hansen, Ole
2011-01-01
. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution......The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method...
Homotopy perturbation method for free vibration analysis of beams on elastic foundation
International Nuclear Information System (INIS)
Ozturk, Baki; Coskun, Safa Bozkurt; Koc, Mehmet Zahid; Atay, Mehmet Tarik
2010-01-01
In this study, the homotopy perturbation method (HPM) is applied for free vibration analysis of beam on elastic foundation. This numerical method is applied on a previously available case study. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, N r . The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for the case considered in this study and the differential transform method (DTM) results available in the literature.
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Claude Rodrigue Bambe Moutsinga
2018-01-01
Full Text Available Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method for solving systems of stiff Riccati differential equations. In this technique, a combination of Laplace transform and homotopy perturbation methods is considered as an algorithm to the exact solution of the nonlinear Riccati equations. The resulting technique is applied to solving stiff diffusion model problems that include interest rates models as well as two and three-factor stochastic volatility models. We show that the present approach is relatively easy, efficient and highly accurate.
Laplace transform homotopy perturbation method for the approximation of variational problems.
Filobello-Nino, U; Vazquez-Leal, H; Rashidi, M M; Sedighi, H M; Perez-Sesma, A; Sandoval-Hernandez, M; Sarmiento-Reyes, A; Contreras-Hernandez, A D; Pereyra-Diaz, D; Hoyos-Reyes, C; Jimenez-Fernandez, V M; Huerta-Chua, J; Castro-Gonzalez, F; Laguna-Camacho, J R
2016-01-01
This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its modifications in order to find analytical approximate solutions for the linear and nonlinear differential equations which arise from some variational problems. As case study we will solve four ordinary differential equations, and we will show that the proposed solutions have good accuracy, even we will obtain an exact solution. In the sequel, we will see that the square residual error for the approximate solutions, belongs to the interval [0.001918936920, 0.06334882582], which confirms the accuracy of the proposed methods, taking into account the complexity and difficulty of variational problems.
Numerical simulation of the regularized long wave equation by He's homotopy perturbation method
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Inc, Mustafa [Department of Mathematics, Firat University, 23119 Elazig (Turkey)], E-mail: minc@firat.edu.tr; Ugurlu, Yavuz [Department of Mathematics, Firat University, 23119 Elazig (Turkey)
2007-09-17
In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions.
Numerical simulation of the regularized long wave equation by He's homotopy perturbation method
International Nuclear Information System (INIS)
Inc, Mustafa; Ugurlu, Yavuz
2007-01-01
In this Letter, we present the homotopy perturbation method (shortly HPM) for obtaining the numerical solution of the RLW equation. We obtain the exact and numerical solutions of the Regularized Long Wave (RLW) equation for certain initial condition. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of other methods have led us to significant consequences. The numerical solutions are compared with the known analytical solutions
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H. Vazquez-Leal
2014-01-01
Full Text Available We present a homotopy continuation method (HCM for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points. The results show that HCM can find multiple solutions within a single homotopy trajectory. Furthermore, we take advantage of the fact that homotopy trajectories are PWL curves meant to replace the multidimensional interpolation and fine tuning stages of the path tracking algorithm with a simple and highly accurate procedure based on the parametric straight line equation.
International Nuclear Information System (INIS)
Esmaeilpour, M.; Ganji, D.D.
2007-01-01
In this Letter, the problem of forced convection over a horizontal flat plate is presented and the homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations
International Nuclear Information System (INIS)
Fathizadeh, M.; Aroujalian, A.
2012-01-01
The boundary layer convective heat transfer equations with low pressure gradient over a flat plate are solved using Homotopy Perturbation Method, which is one of the semi-exact methods. The nonlinear equations of momentum and energy solved simultaneously via Homotopy Perturbation Method are in good agreement with results obtained from numerical methods. Using this method, a general equation in terms of Pr number and pressure gradient (λ) is derived which can be used to investigate velocity and temperature profiles in the boundary layer.
DEFF Research Database (Denmark)
Ganji, D.D; Miansari, Mo; B, Ganjavi
2008-01-01
In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...
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R. Darzi
2010-01-01
Full Text Available We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
Darzi R; Neamaty A
2010-01-01
We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both linear and nonlinear problems without linearization or discretization. The results show that both methods are simple and effective.
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U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Energy Technology Data Exchange (ETDEWEB)
Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J [Intelligent System Research Group, Faculty of Electrical and Computer Engineering, Babol, Noushirvani University of Technology, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Department of Mathematics, Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com
2009-10-15
The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.
International Nuclear Information System (INIS)
Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J; Ranjbar, A; Momani, S
2009-01-01
The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.
Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.
2009-10-01
The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.
Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Marquez, A.; Neipp, C.
2008-01-01
We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems
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Aboozar Heydari
2017-09-01
Full Text Available In this paper, the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated. The rotor is modeled as a rigid body that is supported by two magnetic bearings with eight-polar structures. The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations (ODEs are derived, and for solving these equations, the homotopy perturbation method (HPM is used. By applying HPM, the possibility of presenting a harmonic semi-analytical solution, is provided. In fact, with equality the coefficient of auxiliary parameter (p, the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects. By considering some initial condition for displacement and velocity in the horizontal and vertical directions, free vibration analysis is done and next, the forced vibration analysis under the effect of harmonic forces also is investigated. Likewise, various parameters on the vibration behavior of rotor are studied. Changes in amplitude and response phase per excitation frequency are investigated. Results show that by increasing excitation frequency, the motion amplitude is also increases and by passing the critical speed, it decreases. Also it shows that the magnetic bearing system performance is in stable maintenance of rotor. The parameters affecting on vibration behavior, has been studied and by comparison the results with the other references, which have a good precision up to 2nd order of embedding parameter, it implies the accuracy of this method in current research.
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D. Olvera
2015-01-01
Full Text Available We expand the application of the enhanced multistage homotopy perturbation method (EMHPM to solve delay differential equations (DDEs with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.
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Pranab Kanti Roy
2015-09-01
Full Text Available This work aimed at studying the effects of environmental temperature and surface emissivity parameter on the temperature distribution, efficiency and heat transfer rate of a conductive–radiative fin. The Homotopy Perturbation Method (HPM being one of the semi-numerical methods for highly nonlinear and inhomogeneous equations, the local temperature distribution efficiencies and heat transfer rates are obtained using HPM in which Newton–Raphson method is used for the insulated boundary condition. It is found that the results of the present works are in good agreement with results available in the literature.
Directory of Open Access Journals (Sweden)
Saeed Dinarvand
2012-01-01
Full Text Available The steady three-dimensional flow of condensation or spraying on inclined spinning disk is studied analytically. The governing nonlinear equations and their associated boundary conditions are transformed into the system of nonlinear ordinary differential equations. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM. The velocity and temperature profiles are shown and the influence of Prandtl number on the heat transfer and Nusselt number is discussed in detail. The validity of our solutions is verified by the numerical results. Unlike free surface flows on an incline, this through flow is highly affected by the spray rate and the rotation of the disk.
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
International Nuclear Information System (INIS)
Hojjati, M.H.; Jafari, S.
2008-01-01
In this work, two powerful analytical methods, namely homotopy perturbation method (HPM) and Adomian's decomposition method (ADM), are introduced to obtain distributions of stresses and displacements in rotating annular elastic disks with uniform and variable thicknesses and densities. The results obtained by these methods are then compared with the verified variational iteration method (VIM) solution. He's homotopy perturbation method which does not require a 'small parameter' has been used and a homotopy with an imbedding parameter p element of [0,1] is constructed. The method takes the full advantage of the traditional perturbation methods and the homotopy techniques and yields a very rapid convergence of the solution. Adomian's decomposition method is an iterative method which provides analytical approximate solutions in the form of an infinite power series for nonlinear equations without linearization, perturbation or discretization. Variational iteration method, on the other hand, is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. This study demonstrates the ability of the methods for the solution of those complicated rotating disk cases with either no or difficult to find fairly exact solutions without the need to use commercial finite element analysis software. The comparison among these methods shows that although the numerical results are almost the same, HPM is much easier, more convenient and efficient than ADM and VIM
International Nuclear Information System (INIS)
Abbasbandy, S.
2009-01-01
Solitary wave solutions to the modified form of Camassa-Holm (CH) equation are sought. In this work, the homotopy analysis method (HAM), one of the most effective method, is applied to obtain the soliton wave solutions with and without continuity of first derivatives at crest
Tripathi, Rajnee; Mishra, Hradyesh Kumar
2016-01-01
In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type differential equations and use their appropriate comparisons with exact solutions. In the current study, some examples are better than other existing methods with their nearer results in the form of power series. The Laplace transform used to accelerate the convergence of power series and the results are shown in the tables and graphs which have good agreement with the other existing method in the literature. The results show that LT-HPM is very effective and easy to implement.
Arslanturk, Cihat
2011-02-01
Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.
Homotopy decomposition method for solving one-dimensional time-fractional diffusion equation
Abuasad, Salah; Hashim, Ishak
2018-04-01
In this paper, we present the homotopy decomposition method with a modified definition of beta fractional derivative for the first time to find exact solution of one-dimensional time-fractional diffusion equation. In this method, the solution takes the form of a convergent series with easily computable terms. The exact solution obtained by the proposed method is compared with the exact solution obtained by using fractional variational homotopy perturbation iteration method via a modified Riemann-Liouville derivative.
Directory of Open Access Journals (Sweden)
I-Chung Liu
2012-01-01
Full Text Available We have analyzed the effects of variable heat flux and internal heat generation on the flow and heat transfer in a thin film on a horizontal sheet in the presence of thermal radiation. Similarity transformations are used to transform the governing equations to a set of coupled nonlinear ordinary differential equations. The obtained differential equations are solved approximately by the homotopy perturbation method (HPM. The effects of various parameters governing the flow and heat transfer in this study are discussed and presented graphically. Comparison of numerical results is made with the earlier published results under limiting cases.
Melikhov, Sergey A.
2009-06-01
Steenrod homotopy theory is a natural framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; or from a different viewpoint, it studies the topology of the \\lim^1 functor (for inverse sequences of groups). This paper is primarily concerned with the case of compacta, in which Steenrod homotopy coincides with strong shape. An attempt is made to simplify the foundations of the theory and to clarify and improve some of its major results. With geometric tools such as Milnor's telescope compactification, comanifolds (=mock bundles), and the Pontryagin-Thom construction, new simple proofs are obtained for results by Barratt-Milnor, Geoghegan-Krasinkiewicz, Dydak, Dydak-Segal, Krasinkiewicz-Minc, Cathey, Mittag-Leffler-Bourbaki, Fox, Eda-Kawamura, Edwards-Geoghegan, Jussila, and for three unpublished results by Shchepin. An error in Lisitsa's proof of the `Hurewicz theorem in Steenrod homotopy' is corrected. It is shown that over compacta, R.H. Fox's overlayings are equivalent to I.M. James' uniform covering maps. Other results include: \\bullet A morphism between inverse sequences of countable (possibly non-Abelian) groups that induces isomorphisms on \\lim and \\lim^1 is invertible in the pro-category. This implies the `Whitehead theorem in Steenrod homotopy', thereby answering two questions of Koyama. \\bullet If X is an LC_{n-1}-compactum, n\\ge 1, then its n-dimensional Steenrod homotopy classes are representable by maps S^n\\to\
Abou-zeid, Mohamed Y.; Mohamed, Mona A. A.
2017-09-01
This article is an analytic discussion for the motion of power-law nanofluid with heat transfer under the effect of viscous dissipation, radiation, and internal heat generation. The governing equations are discussed under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using homotopy perturbation method. Results for the behaviours of the axial velocity, temperature, and nanoparticles as well as the skin friction coefficient, reduced Nusselt number, and Sherwood number with other physical parameters are obtained graphically and analytically. It is found that as the power-law exponent increases, both the axial velocity and temperature increase, whereas nanoparticles decreases. These results may have applicable importance in the research discussions of nanofluid flow in channels with small diameters under the effect of different temperature distributions.
International Nuclear Information System (INIS)
Melikhov, Sergey A
2009-01-01
Steenrod homotopy theory is a natural framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; or from a different viewpoint, it studies the topology of the lim 1 functor (for inverse sequences of groups). This paper is primarily concerned with the case of compacta, in which Steenrod homotopy coincides with strong shape. An attempt is made to simplify the foundations of the theory and to clarify and improve some of its major results. With geometric tools such as Milnor's telescope compactification, comanifolds (=mock bundles), and the Pontryagin-Thom construction, new simple proofs are obtained for results by Barratt-Milnor, Geoghegan-Krasinkiewicz, Dydak, Dydak-Segal, Krasinkiewicz-Minc, Cathey, Mittag-Leffler-Bourbaki, Fox, Eda-Kawamura, Edwards-Geoghegan, Jussila, and for three unpublished results by Shchepin. An error in Lisitsa's proof of the 'Hurewicz theorem in Steenrod homotopy' is corrected. It is shown that over compacta, R.H. Fox's overlayings are equivalent to I.M. James' uniform covering maps. Other results include: A morphism between inverse sequences of countable (possibly non-Abelian) groups that induces isomorphisms on lim and lim 1 is invertible in the pro-category. This implies the 'Whitehead theorem in Steenrod homotopy', thereby answering two questions of Koyama. If X is an LC n-1 -compactum, n≥1, then its n-dimensional Steenrod homotopy classes are representable by maps S n →X, provided that X is simply connected. The assumption of simple connectedness cannot be dropped, by a well-known result of Dydak and Zdravkovska. A connected compactum is Steenrod connected (=pointed 1-movable), if and only if every uniform covering space of it has countably many uniform connected components. Bibliography: 117 titles.
Energy Technology Data Exchange (ETDEWEB)
Melikhov, Sergey A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2009-06-30
Steenrod homotopy theory is a natural framework for doing algebraic topology on general spaces in terms of algebraic topology of polyhedra; or from a different viewpoint, it studies the topology of the lim {sup 1} functor (for inverse sequences of groups). This paper is primarily concerned with the case of compacta, in which Steenrod homotopy coincides with strong shape. An attempt is made to simplify the foundations of the theory and to clarify and improve some of its major results. With geometric tools such as Milnor's telescope compactification, comanifolds (=mock bundles), and the Pontryagin-Thom construction, new simple proofs are obtained for results by Barratt-Milnor, Geoghegan-Krasinkiewicz, Dydak, Dydak-Segal, Krasinkiewicz-Minc, Cathey, Mittag-Leffler-Bourbaki, Fox, Eda-Kawamura, Edwards-Geoghegan, Jussila, and for three unpublished results by Shchepin. An error in Lisitsa's proof of the 'Hurewicz theorem in Steenrod homotopy' is corrected. It is shown that over compacta, R.H. Fox's overlayings are equivalent to I.M. James' uniform covering maps. Other results include: A morphism between inverse sequences of countable (possibly non-Abelian) groups that induces isomorphisms on lim and lim {sup 1} is invertible in the pro-category. This implies the 'Whitehead theorem in Steenrod homotopy', thereby answering two questions of Koyama. If X is an LC{sub n-1}-compactum, n{>=}1, then its n-dimensional Steenrod homotopy classes are representable by maps S{sup n}{yields}X, provided that X is simply connected. The assumption of simple connectedness cannot be dropped, by a well-known result of Dydak and Zdravkovska. A connected compactum is Steenrod connected (=pointed 1-movable), if and only if every uniform covering space of it has countably many uniform connected components. Bibliography: 117 titles.
A Mathematical Model for the Dynamics of Zika Virus via Homotopy ...
African Journals Online (AJOL)
ADOWIE PERE
Method was used to obtain the approximate solution of the model. ... Keywords: Homotopy Perturbation method, Zika virus, Modelling, Numerical ..... infected class with the graph for h ... the applications of Homotopy Perturbation Method.
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.
2009-01-01
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.
Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method
International Nuclear Information System (INIS)
Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A
2009-01-01
A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.
Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations
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Bahman Ghazanfari
2013-08-01
Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.
Jardine, John F
2015-01-01
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, n...
Modified method of perturbed stationary states. I
International Nuclear Information System (INIS)
Green, T.A.
1978-10-01
The reaction coordinate approach of Mittleman is used to generalize the method of Perturbed Stationary States. A reaction coordinate is defined for each state in the scattering expansion in terms of parameters which depend on the internuclear separation. These are to be determined from a variational principle described by Demkov. The variational result agrees with that of Bates and McCarroll in the limit of separated atoms, but is generally different elsewhere. The theory is formulated for many-electron systems, and the construction of the scattering expansion is discussed for simple one-, two-, and three-electron systsm. The scattering expansion and the Lagrangian for the radial scattering functions are given in detail for a heteronuclear one-electron system. 2 figures
Modified potentials in many-body perturbation theory
International Nuclear Information System (INIS)
Silver, D.M.; Bartlett, R.J.
1976-01-01
Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential
Modified perturbation theory for strongly correlated electron systems
International Nuclear Information System (INIS)
Takagi, Osamu; Saso, Tetsuro
1999-01-01
We propose a modified scheme for calculating the single-particle excitation spectrum of the impurity Anderson model. It is based on the second order perturbation theory, but modifies the self-energy so as to reproduce the correct atomic limit and to fulfill the Friedel sum rule. Therefore, it offers a simple scheme valid over wide range of excitation energy and parameters, and would be useful also for potential application to the lattice problems. (author)
Synchronization of modified Colpitts oscillators with structural perturbations
Energy Technology Data Exchange (ETDEWEB)
Kammogne, Soup Tewa; Fotsin, H B, E-mail: hbfotsin@yahoo.fr [Laboratoire d' electronique, Departement de Physique, Faculte des sciences, Universite de Dschang, PO Box 067, Dschang (Cameroon)
2011-06-01
This paper deals with the problem of the synchronization of uncertain modified Colpitts oscillators. Considering the effect of external disturbances on the system parameters and nonlinear control inputs, a robust controller based on Lyapunov theory is designed for the output synchronization between a slave system and a master system in order to ensure the synchronization of uncertain modified Colpitts oscillator systems. This approach was chosen not only to guarantee a stable synchronization but also to reduce the effect of external perturbation. Nonadaptive feedback synchronization with only one controller for the system is investigated. Numerical simulations are performed to confirm the efficiency of the proposed control scheme.
International Nuclear Information System (INIS)
Boya, L.J.; Carinena, J.F.; Mateos, J.
1978-01-01
Starting from classical field theory with a Lagrangian, solitons are identified with solutions of the field equations which satisfy peculiar boundary conditions. The symmetry group which causes the degenerate vacuum is taken generally internal, that is, not operating in space-time. Gauge symmetry plays a dominant role. A precise definition of solitons is given and it is shown how to study some continuous mappings of the ''distant'' parts of space on the set of degenerate vacua. A marvellous instrument, the exact homotopy sequence, is applied to calculate homotopy groups of some higher-dimensional manifolds
Introduction to homotopy theory
Selick, Paul
2008-01-01
This text is based on a one-semester graduate course taught by the author at The Fields Institute in fall 1995 as part of the homotopy theory program which constituted the Institute's major program that year. The intent of the course was to bring graduate students who had completed a first course in algebraic topology to the point where they could understand research lectures in homotopy theory and to prepare them for the other, more specialized graduate courses being held in conjunction with the program. The notes are divided into two parts: prerequisites and the course proper. Part I, the pr
Fermi interaction. Conservation of vector current and modified perturbation theory
International Nuclear Information System (INIS)
Rochev, V.E.
1983-01-01
The Fermi interaction (anti psi ysub(n) psi)sup(2) is investigated with the method of auxilary field. The analogues of the Ward-Takahashi electrodynamical identities and the gauge transformations of Green functions, that are the consequence of the conservation of vector current, have been obtained. The gauge function for the spinor propagator is the exponential superpropagator. The arguments are given in favour of the existence of a modified perturbation theory, which is finite in every order and non-analytical over its coupling constant, for the four-fermion interaction. The non-analytical part is defined unambiguously, and the analytical part contains a set of finite dimensionless constants to define which non-perturbative information is needed. The simplest model (the chain approximation) for the non-stable vector bound state is considered
Czech Academy of Sciences Publication Activity Database
Markl, Martin
2002-01-01
Roč. 69, - (2002), s. 161-180 ISSN 0009-725X. [Winter School "Geometry and Physics" /21./. Srní, 13.01.2001-20.01.2001] R&D Projects: GA ČR GA201/99/0675 Keywords : colored operad%cofibrant model%homotopy diagram Subject RIV: BA - General Mathematics
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2014-01-01
Full Text Available En este artículo, el método modificado de perturbación homotópica con distribución de no linealidades (MNDHPM es utilizado para encontrar soluciones en series de potencias de ecuaciones diferenciales ordinarias, tanto lineales como no lineales. Se verá que el método es particularmente relevante en algunos casos de ecuaciones con coeficientes no polinomiales e inhomogéneas con términos no homogéneos no polinomiales.
Ferromagnetism in the Hubbard model: a modified perturbation theory
International Nuclear Information System (INIS)
Gangadhar Reddy, G.; Ramakanth, A.; Nolting, W.
2005-01-01
We study the possibility of ferromagnetism in the Hubbard model using the modified perturbation theory. In this approach an Ansatz is made for the self-energy of the electron which contains the second order contribution developed around the Hartree-Fock solution and two parameters. The parameters are fixed by using a moment method. This self energy satisfies several known exact limiting cases. Using this self energy, the Curie temperature T c as a function of band filling n is investigated. It is found that T c falls off abruptly as n approaches half filling. The results are in qualitative agreement with earlier calculations using other approximation schemes. (author)
Dynamical quark and gluon condensates from a modified perturbative QCD
International Nuclear Information System (INIS)
Cabo Montes de Oca, A.; Martinez Pedrera, D.
2004-12-01
As it was suggested by previous works on a modified perturbation expansion for QCD, the possibility for the generation of large quark condensates in the massless version of the theory is explored. For this purpose, it is firstly presented a way to well define the Feynman diagrams at any number of loops by just employing dimensional regularization. After that, the calculated zero and one loop corrections to the effective potential indicate a strong instability of the system under the generation of quark condensates even in the absence of the gluon one. The quark condensate dependence of particular two loop terms does not modify the instability picture arising at one loop. The results suggest a possible mechanism for a sort of Top Condensate Model to be a dynamically fixed effective action for massless QCD. The inability of lattice calculations in detecting this possibility could be related to the current limitations in treating the fermion determinants. (author)
An introduction to A1-homotopy theory
International Nuclear Information System (INIS)
Morel, F.
2003-01-01
This contribution covers simplicial sheaves, Quillen's homotopical algebra, unstable A 1 homotopy theory, connectivity and A 1 -localisation, stable A 1 homotopy theory of S 1 -spectra and P 1 -spectra
Modalities in homotopy type theory
DEFF Research Database (Denmark)
Rijke, Egbert; Shulman, Michael; Spitters, Bas
2017-01-01
Univalent homotopy type theory (HoTT) may be seen as a language for the category of ∞-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the theory of factorization systems, reflective subuniverses......, and modalities in homotopy type theory, including their construction using a "localization" higher inductive type. This produces in particular the (n-connected, n-truncated) factorization system as well as internal presentations of subtoposes, through lex modalities. We also develop the semantics...
Open-closed homotopy algebra in mathematical physics
International Nuclear Information System (INIS)
Kajiura, Hiroshige; Stasheff, Jim
2006-01-01
In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A ∞ algebras) by closed strings (L ∞ algebras)
On numerical solution of Burgers' equation by homotopy analysis method
International Nuclear Information System (INIS)
Inc, Mustafa
2008-01-01
In this Letter, we present the Homotopy Analysis Method (shortly HAM) for obtaining the numerical solution of the one-dimensional nonlinear Burgers' equation. The initial approximation can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Convergence of the solution and effects for the method is discussed. The comparison of the HAM results with the Homotopy Perturbation Method (HPM) and the results of [E.N. Aksan, Appl. Math. Comput. 174 (2006) 884; S. Kutluay, A. Esen, Int. J. Comput. Math. 81 (2004) 1433; S. Abbasbandy, M.T. Darvishi, Appl. Math. Comput. 163 (2005) 1265] are made. The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. The numerical solutions are compared with the known analytical and some numerical solutions
Directory of Open Access Journals (Sweden)
Nikhil Choudhary
2013-04-01
Full Text Available Objectives: To check and compare the effectiveness of modified agility and perturbation training over conventional physical therapy in patients with knee osteoarthritis. Methods: Subjects were screened on the basis of inclusion and exclusion criteria and a total of 50 subjects were recruited for the study. They were randomly divided into Group A and group B with n=25 each. Results: Group receiving conventional knee exercises with modified agility and perturbation training showed statistically significant results. Discussion: It was found that supplementing rehabilitation programs for people with knee OA with a modified agility and perturbation training program assist them in returning to higher levels of physical activity with less pain and instability following rehabilitation.
An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation
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Hakeem Ullah
2014-01-01
Full Text Available We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM. We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM and homotopy perturbation method (HPM solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.
Sigma Terms and Strangeness Contents of Baryon Octet in Modified Chiral Perturbation Theory
Institute of Scientific and Technical Information of China (English)
LI Xiao-Ya; L(U) Xiao-Fu
2006-01-01
In the frame work of chiral perturbation theory, a modified effective Lagrangian for meson-baryon system is constructed, where the SU(3) breaking effect for meson is considered. The difference between physical and chiral limit decay constants is taken into account. Calculated to one loop at O(p3), the sigma terms and strangeness contents of baryon octet are obtained.
Homotopy theory the mathematical works of J. H. C. whitehead
James, I M
1962-01-01
Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes.This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are
Homotopy Theory of C*-Algebras
Ostvaer, Paul Arne
2010-01-01
Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It
Rational homotopy theory and differential forms
Griffiths, Phillip
2013-01-01
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham's theorem on simplicial complexes. In addition, Sullivan's results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma*Presentation of a natu
DEFF Research Database (Denmark)
Nesseris, Savvas
2009-01-01
We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant $G_{eff}$ and two parameters $\\Sigma$ and $\\eta$, which along with the perturbation equation...... of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation...... for the scale factor $a$ in terms of time $t$ and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model....
International Nuclear Information System (INIS)
Nesseris, Savvas
2009-01-01
We consider theories with an arbitrary coupling between matter and gravity and obtain the perturbation equation of matter on subhorizon scales. Also, we derive the effective gravitational constant G eff and two parameters Σ and η, which along with the perturbation equation of the matter density are useful to constrain the theory from growth factor and weak lensing observations. Finally, we use a completely solvable toy model which exhibits nontrivial phenomenology to investigate specific features of the theory. We obtain the analytic solution of the modified Friedmann equation for the scale factor a in terms of time t and use the age of the oldest star clusters and the primordial nucleosynthesis bounds in order to constrain the parameters of our toy model.
Determination of Periodic Solution for Tapered Beams with Modified Iteration Perturbation Method
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Mashinchi Joubari
2015-01-01
Full Text Available In this paper, we implemented the Modified Iteration Perturbation Method (MIPM for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need to complicated calculations. Comparing the results of the MIPM with the exact solution shows that this method is effective and convenient. Also, it is predicated that MIPM can be potentially used in the analysis of strongly nonlinear oscillation problems accurately.
Elgohary, T.; Kim, D.; Turner, J.; Junkins, J.
2014-09-01
Several methods exist for integrating the motion in high order gravity fields. Some recent methods use an approximate starting orbit, and an efficient method is needed for generating warm starts that account for specific low order gravity approximations. By introducing two scalar Lagrange-like invariants and employing Leibniz product rule, the perturbed motion is integrated by a novel recursive formulation. The Lagrange-like invariants allow exact arbitrary order time derivatives. Restricting attention to the perturbations due to the zonal harmonics J2 through J6, we illustrate an idea. The recursively generated vector-valued time derivatives for the trajectory are used to develop a continuation series-based solution for propagating position and velocity. Numerical comparisons indicate performance improvements of ~ 70X over existing explicit Runge-Kutta methods while maintaining mm accuracy for the orbit predictions. The Modified Chebyshev Picard Iteration (MCPI) is an iterative path approximation method to solve nonlinear ordinary differential equations. The MCPI utilizes Picard iteration with orthogonal Chebyshev polynomial basis functions to recursively update the states. The key advantages of the MCPI are as follows: 1) Large segments of a trajectory can be approximated by evaluating the forcing function at multiple nodes along the current approximation during each iteration. 2) It can readily handle general gravity perturbations as well as non-conservative forces. 3) Parallel applications are possible. The Picard sequence converges to the solution over large time intervals when the forces are continuous and differentiable. According to the accuracy of the starting solutions, however, the MCPI may require significant number of iterations and function evaluations compared to other integrators. In this work, we provide an efficient methodology to establish good starting solutions from the continuation series method; this warm start improves the performance of the
Bordism, stable homotopy and adams spectral sequences
Kochman, Stanley O
1996-01-01
This book is a compilation of lecture notes that were prepared for the graduate course "Adams Spectral Sequences and Stable Homotopy Theory" given at The Fields Institute during the fall of 1995. The aim of this volume is to prepare students with a knowledge of elementary algebraic topology to study recent developments in stable homotopy theory, such as the nilpotence and periodicity theorems. Suitable as a text for an intermediate course in algebraic topology, this book provides a direct exposition of the basic concepts of bordism, characteristic classes, Adams spectral sequences, Brown-Peter
A master identity for homotopy Gerstenhaber algebras
International Nuclear Information System (INIS)
Akman, F.
2000-01-01
We produce a master identity {m}{m,m,..}=0 for a certain type of homotopy Gerstenhaber algebras, in particular suitable for the prototype, namely the Hochschild complex of an associative algebra. This algebraic master identity was inspired by the work of Getzler-Jones and Kimura-Voronov-Zuckerman in the context of topological conformal field theories. To this end, we introduce the notion of a ''partitioned multilinear map'' and explain the mechanics of composing such maps. In addition, many new examples of pre-Lie algebras and homotopy Gerstenhaber algebras are given. (orig.)
A Modified Computational Scheme for the Stochastic Perturbation Finite Element Method
Directory of Open Access Journals (Sweden)
Feng Wu
Full Text Available Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
Quark masses from quark-gluon condensates in a modified perturbative QCD
Cabo-Montes de Oca, Alejandro
2003-01-01
In this note, it is argued that the mass matrix for the six quarks can be generated in first approximation by introducing fermion condensates on the same lines as was done before for gluons, within the modified perturbative expansion for QCD proposed in former works. Thus, the results point in the direction of the conjectured link of the approximate `Democratic' symmetry of the quark mass matrix and `gap' effects similar to the ones occuring in superconductivity. The condensates are introduced here non-dynamically and therefore the question of the possibility for their spontaneous generation remains open. However, possible ways out of the predicted lack of the `Democratic' symmetry of the condensates resulting from the spontaneous breaking of the flavour symmetry are suggested. They come from an analysis based on the Cornwall--Jackiw--Tomboulis (CJT) effective potential for composite operators
Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis
Directory of Open Access Journals (Sweden)
Shahram Shahlaei-Far
Full Text Available Abstract This study analyzes the fourth-order nonlinear free vibration of a Timoshenko beam. We discretize the governing differential equation by Galerkin's procedure and then apply the homotopy analysis method (HAM to the obtained ordinary differential equation of the generalized coordinate. We derive novel analytical solutions for the nonlinear natural frequency and displacement to investigate the effects of rotary inertia, shear deformation, pre-tensile loads and slenderness ratios on the beam. In comparison to results achieved by perturbation techniques, this study demonstrates that a first-order approximation of HAM leads to highly accurate solutions, valid for a wide range of amplitude vibrations, of a high-order strongly nonlinear problem.
Experiments with conjugate gradient algorithms for homotopy curve tracking
Irani, Kashmira M.; Ribbens, Calvin J.; Watson, Layne T.; Kamat, Manohar P.; Walker, Homer F.
1991-01-01
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
Periodic diffeomorphisms on homotopy E (4) surfaces
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 124; Issue 3. Periodic Diffeomorphisms on Homotopy (4) Surfaces. Hongxia Li. Volume 124 Issue 3 August 2014 pp 437-445. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/pmsc/124/03/0437-0445 ...
International Nuclear Information System (INIS)
Yabushita, Kazuki; Yamashita, Mariko; Tsuboi, Kazuhiro
2007-01-01
We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 x 10 3 ∼ 2 x 10 5 (for instance, a sphere) for practical situations, such as throwing a ball. It has been considered that the equations of motion of this case are unsolvable for a general projectile angle, although some solutions have been obtained for a small projectile angle using perturbation techniques. To obtain a general analytic solution, we apply Liao's homotopy analysis method to this problem. The homotopy analysis method, which is different from a perturbation technique, can be applied to a problem which does not include small parameters. We apply the homotopy analysis method for not only governing differential equations, but also an algebraic equation of a velocity vector to extend the radius of convergence. Ultimately, we obtain the analytic solution to this problem and investigate the validation of the solution
On gauge invariant cosmological perturbations in UV-modified Hořava gravity
Shin, Sunyoung; Park, Mu-In
2017-12-01
We consider gauge invariant cosmological perturbations in UV-modified, z = 3 (non-projectable) Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. In order to exhibit its dynamical degrees of freedom, we consider the Hamiltonian reduction method and find that, by solving all the constraint equations, the degrees of freedom are the same as those of Einstein gravity: one scalar and two tensor (graviton) modes when a scalar matter field presents. However, we confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology. Moreover, we find that tensor and scalar fluctuations travel differently in UV, generally. We present also some clarifying remarks about confusing points in the literatures.
Applying homotopy analysis method for solving differential-difference equation
International Nuclear Information System (INIS)
Wang Zhen; Zou Li; Zhang Hongqing
2007-01-01
In this Letter, we apply the homotopy analysis method to solving the differential-difference equations. A simple but typical example is applied to illustrate the validity and the great potential of the generalized homotopy analysis method in solving differential-difference equation. Comparisons are made between the results of the proposed method and exact solutions. The results show that the homotopy analysis method is an attractive method in solving the differential-difference equations
Spaces of homotopy self-equivalences a survey
Rutter, John W
1997-01-01
This survey covers groups of homotopy self-equivalence classes of topological spaces, and the homotopy type of spaces of homotopy self-equivalences. For manifolds, the full group of equivalences and the mapping class group are compared, as are the corresponding spaces. Included are methods of calculation, numerous calculations, finite generation results, Whitehead torsion and other areas. Some 330 references are given. The book assumes familiarity with cell complexes, homology and homotopy. Graduate students and established researchers can use it for learning, for reference, and to determine the current state of knowledge.
Homotopy based Surface Reconstruction with Application to Acoustic Signals
DEFF Research Database (Denmark)
Sharma, Ojaswa; Anton, François
2011-01-01
reconstruct information between any pair of successive cross sections are derived. The zero level set of the resulting homotopy field generates the desired surface. Four types of homotopies are suggested that are well suited to generate a smooth surface. We also provide derivation of necessary higher order...
MATHEMATICAL MODEL OF CATALYTIC PROCESSES AT MODIFIED ELECTRODES
Directory of Open Access Journals (Sweden)
Femila Mercy Rani Joseph
Full Text Available A mathematical modeling of electrocatalytic processes taking place at modified electrodes is discussed. In this paper we obtained the approximate analytical solutions for the nonlinear equations under non steady state conditions using homotopy perturbation method. Simple and approximate polynomial expressions for the concentration of reactant, product and charge carrier were obtained in terms of diffusion coefficient and rate constant. In this work the numerical simulation of the problem is reported using Scilab program. In this manuscript analytical results are compared with simulation results and satisfactory agreement is noted.
Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity
Energy Technology Data Exchange (ETDEWEB)
Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)
2017-06-15
It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)
A modified variation-perturbation approach to zero-point vibrational motion
DEFF Research Database (Denmark)
Åstrand, Per-Olof; Ruud, K.; Sundholm, D.
2000-01-01
We present a detailed investigation of the perturbation approach for calculating zero-point vibrational contributions to molecular properties. It is demonstrated that if the sum of the potential energy and the zero-point vibrational energy is regarded as an effective potential energy, the leading...
Homotopy analysis method for neutron diffusion calculations
International Nuclear Information System (INIS)
Cavdar, S.
2009-01-01
The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on a fundamental concept in differential geometry and topology, the homotopy. It has proved useful for problems involving algebraic, linear/non-linear, ordinary/partial differential and differential-integral equations being an analytic, recursive method that provides a series sum solution. It has the advantage of offering a certain freedom for the choice of its arguments such as the initial guess, the auxiliary linear operator and the convergence control parameter, and it allows us to effectively control the rate and region of convergence of the series solution. HAM is applied for the fixed source neutron diffusion equation in this work, which is a part of our research motivated by the question of whether methods for solving the neutron diffusion equation that yield straightforward expressions but able to provide a solution of reasonable accuracy exist such that we could avoid analytic methods that are widely used but either fail to solve the problem or provide solutions through many intricate expressions that are likely to contain mistakes or numerical methods that require powerful computational resources and advanced programming skills due to their very nature or intricate mathematical fundamentals. Fourier basis are employed for expressing the initial guess due to the structure of the problem and its boundary conditions. We present the results in comparison with other widely used methods of Adomian Decomposition and Variable Separation.
Perturbative analysis in higher-spin theories
Energy Technology Data Exchange (ETDEWEB)
Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2016-07-28
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.
Note on the End Game in Homotopy Zero Curve Tracking
Sosonkina, Masha; Watson, Layne T.; Stewart, David E.
1995-01-01
Homotopy algorithms to solve a nonlinear system of equations f(x)=0 involve tracking the zero curve of a homotopy map p(a,theta,x) from theta=0 until theta=1. When the algorithm nears or crosses the hyperplane theta=1, an "end game" phase is begun to compute the solution x(bar) satisfying p(a,theta,x(bar))=f(x(bar))=0. This note compares several end game strategies, including the one implemented in the normal flow code FIXPNF in the homotopy software package HOMPACK.
Solving system of DAEs by homotopy analysis method
International Nuclear Information System (INIS)
Awawdeh, Fadi; Jaradat, H.M.; Alsayyed, O.
2009-01-01
Homotopy analysis method (HAM) is applied to systems of differential-algebraic equations (DAEs). The HAM is proved to be very effective, simple and convenient to give approximate analytical solutions to DAEs.
Homotopy Lie superalgebra in Yang-Mills theory
International Nuclear Information System (INIS)
Zeitlin, Anton M.
2007-01-01
The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
International Nuclear Information System (INIS)
Hermant, Audrey
2010-01-01
This paper deals with optimal control problems with a regular second-order state constraint and a scalar control, satisfying the strengthened Legendre-Clebsch condition. We study the stability of structure of stationary points. It is shown that under a uniform strict complementarity assumption, boundary arcs are stable under sufficiently smooth perturbations of the data. On the contrary, nonreducible touch points are not stable under perturbations. We show that under some reasonable conditions, either a boundary arc or a second touch point may appear. Those results allow us to design an homotopy algorithm which automatically detects the structure of the trajectory and initializes the shooting parameters associated with boundary arcs and touch points.
Fresse, Benoit
2017-01-01
The ultimate goal of this book is to explain that the Grothendieck-Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck-Teichmüller group in the case of the ...
Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
Directory of Open Access Journals (Sweden)
Marinca Vasile
2017-10-01
Full Text Available Dynamic response time is an important feature for determining the performance of magnetorheological (MR dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.
Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu
2017-10-01
Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.
On Gauge Invariant Cosmological Perturbations in UV-modified Hořava Gravity: A Brief Introduction
Park, Mu-In
2018-01-01
We revisit gauge invariant cosmological perturbations in UV-modified, z = 3 Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. We confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology.
On Gauge Invariant Cosmological Perturbations in UV-modified Hořava Gravity: A Brief Introduction*
Directory of Open Access Journals (Sweden)
Park Mu-In
2018-01-01
Full Text Available We revisit gauge invariant cosmological perturbations in UV-modified, z = 3 Hořava gravity with one scalar matter field, which has been proposed as a renormalizable gravity theory without the ghost problem in four dimensions. We confirm that there is no extra graviton modes and general relativity is recovered in IR, which achieves the consistency of the model. From the UV-modification terms which break the detailed balance condition in UV, we obtain scale-invariant power spectrums for non-inflationary backgrounds, like the power-law expansions, without knowing the details of early expansion history of Universe. This could provide a new framework for the Big Bang cosmology.
Loop homotopy algebras in closed string field theory
International Nuclear Information System (INIS)
Markl, M.
2001-01-01
Barton Zwiebach (1993) constructed ''string products'' on the Hilbert space of a combined conformal field theory of matter and ghosts, satisfying the ''main identity''. It has been well known that the ''tree level'' of the theory gives an example of a strongly homotopy Lie algebra (though, as we will see later, this is not the whole truth). Strongly homotopy Lie algebras are now well-understood objects. On the one hand, strongly homotopy Lie algebra is given by a square zero coderivation on the cofree cocommutative connected coalgebra on the other hand, strongly homotopy Lie algebras are algebras over the cobar dual of the operad Com for commutative algebras. No such characterization of the structure of string products for arbitrary genera has been available, though there are two series of papers directly pointing towards the requisite characterization. As far as the characterization in terms of (co)derivations is concerned, we need the concept of higher order (co)derivations. For our characterization we need to understand the behavior of these higher (co)derivations on (co)free (co)algebras. The necessary machinery for the operadic approach is that of modular operads. We also indicate how to adapt the loop homotopy structure to the case of open string field theory. (orig.)
Mondal, Argha; Upadhyay, Ranjit Kumar
2017-11-01
In this paper, an attempt has been made to understand the activity of mean membrane voltage and subsidiary system variables with moment equations (i.e., mean, variance and covariance's) under noisy environment. We consider a biophysically plausible modified Hindmarsh-Rose (H-R) neural system injected by an applied current exhibiting spiking-bursting phenomenon. The effects of predominant parameters on the dynamical behavior of a modified H-R system are investigated. Numerically, it exhibits period-doubling, period halving bifurcation and chaos phenomena. Further, a nonlinear system has been analyzed for the first and second order moments with additive stochastic perturbations. It has been solved using fourth order Runge-Kutta method and noisy systems by Euler's scheme. It has been demonstrated that the firing properties of neurons to evoke an action potential in a certain parameter space of the large exact systems can be estimated using an approximated model. Strong stimulation can cause a change in increase or decrease of the firing patterns. Corresponding to a fixed set of parameter values, the firing behavior and dynamical differences of the collective variables of a large, exact and approximated systems are investigated.
Directory of Open Access Journals (Sweden)
Venmathi Mahendran
2017-07-01
Full Text Available This paper presents the modified perturb and observe (P&O maximum power point tracking (MPPT method for photovoltaic (PV fed three-port DC‐DC converter in PV/battery hybrid system. The proposed MPPT technique reduces the drift problem which occurs in the conventional MPPT methods by including the data of change in current (ΔI in addition to the data used in the conventional P&O algorithm. The drift phenomenon and its effects are clearly demonstrated in this paper. The ability of the proposed P&O method to address this issue is proved by comparing the conventional P&O algorithm in different modes of operation. The performance assessment includes peak overshoot, settling time, MPP ratio and stability. The experimental validation was implemented using DSPIC30F4011 microcontroller. From the analysis and results, it could be seen that the modified P&O showed better performance in terms of accuracy in tracking the maximum power, less tracking time, high MPP ratio and reduced drift in the changing weather conditions.
Homotopy analysis solutions of point kinetics equations with one delayed precursor group
International Nuclear Information System (INIS)
Zhu Qian; Luo Lei; Chen Zhiyun; Li Haofeng
2010-01-01
Homotopy analysis method is proposed to obtain series solutions of nonlinear differential equations. Homotopy analysis method was applied for the point kinetics equations with one delayed precursor group. Analytic solutions were obtained using homotopy analysis method, and the algorithm was analysed. The results show that the algorithm computation time and precision agree with the engineering requirements. (authors)
Internal Universes in Models of Homotopy Type Theory
DEFF Research Database (Denmark)
Licata, Daniel R.; Orton, Ian; Pitts, Andrew M.
2018-01-01
We show that universes of fibrations in various models of homotopy type theory have an essentially global character: they cannot be described in the internal language of the presheaf topos from which the model is constructed. We get around this problem by extending the internal language with a mo...... that the interval in cubical sets does indeed have. This leads to a completely internal development of models of homotopy type theory within what we call crisp type theory.......We show that universes of fibrations in various models of homotopy type theory have an essentially global character: they cannot be described in the internal language of the presheaf topos from which the model is constructed. We get around this problem by extending the internal language...
Complex cobordism and stable homotopy groups of spheres
Ravenel, Douglas C
2003-01-01
Since the publication of its first edition, this book has served as one of the few available on the classical Adams spectral sequence, and is the best account on the Adams-Novikov spectral sequence. This new edition has been updated in many places, especially the final chapter, which has been completely rewritten with an eye toward future research in the field. It remains the definitive reference on the stable homotopy groups of spheres. The first three chapters introduce the homotopy groups of spheres and take the reader from the classical results in the field though the computational aspects
Symplectic S5 action on symplectic homotopy K3 surfaces
Indian Academy of Sciences (India)
HONGXIA LI
Let X be a symplectic homotopy K3 surface and G = S5 act on X symplectically. In this paper, we give a weak classification of the G action on X by discussing the fixed-point set structure. Besides, we analyse the exoticness of smooth structures of X under the action of G. Keywords. K3 surfaces; symplectic actions; exotic ...
Homotopy Type of Neighborhood Complexes of Kneser Graphs, KG
Indian Academy of Sciences (India)
3
2017-04-12
Apr 12, 2017 ... Abstract. Schrijver identified a family of vertex critical subgraphs of the. Kneser graphs called the stable Kneser graphs SGn,k. Björner and de Longueville proved that the neighborhood complex of the stable. Kneser graph SGn,k is homotopy equivalent to a k−sphere. In this article, we prove that the ...
On convergence of homotopy analysis method and its application to ...
African Journals Online (AJOL)
In this paper, we have used the homotopy analysis method (HAM) to obtain approximate solution of fractional integro-differential equations (FIDEs). Convergence of HAM is considered for this kind of equations. Also some examples are given to illustrate the high efficiency and precision of HAM. Keywords: Fractional ...
Classification of smooth structures on a homotopy complex ...
Indian Academy of Sciences (India)
Abstract. We classify, up to diffeomorphism, all closed smooth manifolds homeo- morphic to the complex projective n-space CPn, where n = 3 and 4. Let M2n be a closed smooth 2n-manifold homotopy equivalent to CPn. We show that, up to diffeo- morphism, M6 has a unique differentiable structure and M8 has at most two ...
Classification of smooth structures on a homotopy complex ...
Indian Academy of Sciences (India)
We classify, up to diffeomorphism, all closed smooth manifolds homeomorphic to the complex projective n -space C P n , where n = 3 and 4. Let M 2 n be a closed smooth 2 n -manifold homotopy equivalent to C P n . We show that, up to diffeomorphism, M 6 has a unique differentiable structure and M 8 has at most two ...
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
On the singular perturbations for fractional differential equation.
Atangana, Abdon
2014-01-01
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
On the Singular Perturbations for Fractional Differential Equation
Directory of Open Access Journals (Sweden)
Abdon Atangana
2014-01-01
Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
Homotopy Lie algebras associated with a proto-bialgebra
International Nuclear Information System (INIS)
Bangoura, Momo
2003-10-01
Motivated by the search for examples of homotopy Lie algebras, to any Lie proto-bialgebra structure on a finite-dimensional vector space F, we associate two homotopy Lie algebra structures defined on the suspension of the exterior algebra of F and that of its dual F*, respectively, with a 0-ary map corresponding to the image of the empty set. In these algebras, all n-ary brackets for n ≥ 4 vanish. More generally, to any element of odd degree in Λ(F*+F), we associate a set of n-ary skew-symmetric mappings on the suspension of ΛF (resp. Λ F*), which satisfy the generalized Jacobi identities if the given element is of square zero. (author)
Higher Inductive Types as Homotopy-Initial Algebras
2016-08-01
correspondence between Martin -Löf’s constructive type theory and ab- stract homotopy theory. We have a powerful interplay between these disciplines - we can...inductive types we call W-quotients which generalize Martin -Löf’s well-founded trees to a higher- dimensional setting. We have shown that a...27]). Among the most studied type theories is Martin -Löf’s intuition- istic type theory ([20, 22]), also known as constructive or dependent type
On the homotopy equivalence of simple AI-algebras
International Nuclear Information System (INIS)
Aristov, O Yu
1999-01-01
Let A and B be simple unital AI-algebras (an AI-algebra is an inductive limit of C*-algebras of the form BigOplus i k C([0,1],M N i ). It is proved that two arbitrary unital homomorphisms from A into B such that the corresponding maps K 0 A→K 0 B coincide are homotopic. Necessary and sufficient conditions on the Elliott invariant for A and B to be homotopy equivalent are indicated. Moreover, two algebras in the above class having the same K-theory but not homotopy equivalent are constructed. A theorem on the homotopy of approximately unitarily equivalent homomorphisms between AI-algebras is used in the proof, which is deduced in its turn from a generalization to the case of AI-algebras of a theorem of Manuilov stating that a unitary matrix almost commuting with a self-adjoint matrix h can be joined to 1 by a continuous path consisting of unitary matrices almost commuting with h
Yi, X.; Vries, de H.I.; Siudeja, K.; Rana, A.; Lemstra, W.; Brunsting, J.F.; Kok, R.J.M.; Smulders, Y.M.; Schaefer, M.; Dijk, F.; Shang, Y.F.; Eggen, B.J.L.; Kampinga, H.H.; Sibon, O.C.M.
2009-01-01
Hydroxyurea, a well-known DNA replication inhibitor, induces cell cycle arrest and intact checkpoint functions are required to survive DNA replication stress induced by this genotoxic agent. Perturbed DNA synthesis also results in elevated levels of DNA damage. It is unclear how organisms prevent
Yi, Xia; Vries, Hilda I. de; Siudeja, Katarzyna; Rana, Anil; Lemstra, Willy; Brunsting, Jeanette F.; Kok, Rob M.; Smulders, Yvo M.; Schaefer, Matthias; Dijk, Freark; Shang, Yongfeng; Eggen, Bart J.L.; Kampinga, Harm H.; Sibon, Ody C.M.
Hydroxyurea, a well-known DNA replication inhibitor, induces cell cycle arrest and intact checkpoint functions are required to survive DNA replication stress induced by this genotoxic agent. Perturbed DNA synthesis also results in elevated levels of DNA damage. It is unclear how organisms prevent
Directory of Open Access Journals (Sweden)
Amin Saif
2016-10-01
Full Text Available In this paper we generalize the retracting property in homotopy theory for topological semigroups by introducing the notions of deformation S-retraction with its weaker forms and ES-homotopy extension property. Furthermore, the covering homotopy theorems for S-maps into Sχ-fibrations and Sχ-cofibrations are introduced and pullbacks for Sχ-fibrations behave properly.
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H. Jafari
2010-07-01
Full Text Available In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM.Comparisons are made between the Adomian decomposition method (ADM, the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.
Application of Homotopy Analysis Method to Solve Relativistic Toda Lattice System
International Nuclear Information System (INIS)
Wang Qi
2010-01-01
In this letter, the homotopy analysis method is successfully applied to solve the Relativistic Toda lattice system. Comparisons are made between the results of the proposed method and exact solutions. Analysis results show that homotopy analysis method is a powerful and easy-to-use analytic tool to solve systems of differential-difference equations. (general)
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X. Zhao
2012-01-01
Full Text Available A combined interior point homotopy continuation method is proposed for solving general multiobjective programming problem. We prove the existence and convergence of a smooth homotopy path from almost any interior initial interior point to a solution of the KKT system under some basic assumptions.
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Calebe A. Matias
2017-07-01
Full Text Available The purpose of the present study is to simulate and analyze an isolated full-bridge DC/DC boost converter, for photovoltaic panels, running a modified perturb and observe maximum power point tracking method. The zero voltage switching technique was used in order to minimize the losses of the converter for a wide range of solar operation. The efficiency of the power transfer is higher than 90% for large solar operating points. The panel enhancement due to the maximum power point tracking algorithm is 5.06%.
Homotopy theory of modules over diagrams of rings
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J. P. C. Greenlees
2014-09-01
Full Text Available Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories ℳ( (as runs through the diagram, we consider the category of diagrams where the object ( at comes from ℳ(. We develop model structures on such categories of diagrams and Quillen adjunctions that relate categories based on different diagram shapes. Under certain conditions, cellularizations (or right Bousfield localizations of these adjunctions induce Quillen equivalences. As an application we show that a cellularization of a category of modules over a diagram of ring spectra (or differential graded rings is Quillen equivalent to modules over the associated inverse limit of the rings. Another application of the general machinery here is given in work by the authors on algebraic models of rational equivariant spectra. Some of this material originally appeared in the preprint “An algebraic model for rational torus-equivariant stable homotopy theory”, arXiv:1101.2511, but has been generalized here.
Linear homotopy solution of nonlinear systems of equations in geodesy
Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.
2010-01-01
A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.
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Z. Pashazadeh Atabakan
2013-01-01
Full Text Available Spectral homotopy analysis method (SHAM as a modification of homotopy analysis method (HAM is applied to obtain solution of high-order nonlinear Fredholm integro-differential problems. The existence and uniqueness of the solution and convergence of the proposed method are proved. Some examples are given to approve the efficiency and the accuracy of the proposed method. The SHAM results show that the proposed approach is quite reasonable when compared to homotopy analysis method, Lagrange interpolation solutions, and exact solutions.
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S.Z.Mohammad Noor
2016-06-01
Full Text Available This paper presents an implementation of Single-phase Single stage String inverter for Grid connected Photovoltaic (PV system. The proposed system uses Modified Perturb and Observe (P&O algorithm implemented using Fuzzy Logic Control (FLC as Maximum Power Point Tracking (MPPT. The inverter is designed for 340W system using two series of STP170s24/Ac PV modules. The MPPT unit keeps tracking the maximum power from the PV array by changing the modulation index and the phase angle of inverter’s output voltage. The simulation model is developed using Matlab/Simulink to evaluate the performance of the converter. Selected experimental results are also presented in this paper.
Homotopy analysis approach for nonlinear piezoelectric vibration energy harvesting
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Shahlaei-Far Shahram
2016-01-01
Full Text Available Piezoelectric energy harvesting from a vertical geometrically nonlinear cantilever beam with a tip mass subject to transverse harmonic base excitations is analyzed. One piezoelectric patch is placed on the slender beam to convert the tension and compression into electrical voltage. Applying the homotopy analysis method to the coupled electromechanical governing equations, we derive analytical solutions for the horizontal displacement of the tip mass and consequently the output voltage from the piezoelectric patch. Analytical approximation for the frequency response and phase of the geometrically forced nonlinear vibration system are also obtained. The research aims at a rigorous analytical perspective on a nonlinear problem which has previously been solely investigated by numerical and experimental methods.
Solving the discrete KdV equation with homotopy analysis method
International Nuclear Information System (INIS)
Zou, L.; Zong, Z.; Wang, Z.; He, L.
2007-01-01
In this Letter, we apply the homotopy analysis method to differential-difference equations. We take the discrete KdV equation as an example, and successfully obtain double periodic wave solutions and solitary wave solutions. It illustrates the validity and the great potential of the homotopy analysis method in solving discrete KdV equation. Comparisons are made between the results of the proposed method and exact solutions. The results reveal that the proposed method is very effective and convenient
On Solution of a Fractional Diffusion Equation by Homotopy Transform Method
International Nuclear Information System (INIS)
Salah, A.; Hassan, S.S.A.
2012-01-01
The homotopy analysis transform method (HATM) is applied in this work in order to find the analytical solution of fractional diffusion equations (FDE). These equations are obtained from standard diffusion equations by replacing a second-order space derivative by a fractional derivative of order α and a first order time derivative by a fractional derivative. Furthermore, some examples are given. Numerical results show that the homotopy analysis transform method is easy to implement and accurate when applied to a fractional diffusion equations.
Application of Homotopy Perturbation and Variational Iteration Methods to SIR Epidemic Model
DEFF Research Database (Denmark)
Ghotbi, Abdoul R.; Barari, Amin; Omidvar, M.
2011-01-01
effective strategy against childhood diseases, the development of the framework that would predict the optimal vaccine coverage level needed to prevent the spread of diseases is crucial. The SIR model is a standard compartmental model that has been used to describe many epidemiological diseases...
On the complexity of a combined homotopy interior method for convex programming
Yu, Bo; Xu, Qing; Feng, Guochen
2007-03-01
In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.
Stability of gradient semigroups under perturbations
Aragão-Costa, E. R.; Caraballo, T.; Carvalho, A. N.; Langa, J. A.
2011-07-01
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).
Stability of gradient semigroups under perturbations
International Nuclear Information System (INIS)
Aragão-Costa, E R; Carvalho, A N; Caraballo, T; Langa, J A
2011-01-01
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space)
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Mehmet Tarik Atay
2013-01-01
Full Text Available The Variational Iteration Method (VIM and Modified Variational Iteration Method (MVIM are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM and the Modified Variational Iteration Method (MVIM are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.
Winding numbers in homotopy theory from integers to reals
International Nuclear Information System (INIS)
Mekhfi, M.
1993-07-01
In Homotopy Theory (HT) we define paths on a given topological space. Closed paths prove to be construction elements of a group (the fundamental group) Π 1 and carry charges, the winding numbers. The charges are integers as they indicate how many times closed paths encircle a given hole (or set of holes). Open paths as they are defined in (HT) do not possess any groups structure and as such they are less useful in topology. In the present paper we enlarge the concept of a path in such a way that both types of paths do possess a group structure. In this broad sense we have two fundamental groups the Π i = Z group and the SO(2) group of rotations but the latter has the global property that there is no periodicity in the rotation angle. There is also two charge operators W and W λ whose eigenvalues are either integers or reals depending respectively on the paths being closed or open. Also the SO(2) group and the real charge operator W λ are not independently defined but directly related respectively to the Π i group and to the integer charge operator W. Thus well defined links can be established between seemingly different groups and charges. (author). 3 refs, 1 fig
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Hamid M. Sedighi
Full Text Available This paper investigates the dynamic pull-in instability of vibrating micro-beams undergoing large deflection under electrosatically actuation. The governing equation of motion is derived based on the modified couple stress theory. Homotopy Perturbation Method is employed to produce the high accuracy approximate solution as well as the second-order frequency- amplitude relationship. The nonlinear governing equation of micro beam vibrations predeformed by an electric field includes both even and odd nonlinearities. The influences of basic non-dimensional parameters on the pull-in instability as well as the natural frequency are studied. It is demonstrated that two terms in series expansions are sufficient to produce high accuracy solution of the micro-structure. The accuracy of proposed asymptotic approach is validated via numerical results. The phase portrait of the system exhibits periodic and homoclinic orbits.
A homotopy algorithm for digital optimal projection control GASD-HADOC
Collins, Emmanuel G., Jr.; Richter, Stephen; Davis, Lawrence D.
1993-01-01
The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.
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S. Das
2013-12-01
Full Text Available In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution. Effects of parameters on the convergence of the approximate series solution by minimizing the averaged residual error with the proper choices of parameters are calculated numerically and presented through graphs and tables for different particular cases.
A homotopy method for solving Riccati equations on a shared memory parallel computer
International Nuclear Information System (INIS)
Zigic, D.; Watson, L.T.; Collins, E.G. Jr.; Davis, L.D.
1993-01-01
Although there are numerous algorithms for solving Riccati equations, there still remains a need for algorithms which can operate efficiently on large problems and on parallel machines. This paper gives a new homotopy-based algorithm for solving Riccati equations on a shared memory parallel computer. The central part of the algorithm is the computation of the kernel of the Jacobian matrix, which is essential for the corrector iterations along the homotopy zero curve. Using a Schur decomposition the tensor product structure of various matrices can be efficiently exploited. The algorithm allows for efficient parallelization on shared memory machines
International Nuclear Information System (INIS)
Bartlett, R.; Kirtman, B.; Davidson, E.R.
1978-01-01
After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references
Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy
Majumdar, Apala; Robbins, J.M.; Zyskin, Maxim
2009-01-01
energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1
The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet
International Nuclear Information System (INIS)
Sajid, M.; Hayat, T.
2009-01-01
This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet. The cases of two dimensional and axisymmetric shrinking have been discussed. Exact series solution is obtained using the homotopy analysis method (HAM). The convergence of the obtained series solution is discussed explicitly. The obtained HAM solution is valid for all values of the suction parameter and Hartman number.
A note on the convergence of the Zakharov-Kuznetsov equation by homotopy analysis method
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Amir Fallahzadeh
2014-07-01
Full Text Available In this paper, the convergence of Zakharov-Kuznetsov (ZK equation by homotopy analysis method (HAM is investigated. A theorem is proved to guarantee the convergence of HAMand to find the series solution of this equation via a reliable algorithm.
Abe homotopy classification of topological excitations under the topological influence of vortices
International Nuclear Information System (INIS)
Kobayashi, Shingo; Kobayashi, Michikazu; Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito
2012-01-01
Topological excitations are usually classified by the nth homotopy group π n . However, for topological excitations that coexist with vortices, there are cases in which an element of π n cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of π n corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π 1 on π n . In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κ n . The nth Abe homotopy group κ n is defined as a semi-direct product of π 1 and π n . In this framework, the action of π 1 on π n is understood as originating from noncommutativity between π 1 and π n . We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is S n /K, where S n is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).
Czech Academy of Sciences Publication Activity Database
Červinka, Michal
2010-01-01
Roč. 2010, č. 4 (2010), s. 730-753 ISSN 0023-5954 Institutional research plan: CEZ:AV0Z10750506 Keywords : equilibrium problems with complementarity constraints * homotopy * C-stationarity Subject RIV: BC - Control Systems Theory Impact factor: 0.461, year: 2010 http://library.utia.cas.cz/separaty/2010/MTR/cervinka-on computation of c-stationary points for equilibrium problems with linear complementarity constraints via homotopy method.pdf
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2004-01-01
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Solution of two group neutron diffusion equation by using homotopy analysis method
International Nuclear Information System (INIS)
Cavdar, S.
2010-01-01
The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.
Analysis of a time fractional wave-like equation with the homotopy analysis method
International Nuclear Information System (INIS)
Xu Hang; Cang Jie
2008-01-01
The time fractional wave-like differential equation with a variable coefficient is studied analytically. By using a simple transformation, the governing equation is reduced to two fractional ordinary differential equations. Then the homotopy analysis method is employed to derive the solutions of these equations. The accurate series solutions are obtained. Especially, when h f =h g =-1, these solutions are exactly the same as those results given by the Adomian decomposition method. The present work shows the validity and great potential of the homotopy analysis method for solving nonlinear fractional differential equations. The basic idea described in this Letter is expected to be further employed to solve other similar nonlinear problems in fractional calculus
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Mohammad Almousa
2013-01-01
Full Text Available The aim of this study is to present the use of a semi analytical method called the optimal homotopy asymptotic method (OHAM for solving the linear Fredholm integral equations of the first kind. Three examples are discussed to show the ability of the method to solve the linear Fredholm integral equations of the first kind. The results indicated that the method is very effective and simple.
On accelerated flow of MHD powell-eyring fluid via homotopy analysis method
Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul
2017-09-01
The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.
Homotopy L-infinity spaces and Kuranishi manifolds, I: categorical structures
Tu, Junwu
2016-01-01
Motivated by the definition of homotopy $L_\\infty$ spaces, we develop a new theory of Kuranishi manifolds, closely related to Joyce's recent theory. We prove that Kuranishi manifolds form a $2$-category with invertible $2$-morphisms, and that certain fiber product property holds in this $2$-category. In a subsequent paper, we construct the virtual fundamental cycle of a compact oriented Kuranishi manifold, and prove some of its basic properties. Manifest from this new formulation is the fact ...
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Behzad Ghanbari
2014-01-01
Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
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Uswah Qasim
2016-03-01
Full Text Available A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.
A homotopy analysis method for the option pricing PDE in illiquid markets
E-Khatib, Youssef
2012-09-01
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading the underlying asset does not affect the underlying asset price. This can happen in perfectly liquid markets and it is evidently not viable in markets with imperfect liquidity (illiquid markets). It is well-known that markets with imperfect liquidity are more realistic. Thus, the presence of price impact while studying options is very important. This paper investigates a solution for the option pricing PDE in illiquid markets using the homotopy analysis method.
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Y. M. Chen
2011-01-01
Full Text Available The homotopy analysis method (HAM is employed to propose an approach for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. There are two relative merits of the presented HAM compared with some usual procedures of the HAM. First, a new auxiliary linear operator is constructed. This operator makes it unnecessary to eliminate any secular terms. Furthermore, all the deformation equations are purely linear. Numerical examples show the excellent agreement of the attained solutions with numerical ones. The respective effects of applied voltage, cubic nonlinear stiffness, gap distance, and squeeze film damping on vibration responses are analyzed detailedly.
Communication: Newton homotopies for sampling stationary points of potential energy landscapes
International Nuclear Information System (INIS)
Mehta, Dhagash; Chen, Tianran; Hauenstein, Jonathan D.; Wales, David J.
2014-01-01
One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they all exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor ϕ 4 model and atomic clusters
An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow
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Vasile Marinca
2011-01-01
Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.
Communication: Newton homotopies for sampling stationary points of potential energy landscapes
Energy Technology Data Exchange (ETDEWEB)
Mehta, Dhagash, E-mail: dmehta@nd.edu [Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556 (United States); University Chemical Laboratory, The University of Cambridge, Cambridge CB2 1EW (United Kingdom); Chen, Tianran, E-mail: chentia1@msu.edu [Department of Mathematics, Michigan State University, East Lansing, Michigan 48823 (United States); Hauenstein, Jonathan D., E-mail: hauenstein@nd.edu [Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556 (United States); Wales, David J., E-mail: dw34@cam.ac.uk [University Chemical Laboratory, The University of Cambridge, Cambridge CB2 1EW (United Kingdom)
2014-09-28
One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they all exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor ϕ{sup 4} model and atomic clusters.
International Nuclear Information System (INIS)
Khader, M. M.; Kumar, Sunil; Abbasbandy, S.
2013-01-01
We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology. Such problems are presented as nonlinear differential—difference equations. The proposed method is based on the Laplace transform with the homotopy analysis method (HAM). This method is a powerful tool for solving a large amount of problems. This technique provides a series of functions which may converge to the exact solution of the problem. A good agreement between the obtained solution and some well-known results is obtained
Development of homotopy algorithms for fixed-order mixed H2/H(infinity) controller synthesis
Whorton, M.; Buschek, H.; Calise, A. J.
1994-01-01
A major difficulty associated with H-infinity and mu-synthesis methods is the order of the resulting compensator. Whereas model and/or controller reduction techniques are sometimes applied, performance and robustness properties are not preserved. By directly constraining compensator order during the optimization process, these properties are better preserved, albeit at the expense of computational complexity. This paper presents a novel homotopy algorithm to synthesize fixed-order mixed H2/H-infinity compensators. Numerical results are presented for a four-disk flexible structure to evaluate the efficiency of the algorithm.
Homotopy Algorithm for Fixed Order Mixed H2/H(infinity) Design
Whorton, Mark; Buschek, Harald; Calise, Anthony J.
1996-01-01
Recent developments in the field of robust multivariable control have merged the theories of H-infinity and H-2 control. This mixed H-2/H-infinity compensator formulation allows design for nominal performance by H-2 norm minimization while guaranteeing robust stability to unstructured uncertainties by constraining the H-infinity norm. A key difficulty associated with mixed H-2/H-infinity compensation is compensator synthesis. A homotopy algorithm is presented for synthesis of fixed order mixed H-2/H-infinity compensators. Numerical results are presented for a four disk flexible structure to evaluate the efficiency of the algorithm.
Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation
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Mohammad Hamarsheh
2015-11-01
Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.
Supersingular quantum perturbations
International Nuclear Information System (INIS)
Detwiler, L.C.; Klauder, J.R.
1975-01-01
A perturbation potential is called supersingular whenever generally every matrix element of the perturbation in the unperturbed eigenstates is infinite. It follows that supersingular perturbations do not have conventional perturbation expansions, say for energy eigenvalues. By invoking variational arguments, we determine the asymptotic behavior of the energy eigenvalues for asymptotically small values of the coupling constant of the supersingular perturbation
Stein manifolds and holomorphic mappings the homotopy principle in complex analysis
Forstnerič, Franc
2017-01-01
This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka t...
On perturbation theory for distance dependent statistics.
Energy Technology Data Exchange (ETDEWEB)
Mashkevich, S V
1994-12-31
It is known that perturbation theory for anyons has to be modified near Bose statistics in order to get correct finite results. For ``distance dependent statistics`` or anyons with smeared flux tubes, perturbation theory is in principle applicable directly but gives results which hold for too small values of the statistical parameter and, in particular, are not valid as the flux tube radius tends to zero. In this paper we discuss the way to modify perturbation theory for this situation, which allows to obtain the appropriate results. (author). 6 refs.
Analytic continuation in perturbative QCD
International Nuclear Information System (INIS)
Caprini, Irinel
2002-01-01
We discuss some attempts to improve standard perturbative expansion in QCD by using the analytic continuation in the momentum and the Borel complex planes. We first analyse the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD and the connection between the Landau singularities and the infrared renormalons. By using the analytic continuation in the Borel complex plane, we propose a new perturbative series replacing the standard expansion in powers of the normalized coupling constant a. The new expansion functions have branch point and essential singularities at the origin of the complex a-plane and divergent Taylor expansions in powers of a. On the other hand the modified expansion of the QCD correlators is convergent under rather conservative conditions. (author)
Directory of Open Access Journals (Sweden)
Hoi Ying Wong
2013-01-01
Full Text Available Turbo warrants are liquidly traded financial derivative securities in over-the-counter and exchange markets in Asia and Europe. The structure of turbo warrants is similar to barrier options, but a lookback rebate will be paid if the barrier is crossed by the underlying asset price. Therefore, the turbo warrant price satisfies a partial differential equation (PDE with a boundary condition that depends on another boundary-value problem (BVP of PDE. Due to the highly complicated structure of turbo warrants, their valuation presents a challenging problem in the field of financial mathematics. This paper applies the homotopy analysis method to construct an analytic pricing formula for turbo warrants under stochastic volatility in a PDE framework.
Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy
Majumdar, Apala
2009-10-01
Let O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we evaluate the infimum Dirichlet energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1, ..., sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.
The solution of a coupled system of nonlinear physical problems using the homotopy analysis method
International Nuclear Information System (INIS)
El-Wakil, S A; Abdou, M A
2010-01-01
In this article, the homotopy analysis method (HAM) has been applied to solve coupled nonlinear evolution equations in physics. The validity of this method has been successfully demonstrated by applying it to two nonlinear evolution equations, namely coupled nonlinear diffusion reaction equations and the (2+1)-dimensional Nizhnik-Novikov Veselov system. The results obtained by this method show good agreement with the ones obtained by other methods. The proposed method is a powerful and easy to use analytic tool for nonlinear problems and does not need small parameters in the equations. The HAM solutions contain an auxiliary parameter that provides a convenient way of controlling the convergence region of series solutions. The results obtained here reveal that the proposed method is very effective and simple for solving nonlinear evolution equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems.
Application of homotopy analysis method and inverse solution of a rectangular wet fin
International Nuclear Information System (INIS)
Panda, Srikumar; Bhowmik, Arka; Das, Ranjan; Repaka, Ramjee; Martha, Subash C.
2014-01-01
Highlights: • Solution of a wet fin with is obtained by homotopy analysis method (HAM). • Present HAM results have been well-validated with literature results. • Inverse analysis is done using genetic algorithm. • Measurement error of ±10–12% (approx.) is found to yield satisfactory reconstructions. - Abstract: This paper presents the analytical solution of a rectangular fin under the simultaneous heat and mass transfer across the fin surface and the fin tip, and estimates the unknown thermal and geometrical configurations of the fin using inverse heat transfer analysis. The local temperature field is obtained by using homotopy analysis method for insulated and convective fin tip boundary conditions. Using genetic algorithm, the thermal and geometrical parameters, viz., thermal conductivity of the material, surface heat transfer coefficient and dimensions of the fin have been simultaneously estimated for the prescribed temperature field. Earlier inverse studies on wet fin have been restricted to the analysis of nonlinear governing equation with either insulated tip condition or finite tip temperature only. The present study developed a closed-form solution with the consideration of nonlinearity effects in both governing equation and boundary condition. The study on inverse optimization leads to many feasible combination of fin materials, thermal conditions and fin dimensions. Thus allows the flexibility for designing a fin under wet conditions, based on multiple combinations of fin materials, fin dimensions and thermal configurations to achieve the required heat transfer duty. It is further determined that the allowable measurement error should be limited to ±10–12% in order to achieve satisfactory reconstruction
Developments in perturbation theory
International Nuclear Information System (INIS)
Greenspan, E.
1976-01-01
Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators
Institute of Scientific and Technical Information of China (English)
Daciberg Lima GON(C)ALVES; John GUASCHI
2017-01-01
Let X be a topological space.In this survey the authors consider severaltypes of configuration spaces,namely,the classical (usual) configuration spaces Fn(X)and Dn(X),the orbit configuration spaces FGn(X) and FGn(X)/Sn with respect to a freeaction of a group G on X,and the graph configuration spaces FΓn(X) and FΓn(X)/H,where F is a graph and H is a suitable subgroup of the symmetric group Sn.The orderedconfiguration spaces Fn (X),FGn (X),FΓn(X) are all subsets of the n-fold Cartesian productnП1 X of X with itself,and satisfy FGn(X) (C) Fn(X) (C) Frn(X) (C) nП1 X.If A denotes one of these configuration spaces,the authors analyse the difference between A and nП1 X from a topological and homotopical point of view.The principal results known in the literature concern the usual configuration spaces.The authors are particularly interested in the homomorphism on the level of the homotopy groups of the spaces induced by the inclusion (ι):A → nП1 X,the homotopy type of the homotopy fibre I(ι) of the map (ι) via certain constructions on various spaces that depend on X,and the long exact sequence in homotopy of the fibration involving I(ι) and arising from the inclusion (ι).In this respect,if X is either a surface without boundary,in particular if X is the 2-sphere or the real projective plane,or a space whose universal covering is contractible,or an orbit space Sk/G of the k-dimensional sphere by a free action of a Lie group G,the authors present recent results obtained by themselves for the first case,and in collaboration with Golasi(n)ski for the second and third cases.The authors also briefly indicate some older results relative to the homotopy of these spaces that are related to the problems of interest.In order to motivate various questions,for the remaining types of configuration spaces,a few of their basic properties are described and proved.A list of open questions and problems is given at the end of the paper.
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael
2015-10-24
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael; Calo, Victor M.
2015-01-01
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, N.; Barari, Amin
2011-01-01
equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the Homotopy Analysis Method in comparison with the numerical method in solving this problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear...... conclusion can be drawn from the numerical method results that the HAM provides highly accurate solutions for nonlinear differential equations. Design/methodology/approach - In this paper a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet channel...... is presented and the Homotopy Analysis Method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the Homotopy Analysis Method in comparison...
International Nuclear Information System (INIS)
Alomari, A. K.; Noorani, M. S. M.; Nazar, R.
2008-01-01
We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter ħ, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method
International Nuclear Information System (INIS)
Collins, J.C.
1985-01-01
Progress in quantum chromodynamics in the past year is reviewed in these specific areas: proof of factorization for hadron-hadron collisions, fast calculation of higher order graphs, perturbative Monte Carlo calculations for hadron-hadron scattering, applicability of perturbative methods to heavy quark production, and understanding of the small-x problem. 22 refs
Perturbative and constructive renormalization
International Nuclear Information System (INIS)
Veiga, P.A. Faria da
2000-01-01
These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)
Fresse, Benoit
2017-01-01
The Grothendieck-Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck-Teichmüller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of...
International Nuclear Information System (INIS)
Mueller, A.H.
1986-03-01
A brief review of some of the recent progress in perturbative QCD is given (heavy quark production, small-x physics, minijets and related topics, classical simulations in high energy reactions, coherence and the string effect)
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
of calculations. Results obtained by max–min are compared with Homotopy Analysis Method (HAM), energy balance and numerical solution and it is shown that, simply one term is enough to obtain a highly accurate result in contrast to HAM with just one term in series solution. Finally, the phase plane to show...... the stability of systems is plotted and discussed....
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
of calculations. Results obtained by max–min are compared with Homotopy Analysis Method (HAM), energy balance and numerical solution and it is shown that, simply one term is enough to obtain a highly accurate result in contrast to HAM with just one term in series solution. Finally, the phase plane to show...... the stability of systems is plotted and discussed....
Generalized chiral perturbation theory
International Nuclear Information System (INIS)
Knecht, M.; Stern, J.
1994-01-01
The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs
Directory of Open Access Journals (Sweden)
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
International Nuclear Information System (INIS)
Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75
1992-06-01
The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant α is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a 3 , a 4 , a 5 and a 6 are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs
International Nuclear Information System (INIS)
Ecker, G.
1996-06-01
After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)
Schroedinger operators with singular perturbation potentials
International Nuclear Information System (INIS)
Harrell, E.M. II.
1976-01-01
This is a perturbative analysis of the eigenvalues and eigenfunctions of Schroedinger operators of the form -Δ + A + lambda V, defined on the Hilbert space L 2 (R/sup n/). A is a potential function (a smooth, real multiplication operator), and V is a ''spikelike'' perturbation, i.e., a perturbative potential function which diverges at some finite point. Lambda is a small real or complex parameter. The emphasis is on one-dimensional problems, and in particular the typical example is the ''spiked harmonic oscillator'' Hamiltonian, -d 2 /dx 2 + x 2 + lambda x/sup -α/, where α is a positive constant. An earlier study by L. Detwiler and J. R. Klauder [Phys. Rev. D 11 (1975) 1436] indicated that the lowest-order corrections to the ground-state eigenvalue of the spiked harmonic oscillator with lambda greater than 0 were proportional to lambda ln lambda when α = 3, and to lambda/sup 1/(α-2) when α is greater than 3. These and analogous results for a large class of operators and arbitrary eigenvalues are proved. Explicit constants in a modified perturbation series with a complicated dependence on lambda are determined and exhibited. Higher-order corrections for real lambda and lowest-order corrections for complex lambda are also discussed. While the substance of the dissertation is mathematical, its main applications are to quantum physics. The immediate cause of interest in such problems was the use of their peculiar convergence properties by J. R. Klauder as models for the behavior of nonrenormalizable quantum field theories. However, the results of this study are likely to be of greater importance in chemical or nuclear physics, as positive spikelike perturbations represent repulsive core interactions for quantum mechanical particles. The modified perturbation series are a new calculation technique for this situation
Yang, Paul; Gambino, Nicola; Kock, Joachim
2015-01-01
The two parts of the present volume contain extended conference abstracts corresponding to selected talks given by participants at the "Conference on Geometric Analysis" (thirteen abstracts) and at the "Conference on Type Theory, Homotopy Theory and Univalent Foundations" (seven abstracts), both held at the Centre de Recerca Matemàtica (CRM) in Barcelona from July 1st to 5th, 2013, and from September 23th to 27th, 2013, respectively. Most of them are brief articles, containing preliminary presentations of new results not yet published in regular research journals. The articles are the result of a direct collaboration between active researchers in the area after working in a dynamic and productive atmosphere. The first part is about Geometric Analysis and Conformal Geometry; this modern field lies at the intersection of many branches of mathematics (Riemannian, Conformal, Complex or Algebraic Geometry, Calculus of Variations, PDE's, etc) and relates directly to the physical world, since many natural phenomena...
Preheating curvaton perturbations
International Nuclear Information System (INIS)
Bastero-Gil, M.; Di Clemente, V.; King, S.F.
2005-01-01
We discuss the potentially important role played by preheating in certain variants of the curvaton mechanism in which isocurvature perturbations of a D-flat (and F-flat) direction become converted to curvature perturbations during reheating. We discover that parametric resonance of the isocurvature components amplifies the superhorizon fluctuations by a significant amount. As an example of these effects we develop a particle physics motivated model which involves hybrid inflation with the waterfall field N being responsible for generating the μ term, the right-handed neutrino mass scale, and the Peccei-Quinn symmetry breaking scale. The role of the curvaton field can be played either by usual Higgs field, or the lightest right-handed sneutrino. Our new results show that it is possible to achieve the correct curvature perturbations for initial values of the curvaton fields of order the weak scale. In this model we show that the prediction for the spectral index of the final curvature perturbation only depends on the mass of the curvaton during inflation, where consistency with current observational data requires the ratio of this mass to the Hubble constant to be 0.3
String perturbation theory diverges
International Nuclear Information System (INIS)
Gross, D.J.; Periwal, V.
1988-01-01
We prove that perturbation theory for the bosonic string diverges for arbitrary values of the coupling constant and is not Borel summable. This divergence is independent of the existence of the infinities that occur in the theory due to the presence of tachyons and dilaton tadpoles. We discuss the physical implications of such a divergence
International Nuclear Information System (INIS)
Suslov, I.M.
2005-01-01
Various perturbation series are factorially divergent. The behavior of their high-order terms can be determined by Lipatov's method, which involves the use of instanton configurations of appropriate functional integrals. When the Lipatov asymptotic form is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight into the behavior of the remaining terms of the series, which can be resummed to solve various strong-coupling problems in a certain approximation. This approach is demonstrated by determining the Gell-Mann-Low functions in φ 4 theory, QED, and QCD with arbitrary coupling constants. An overview of the mathematical theory of divergent series is presented, and interpretation of perturbation series is discussed. Explicit derivations of the Lipatov asymptotic form are presented for some basic problems in theoretical physics. A solution is proposed to the problem of renormalon contributions, which hampered progress in this field in the late 1970s. Practical perturbation-series summation schemes are described both for a coupling constant of order unity and in the strong-coupling limit. An interpretation of the Borel integral is given for 'non-Borel-summable' series. Higher order corrections to the Lipatov asymptotic form are discussed
Instantaneous stochastic perturbation theory
International Nuclear Information System (INIS)
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Cosmological perturbations in antigravity
Oltean, Marius; Brandenberger, Robert
2014-10-01
We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.
Solan, Eilon; Vieille, Nicolas
2015-01-01
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.
Scalar cosmological perturbations
International Nuclear Information System (INIS)
Uggla, Claes; Wainwright, John
2012-01-01
Scalar perturbations of Friedmann-Lemaitre cosmologies can be analyzed in a variety of ways using Einstein's field equations, the Ricci and Bianchi identities, or the conservation equations for the stress-energy tensor, and possibly introducing a timelike reference congruence. The common ground is the use of gauge invariants derived from the metric tensor, the stress-energy tensor, or from vectors associated with a reference congruence, as basic variables. Although there is a complication in that there is no unique choice of gauge invariants, we will show that this can be used to advantage. With this in mind our first goal is to present an efficient way of constructing dimensionless gauge invariants associated with the tensors that are involved, and of determining their inter-relationships. Our second goal is to give a unified treatment of the various ways of writing the governing equations in dimensionless form using gauge-invariant variables, showing how simplicity can be achieved by a suitable choice of variables and normalization factors. Our third goal is to elucidate the connection between the metric-based approach and the so-called 1 + 3 gauge-invariant approach to cosmological perturbations. We restrict our considerations to linear perturbations, but our intent is to set the stage for the extension to second-order perturbations. (paper)
Generalized perturbation series
International Nuclear Information System (INIS)
Baird, L.C.; Stinchcomb, G.
1973-01-01
An approximate solution of the Green's function equation may be used to generate an exact solution of the Schroedinger equation. This is accomplished through an iterative procedure. The procedure is equivalent to a perturbation expansion if the approximate Green's function is exact with respect to some reference potential
DEFF Research Database (Denmark)
jora, Renata; Schechter, Joseph; Naeem Shahid, M.
2009-01-01
We study the effects of the perturbation which violates the permutation symmetry of three Majorana neutrinos but preserves the well known (23) interchange symmetry. This is done in the presenceof an arbitrary Majorana phase which serves to insure the degeneracy of the three neutrinos at the unper...... at the unperturbed level....
Quantum system lifetimes and measurement perturbations
International Nuclear Information System (INIS)
Najakov, E.
1977-05-01
The recently proposed description of quantum system decay in terms of repeated measurement perturbations is modified. The possibility of retarded reductions to a unique quantum state, due to ineffective localization of the decay products at initial time measurements, is simply taken into account. The exponential decay law is verified again. A modified equation giving the observed lifetime in terms of unperturbed quantum decay law, measurement frequency and reduction law is derived. It predicts deviations of the observed lifetime from the umperturbed one, together with a dependence on experimental procedures. The influence of different model unperturbed decay laws and reduction laws on this effect is studied
Cosmological perturbations in a family of deformations of general relativity
International Nuclear Information System (INIS)
Krasnov, Kirill; Shtanov, Yuri
2010-01-01
We study linear cosmological perturbations in a previously introduced family of deformations of general relativity characterized by the absence of new degrees of freedom. The homogeneous and isotropic background in this class of theories is unmodified and is described by the usual Friedmann equations. The theory of cosmological perturbations is modified and the relevant deformation parameter has the dimension of length. Gravitational perturbations of the scalar type can be described by a certain relativistic potential related to the matter perturbations just as in general relativity. A system of differential equations describing the evolution of this potential and of the stress-energy density perturbations is obtained. We find that the evolution of scalar perturbations proceeds with a modified effective time-dependent speed of sound, which, contrary to the case of general relativity, does not vanish even at the matter-dominated stage. In a broad range of values of the length parameter controlling the deformation, a specific transition from the regime of modified gravity to the regime of general relativity in the evolution of scalar perturbations takes place during the radiation domination. In this case, the resulting power spectrum of perturbations in radiation and dark matter is suppressed on the comoving spatial scales that enter the Hubble radius before this transition. We estimate the bounds on the deformation parameter for which this suppression does not lead to observable consequences. Evolution of scalar perturbations at the inflationary stage is modified but very slightly and the primordial spectrum generated during inflation is not noticeably different from the one obtained in general relativity
Studying the perturbative Reggeon
International Nuclear Information System (INIS)
Griffiths, S.; Ross, D.A.
2000-01-01
We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ''reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q 2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel. (orig.)
Renormalized Lie perturbation theory
International Nuclear Information System (INIS)
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
Nonperturbative perturbation theory
International Nuclear Information System (INIS)
Bender, C.M.
1989-01-01
In this talk we describe a recently proposed graphical perturbative calculational scheme for quantum field theory. The basic idea is to expand in the power of the interaction term. For example, to solve a λφ 4 theory in d-dimensional space-time, we introduce a small parameter δ and consider a λ(φ 2 ) 1+δ field theory. We show how to expand such a theory as a series in powers of δ. The resulting perturbation series appears to have a finite radius of convergence and numerical results for low-dimensional models are good. We have computed the two-point and four-point Green's functions to second order in powers of δ and the 2n-point Green's functions (n>2) to order δ. We explain how to renormalize the theory and show that, to first order in powers of δ, when δ>0 and d≥4 the theory is free. This conclusion remains valid to second order in powers of δ, and we believe that it remains valid to all orders in powers of δ. The new perturbative scheme is consistent with global supersymmetry invariance. We examine a two-dimensional supersymmetric quantum field theory in which we do not know of any other means for doing analytical calculations. We illustrate the power of this new technique by computing the ground-state energy density E to second order in this new perturbation theory. We show that there is a beautiful and delicate cancellation between infinite classes of graphs which leads to the result that E=0. (orig.)
Perturbed asymptotically linear problems
Bartolo, R.; Candela, A. M.; Salvatore, A.
2012-01-01
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...
Twisting perturbed parafermions
Directory of Open Access Journals (Sweden)
A.V. Belitsky
2017-07-01
Full Text Available The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang–Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6 nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current–current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3 sigma model which is reformulated as perturbed parafermions.
Forecasting with the Standardized Self-Perturbed Kalman Filter
DEFF Research Database (Denmark)
Grassi, Stefano; Nonejad, Nima; Santucci de Magistris, Paolo
We propose and study the finite-sample properties of a modified version of the self-perturbed Kalman filter of Park and Jun (1992) for the on-line estimation of models subject to parameter instability. The perturbation term in the updating equation of the state covariance matrix is now weighted...... compared to other on-line, classical and Bayesian methods. The standardized self-perturbed Kalman filter is adopted to forecast the equity premium on the S&P500 index under several model specifications, and to investigate to what extent and how realized variance can be exploited to predict excess returns....
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Perturbative quantum chromodynamics
1989-01-01
This book will be of great interest to advanced students and researchers in the area of high energy theoretical physics. Being the most complete and updated review volume on Perturbative QCD, it serves as an extremely useful textbook or reference book. Some of the reviews in this volume are the best that have been written on the subject anywhere. Contents: Factorization of Hard Processes in QCD (J C Collins, D E Soper & G Sterman); Exclusive Processes in Quantum Chromodynamics (S J Brodsky & G P Lepage); Coherence and Physics of QCD Jets (Yu L Dokshitzer, V A Khoze & S I Troyan); Pomeron in Qu
Perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Radyushkin, A.V.
1987-01-01
The latest achievements in perturbative quantum chromodynamics (QCD) relating to the progress in factorization of small and large distances are presented. The following problems are concerned: Development of the theory of Sudakov effects on the basis of mean contour formalism. Development of nonlocal condensate formalism. Calculation of hadron wave functions and hadron distribution functions using QCD method of sum rules. Development of the theory of Regge behaviour in QCD, behaviour of structure functions at small x. Study of polarization effects in hadron processes with high momentum transfer
Perturbed effects at radiation physics
International Nuclear Information System (INIS)
Külahcı, Fatih; Şen, Zekâi
2013-01-01
Perturbation methodology is applied in order to assess the linear attenuation coefficient, mass attenuation coefficient and cross-section behavior with random components in the basic variables such as the radiation amounts frequently used in the radiation physics and chemistry. Additionally, layer attenuation coefficient (LAC) and perturbed LAC (PLAC) are proposed for different contact materials. Perturbation methodology provides opportunity to obtain results with random deviations from the average behavior of each variable that enters the whole mathematical expression. The basic photon intensity variation expression as the inverse exponential power law (as Beer–Lambert's law) is adopted for perturbation method exposition. Perturbed results are presented not only in terms of the mean but additionally the standard deviation and the correlation coefficients. Such perturbation expressions provide one to assess small random variability in basic variables. - Highlights: • Perturbation methodology is applied to Radiation Physics. • Layer attenuation coefficient (LAC) and perturbed LAC are proposed for contact materials. • Perturbed linear attenuation coefficient is proposed. • Perturbed mass attenuation coefficient (PMAC) is proposed. • Perturbed cross-section is proposed
Chiral perturbation theory with nucleons
International Nuclear Information System (INIS)
Meissner, U.G.
1991-09-01
I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, πN scattering and the σ-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon
Directory of Open Access Journals (Sweden)
A. Jamali
2016-10-01
Full Text Available Nowadays, municipalities intend to have 3D city models for facility management, disaster management and architectural planning. Indoor models can be reconstructed from construction plans but sometimes, they are not available or very often, they differ from ‘as-built’ plans. In this case, the buildings and their rooms must be surveyed. One of the most utilized methods of indoor surveying is laser scanning. The laser scanning method allows taking accurate and detailed measurements. However, Terrestrial Laser Scanner is costly and time consuming. In this paper, several techniques for indoor 3D building data acquisition have been investigated. For reducing the time and cost of indoor building data acquisition process, the Trimble LaserAce 1000 range finder is used. The proposed approache use relatively cheap equipment: a light Laser Rangefinder which appear to be feasible, but it needs to be tested to see if the observation accuracy is sufficient for the 3D building modelling. The accuracy of the rangefinder is evaluated and a simple spatial model is reconstructed from real data. This technique is rapid (it requires a shorter time as compared to others, but the results show inconsistencies in horizontal angles for short distances in indoor environments. The range finder horizontal angle sensor was calibrated using a least square adjustment algorithm, a polynomial kernel, interval analysis and homotopy continuation.
Directory of Open Access Journals (Sweden)
Yahaya Shagaiya Daniel
2015-09-01
Full Text Available This paper investigates the theoretical influence of buoyancy and thermal radiation on MHD flow over a stretching porous sheet. The model which constituted highly nonlinear governing equations is transformed using similarity solution and then solved using homotopy analysis method (HAM. The analysis is carried out up to the 5th order of approximation and the influences of different physical parameters such as Prandtl number, Grashof number, suction/injection parameter, thermal radiation parameter and heat generation/absorption coefficient and also Hartman number on dimensionless velocity, temperature and the rate of heat transfer are investigated and discussed quantitatively with the aid of graphs. Numerical results obtained are compared with the previous results published in the literature and are found to be in good agreement. It was found that when the buoyancy parameter and the fluid velocity increase, the thermal boundary layer decreases. In case of the thermal radiation, increasing the thermal radiation parameter produces significant increases in the thermal conditions of the fluid temperature which cause more fluid in the boundary layer due to buoyancy effect, causing the velocity in the fluid to increase. The hydrodynamic boundary layer and thermal boundary layer thickness increase as a result of increase in radiation.
Non-perturbative versus perturbative renormalization of lattice operators
International Nuclear Information System (INIS)
Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.
1995-09-01
Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)
Perturbation theories for the dipolar fluids
International Nuclear Information System (INIS)
Lee, L.L.; Chung, T.H.
1983-01-01
We derive here four different perturbation equations for the calculation of the angular pair correlation functions of dipolar fluids; namely, the first order y-expansion, the modified Percus--Yevik (MPY) expansion, the modified hypernetted chain (MHNC) expansion, and the modified linearized hypernetted chain (MLHNC) equation. Both the method of the functional expansion and the method of the cluster integrals are utilized. Comparison with other perturbation theories (e.g., the Melnyk--Smith equation) is made. While none of the theories is exact, as shown by the cluster diagrams, the MLHNC and the MHNC contain more diagrams than, say, the MPY and y-expansion. The y-expansion equation can be improved by including the correction terms to the Kirkwood superposition approximation for the triplet correlation function. For example, the inclusion of the correction term rho∫d4h(14)h(24)h(34) in a formula given by Henderson, is shown to improve substantially the y-expansion equation. We examine the performance of two of the theories: the y-expansion and the MLHNC equation for a Stockmayer (dipolar) fluid with a reduced dipole moment μ/sup asterisk2/ [ = μ 2 /(epsilonsigma 3 )] = 1.0. Comparison with Monte Carlo simulation results of Adams et al. and with other theories (e.g., the QHNC equation) shows that our results are reasonable. Further improvements of the equations are also pointed out
Shivakumara, Tagginahalli N; Chaudhary, Sonam; Kamaraju, Divya; Dutta, Tushar K; Papolu, Pradeep K; Banakar, Prakash; Sreevathsa, Rohini; Singh, Bhupinder; Manjaiah, K M; Rao, Uma
2017-01-01
The complex parasitic strategy of Meloidogyne incognita appears to involve simultaneous expression of its pharyngeal gland-specific effector genes in order to colonize the host plants. Research reports related to effector crosstalk in phytonematodes for successful parasitism of the host tissue is yet underexplored. In view of this, we have used in planta effector screening approach to understand the possible interaction of pioneer genes ( msp-18 and msp-20 , putatively involved in late and early stage of M. incognita parasitism, respectively) with other unrelated effectors such as cell-wall modifying enzymes (CWMEs) in M. incognita . Host-induced gene silencing (HIGS) strategy was used to generate the transgenic eggplants expressing msp-18 and msp-20 , independently. Putative transformants were characterized via qRT-PCR and Southern hybridization assay. SiRNAs specific to msp-18 and msp - 20 were also detected in the transformants via Northern hybridization assay. Transgenic expression of the RNAi constructs of msp-18 and msp-20 genes resulted in 43.64-69.68% and 41.74-67.30% reduction in M. incognita multiplication encompassing 6 and 10 events, respectively. Additionally, transcriptional oscillation of CWMEs documented in the penetrating and developing nematodes suggested the possible interaction among CWMEs and pioneer genes. The rapid assimilation of plant-derived carbon by invading nematodes was also demonstrated using 14 C isotope probing approach. Our data suggests that HIGS of msp-18 and msp-20 , improves nematode resistance in eggplant by affecting the steady-state transcription level of CWME genes in invading nematodes, and safeguard the plant against nematode invasion at very early stage because nematodes may become the recipient of bioactive RNA species during the process of penetration into the plant root.
Perturbation studies on KAHTER
Energy Technology Data Exchange (ETDEWEB)
Rueckert, M.; Jonas, H.; Neef, R. D.
1974-10-15
The paper describes experimental and analytical results by both transport theory and diffusion theory calculations of perturbation tests in the KAHTER pebble bed critical experiment. The fission-weighted adjoint flux is measured from in-core detector responses by introducing a Cf-source into the core. Adjoint-weighted reactivities are calculated and compared to reactivity measurements for the introduction of a fuel and graphite pebble onto the top of the critical pile, the central rod worth, and the effect of replacing B4C with varying amounts of HfC in the central rod. In addition, analytical studies were made of the sensitivity of criticality to the fuel to graphite pebble ratio as measured in tests and of the effect of the upper void cavity as simulated in tests by placing cadmium layer across the top of the pebble pile to force a zero flux boundary condition.
Introduction to perturbation methods
Holmes, M
1995-01-01
This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.
Perturbation theory with instantons
International Nuclear Information System (INIS)
Carruthers, P.; Pinsky, S.S.; Zachariasen, F.
1977-05-01
''Perturbation theory'' rules are developed for calculating the effect of instantons in a pure Yang-Mills theory with no fermions, in the ''dilute gas'' approximation in which the N-instanton solution is assumed to be the sum of N widely separated one-instanton solutions. These rules are then used to compute the gluon propagator and proper vertex function including all orders of the instanton interaction but only to lowest order in the gluon coupling. It is to be expected that such an approximation is valid only for momenta q larger than the physical mass μ. The result is that in this regime instantons cause variations in the propagator and vertex of the form (μ 2 /q 2 )/sup -8π 2 b/ where b is the coefficient in the expansion of the β function: β = bg 3 +...
Singular perturbation of simple eigenvalues
International Nuclear Information System (INIS)
Greenlee, W.M.
1976-01-01
Two operator theoretic theorems which generalize those of asymptotic regular perturbation theory and which apply to singular perturbation problems are proved. Application of these theorems to concrete problems is involved, but the perturbation expansions for eigenvalues and eigenvectors are developed in terms of solutions of linear operator equations. The method of correctors, as well as traditional boundary layer techniques, can be used to apply these theorems. The current formulation should be applicable to highly singular ''hard core'' potential perturbations of the radial equation of quantum mechanics. The theorems are applied to a comparatively simple model problem whose analysis is basic to that of the quantum mechanical problem
International Nuclear Information System (INIS)
Harada, Masayasu
2009-01-01
Chiral perturbation theory has been used for great number of phenomenological analyses in low energy QCD as well as the lattice QCD analyses since the creation of the theory by Weinberg in 1979 followed by its consolidation by Gasser and Leutwyler in 1984 and 85. The theory is now the highly established one as the approach based on the effective field theory to search for Green function including quantum correlations in the frame of the systematic expansion technique using Lagrangian which includes all of the terms allowed by the symmetry. This review has been intended to describe how systematically physical quantities are calculated in the framework of the chiral symmetry. Consequently many of the various phenomenological analyses are not taken up here for which other reports are to be referred. Further views are foreseen to be developed based on the theory in addition to numbers of results reported up to the present. Finally π-π scattering is taken up to discuss to what energy scale the theory is available. (S. Funahashi)
International Nuclear Information System (INIS)
Fabris, J.D.
1977-01-01
The electric quadrupolar interaction in some hafnium complexes, measured at the metal nucleus level is studied. For that purpose, the technique of γ-γ perturbed angular correlation is used: the frequencies of quadrupolar interaction are compared with some hafnium α-hydroxicarboxilates, namely glycolate, lactate, mandelate and benzylate; the influence of the temperature on the quadrupolar coupling on the hafnium tetramandelate is studied; finally, the effects associated with the capture of thermal neutrons by hafnium tetramandelate are examined locally at the nuclear level. The first group of results shows significant differences in a series of complexes derived from glycolic acid. On the other hand, the substitution of the protons in hafnium tetramandelate structure by some alkaline cations permits to verify a correlation between the variations in the quadrupolar coupling and the electronegativities of the substituent elements. Measurements at high temperatures show that this complex is thermally stable at 100 and 150 0 C. It is possible to see the appearance of two distinct sites for the probe nucleus, after heating the sample at 100 0 C for prolonged time. This fact is attributed to a probable interconversion among the postulated structural isomers for the octacoordinated compounds. Finally, measurements of angular correlation on the irradiated complex show that there is an effective destruction of the target molecule by neutron capture [pt
Perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Brodsky, S.J.
1979-12-01
The application of QCD to hadron dynamics at short distances, where asymptotic freedom allows a systematic perturbative approach, is addressed. The main theme of the approach is to incorporate systematically the effects of the hadronic wave function in large momentum transfer exclusive and inclusive reactions. Although it is conventional to treat the hadron as a classical source of on-shell quarks, there are important dynamical effects due to hadronic constituent structure which lead to a broader testing ground for QCD. QCD predictions are discussed for exclusive processes and form factors at large momentum transfer in which the short-distance behavior and the finite compositeness of the hadronic wave functions play crucial roles. Many of the standard tests of QCD are reviewed including the predictions for R = sigma/sub e + e - →had//sigma/sub e + e - →μ + μ - /, the structure functions of hadrons and photons, jet phenomena, and the QCD corrections to deep inelastic processes. The exclusive-inclusive connection in QCD, the effects of power-law scale-breaking contributions, and the important role of the available energy in controlling logarithmic scale violations are also discussed. 150 references, 44 figures
Lattice regularized chiral perturbation theory
International Nuclear Information System (INIS)
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
CERN. Geneva
2013-01-01
Perturbative QCD is the general theoretical framework for describing hard scattering processes yielding multiparticle production at hadron colliders. In these lectures, we shall introduce fundamental features of perturbative QCD and describe its application to several high energy collider processes, including jet production in electron-positron annihilation, deep inelastic scattering, Higgs boson and gauge boson production at the LHC.
Propagation of Ion Acoustic Perturbations
DEFF Research Database (Denmark)
Pécseli, Hans
1975-01-01
Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered.......Equations describing the propagation of ion acoustic perturbations are considered, using the assumption that the electrons are Boltzman distributed and isothermal at all times. Quasi-neutrality is also considered....
On summation of perturbation expansions
International Nuclear Information System (INIS)
Horzela, A.
1985-04-01
The problem of the restoration of physical quantities defined by divergent perturbation expansions is analysed. The Pad'e and Borel summability is proved for alternating perturbation expansions with factorially growing coefficients. The proof is based on the methods of the classical moments theory. 17 refs. (author)
Continual integral in perturbation theory
International Nuclear Information System (INIS)
Slavnov, A.A.
1975-01-01
It is shown that all results obtained by means of continual integration within the framework of perturbation theory are completely equivalent to those obtained by the usual diagram technique and are therfore just as rigorous. A rigorous justification is given for the rules for operating with continual integrals in perturbation theory. (author)
On dark energy isocurvature perturbation
International Nuclear Information System (INIS)
Liu, Jie; Zhang, Xinmin; Li, Mingzhe
2011-01-01
Determining the equation of state of dark energy with astronomical observations is crucially important to understand the nature of dark energy. In performing a likelihood analysis of the data, especially of the cosmic microwave background and large scale structure data the dark energy perturbations have to be taken into account both for theoretical consistency and for numerical accuracy. Usually, one assumes in the global fitting analysis that the dark energy perturbations are adiabatic. In this paper, we study the dark energy isocurvature perturbation analytically and discuss its implications for the cosmic microwave background radiation and large scale structure. Furthermore, with the current astronomical observational data and by employing Markov Chain Monte Carlo method, we perform a global analysis of cosmological parameters assuming general initial conditions for the dark energy perturbations. The results show that the dark energy isocurvature perturbations are very weakly constrained and that purely adiabatic initial conditions are consistent with the data
Perturbation analysis of a parametrically changed sine-Gordon equation
DEFF Research Database (Denmark)
Sakai, S.; Samuelsen, Mogens Rugholm; Olsen, O. H.
1987-01-01
A long Josephson junction with a spatially varying inductance is a physical manifestation of a modified sine-Gordon equation with parametric perturbation. Soliton propagation in such Josephson junctions is discussed. First, for an adiabatic model where the inductance changes smoothly compared...
Disformal transformation of cosmological perturbations
Directory of Open Access Journals (Sweden)
Masato Minamitsuji
2014-10-01
Full Text Available We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (nonconservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame.
Disformal transformation of cosmological perturbations
International Nuclear Information System (INIS)
Minamitsuji, Masato
2014-01-01
We investigate the gauge-invariant cosmological perturbations in the gravity and matter frames in the general scalar–tensor theory where two frames are related by the disformal transformation. The gravity and matter frames are the extensions of the Einstein and Jordan frames in the scalar–tensor theory where two frames are related by the conformal transformation, respectively. First, it is shown that the curvature perturbation in the comoving gauge to the scalar field is disformally invariant as well as conformally invariant, which gives the predictions from the cosmological model where the scalar field is responsible both for inflation and cosmological perturbations. Second, in case that the disformally coupled matter sector also contributes to curvature perturbations, we derive the evolution equations of the curvature perturbation in the uniform matter energy density gauge from the energy (non)conservation in the matter sector, which are independent of the choice of the gravity sector. While in the matter frame the curvature perturbation in the uniform matter energy density gauge is conserved on superhorizon scales for the vanishing nonadiabatic pressure, in the gravity frame it is not conserved even if the nonadiabatic pressure vanishes. The formula relating two frames gives the amplitude of the curvature perturbation in the matter frame, once it is evaluated in the gravity frame
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
Instabilities in mimetic matter perturbations
Energy Technology Data Exchange (ETDEWEB)
Firouzjahi, Hassan; Gorji, Mohammad Ali [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Mansoori, Seyed Ali Hosseini, E-mail: firouz@ipm.ir, E-mail: gorji@ipm.ir, E-mail: shosseini@shahroodut.ac.ir, E-mail: shossein@ipm.ir [Physics Department, Shahrood University of Technology, P.O. Box 3619995161 Shahrood (Iran, Islamic Republic of)
2017-07-01
We study cosmological perturbations in mimetic matter scenario with a general higher derivative function. We calculate the quadratic action and show that both the kinetic term and the gradient term have the wrong sings. We perform the analysis in both comoving and Newtonian gauges and confirm that the Hamiltonians and the associated instabilities are consistent with each other in both gauges. The existence of instabilities is independent of the specific form of higher derivative function which generates gradients for mimetic field perturbations. It is verified that the ghost instability in mimetic perturbations is not associated with the higher derivative instabilities such as the Ostrogradsky ghost.
Perturbation theory of effective Hamiltonians
International Nuclear Information System (INIS)
Brandow, B.H.
1975-01-01
This paper constitutes a review of the many papers which have used perturbation theory to derive ''effective'' or ''model'' Hamiltonians. It begins with a brief review of nondegenerate and non-many-body perturbation theory, and then considers the degenerate but non-many-body problem in some detail. It turns out that the degenerate perturbation problem is not uniquely defined, but there are some practical criteria for choosing among the various possibilities. Finally, the literature dealing with the linked-cluster aspects of open-shell many-body systems is reviewed. (U.S.)
The theory of singular perturbations
De Jager, E M
1996-01-01
The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathemat
The power of perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Serone, Marco [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy); Spada, Gabriele [SISSA International School for Advanced Studies and INFN Trieste, Via Bonomea 265, 34136, Trieste (Italy); Villadoro, Giovanni [Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste (Italy)
2017-05-10
We study quantum mechanical systems with a discrete spectrum. We show that the asymptotic series associated to certain paths of steepest-descent (Lefschetz thimbles) are Borel resummable to the full result. Using a geometrical approach based on the Picard-Lefschetz theory we characterize the conditions under which perturbative expansions lead to exact results. Even when such conditions are not met, we explain how to define a different perturbative expansion that reproduces the full answer without the need of transseries, i.e. non-perturbative effects, such as real (or complex) instantons. Applications to several quantum mechanical systems are presented.
Tunnelling instability via perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Graffi, S. (Bologna Univ. (Italy). Dip. di Matematica); Grecchi, V. (Moderna Univ. (Italy). Dip. di Matematica); Jona-Lasinio, G. (Paris-11 Univ., 91 - Orsay (France). Lab. de Physique Theorique et Hautes Energies)
1984-10-21
The semiclassical limit of low lying states in a multiwell potential is studied by rigorous perturbative techniques. In particular tunnelling instability and localisation of wave functions is obtained in a simple way under small deformations of symmetric potentials.
Perturbation theory of quantum resonances
Czech Academy of Sciences Publication Activity Database
Durand, P.; Paidarová, Ivana
2016-01-01
Roč. 135, č. 7 (2016), s. 159 ISSN 1432-2234 Institutional support: RVO:61388955 Keywords : Partitioning technique * Analytic continuation * Perturbative expansion Subject RIV: CF - Physical ; Theoretical Chemistry
Perturbation Theory of Embedded Eigenvalues
DEFF Research Database (Denmark)
Engelmann, Matthias
project gives a general and systematic approach to analytic perturbation theory of embedded eigenvalues. The spectral deformation technique originally developed in the theory of dilation analytic potentials in the context of Schrödinger operators is systematized by the use of Mourre theory. The group...... of dilations is thereby replaced by the unitary group generated y the conjugate operator. This then allows to treat the perturbation problem with the usual Kato theory.......We study problems connected to perturbation theory of embedded eigenvalues in two different setups. The first part deals with second order perturbation theory of mass shells in massive translation invariant Nelson type models. To this end an expansion of the eigenvalues w.r.t. fiber parameter up...
Perturbative tests of quantum chromodynamics
International Nuclear Information System (INIS)
Michael, C.
1978-01-01
A review is given of perturbation theory results for quantum chromodynamics and of tests in deep inelastic lepton scattering, electron-positron annihilation, hadronic production of massive dileptons and hadronic large-momentum-transfer processes. (author)
Large-order perturbation theory
International Nuclear Information System (INIS)
Wu, T.T.
1982-01-01
The original motivation for studying the asymptotic behavior of the coefficients of perturbation series came from quantum field theory. An overview is given of some of the attempts to understand quantum field theory beyond finite-order perturbation series. At least is the case of the Thirring model and probably in general, the full content of a relativistic quantum field theory cannot be recovered from its perturbation series. This difficulty, however, does not occur in quantum mechanics, and the anharmonic oscillator is used to illustrate the methods used in large-order perturbation theory. Two completely different methods are discussed, the first one using the WKB approximation, and a second one involving the statistical analysis of Feynman diagrams. The first one is well developed and gives detailed information about the desired asymptotic behavior, while the second one is still in its infancy and gives instead information about the distribution of vertices of the Feynman diagrams
Review of chiral perturbation theory
Indian Academy of Sciences (India)
Abstract. A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
Perturbation theory in light-cone gauge
International Nuclear Information System (INIS)
Vianello, Eliana
2000-01-01
Perturbation calculations are presented for the light-cone gauge Schwinger model. Eigenstates can be calculated perturbatively but the perturbation theory is nonstandard. We hope to extend the work to QCD 2 to resolve some outstanding issues in those theories
Non-adiabatic perturbations in Ricci dark energy model
International Nuclear Information System (INIS)
Karwan, Khamphee; Thitapura, Thiti
2012-01-01
We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included
Convergence and analytic properties of manifestly finite perturbation theory
International Nuclear Information System (INIS)
Mtingwa, S.K.
1979-01-01
The author discusses more carefully the ultraviolet convergence properties of Feynman diagrams in recently proposed manifestly finite perturbation expansions. Speccifically, he refines one of the constraints on the γ's-the noncanonical dimensions-such that, when satisfied, any general product-type interaction of massive scalar, fermion and vector fields yields finite perturbation expansions requiring no conventional renormalization procedure. Moreover, the analytic properties of the Feynman integrals in the theory are discussed and concluded with remarks on the necessity of a modified Kaellen-Lehmann representation
Directory of Open Access Journals (Sweden)
Lavrenov Roman
2017-01-01
Full Text Available Our research focuses on operation of a heterogeneous robotic group that carries out point-to point navigation in GPS-denied dynamic environment, applying a combined local and global planning approach. In this paper, we introduce a homotopy-based high-level planner, which uses a modified splinebased path-planning algorithm. The algorithm utilizes Voronoi graph for global planning and a set of optimization criteria for local improvements of selected paths. The simulation was implemented in Matlab environment.
Base case and perturbation scenarios
Energy Technology Data Exchange (ETDEWEB)
Edmunds, T
1998-10-01
This report describes fourteen energy factors that could affect electricity markets in the future (demand, process, source mix, etc.). These fourteen factors are believed to have the most influence on the State's energy environment. A base case, or most probable, characterization is given for each of these fourteen factors over a twenty year time horizon. The base case characterization is derived from quantitative and qualitative information provided by State of California government agencies, where possible. Federal government databases are nsed where needed to supplement the California data. It is envisioned that a initial selection of issue areas will be based upon an evaluation of them under base case conditions. For most of the fourteen factors, the report identities possible perturbations from base case values or assumptions that may be used to construct additional scenarios. Only those perturbations that are plausible and would have a significant effect on energy markets are included in the table. The fourteen factors and potential perturbations of the factors are listed in Table 1.1. These perturbations can be combined to generate internally consist.ent. combinations of perturbations relative to the base case. For example, a low natural gas price perturbation should be combined with a high natural gas demand perturbation. The factor perturbations are based upon alternative quantitative forecasts provided by other institutions (the Department of Energy - Energy Information Administration in some cases), changes in assumptions that drive the quantitative forecasts, or changes in assumptions about the structure of the California energy markets. The perturbations are intended to be used for a qualitative reexamination of issue areas after an initial evaluation under the base case. The perturbation information would be used as a "tiebreaker;" to make decisions regarding those issue areas that were marginally accepted or rejected under the base case. Hf a
Perturbation theory in large order
International Nuclear Information System (INIS)
Bender, C.M.
1978-01-01
For many quantum mechanical models, the behavior of perturbation theory in large order is strikingly simple. For example, in the quantum anharmonic oscillator, which is defined by -y'' + (x 2 /4 + ex 4 /4 - E) y = 0, y ( +- infinity) = 0, the perturbation coefficients, A/sub n/, in the expansion for the ground-state energy, E(ground state) approx. EPSILON/sub n = 0//sup infinity/ A/sub n/epsilon/sup n/, simplify dramatically as n → infinity: A/sub n/ approx. (6/π 3 )/sup 1/2/(-3)/sup n/GAMMA(n + 1/2). Methods of applied mathematics are used to investigate the nature of perturbation theory in quantum mechanics and show that its large-order behavior is determined by the semiclassical content of the theory. In quantum field theory the perturbation coefficients are computed by summing Feynman graphs. A statistical procedure in a simple lambda phi 4 model for summing the set of all graphs as the number of vertices → infinity is presented. Finally, the connection between the large-order behavior of perturbation theory in quantum electrodynamics and the value of α, the charge on the electron, is discussed. 7 figures
Sayevand, K.; Pichaghchi, K.
2018-04-01
In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.
Perturbations of the Friedmann universe
International Nuclear Information System (INIS)
Novello, M.; Salim, J.M.; Heintzmann, H.
1982-01-01
Correcting and extending previous work by Hawking (1966) and Olson (1976) the complete set of perturbation equations of a Friedmann Universe in the quasi-Maxwellian form is derived and analized. The formalism is then applied to scalar, vector and tensor perturbations of a phenomenological fluid, which is modelled such as to comprise shear and heat flux. Depending on the equation of state of the background it is found that there exist unstable (growing) modes of purely rotational character. It is further found that (to linear order at least) any vortex perturbation is equivalent to a certain heat flux vector. The equation for the gravitational waves are derived in a completely equivalent method as in case of the propagation, in a curved space-time, of electromagnetic waves in a plasma endowed with some definite constitutive relations. (Author) [pt
Perturbative coherence in field theory
International Nuclear Information System (INIS)
Aldrovandi, R.; Kraenkel, R.A.
1987-01-01
A general condition for coherent quantization by perturbative methods is given, because the basic field equations of a fild theory are not always derivable from a Lagrangian. It's seen that non-lagrangian models way have well defined vertices, provided they satisfy what they call the 'coherence condition', which is less stringent than the condition for the existence of a Lagrangian. They note that Lagrangian theories are perturbatively coherent, in the sense that they have well defined vertices, and that they satisfy automatically that condition. (G.D.F.) [pt
Mabood, Fazle; Khan, Waqar A; Ismail, Ahmad Izani Md
2013-01-01
In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.
Cosmological perturbation theory and quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Brunetti, Romeo [Dipartimento di Matematica, Università di Trento,Via Sommarive 14, 38123 Povo TN (Italy); Fredenhagen, Klaus [II Institute für Theoretische Physik, Universität Hamburg,Luruper Chaussee 149, 22761 Hamburg (Germany); Hack, Thomas-Paul [Institute für Theoretische Physik, Universität Leipzig,Brüderstr. 16, 04103 Leipzig (Germany); Pinamonti, Nicola [Dipartimento di Matematica, Università di Genova,Via Dodecaneso 35, 16146 Genova (Italy); INFN, Sezione di Genova,Via Dodecaneso 33, 16146 Genova (Italy); Rejzner, Katarzyna [Department of Mathematics, University of York,Heslington, York YO10 5DD (United Kingdom)
2016-08-04
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well.
Chaotic inflation with metric and matter perturbations
International Nuclear Information System (INIS)
Feldman, H.A.; Brandenberger, R.H.
1989-01-01
A perturbative scheme to analyze the evolution of both metric and scalar field perturbations in an expanding universe is developed. The scheme is applied to study chaotic inflation with initial metric and scalar field perturbations present. It is shown that initial gravitational perturbations with wavelength smaller than the Hubble radius rapidly decay. The metric simultaneously picks up small perturbations determined by the matter inhomogeneities. Both are frozen in once the wavelength exceeds the Hubble radius. (orig.)
Disconnected rational homotopy theory
Czech Academy of Sciences Publication Activity Database
Lazarev, A.; Markl, Martin
2015-01-01
Roč. 283, 1 October (2015), s. 303-361 ISSN 0001-8708 Institutional support: RVO:67985840 Keywords : closed model category * differential graded Lie algebra * Maurer-Cartan simplicial set Subject RIV: BA - General Mathematics Impact factor: 1.405, year: 2015 http://www.sciencedirect.com/science/article/pii/S0001870815002479
Effects of thermal inflation on small scale density perturbations
Energy Technology Data Exchange (ETDEWEB)
Hong, Sungwook E. [School of Physics, Korea Institute for Advanced Study, 85 Hoegiro, Seoul 130-722 (Korea, Republic of); Lee, Hyung-Joo; Lee, Young Jae; Stewart, Ewan D. [Department of Physics, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-338 (Korea, Republic of); Zoe, Heeseung, E-mail: swhong@kias.re.kr, E-mail: ohsk111@kaist.ac.kr, E-mail: noasac@kaist.ac.kr, E-mail: jcap@profstewart.org, E-mail: heezoe@dgist.ac.kr [School of Basic Science, Daegu Gyeongbuk Institute of Science and Technology (DGIST), 333 Techno jungang-daero, Daegu 711-873 (Korea, Republic of)
2015-06-01
In cosmological scenarios with thermal inflation, extra eras of moduli matter domination, thermal inflation and flaton matter domination exist between primordial inflation and the radiation domination of Big Bang nucleosynthesis. During these eras, cosmological perturbations on small scales can enter and re-exit the horizon, modifying the power spectrum on those scales. The largest modified scale, k{sub b}, touches the horizon size when the expansion changes from deflation to inflation at the transition from moduli domination to thermal inflation. We analytically calculate the evolution of perturbations from moduli domination through thermal inflation and evaluate the curvature perturbation on the constant radiation density hypersurface at the end of thermal inflation to determine the late time curvature perturbation. Our resulting transfer function suppresses the power spectrum by a factor 0∼ 5 at k >> k{sub b}, with k{sub b} corresponding to anywhere from megaparsec to subparsec scales depending on the parameters of thermal inflation. Thus, thermal inflation might be constrained or detected by small scale observations such as CMB distortions or 21cm hydrogen line observations.
Basics of QCD perturbation theory
International Nuclear Information System (INIS)
Soper, D.E.
1997-01-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs
Current issues in perturbative QCD
International Nuclear Information System (INIS)
Hinchliffe, I.
1994-12-01
This review talk discusses some issues of active research in perturbative QCD. The following topics are discussed: (1) current value of αs; (2) heavy quark production in hadron collisions; (3) production of Ψ and Υ in p anti p collisions; (4) prompt photon production; (5) small-x and related phenomena; and (6) particle multiplicity in heavy quark jets
New results in perturbative QCD
International Nuclear Information System (INIS)
Ellis, R.K.
1986-01-01
Three topics in perturbative QCD important for Super-collider physics are reviewed. The topics are: 1. (2 → 2) jet phenomena calculated in O(αs 3 ). 2. New techniques for the calculation of tree graphs. 3. Color coherence in jet phenomena. 31 references, 6 figures
Perturbation theory from stochastic quantization
International Nuclear Information System (INIS)
Hueffel, H.
1984-01-01
By using a diagrammatical method it is shown that in scalar theories the stochastic quantization method of Parisi and Wu gives the usual perturbation series in Feynman diagrams. It is further explained how to apply the diagrammatical method to gauge theories, discussing the origin of ghost effects. (Author)
Seven topics in perturbative QCD
International Nuclear Information System (INIS)
Buras, A.J.
1980-09-01
The following topics of perturbative QCD are discussed: (1) deep inelastic scattering; (2) higher order corrections to e + e - annihilation, to photon structure functions and to quarkonia decays; (3) higher order corrections to fragmentation functions and to various semi-inclusive processes; (4) higher twist contributions; (5) exclusive processes; (6) transverse momentum effects; (7) jet and photon physics
Reggeon interactions in perturbative QCD
International Nuclear Information System (INIS)
Kirschner, R.
1994-08-01
We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases. (orig.)
Basics of QCD perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soper, D.E. [Univ. of Oregon, Eugene, OR (United States). Inst. of Theoretical Science
1997-06-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.
Status of chiral perturbation theory
International Nuclear Information System (INIS)
Ecker, G.
1996-10-01
A survey is made of semileptonic and nonleptonic kaon decays in the framework of chiral perturbation theory. The emphasis is on what has been done rather than how it was done. The theoretical predictions are compared with available experimental results. (author)
Principles of chiral perturbation theory
International Nuclear Information System (INIS)
Leutwyler, H.
1995-01-01
An elementary discussion of the main concepts used in chiral perturbation theory is given in textbooks and a more detailed picture of the applications may be obtained from the reviews. Concerning the foundations of the method, the literature is comparatively scarce. So, I will concentrate on the basic concepts and explain why the method works. (author)
Superfield perturbation theory and renormalization
International Nuclear Information System (INIS)
Delbourgo, R.
1975-01-01
The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond
Chiral symmetry in perturbative QCD
International Nuclear Information System (INIS)
Trueman, T.L.
1979-04-01
The chiral symmetry of quantum chromodynamics with massless quarks is unbroken in perturbation theory. Dimensional regularization is used. The ratio of the vector and axial vector renormalization constante is shown to be independent of the renormalization mass. The general results are explicitly verified to fourth order in g, the QCD coupling constant
Perturbative QCD and exclusive processes
International Nuclear Information System (INIS)
Bennett, J.; Hawes, F.; Zhao, M.; Zyla, P.
1991-01-01
The authors discuss perturbation theory as applied to particle physics calculations. In particle physics one is generally interested in the scattering amplitude for a system going from some initial state to a final state. The intermediate state or states are unknown. To get the scattering amplitude it is necessary to sum the contributions from processes which pass through all possible intermediate states. Intermediate states involve the exchange of intermediate vector bosons between the particles, and with this interaction is associated a coupling constant α. Each additional boson exchange involves an additional contribution of α to the coupling. If α is less than 1, one can see that the relative contribution of higher order processes is less and less important as α falls. In QCD the gluons serve as the intermediate vector bosons exchanged by quarks and gluons, and the interaction constant is not really a constant, but depends upon the distance between the particles. At short distances the coupling is small, and one can assume perturbative expansions may converge rapidly. Exclusive scattering processes, as opposed to inclusive, are those in which all of the final state products are detected. The authors then discuss the application of perturbative QCD to the deuteron. The issues of chiral conservation and color transparancy are also discussed, in the scheme of large Q 2 interations, where perturbative QCD should be applicable
Perturbative treatment of nuclear rotations
International Nuclear Information System (INIS)
Civitarese, O.
1980-01-01
In this work, it is described the case corresponding to perturbative quantum treatment of a fermion system in free rotation and the divergences which resulted from the 'break' in symmetry, associated by the adoption of a deformed basis as a non pertubed solution. (A.C.A.S.) [pt
Sound Attenuation in Elliptic Mufflers Using a Regular Perturbation Method
Banerjee, Subhabrata; Jacobi, Anthony M.
2012-01-01
The study of sound attenuation in an elliptical chamber involves the solution of the Helmholtz equation in elliptic coordinate systems. The Eigen solutions for such problems involve the Mathieu and the modified Mathieu functions. The computation of such functions poses considerable challenge. An alternative method to solve such problems had been proposed in this paper. The elliptical cross-section of the muffler has been treated as a perturbed circle, enabling the use of a regular perturbatio...
Non-perturbative Green functions in quantum gauge theories
International Nuclear Information System (INIS)
Shabanov, S.V.
1991-01-01
Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tensing to zero at spatial infinity. 20 refs
Adaptation of reach-to-grasp movement in response to force perturbations.
Rand, M K; Shimansky, Y; Stelmach, G E; Bloedel, J R
2004-01-01
This study examined how reach-to-grasp movements are modified during adaptation to external force perturbations applied on the arm during reach. Specifically, we examined whether the organization of these movements was dependent upon the condition under which the perturbation was applied. In response to an auditory signal, all subjects were asked to reach for a vertical dowel, grasp it between the index finger and thumb, and lift it a short distance off the table. The subjects were instructed to do the task as fast as possible. The perturbation was an elastic load acting on the wrist at an angle of 105 deg lateral to the reaching direction. The condition was modified by changing the predictability with which the perturbation was applied in a given trial. After recording unperturbed control trials, perturbations were applied first on successive trials (predictable perturbations) and then were applied randomly (unpredictable perturbations). In the early predictable perturbation trials, reach path length became longer and reaching duration increased. As more predictable perturbations were applied, the reach path length gradually decreased and became similar to that of control trials. Reaching duration also decreased gradually as the subjects adapted by exerting force against the perturbation. In addition, the amplitude of peak grip aperture during arm transport initially increased in response to repeated perturbations. During the course of learning, it reached its maximum and thereafter slightly decreased. However, it did not return to the normal level. The subjects also adapted to the unpredictable perturbations through changes in both arm transport and grasping components, indicating that they can compensate even when the occurrence of the perturbation cannot be predicted during the inter-trial interval. Throughout random perturbation trials, large grip aperture values were observed, suggesting that a conservative aperture level is set regardless of whether the
Perturbations in electromagnetic dark energy
International Nuclear Information System (INIS)
Jiménez, Jose Beltrán; Maroto, Antonio L.; Koivisto, Tomi S.; Mota, David F.
2009-01-01
It has been recently proposed that the presence of a temporal electromagnetic field on cosmological scales could explain the phase of accelerated expansion that the universe is currently undergoing. The field contributes as a cosmological constant and therefore, the homogeneous cosmology produced by such a model is exactly the same as that of ΛCDM. However, unlike a cosmological constant term, electromagnetic fields can acquire perturbations which in principle could affect CMB anisotropies and structure formation. In this work, we study the evolution of inhomogeneous scalar perturbations in this model. We show that provided the initial electromagnetic fluctuations generated during inflation are small, the model is perfectly compatible with both CMB and large scale structure observations at the same level of accuracy as ΛCDM
Perturbative instabilities in Horava gravity
International Nuclear Information System (INIS)
Bogdanos, Charalampos; Saridakis, Emmanuel N
2010-01-01
We investigate the scalar and tensor perturbations in Horava gravity, with and without detailed balance, around a flat background. Once both types of perturbations are taken into account, it is revealed that the theory is plagued by ghost-like scalar instabilities in the range of parameters which would render it power-counting renormalizable, that cannot be overcome by simple tricks such as analytic continuation. Implementing a consistent flow between the UV and IR limits seems thus more challenging than initially presumed, regardless of whether the theory approaches general relativity at low energies or not. Even in the phenomenologically viable parameter space, the tensor sector leads to additional potential problems, such as fine-tunings and super-luminal propagation.
The status of perturbative QCD
International Nuclear Information System (INIS)
Ellis, R.K.
1988-10-01
The advances in perturbative QCD are reviewed. The status of determinations of the coupling constant α/sub S/ and the parton distribution functions is presented. New theoretical results on the spin dependent structure functions of the proton are also reviewed. The theoretical description of the production of vector bosons, jets and heavy quarks is outlined with special emphasis on new results. Expected rates for top quark production at hadronic colliders are presented. 111 refs., 8 figs
Scalar perturbations and conformal transformation
International Nuclear Information System (INIS)
Fabris, J.C.; Tossa, J.
1995-11-01
The non-minimal coupling of gravity to a scalar field can be transformed into a minimal coupling through a conformal transformation. We show how to connect the results of a perturbation calculation, performed around a Friedman-Robertson-Walker background solution, before and after the conformal transformation. We work in the synchronous gauge, but we discuss the implications of employing other frames. (author). 16 refs
Perturbative QCD at finite temperature
International Nuclear Information System (INIS)
Altherr, T.
1989-03-01
We discuss an application of finite temperature QCD to lepton-pair production in a quark-gluon plasma. The perturbative calculation is performed within the realtime formalism. After cancellation of infrared and mass singularities, the corrections at O (α s ) are found to be very small in the region where the mass of the Drell-Yan pair is much larger than the temperature of the plasma. Interesting effects, however, appear at the annihilation threshold of the thermalized quarks
Vermaas, Willem F J.
2014-06-17
Disclosed is a modified photoautotrophic bacterium comprising genes of interest that are modified in terms of their expression and/or coding region sequence, wherein modification of the genes of interest increases production of a desired product in the bacterium relative to the amount of the desired product production in a photoautotrophic bacterium that is not modified with respect to the genes of interest.
Gauge-invariant cosmological density perturbations
International Nuclear Information System (INIS)
Sasaki, Misao.
1986-06-01
Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)
Perturbation of an exact strong gravity solution
International Nuclear Information System (INIS)
Baran, S.A.
1982-10-01
Perturbations of an exact strong gravity solution are investigated. It is shown, by using the new multipole expansions previously presented, that this exact and static spherically symmetric solution is stable under odd parity perturbations. (author)
Analytic perturbation theory in analyzing some QCD observables
International Nuclear Information System (INIS)
Shirkov, D.V.
2001-01-01
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD - ghost singularities and with the resume of this trouble solution within the APT. By a few examples in the various energy and momentum transfer regions (with the flavor number f = 3, 4 and 5) we demonstrate the effect of improved convergence of the APT modified perturbative QCD expansion. Our first observation is that in the APT analysis the three-loop contribution (of an order of α s 3 ) is as a rule numerically inessential. This raises hope for practical solving the well-known problem of asymptotic nature of common QFT perturbation series. The second conclusion is that a common perturbative analysis of time-like events with the big π 2 term in the π 2 coefficient is not adequate at s ≤ 2 GeV 2 . In particular, this relates to τ decay. Then, for the 'high' (f = 5) region it is shown that the common two-loop (NLO, NLLA) perturbation approximation widely used there (at 10 GeV ≤ √s ≤ 170 GeV) for analysis of shape/events data contains a systematic negative error of a 1 - 2 per cent level for the extracted α bar s (2) values. Our physical conclusion is that the α bar s (M Z 2 ) value averaged over the f = 5 data s (M Z 2 )> APT; f= 5 ≅ 0.124 appreciably differs from the currently accepted 'world average' (= 0.118)
Adiabatic perturbations in pre-big bang models: Matching conditions and scale invariance
International Nuclear Information System (INIS)
Durrer, Ruth; Vernizzi, Filippo
2002-01-01
At low energy, the four-dimensional effective action of the ekpyrotic model of the universe is equivalent to a slightly modified version of the pre-big bang model. We discuss cosmological perturbations in these models. In particular we address the issue of matching the perturbations from a collapsing to an expanding phase. We show that, under certain physically motivated and quite generic assumptions on the high energy corrections, one obtains n=0 for the spectrum of scalar perturbations in the original pre-big bang model (with a vanishing potential). With the same assumptions, when an exponential potential for the dilaton is included, a scale invariant spectrum (n=1) of adiabatic scalar perturbations is produced under very generic matching conditions, both in a modified pre-big bang and ekpyrotic scenario. We also derive the resulting spectrum for arbitrary power law scale factors matched to a radiation-dominated era
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S(⋅) may not be densely defined and the perturbation operator is a bounded linear operator from ¯D(A) into () such that = ...
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S ( ⋅ ) may not be densely defined and the perturbation operator is a bounded linear operator from D ( A ) ¯ into () such that = on D ( A ) ¯ ...
FRW Cosmological Perturbations in Massive Bigravity
Comelli, D; Pilo, L
2014-01-01
Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.
International Nuclear Information System (INIS)
Budgor, A.B.; West, B.J.
1978-01-01
We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation
Electrostatic probes driven by broad band high power and propagation of the turbulent perturbation
International Nuclear Information System (INIS)
Wang Zhijiang; Sun Xuan; Wan Shude; Wen Yizhi; Yu Changxuan; Liu Wandong; Wang Cheng; Pan Gesheng
2003-01-01
A high dynamic output, broad-band power source for driving electrostatic probes in the investigation on propagation of turbulent perturbation has been built and used successfully in experiments on the KT-5C tokamak. The details of the experiment setup as well as some preliminary results are presented. Detections both from the small size magnetic probes and electrostatic probes indicate that the modified perturbation excited by the power source may propagate electrostatically, and electromagnetically as well
Dimensional perturbation theory for the two-electron atom
International Nuclear Information System (INIS)
Goodson, D.Z.
1987-01-01
Perturbation theory in δ = 1/D, where D is the dimensionality of space, is applied to the two-electron atom. In Chapter 1 an efficient procedure for calculating the coefficients of the perturbation series for the ground-state energy is developed using recursion relations between the moments of the coordinate operators. Results through tenth order are presented. The series is divergent, but Pade summation gives results comparable in accuracy to the best configuration-interaction calculations. The singularity structure of the Pade approximants confirms the hypothesis that the energy as a function of δ has an infinite sequence of poles on the negative real axis that approaches an essential singularity at δ = O. The essential singularity causes the divergence of the perturbation series. There are also two poles at δ = 1 that slow the asymptotic convergence of the low-order terms. In Chapter 2, various techniques are demonstrated for removing the effect of these poles, and accurate results are thereby obtained, even at very low order. In Chapter 3, the large D limit of the correlation energy (CE) is investigated. In the limit D → infinity it is only 35% smaller than at D = 3. It can be made to vanish in the limit by modifying the Hartree-Fock (HF) wavefunction. In Chapter 4, perturbation theory is applied to the Hooke's-law model of the atom. Prospects for treating more-complicated systems are briefly discussed
Tensor perturbations during inflation in a spatially closed Universe
Energy Technology Data Exchange (ETDEWEB)
Bonga, Béatrice; Gupt, Brajesh; Yokomizo, Nelson, E-mail: bpb165@psu.edu, E-mail: bgupt@gravity.psu.edu, E-mail: yokomizo@gravity.psu.edu [Institute for Gravitation and the Cosmos and Physics Department, The Pennsylvania State University, 104 Lavey Lab, University Park, PA 16802 (United States)
2017-05-01
In a recent paper [1], we studied the evolution of the background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature and spatial topology S{sup 3}. Due to the spatial curvature, the early phase of slow-roll inflation is modified, leading to suppression of power in the scalar power spectrum at large angular scales. In this paper, we extend the analysis to include tensor perturbations. We find that, similarly to the scalar perturbations, the tensor power spectrum also shows suppression for long wavelength modes. The correction to the tensor spectrum is limited to the very long wavelength modes, therefore the resulting observable CMB B-mode polarization spectrum remains practically the same as in the standard scenario with flat spatial sections. However, since both the tensor and scalar power spectra are modified, there are scale dependent corrections to the tensor-to-scalar ratio that leads to violation of the standard slow-roll consistency relation.
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
International Nuclear Information System (INIS)
Childs, R.L.
1979-01-01
Perturbation theory for changes in linear and bilinear functionals of the forward and adjoint fluxes in a critical reactor has been implemented using two-dimensional discrete ordinates transport theory. The computer program DOT IV was modified to calculate the generalized functions Λ and Λ*. Demonstration calculations were performed for changes in a reaction-rate ratio and a reactivity worth caused by system perturbations. The perturbation theory predictions agreed with direct calculations to within about 2%. A method has been developed for calculating higher lambda eigenvalues and eigenfunctions using techniques similar to those developed for generalized functions. Demonstration calculations have been performed to obtain these eigenfunctions
Development of the Lunar and Solar Perturbations in the Motion of an Artificial Satellite
Musen, P.; Bailie, A.; Upton, E.
1961-01-01
Problems relating to the influence of lunar and solar perturbations on the motion of artificial satellites are analyzed by an extension of Cayley's development of the perturbative function in the lunar theory. In addition, the results are modified for incorporation into the Hansen-type theory used by the NASA Space Computing Center. The theory is applied to the orbits of the Vanguard I and Explorer VI satellites, and the results of detailed computations for these satellites are given together with a physical description of the perturbations in terms of resonance effects.
Roles of dark energy perturbations in dynamical dark energy models: can we ignore them?
Park, Chan-Gyung; Hwang, Jai-chan; Lee, Jae-heon; Noh, Hyerim
2009-10-09
We show the importance of properly including the perturbations of the dark energy component in the dynamical dark energy models based on a scalar field and modified gravity theories in order to meet with present and future observational precisions. Based on a simple scaling scalar field dark energy model, we show that observationally distinguishable substantial differences appear by ignoring the dark energy perturbation. By ignoring it the perturbed system of equations becomes inconsistent and deviations in (gauge-invariant) power spectra depend on the gauge choice.
Hadronic Structure from Perturbative Dressing
Energy Technology Data Exchange (ETDEWEB)
Arash, Firooz [Physics Department, Tafresh University, Tafresh, Iran and Center for theoretical physics and Mathematics, AEOI, P.O. Box 11365-8486, Tehran (Iran, Islamic Republic of)]. E-mail: farash@cic.aut.ac.ir
2005-09-15
Perturbative dressing of a valence quark in QCD produces the internal structure of an extended object, the so-called Valon. The valon structure is universal and independent of the hosting hadron. Polarized and unpolarized proton and pion structure functions are calculated in the valon representation. One finds that although all the available data on g{sub 1}{sup p,n,d} are easily reproduced, a sizable orbital angular momentum associated with the partonic structure of the valon is required in order to have a spin 1/2 valon.
Perturbations in loop quantum cosmology
International Nuclear Information System (INIS)
Nelson, W; Agullo, I; Ashtekar, A
2014-01-01
The era of precision cosmology has allowed us to accurately determine many important cosmological parameters, in particular via the CMB. Confronting Loop Quantum Cosmology with these observations provides us with a powerful test of the theory. For this to be possible, we need a detailed understanding of the generation and evolution of inhomogeneous perturbations during the early, quantum gravity phase of the universe. Here, we have described how Loop Quantum Cosmology provides a completion of the inflationary paradigm, that is consistent with the observed power spectra of the CMB
Perturbation calculations with Wilson loop
International Nuclear Information System (INIS)
Peixoto Junior, L.B.
1984-01-01
We present perturbative calculations with the Wilson loop (WL). The dimensional regularization method is used with a special attention concerning to the problem of divergences in the WL expansion in second and fourth orders, in three and four dimensions. We show that the residue in the pole, in 4d, of the fourth order graphs contribution sum is important for the charge renormalization. We compute up to second order the exact expression of the WL, in three-dimensional gauge theories with topological mass as well as its assimptotic behaviour for small and large distances. the author [pt
Mobile ankle and knee perturbator.
Andersen, Jacob Buus; Sinkjaer, Thomas
2003-10-01
A mobile ankle and knee perturbator has been developed. It consists of a functional joint with an integrated clutch. Four Bowden wires connect the joint to a powerful motor and a double pneumatic cylinder. When needed during any time of the gait cycle, it is possible to impose an ankle rotation by engaging the clutch and rotating the ankle or knee joint with a predefined displacement. The system is designed to investigate electrophysiological and biomechanical features of the human ankle or knee joint during gait.
"Phonon" scattering beyond perturbation theory
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
Perturbation theory for Alfven wave
International Nuclear Information System (INIS)
Yoshida, Z.; Mahajan, S.M.
1995-01-01
The Alfven wave is the dominant low frequency transverse mode of a magnetized plasma. The Alfven wave propagation along the magnetic field, and displays a continuous spectrum even in a bounded plasma. This is essentially due to the degeneracy of the wave characteristics, i.e. the frequency (ω) is primarily determined by the wave number in the direction parallel to the ambient magnetic field (k parallel ) and is independent of the perpendicular wavenumbers. The characteristics, that are the direction along which the wave energy propagates, are identical to the ambient magnetic field lines. Therefore, the spectral structure of the Alfven wave has a close relationship with the geometric structure of the magnetic field lines. In an inhomogeneous plasma, the Alfven resonance constitutes a singularity for the defining wave equation; this results in a singular eigenfunction corresponding to the continuous spectrum. The aim of this review is to present an overview of the perturbation theory for the Alfven wave. Emphasis is placed on those perturbations of the continuous spectrum which lead to the creation of point spectra. Such qualitative changes in the spectrum are relevant to many plasma phenomena
Dynamics of linear perturbations in f(R) gravity
International Nuclear Information System (INIS)
Bean, Rachel; Bernat, David; Pogosian, Levon; Silvestri, Alessandra; Trodden, Mark
2007-01-01
We consider predictions for structure formation from modifications to general relativity in which the Einstein-Hilbert action is replaced by a general function of the Ricci scalar. We work without fixing a gauge, as well as in explicit popular coordinate choices, appropriate for the modification of existing cosmological code. We present the framework in a comprehensive and practical form that can be directly compared to standard perturbation analyses. By considering the full evolution equations, we resolve perceived instabilities previously suggested, and instead find a suppression of perturbations. This result presents significant challenges for agreement with current cosmological structure formation observations. The findings apply to a broad range of forms of f(R) for which the modification becomes important at low curvatures, disfavoring them in comparison with the ΛCDM scenario. As such, these results provide a powerful method to rule out a wide class of modified gravity models aimed at providing an alternative explanation to the dark energy problem
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
International Nuclear Information System (INIS)
Finster, Felix; Grotz, Andreas
2010-01-01
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
The causal perturbation expansion revisited: Rescaling the interacting Dirac sea
Finster, Felix; Grotz, Andreas
2010-07-01
The causal perturbation expansion defines the Dirac sea in the presence of a time-dependent external field. It yields an operator whose image generalizes the vacuum solutions of negative energy and thus gives a canonical splitting of the solution space into two subspaces. After giving a self-contained introduction to the ideas and techniques, we show that this operator is, in general, not idempotent. We modify the standard construction by a rescaling procedure giving a projector on the generalized negative-energy subspace. The resulting rescaled causal perturbation expansion uniquely defines the fermionic projector in terms of a series of distributional solutions of the Dirac equation. The technical core of the paper is to work out the combinatorics of the expansion in detail. It is also shown that the fermionic projector with interaction can be obtained from the free projector by a unitary transformation. We finally analyze the consequences of the rescaling procedure on the light-cone expansion.
A Schwarz alternating procedure for singular perturbation problems
Energy Technology Data Exchange (ETDEWEB)
Garbey, M. [Universit Claude Bernard Lyon, Villeurbanne (France); Kaper, H.G. [Argonne National Lab., IL (United States)
1994-12-31
The authors show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. They give sharp estimates for the optimal position of the domain boundaries and present convergence rates of the algorithm for various second-order singular perturbation problems. The splitting of the operator is domain-dependent, and the iterative solution of each subproblem is based on a modified asymptotic expansion of the operator. They show that this asymptotic-induced method leads to a family of efficient massively parallel algorithms and report on implementation results for a turning-point problem and a combustion problem.
Perturbations i have Known and Loved
Field, Robert W.
2011-06-01
A spectroscopic perturbation is a disruption of a ^1Σ-^1Σ-like regular pattern that can embody level-shifts, extra lines, and intensity anomalies. Once upon a time, when a band was labeled ``perturbed,'' it was considered worthless because it could at best yield molecular constants unsuited for archival tables. Nevertheless, a few brave spectroscopists, notably Albin Lagerqvist and Richard Barrow, collected perturbations because they knew that the pattern of multiple perturbations formed an intricate puzzle that would eventually reveal the presence and electronic symmetry of otherwise unobservable electronic states. There are many kinds of patterns of broken patterns. In my PhD thesis I showed how to determine absolute vibrational assignments for the perturber from patterns among the observed values of perturbation matrix elements. When a ^3Π state is perturbed, its six (Ω, parity) components capture a pattern of level shifts and intensity anomalies that reveals more about the nature of the perturber than a simple perturbation of the single component of a ^1Σ state. In perturbation-facilitated OODR, a perturbed singlet level acts as a spectroscopic doorway through which the entire triplet manifold may be systematically explored. For polyatomic molecule vibrations, a vibrational polyad (a group of mutually perturbing vibrational levels, among which the perturbation matrix elements are expected to follow harmonic oscillator scaling rules) can contain more components than a ^3Π state and intrapolyad patterns can be exquisitely sensitive not merely to the nature of an interloper within the polyad but also to the eigenvector character of the vibronic state from which the polyad is viewed. Variation of scaled polyad interaction parameters from one polyad to the next, a pattern of patterns, can signal proximity to an isomerization barrier. Everything in Rydberg-land seems to scale as N⋆-3, yet a trespassing valence state causes all scaling and propensity rules go
New Methods in Non-Perturbative QCD
Energy Technology Data Exchange (ETDEWEB)
Unsal, Mithat [North Carolina State Univ., Raleigh, NC (United States)
2017-01-31
In this work, we investigate the properties of quantum chromodynamics (QCD), by using newly developing mathematics and physics formalisms. Almost all of the mass in the visible universe emerges from a quantum chromodynamics (QCD), which has a completely negligible microscopic mass content. An intimately related issue in QCD is the quark confinement problem. Answers to non-perturbative questions in QCD remained largely elusive despite much effort over the years. It is also believed that the usual perturbation theory is inadequate to address these kinds of problems. Perturbation theory gives a divergent asymptotic series (even when the theory is properly renormalized), and there are non-perturbative phenomena which never appear at any order in perturbation theory. Recently, a fascinating bridge between perturbation theory and non-perturbative effects has been found: a formalism called resurgence theory in mathematics tells us that perturbative data and non-perturbative data are intimately related. Translating this to the language of quantum field theory, it turns out that non-perturbative information is present in a coded form in perturbation theory and it can be decoded. We take advantage of this feature, which is particularly useful to understand some unresolved mysteries of QCD from first principles. In particular, we use: a) Circle compactifications which provide a semi-classical window to study confinement and mass gap problems, and calculable prototypes of the deconfinement phase transition; b) Resurgence theory and transseries which provide a unified framework for perturbative and non-perturbative expansion; c) Analytic continuation of path integrals and Lefschetz thimbles which may be useful to address sign problem in QCD at finite density.
A finite element formulation for perturbation theory calculations
International Nuclear Information System (INIS)
Ozgener, B.; Kaluc, S.
2004-01-01
Full text: When the introduced change in the configuration of a nuclear system is neutronically not too significant, the use of the perturbation theory approximation ('the perturbation theory method' or PTM) is usually considered as an alternative to the recalculation of the effective multiplication factor (K eff ) of the modified system ('the diffusion theory method' or DTM) for the determination of the ensuing change in reactivity. In the DTM, the change in reactivity due to the introduced change can be calculated by the multigroup diffusion theory by performing two K eff determinations, one for the original and one for the modified system. The accuracy of this method is only limited by the approximations inherent in the multigroup diffusion theory and the numerical method employed for its solution. The error stemming from the numerical approximation can be nearly eliminated by utilizing a fine enough spatial mesh ad an 'exact' solution is nearly possible. Its basic disadvantage relative to the PTM is the necessity of a new K eff calculation for every change in the configuration no matter how small. On the other hand, if we use PTM, with an only one-time calculation of the flux and the adjoint flux of the original system, the change in reactivity due to any kind of perturbation can be approximately calculated using the changes in the cross section data in the perturbation theory reactivity formula. The accuracy of the PTM is restricted by the size and location of the induced change. In this work, our aim is to assess the accuracy of PTM relative to the DTM and determine criteria for the justification of its use. For all required solutions of the normal and adjoint multigroup diffusion equations, we choose the finite element method (FEM) as our numerical method and a 1-D cylindrical geometry model. The underlying theory is implemented in our FORTRAN program PERTURB. The validation of PERTURB is carried out via comparisons with analytical solutions for bare and
Phytochemicals perturb membranes and promiscuously alter protein function.
Ingólfsson, Helgi I; Thakur, Pratima; Herold, Karl F; Hobart, E Ashley; Ramsey, Nicole B; Periole, Xavier; de Jong, Djurre H; Zwama, Martijn; Yilmaz, Duygu; Hall, Katherine; Maretzky, Thorsten; Hemmings, Hugh C; Blobel, Carl; Marrink, Siewert J; Koçer, Armağan; Sack, Jon T; Andersen, Olaf S
2014-08-15
A wide variety of phytochemicals are consumed for their perceived health benefits. Many of these phytochemicals have been found to alter numerous cell functions, but the mechanisms underlying their biological activity tend to be poorly understood. Phenolic phytochemicals are particularly promiscuous modifiers of membrane protein function, suggesting that some of their actions may be due to a common, membrane bilayer-mediated mechanism. To test whether bilayer perturbation may underlie this diversity of actions, we examined five bioactive phenols reported to have medicinal value: capsaicin from chili peppers, curcumin from turmeric, EGCG from green tea, genistein from soybeans, and resveratrol from grapes. We find that each of these widely consumed phytochemicals alters lipid bilayer properties and the function of diverse membrane proteins. Molecular dynamics simulations show that these phytochemicals modify bilayer properties by localizing to the bilayer/solution interface. Bilayer-modifying propensity was verified using a gramicidin-based assay, and indiscriminate modulation of membrane protein function was demonstrated using four proteins: membrane-anchored metalloproteases, mechanosensitive ion channels, and voltage-dependent potassium and sodium channels. Each protein exhibited similar responses to multiple phytochemicals, consistent with a common, bilayer-mediated mechanism. Our results suggest that many effects of amphiphilic phytochemicals are due to cell membrane perturbations, rather than specific protein binding.
Perturbativity in the seesaw mechanism
International Nuclear Information System (INIS)
Asaka, Takehiko; Tsuyuki, Takanao
2016-01-01
We consider the Standard Model extended by right-handed neutrinos to explain massive neutrinos through the seesaw mechanism. The new fermion can be observed when it has a sufficiently small mass and large mixings to left-handed neutrinos. If such a particle is the lightest right-handed neutrino, its contribution to the mass matrix of active neutrinos needs to be canceled by that of a heavier one. Yukawa couplings of the heavier one are then larger than those of the lightest one. We show that the perturbativity condition gives a severe upper bound on the mixing of the lightest right-handed neutrino, depending on the masses of heavier ones. Models of high energy phenomena, such as leptogenesis, can be constrained by low energy experiments.
Initial conditions for cosmological perturbations
Ashtekar, Abhay; Gupt, Brajesh
2017-02-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations.
Initial conditions for cosmological perturbations
International Nuclear Information System (INIS)
Ashtekar, Abhay; Gupt, Brajesh
2017-01-01
Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations . (paper)
Curvature perturbations from dimensional decoupling
Giovannini, Massimo
2005-01-01
The scalar modes of the geometry induced by dimensional decoupling are investigated. In the context of the low energy string effective action, solutions can be found where the spatial part of the background geometry is the direct product of two maximally symmetric Euclidean manifolds whose related scale factors evolve at a dual rate so that the expanding dimensions first accelerate and then decelerate while the internal dimensions always contract. After introducing the perturbative treatment of the inhomogeneities, a class of five-dimensional geometries is discussed in detail. Quasi-normal modes of the system are derived and the numerical solution for the evolution of the metric inhomogeneities shows that the fluctuations of the internal dimensions provide a term that can be interpreted, in analogy with the well-known four-dimensional situation, as a non-adiabatic pressure density variation. Implications of this result are discussed with particular attention to string cosmological scenarios.
Effects of 3D magnetic perturbations on toroidal plasmas
International Nuclear Information System (INIS)
Callen, J.D.
2011-01-01
stochasticity and increase plasma transport in the edge of H-mode plasmas. These various effects of 3D fields can be used to modify directly the plasma toroidal rotation (and possibly transport via multiple RMPs for controlling edge localized modes) and indirectly anomalous plasma transport. The present understanding and modelling of these various 3D magnetic field perturbation effects including for test blanket modules in ITER are summarized. Finally, implications of the present understanding and key open issues for developing a predictive capability of them for ITER are discussed. (topical review)
Closed form bound-state perturbation theory
Directory of Open Access Journals (Sweden)
Ollie J. Rose
1980-01-01
Full Text Available The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.
Kato expansion in quantum canonical perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Nikolaev, Andrey, E-mail: Andrey.Nikolaev@rdtex.ru [Institute of Computing for Physics and Technology, Protvino, Moscow Region, Russia and RDTeX LTD, Moscow (Russian Federation)
2016-06-15
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Perturbative spacetimes from Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Kato expansion in quantum canonical perturbation theory
International Nuclear Information System (INIS)
Nikolaev, Andrey
2016-01-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Perturbation methods for power and reactivity reconstruction
International Nuclear Information System (INIS)
Palmiotti, G.; Salvatores, M.; Estiot, J.C.; Broccoli, U.; Bruna, G.; Gomit, J.M.
1987-01-01
This paper deals with recent developments and applications in perturbation methods. Two types of methods are used. The first one is an explicit method, which allows the explicit reconstruction of a perturbed flux using a linear combination of a library of functions. In our application, these functions are the harmonics (i.e. the high order eigenfunctions of the system). The second type is based on the Generalized Perturbation Theory GPT and needs the calculation of an importance function for each integral parameter of interest. Recent developments of a particularly useful high order formulation allows to obtain satisfactory results also for very large perturbations
On adiabatic perturbations in the ekpyrotic scenario
International Nuclear Information System (INIS)
Linde, A.; Mukhanov, V.; Vikman, A.
2010-01-01
In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario
Nonrelativistic hyperfine splitting in muonic helium by adiabatic perturbation theory
International Nuclear Information System (INIS)
Drachman, R.J.
1980-01-01
Huang and Hughes have recently discussed the hyperfine splitting Δν of muonic helium (α ++ μ - e - ) using a variational approach. In this paper, the Born-Oppenheimer approximation is used to simplify the evaluation of Δν in the nonrelativistic limit. The first-order perturbed wave function of the electron is obtained in closed form by slightly modifying the method used by Dalgarno and Lynn. The result Δν=4450 MHz, is quite close to the published result of Huang and Hughes 4455.2 +- 1 MHz, which required a very large Hylleraas expansion as well as considerable extrapolation
Non-perturbative Debye mass in finite-T QCD
Kajantie, Keijo; Peisa, J; Rajantie, A; Rummukainen, K; Shaposhnikov, Mikhail E
1997-01-01
Employing a non-perturbative gauge invariant definition of the Debye screening mass m_D in the effective field theory approach to finite T QCD, we use 3d lattice simulations to determine the leading O(g^2) and to estimate the next-to-leading O(g^3) corrections to m_D in the high temperature region. The O(g^2) correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD.
Kaplan-Narayanan-Neuberger lattice fermions pass a perturbative test
International Nuclear Information System (INIS)
Aoki, S.; Levien, R.B.
1995-01-01
We test perturbatively a recent scheme for implementing chiral fermions on the lattice, proposed by Kaplan and modified by Narayanan and Neuberger, using as our testing ground the chiral Schwinger model. The scheme is found to reproduce the desired form of the effective action, whose real part is gauge invariant and whose imaginary part gives the correct anomaly in the continuum limit, once technical problems relating to the necesary infinite extent of the extra dimension are properly addressed. The indications from this study are that the Kaplan-Narayanan-Neuberger scheme has a good chance at being a correct lattice regularization of chiral gauge theories
Smoothing expansion rate data to reconstruct cosmological matter perturbations
Energy Technology Data Exchange (ETDEWEB)
Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C., E-mail: javierernesto@on.br, E-mail: alcaniz@on.br, E-mail: jcarvalho@on.br [Departamento de Astronomia, Observatório Nacional, Rua Gal. José Cristino, 77, Rio de Janeiro, RJ 20921-400 (Brazil)
2017-08-01
The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analyzing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ( H ( z )) from model-independent cosmic chronometers and high- z quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the H ( z ) reconstruction and realistic values of Ω {sub m} {sub 0} and σ{sub 8} from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and f σ{sub 8}( z ) from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct f σ{sub 8}( z ). For this case, we find a ∼ 3σ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.
Smoothing expansion rate data to reconstruct cosmological matter perturbations
International Nuclear Information System (INIS)
Gonzalez, J.E.; Alcaniz, J.S.; Carvalho, J.C.
2017-01-01
The existing degeneracy between different dark energy and modified gravity cosmologies at the background level may be broken by analyzing quantities at the perturbative level. In this work, we apply a non-parametric smoothing (NPS) method to reconstruct the expansion history of the Universe ( H ( z )) from model-independent cosmic chronometers and high- z quasar data. Assuming a homogeneous and isotropic flat universe and general relativity (GR) as the gravity theory, we calculate the non-relativistic matter perturbations in the linear regime using the H ( z ) reconstruction and realistic values of Ω m 0 and σ 8 from Planck and WMAP-9 collaborations. We find a good agreement between the measurements of the growth rate and f σ 8 ( z ) from current large-scale structure observations and the estimates obtained from the reconstruction of the cosmic expansion history. Considering a recently proposed null test for GR using matter perturbations, we also apply the NPS method to reconstruct f σ 8 ( z ). For this case, we find a ∼ 3σ tension (good agreement) with the standard relativistic cosmology when the Planck (WMAP-9) priors are used.
Perturbed angular correlations and distributions
International Nuclear Information System (INIS)
Makaryunas, K.
1976-01-01
The present index comprises original works and review papers on the perturbed angular correlations (PAC) and distributions (PAD). The articles published in the Soviet and foreign journals as well as the materials of conferences, monographs and collections published in the USSR and abroad, the preprints produced by various institutes and abstracts of disertations are included from 1948 up to 1973. The whole material compiled in this index is divided into three parts. Part one is a bibliographic index. All papers in this part are divided into three sections. Section one comprises the papers devoted to the theoretical works on PAC, review papers, monographs, materials of conferences. Section two deals with the works of methodical character where correlation spectrometers as well as the treatment of experimental data are described. In section three experimental works with concrete nuclei are compiled. Part two gives the characteristic of works performed with concrete nuclei. This part is presented in the form of the table in which the works are systematized according to the chemical elements and isotopes. The table shows the characteristics of the nuclear levels used in the investigations by PAC as well as brief characteristics of experiments and results obtained. Part three - appendix contains alphabetic index of the authors, the list of the used editions with the abbreviations of the titles of these editions. The lists indicating the dynamic of the quantity of works on PAC and the distribution according to the literature sources are also given
Importance of Plasma Response to Non-axisymmetric Perturbations in Tokamaks
International Nuclear Information System (INIS)
Park, Jong-kyu; Boozer, Allen H.; Menard, Jonathan E.; Garofalo, Andrea M.; Schaffer, Michael J.; Hawryluk, Richard J.; Kaye, Stanley M.; Gerhardt, Stefan P.; Sabbagh, Steve A. and the NSTX Team
2009-01-01
Tokamaks are sensitive to deviations from axisymmetry as small as (delta)B/B 0 ∼ 10 -4 . These non-axisymmetric perturbations greatly modify plasma confinement and performance by either destroying magnetic surfaces with subsequent locking or deforming magnetic surfaces with associated non-ambipolar transport. The Ideal Perturbed Equilibrium Code (IPEC) calculates ideal perturbed equilibria and provides important basis for understanding the sensitivity of tokamak plasmas to perturbations. IPEC calculations indicate that the ideal plasma response, or equivalently the effect by ideally perturbed plasma currents, is essential to explain locking experiments on National Spherical Torus eXperiment (NSTX) and DIII-D. The ideal plasma response is also important for Neoclassical Toroidal Viscosity (NTV) in non-ambipolar transport. The consistency between NTV theory and magnetic braking experiments on NSTX and DIII-D can be improved when the variation in the field strength in IPEC is coupled with generalized NTV theory. These plasma response effects will be compared with the previous vacuum superpositions to illustrate the importance. However, plasma response based on ideal perturbed equilibria is still not sufficiently accurate to predict the details of NTV transport, and can be inconsistent when currents associated with a toroidal torque become comparable to ideal perturbed currents
Massive states in chiral perturbation theory
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Mallik, S [Saha Inst. of Nuclear Physics, Calcutta (India)
1995-08-01
It is shown that the chiral nonanalytic terms generated by {Delta}{sub 33} resonance in the nucleon self-energy is reproduced in chiral perturbation theory by perturbing appropriate local operators contained in the pion-nucleon effective Lagrangian itself. (orig.)
On the non-perturbative effects
International Nuclear Information System (INIS)
Manjavidze, J.; Voronyuk, V.
2004-01-01
The quantum correspondence principle based on the time reversibility is adopted to take into account the non-Abelian symmetry constrains. The main properties of the new strong-coupling perturbation theory which take into account non-perturbative effects are described. (author)
Scalar Quantum Electrodynamics: Perturbation Theory and Beyond
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Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.
2006-01-01
In this article, we calculate scalar propagator in arbitrary dimensions and gauge and the three-point scalar-photon vertex in arbitrary dimensions and Feynman gauge, both at the one loop level. We also discuss constraints on their non perturbative structure imposed by requirements of gauge invariance and perturbation theory
International Nuclear Information System (INIS)
Wu, C.W.
2003-01-01
In a recent paper, wavelet analysis is used to perturb the coupling matrix in an array of identical chaotic systems in order to improve its synchronization. When the coupling matrix is symmetric, the synchronization criterion is determined by the second smallest eigenvalue λ 2 of the coupling matrix and the problem is reduced to studying how λ 2 of the coupling matrix changes with perturbation. In the aforementioned paper, a small percentage of the wavelet coefficients are modified. However, this results in a perturbed matrix where every element is modified and nonzero. The purpose of this Letter is to present some results on the change of λ 2 due to perturbation. In particular, we show that as the number of systems n→∞, perturbations which only add local coupling will not change λ 2 . On the other hand, we show that there exists perturbations which modify an arbitrarily small percentage of matrix elements, each of which is changed by an arbitrarily small amount and yet can make λ 2 arbitrarily large. These results give conditions on what the perturbation should be in order to improve the synchronizability in an array of coupled chaotic systems. This analysis allows us to justify and explain some of the synchronization phenomena observed in a recently studied network where random coupling is added to a locally connected array. We propose to classify various classes of coupling matrices such as small world networks and scale free networks according to their synchronizability in the limit. Finally, we briefly discuss the case of time-varying coupling
African Journals Online (AJOL)
Application of homotopy perturbation method for the large angle period of a nonlinear oscillator. Abstract · Vol 15 (2009) - Articles Application of modified power series method for the solution of system of differential equations. Abstract · Vol 16 (2010) - Articles An Efficient Algorithm for Solving the Telegraph Equation.
Salas, M. D.; Kuehn, M. S.
1994-01-01
Original version of program incorporated into program SRGULL (LEW-15093) for use on National Aero-Space Plane project, its duty being to model forebody, inlet, and nozzle portions of vehicle. However, real-gas chemistry effects in hypersonic flow fields limited accuracy of that version, because it assumed perfect-gas properties. As a result, SEAGULL modified according to real-gas equilibrium-chemistry methodology. This program analyzes two-dimensional, hypersonic flows of real gases. Modified version of SEAGULL maintains as much of original program as possible, and retains ability to execute original perfect-gas version.
Accommodation of the spinal cat to a tripping perturbation
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Hui eZhong
2012-05-01
Full Text Available Adult cats with a complete spinal cord transection at T12-T13 can relearn over a period of days-to-weeks how to generate full weight-bearing stepping on a treadmill or standing ability if trained specifically for that task. In the present study, we assessed short-term (msec-min adaptations by repetitively imposing a mechanical perturbation on the hindlimb of chronic spinal cats by placing a rod in the path of the leg during the swing phase to trigger a tripping response. The kinematics and EMG were recorded during control (10 steps, trip (1 to 60 steps with various patterns and then release (without any tripping stimulus, 10 to 20 steps sequences. Our data show that the activation patterns and kinematics of the hindlimb in the step cycle immediately following the initial trip (mechanosensory stimulation of the dorsal surface of the paw was modified in a way that increased the probability of avoiding the obstacle in the subsequent step. This indicates that the spinal sensorimotor circuitry reprogrammed the trajectory of the swing following a perturbation prior to the initiation of the swing phase of the subsequent step, in effect attempting to avoid the re-occurrence of the perturbation. The average height of the release steps was elevated compared to control regardless of the pattern and the length of the trip sequences. In addition, the average impact force on the tripping rod tended to be lower with repeated exposure to the tripping stimulus. EMG recordings suggest that the semitendinosus, a primary knee flexor, was a major contributor to the adaptive tripping response. These results demonstrate that the lumbosacral locomotor circuitry can modulate the activation patterns of the hindlimb motor pools within the time frame of single step in a manner that tends to minimize repeated perturbations. Furthermore, these adaptations remained evident for a number of steps after removal of the mechanosensory stimulation.
Shishkin, G. I.
2015-11-01
An initial-boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation with a perturbation parameter ɛ (ɛ ∈ (0, 1]) multiplying the highest order derivative. The stability of a standard difference scheme based on monotone approximations of the problem on a uniform mesh is analyzed, and the behavior of discrete solutions in the presence of perturbations is examined. The scheme does not converge ɛ-uniformly in the maximum norm as the number of its grid nodes is increased. When the solution of the difference scheme converges, which occurs if N -1 ≪ ɛ and N -1 0 ≪ 1, where N and N 0 are the numbers of grid intervals in x and t, respectively, the scheme is not ɛ-uniformly well conditioned or stable to data perturbations in the grid problem and to computer perturbations. For the standard difference scheme in the presence of data perturbations in the grid problem and/or computer perturbations, conditions on the "parameters" of the difference scheme and of the computer (namely, on ɛ, N, N 0, admissible data perturbations in the grid problem, and admissible computer perturbations) are obtained that ensure the convergence of the perturbed solutions. Additionally, the conditions are obtained under which the perturbed numerical solution has the same order of convergence as the solution of the unperturbed standard difference scheme.
Strings as perturbations of evolving spin networks
International Nuclear Information System (INIS)
Smolin, Lee
2000-01-01
One step in the construction of a background independent formulation of string theory is detailed, in which it is shown how perturbative strings may arise as small fluctuations around histories in a formulation of non-perturbative dynamics of spin networks due to Markopoulou. In this formulation the dynamics of spin network states and their generalizations is described in terms of histories which have discrete analogues of the causal structure and many fingered time of Lorentzian spacetimes. Perturbations of these histories turn out to be described in terms of spin systems defined on 2-dimensional timelike surfaces embedded in the discrete spacetime. When the history has a classical limit which is Minkowski spacetime, the action of the perturbation theory is given to leading order by the spacetime area of the surface, as in bosonic string theory. This map between a non-perturbative formulation of quantum gravity and a 1+1 dimensional theory generalizes to a large class of theories in which the group SU(2) i s extended to any quantum group or supergroup. It is argued that a necessary condition for the non-perturbative theory to have a good classical limit is that the resulting 1+1 dimensional theory defines a consistent and stable perturbative string theory
Perturbation analysis of linear control problems
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Petkov, Petko; Konstantinov, Mihail
2017-01-01
The paper presents a brief overview of the technique of splitting operators, proposed by the authors and intended for perturbation analysis of control problems involving unitary and orthogonal matrices. Combined with the technique of Lyapunov majorants and the implementation of the Banach and Schauder fixed point principles, it allows to obtain rigorous non-local perturbation bounds for a set of sensitivity analysis problems. Among them are the reduction of linear systems into orthogonal canonical forms, the feedback synthesis problem and pole assignment problem in particular, as well as other important problems in control theory and linear algebra. Key words: perturbation analysis, canonical forms, feedback synthesis
Kerr-CFT and gravitational perturbations
International Nuclear Information System (INIS)
Dias, Oscar J.C.; Reall, Harvey S.; Santos, Jorge E.
2009-01-01
Motivated by the Kerr-CFT conjecture, we investigate perturbations of the near-horizon extreme Kerr spacetime. The Teukolsky equation for a massless field of arbitrary spin is solved. Solutions fall into two classes: normal modes and traveling waves. Imposing suitable (outgoing) boundary conditions, we find that there are no unstable modes. The explicit form of metric perturbations is obtained using the Hertz potential formalism, and compared with the Kerr-CFT boundary conditions. The energy and angular momentum associated with scalar field and gravitational normal modes are calculated. The energy is positive in all cases. The behaviour of second order perturbations is discussed.
Resolution of ambiguities in perturbative QCD
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Nakkagawa, Hisao; Niegawa, Akira.
1984-01-01
In the perturbative QCD analyses of the deeply inelastic processes, the coupling constant depends on at least two mass-scales, the renormalization scale and the factorization scale. By integrating the coupled renormalization group equations with respect to these two mass-scales, the running coupling constant is defined. A perturbative approximation then introduces a new ambiguity, the integration-path dependence, into the theory. We show that the problem of this new ambiguity is resolved by imposing Stevenson's principle of minimal sensitivity. Together with the analogous analysis of the operator matrix element or the cut vertex, we can completely solve the problem of getting an unambiguous perturbative QCD prediction. (author)
Mass generation in perturbed massless integrable models
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Controzzi, D.; Mussardo, G.
2005-01-01
We extend form-factor perturbation theory to non-integrable deformations of massless integrable models, in order to address the problem of mass generation in such systems. With respect to the standard renormalisation group analysis this approach is more suitable for studying the particle content of the perturbed theory. Analogously to the massive case, interesting information can be obtained already at first order, such as the identification of the operators which create a mass gap and those which induce the confinement of the massless particles in the perturbed theory
Non-perturbative effects in supersymmetry
International Nuclear Information System (INIS)
Veneziano, G.
1987-01-01
Some non perturbative aspects of globally supersymmetric (SUSY) gauge theories are discussed. These share with their non-supersymmetric analogues interesting non perturbative features, such as the spontaneous breaking of chiral symmetries via condensates. What is peculiar about supersymmetric theories, however, is that one is able to say a lot about non-perturbative effects even without resorting to elaborate numerical calculations: general arguments, supersymmetric and chiral Ward identities and analytic, dynamical calculations will turn out to effectively determine most of the supersymmetric vacuum properties. 28 references, 5 figures
Solitonic Integrable Perturbations of Parafermionic Theories
Fernández-Pousa, C R; Hollowood, Timothy J; Miramontes, J L
1997-01-01
The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.
Critical behaviors of gravity under quantum perturbations
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ZHANG Hongsheng
2014-02-01
Full Text Available Phase transition and critical phenomenon is a very interesting topic in thermodynamics and statistical mechanics. Gravity is believed to have deep and inherent relation to thermodynamics. Near the critical point,the perturbation becomes significant. Thus for ordinary matter (governed by interactions besides gravity the critical behavior will become very different if we ignore the perturbations around the critical point,such as mean field theory. We find that the critical exponents for RN-AdS spacetime keep the same values even when we consider the full quantum perturbations. This indicates a key difference between gravity and ordinary thermodynamic system.
Observational tests of modified gravity
International Nuclear Information System (INIS)
Jain, Bhuvnesh; Zhang Pengjie
2008-01-01
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the Universe. Modified gravity theories have richer observational consequences for large-scale structures than conventional dark energy models, in that different observables are not described by a single growth factor even in the linear regime. We examine the relationships between perturbations in the metric potentials, density and velocity fields, and discuss strategies for measuring them using gravitational lensing, galaxy cluster abundances, galaxy clustering/dynamics, and the integrated Sachs-Wolfe effect. We show how a broad class of gravity theories can be tested by combining these probes. A robust way to interpret observations is by constraining two key functions: the ratio of the two metric potentials, and the ratio of the gravitational 'constant' in the Poisson equation to Newton's constant. We also discuss quasilinear effects that carry signatures of gravity, such as through induced three-point correlations. Clustering of dark energy can mimic features of modified gravity theories and thus confuse the search for distinct signatures of such theories. It can produce pressure perturbations and anisotropic stresses, which break the equality between the two metric potentials even in general relativity. With these two extra degrees of freedom, can a clustered dark energy model mimic modified gravity models in all observational tests? We show with specific examples that observational constraints on both the metric potentials and density perturbations can in principle distinguish modifications of gravity from dark energy models. We compare our result with other recent studies that have slightly different assumptions (and apparently contradictory conclusions).
Stability under persistent perturbation by white noise
International Nuclear Information System (INIS)
Kalyakin, L
2014-01-01
Deterministic dynamical system which has an asymptotical stable equilibrium is considered under persistent perturbation by white noise. It is well known that if the perturbation does not vanish in the equilibrium position then there is not Lyapunov's stability. The trajectories of the perturbed system diverge from the equilibrium to arbitrarily large distances with probability 1 in finite time. New concept of stability on a large time interval is discussed. The length of interval agrees the reciprocal quantity of the perturbation parameter. The measure of stability is the expectation of the square distance from the trajectory till the equilibrium position. The method of parabolic equation is applied to both estimate the expectation and prove such stability. The main breakthrough is the barrier function derived for the parabolic equation. The barrier is constructed by using the Lyapunov function of the unperturbed system
Inflation and the theory of cosmological perturbations
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Riotto, A.
2003-01-01
These lectures provide a pedagogical introduction to inflation and the theory of cosmological perturbations generated during inflation which are thought to be the origin of structure in the universe. (author)
't Hooft loops and perturbation theory
De Forcrand, Philippe; Noth, D; Forcrand, Philippe de; Lucini, Biagio; Noth, David
2005-01-01
We show that high-temperature perturbation theory describes extremely well the area law of SU(N) spatial 't Hooft loops, or equivalently the tension of the interface between different Z_N vacua in the deconfined phase. For SU(2), the disagreement between Monte Carlo data and lattice perturbation theory for sigma(T)/T^2 is less than 2%, down to temperatures O(10) T_c. For SU(N), N>3, the ratios of interface tensions, (sigma_k/sigma_1)(T), agree with perturbation theory, which predicts tiny deviations from the ratio of Casimirs, down to nearly T_c. In contrast, individual tensions differ markedly from the perturbative expression. In all cases, the required precision Monte Carlo measurements are made possible by a simple but powerful modification of the 'snake' algorithm.
Isocurvature perturbations in the Ekpyrotic Universe
International Nuclear Information System (INIS)
Notari, A.; Riotto, A.
2002-01-01
The Ekpyrotic scenario assumes that our visible Universe is a boundary brane in a five-dimensional bulk and that the hot Big Bang occurs when a nearly supersymmetric five-brane travelling along the fifth dimension collides with our visible brane. We show that the generation of isocurvature perturbations is a generic prediction of the Ekpyrotic Universe. This is due to the interactions in the kinetic terms between the brane modulus parameterizing the position of the five-brane in the bulk and the dilaton and volume moduli. We show how to separate explicitly the adiabatic and isocurvature modes by performing a rotation in field space. Our results indicate that adiabatic and isocurvature perturbations might be cross-correlated and that curvature perturbations might be entirely seeded by isocurvature perturbations
Simple Perturbation Example for Quantum Chemistry.
Goodfriend, P. L.
1985-01-01
Presents a simple example that illustrates various aspects of the Rayleigh-Schrodinger perturbation theory. The example is a particularly good one because it is straightforward and can be compared with both the exact solution and with experimental data. (JN)
SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.
Thiede, Erik; VAN Koten, Brian; Weare, Jonathan
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.
Renormalization scheme-invariant perturbation theory
International Nuclear Information System (INIS)
Dhar, A.
1983-01-01
A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)
Cosmological perturbations in the new Higgs inflation
Energy Technology Data Exchange (ETDEWEB)
Germani, Cristiano [Arnold Sommerfeld Center, Ludwig-Maximilians-University, Theresienstr, 37 80333 Muenchen (Germany); Kehagias, Alex, E-mail: cristiano.germani@lmu.de, E-mail: kehagias@central.ntua.gr [Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece)
2010-05-01
We study the cosmological perturbations created during the New Higgs inflationary phase. In the New Higgs Inflation, the Higgs boson is kinetically coupled to the Einstein tensor and only three perturbative degrees of freedom, a scalar and two tensorial (gravitational waves), propagate during Inflation. Scalar perturbations are found to match the latest WMAP-7yrs data within Standard Model Higgs parameters. Primordial gravitational waves also, although propagating with superluminal speed, are consistent with present data. Finally, we estimate the values of the parameter of the New Higgs Inflation in relation to the Higgs mass, the spectral index and amplitude of the primordial scalar perturbations showing that the unitarity bound of the theory is not violated.
Prospects of inflation with perturbed throat geometry
International Nuclear Information System (INIS)
Ali, Amna; Chingangbam, R.; Panda, Sudhakar; Sami, M.
2009-01-01
We study brane inflation in a warped deformed conifold background that includes general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. We focus specifically, on the perturbation by chiral operator of dimension 3/2 in the CFT. We find that the effective potential in this case can give rise to required number of e-foldings and the spectral index n S consistent with observation. The tensor to scalar ratio of perturbations is generally very low in this scenario. The COBE normalization, however, poses certain difficulties which can be circumvented provided model parameters are properly fine tuned. We find the numerical values of parameters which can give rise to enough inflation, observationally consistent values of density perturbations, scalar to tensor ratio of perturbations and the spectral index n S .
Discrete state perturbation theory via Green's functions
International Nuclear Information System (INIS)
Rubinson, W.
1975-01-01
The exposition of stationary-state perturbation theory via the Green's function method in Goldberger and Watson's Collision Theory is reworked in a way that makes explicit its mathematical basis. It is stressed that the theory consists of the construction of, and manipulations on, a mathematical identity. The perturbation series fall out of the identity almost immediately. The logical status of the method is commented on
Algebraic renormalization. Perturbative renormalization, symmetries and anomalies
International Nuclear Information System (INIS)
Piguet, O.
1995-01-01
This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)
A new perturbative approach to QCD
International Nuclear Information System (INIS)
Pervushin, V.N.; Kallies, W.; Sarikov, N.A.
1988-01-01
For the description of bound states in QED and QCD the physical perturbation theory on the spatial components of the vector over the exact solution, defined by the time one, is proposed. It is shown this perturbation theory in QCD can be redefined so that it reproduces the main elements of hadron physics: confinement, spectroscopy of light and heavy quarkonia, dual-resonance amplitudes, chiral Lagrangians and the parton model
Cylindrical dust acoustic waves with transverse perturbation
International Nuclear Information System (INIS)
Xue Jukui
2003-01-01
The nonlinear dust acoustic waves in dusty plasmas with the combined effects of bounded cylindrical geometry and the transverse perturbation are studied. Using the perturbation method, a cylindrical Kadomtsev-Petviashvili (CKP) equation that describes the dust acoustic waves is deduced for the first time. A particular solution of this CKP equation is also obtained. It is shown that the dust acoustic solitary waves can exist in the CKP equation
The triangulation in a perturbed Friedmann universe
International Nuclear Information System (INIS)
Kasai, Masumi.
1987-12-01
A formula for the parallax distance in a general space-time is shown and it is applied to the linearly perturbed Friedmann universe. Its invariance under any coordinate-gauge transformations and any infinitesimal affine transformations is also shown. Then it is applied to the Einstein-de Sitter background model, and it is found that the perturbed space-time behaves as a Friedmann-like universe with the direction-dependent H 0 and q 0 . (author)
Alternative perturbation approaches in classical mechanics
International Nuclear Information System (INIS)
Amore, Paolo; Raya, Alfredo; Fernandez, Francisco M
2005-01-01
We discuss two alternative methods, based on the Lindstedt-Poincare technique, for the removal of secular terms from the equations of perturbation theory. We calculate the period of an anharmonic oscillator by means of both approaches and show that one of them is more accurate for all values of the coupling constant. We believe that present discussion and comparison may be a suitable exercise for teaching perturbation theory in advanced undergraduate courses on classical mechanics
Double soft theorem for perturbative gravity
Saha, Arnab
2016-01-01
Following up on the recent work of Cachazo, He and Yuan \\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in perturbative gravity. We show that the double soft theorem derived using CHY formula precisely matches with the perturbative computation involving Feynman diagrams. In particular, we find how certain delicate limits of Feynman diagrams play an important role in obtaining this equivalence.
On perturbations of a quintom bounce
International Nuclear Information System (INIS)
Cai Yifu; Qiu Taotao; Zhang Xinmin; Brandenberger, Robert; Piao Yunsong
2008-01-01
A quintom universe with an equation of state crossing the cosmological constant boundary can provide a bouncing solution dubbed the quintom bounce and thus resolve the big bang singularity. In this paper, we investigate the cosmological perturbations of the quintom bounce both analytically and numerically. We find that the fluctuations in the dominant mode in the post-bounce expanding phase couple to the growing mode of the perturbations in the pre-bounce contracting phase
Introduction to non-perturbative heavy quark effective theory
International Nuclear Information System (INIS)
Sommer, R.
2010-08-01
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti Λ and λ 1 lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m) n+1 if the theory was treated including (1/m) n terms. Clearly, the weakest point of HQET is that it intrinsically is an expansion. In practise, carrying it
Introduction to non-perturbative heavy quark effective theory
Energy Technology Data Exchange (ETDEWEB)
Sommer, R. [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2010-08-15
My lectures on the effective field theory for heavy quarks, an expansion around the static limit, concentrate on the motivation and formulation of HQET, its renormalization and discretization. This provides the basis for understanding that and how this effective theory can be formulated fully non-perturbatively in the QCD coupling, while by the very nature of an effective field theory, it is perturbative in the expansion parameter 1/m. After the couplings in the effective theory have been determined, the result at a certain order in 1/m is unique up to higher order terms in 1/m. In particular the continuum limit of the lattice regularized theory exists and leaves no trace of how it was regularized. In other words, the theory yields an asymptotic expansion of the QCD observables in 1/m - as usual in a quantum field theory modified by powers of logarithms. None of these properties has been shown rigorously (e.g. to all orders in perturbation theory) but perturbative computations and recently also non-perturbative lattice results give strong support to this ''standard wisdom''. A subtle issue is that a theoretically consistent formulation of the theory is only possible through a non-perturbative matching of its parameters with QCD at finite values of 1/m. As a consequence one finds immediately that the splitting of a result for a certain observable into, for example, lowest order and first order is ambiguous. Depending on how the matching between effective theory and QCD is done, a first order contribution may vanish and appear instead in the lowest order. For example, the often cited phenomenological HQET parameters anti {lambda} and {lambda}{sub 1} lack a unique non-perturbative definition. But this does not affect the precision of the asymptotic expansion in 1/m. The final result for an observable is correct up to order (1/m){sup n+1} if the theory was treated including (1/m){sup n} terms. Clearly, the weakest point of HQET is that it
Computer fan performance enhancement via acoustic perturbations
Energy Technology Data Exchange (ETDEWEB)
Greenblatt, David, E-mail: davidg@technion.ac.il [Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa (Israel); Avraham, Tzahi; Golan, Maayan [Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa (Israel)
2012-04-15
Highlights: Black-Right-Pointing-Pointer Computer fan effectiveness was increased by introducing acoustic perturbations. Black-Right-Pointing-Pointer Acoustic perturbations controlled blade boundary layer separation. Black-Right-Pointing-Pointer Optimum frequencies corresponded with airfoils studies. Black-Right-Pointing-Pointer Exploitation of flow instabilities was responsible for performance improvements. Black-Right-Pointing-Pointer Peak pressure and peak flowrate were increased by 40% and 15% respectively. - Abstract: A novel technique for increasing computer fan effectiveness, based on introducing acoustic perturbations onto the fan blades to control boundary layer separation, was assessed. Experiments were conducted in a specially designed facility that simultaneously allowed characterization of fan performance and introduction of the perturbations. A parametric study was conducted to determine the optimum control parameters, namely those that deliver the largest increase in fan pressure for a given flowrate. The optimum reduced frequencies corresponded with those identified on stationary airfoils and it was thus concluded that the exploitation of Kelvin-Helmholtz instabilities, commonly observed on airfoils, was responsible for the fan blade performance improvements. The optimum control inputs, such as acoustic frequency and sound pressure level, showed some variation with different fan flowrates. With the near-optimum control conditions identified, the full operational envelope of the fan, when subjected to acoustic perturbations, was assessed. The peak pressure and peak flowrate were increased by up to 40% and 15% respectively. The peak fan efficiency increased with acoustic perturbations but the overall system efficiency was reduced when the speaker input power was accounted for.
Secondary isocurvature perturbations from acoustic reheating
Ota, Atsuhisa; Yamaguchi, Masahide
2018-06-01
The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates during the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.
Computer fan performance enhancement via acoustic perturbations
International Nuclear Information System (INIS)
Greenblatt, David; Avraham, Tzahi; Golan, Maayan
2012-01-01
Highlights: ► Computer fan effectiveness was increased by introducing acoustic perturbations. ► Acoustic perturbations controlled blade boundary layer separation. ► Optimum frequencies corresponded with airfoils studies. ► Exploitation of flow instabilities was responsible for performance improvements. ► Peak pressure and peak flowrate were increased by 40% and 15% respectively. - Abstract: A novel technique for increasing computer fan effectiveness, based on introducing acoustic perturbations onto the fan blades to control boundary layer separation, was assessed. Experiments were conducted in a specially designed facility that simultaneously allowed characterization of fan performance and introduction of the perturbations. A parametric study was conducted to determine the optimum control parameters, namely those that deliver the largest increase in fan pressure for a given flowrate. The optimum reduced frequencies corresponded with those identified on stationary airfoils and it was thus concluded that the exploitation of Kelvin–Helmholtz instabilities, commonly observed on airfoils, was responsible for the fan blade performance improvements. The optimum control inputs, such as acoustic frequency and sound pressure level, showed some variation with different fan flowrates. With the near-optimum control conditions identified, the full operational envelope of the fan, when subjected to acoustic perturbations, was assessed. The peak pressure and peak flowrate were increased by up to 40% and 15% respectively. The peak fan efficiency increased with acoustic perturbations but the overall system efficiency was reduced when the speaker input power was accounted for.
Cosmological perturbations in theories with non-minimal coupling between curvature and matter
International Nuclear Information System (INIS)
Bertolami, Orfeu; Frazão, Pedro; Páramos, Jorge
2013-01-01
In this work, we examine how the presence of a non-minimal coupling between spacetime curvature and matter affects the evolution of cosmological perturbations on a homogeneous and isotropic Universe, and hence the formation of large-scale structure. This framework places constraints on the terms which arise due to the coupling with matter and, in particular, on the modified growth of matter density perturbations. We derive approximate analytical solutions for the evolution of matter overdensities during the matter dominated era and discuss the compatibility of the obtained results with the hypothesis that the late time acceleration of the Universe is driven by a non-minimal coupling
International Nuclear Information System (INIS)
Ma Jun; Wang Chunni; Li Yanlong; Pu Zhongsheng; Jin Wuyin
2008-01-01
This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhugh–Nagumo (MFHN) model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally. (general)
Influence of resonant magnetic perturbations on transient heat load deposition and fast ion losses
International Nuclear Information System (INIS)
Rack, Michael Thomas
2014-01-01
Thermonuclear fusion is the energy conversion process which keeps the sun shining. For the last six decades, researchers have been investigating the physics involved in order to enable the usage of this energy supply on Earth. The most promising candidates for fusion power plants are based on magnetic confinement of plasma to provide the ideal conditions for efficient thermonuclear fusion in well controlled surroundings. One important aspect is the control of instabilities that occur in the edge region of the plasma and lead to an ejection of huge amounts of energy. Magnetic perturbation fields which are resonant in the plasma edge are found to modify the plasma favourably and reduce the impact of these instabilities. This dissertation focuses on the effects of resonant magnetic perturbation fields on the ejected energy as well as on the drawbacks of these perturbation fields. The transient energy ejection which is triggered by the instabilities causes extreme heat loads on the wall components in fusion devices. Therefore, it is crucial to understand how resonant magnetic perturbation fields affect the heat load deposition. Furthermore, the impact of resonant magnetic perturbation fields on the confinement of fast ions is an important aspect as fast ions are still required to be well confined in order to avoid additional wall loads and increase the fusion efficiency. Recent upgrades on the Joint European Torus allow for a detailed study of the heat load deposition profiles caused by transient events. Throughout this work, the new features are used for the study of the modifications of the transient heat load depositions that occur if resonant magnetic perturbation fields are applied. This leads to a further understanding of the processes involved during the plasma edge instabilities. Additionally, an alternative method using lower hybrid waves for applying resonant magnetic perturbations is investigated. Furthermore, a new diagnostic, capable of detecting fast ion
Influence of resonant magnetic perturbations on transient heat load deposition and fast ion losses
Energy Technology Data Exchange (ETDEWEB)
Rack, Michael Thomas
2014-07-11
Thermonuclear fusion is the energy conversion process which keeps the sun shining. For the last six decades, researchers have been investigating the physics involved in order to enable the usage of this energy supply on Earth. The most promising candidates for fusion power plants are based on magnetic confinement of plasma to provide the ideal conditions for efficient thermonuclear fusion in well controlled surroundings. One important aspect is the control of instabilities that occur in the edge region of the plasma and lead to an ejection of huge amounts of energy. Magnetic perturbation fields which are resonant in the plasma edge are found to modify the plasma favourably and reduce the impact of these instabilities. This dissertation focuses on the effects of resonant magnetic perturbation fields on the ejected energy as well as on the drawbacks of these perturbation fields. The transient energy ejection which is triggered by the instabilities causes extreme heat loads on the wall components in fusion devices. Therefore, it is crucial to understand how resonant magnetic perturbation fields affect the heat load deposition. Furthermore, the impact of resonant magnetic perturbation fields on the confinement of fast ions is an important aspect as fast ions are still required to be well confined in order to avoid additional wall loads and increase the fusion efficiency. Recent upgrades on the Joint European Torus allow for a detailed study of the heat load deposition profiles caused by transient events. Throughout this work, the new features are used for the study of the modifications of the transient heat load depositions that occur if resonant magnetic perturbation fields are applied. This leads to a further understanding of the processes involved during the plasma edge instabilities. Additionally, an alternative method using lower hybrid waves for applying resonant magnetic perturbations is investigated. Furthermore, a new diagnostic, capable of detecting fast ion
Li, Fei; Li, Peng; Xu, Wenjian; Peng, Yuxing; Bo, Xiaochen; Wang, Shengqi
2010-01-15
The propagation of perturbations in protein concentration through a protein interaction network (PIN) can shed light on network dynamics and function. In order to facilitate this type of study, PerturbationAnalyzer, which is an open source plugin for Cytoscape, has been developed. PerturbationAnalyzer can be used in manual mode for simulating user-defined perturbations, as well as in batch mode for evaluating network robustness and identifying significant proteins that cause large propagation effects in the PINs when their concentrations are perturbed. Results from PerturbationAnalyzer can be represented in an intuitive and customizable way and can also be exported for further exploration. PerturbationAnalyzer has great potential in mining the design principles of protein networks, and may be a useful tool for identifying drug targets. PerturbationAnalyzer can be accessed from the Cytoscape web site http://www.cytoscape.org/plugins/index.php or http://biotech.bmi.ac.cn/PerturbationAnalyzer. Supplementary data are available at Bioinformatics online.
Energy Technology Data Exchange (ETDEWEB)
Martin, Ina; French, Roger H.
2018-03-19
Our project objective in the first and only Budget Period was to demonstrate the potential of nm-scale organofunctional silane coatings as a method of extending the lifetime of PV materials and devices. Specifically, the target was to double the lifetime performance of a laminated Cu(In,Ga)Se2 (CIGS) cell under real-world and accelerated aging exposure conditions. Key findings are that modification of aluminum-doped zinc oxide (AZO) films (materials used as transparent conductive oxide (TCO) top contacts) resulted in decreased degradation of optical and electrical properties under damp heat (DH) exposure compared to un-modified AZO. The most significant finding is that modification of the AZO top contact of full CIGS devices resulted in significantly improved properties under DH exposure compared to un-modified devices, by a factor of 4 after 1000 h. Results of this one-year project have demonstrated that surface functionalization is a viable pathway for extending the lifetime of state-of-the-art CIGS devices.
Stepping stability: effects of sensory perturbation
Directory of Open Access Journals (Sweden)
Krebs David E
2005-05-01
Full Text Available Abstract Background Few tools exist for quantifying locomotor stability in balance impaired populations. The objective of this study was to develop and evaluate a technique for quantifying stability of stepping in healthy people and people with peripheral (vestibular hypofunction, VH and central (cerebellar pathology, CB balance dysfunction by means a sensory (auditory perturbation test. Methods Balance impaired and healthy subjects performed a repeated bench stepping task. The perturbation was applied by suddenly changing the cadence of the metronome (100 beat/min to 80 beat/min at a predetermined time (but unpredictable by the subject during the trial. Perturbation response was quantified by computing the Euclidian distance, expressed as a fractional error, between the anterior-posterior center of gravity attractor trajectory before and after the perturbation was applied. The error immediately after the perturbation (Emax, error after recovery (Emin and the recovery response (Edif were documented for each participant, and groups were compared with ANOVA. Results Both balance impaired groups exhibited significantly higher Emax (p = .019 and Emin (p = .028 fractional errors compared to the healthy (HE subjects, but there were no significant differences between CB and VH groups. Although response recovery was slower for CB and VH groups compared to the HE group, the difference was not significant (p = .051. Conclusion The findings suggest that individuals with balance impairment have reduced ability to stabilize locomotor patterns following perturbation, revealing the fragility of their impairment adaptations and compensations. These data suggest that auditory perturbations applied during a challenging stepping task may be useful for measuring rehabilitation outcomes.
Perturbations of ultralight vector field dark matter
Energy Technology Data Exchange (ETDEWEB)
Cembranos, J.A.R.; Maroto, A.L.; Jareño, S.J. Núñez [Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid (Spain)
2017-02-13
We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k{sup 2}≪Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k{sup 2}≫Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c{sub s}{sup 2}≃k{sup 2}/m{sup 2}a{sup 2}. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ−Ψ)/Φ∼c{sub s}{sup 2}. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ∼c{sub s}{sup 2}. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-09-01
Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.
Application of linear and higher perturbation theory in reactor physics
International Nuclear Information System (INIS)
Woerner, D.
1978-01-01
For small perturbations in the material composition of a reactor according to the first approximation of perturbation theory the eigenvalue perturbation is proportional to the perturbation of the system. This assumption is true for the neutron flux not influenced by the perturbance. The two-dimensional code LINESTO developed for such problems in this paper on the basis of diffusion theory determines the relative change of the multiplication constant. For perturbations varying the neutron flux in the space of energy and position the eigenvalue perturbation is also influenced by this changed neutron flux. In such cases linear perturbation theory yields larger errors. Starting from the methods of calculus of variations there is additionally developed in this paper a perturbation method of calculation permitting in a quick and simple manner to assess the influence of flux perturbation on the eigenvalue perturbation. While the source of perturbations is evaluated in isotropic approximation of diffusion theory the associated inhomogeneous equation may be used to determine the flux perturbation by means of diffusion or transport theory. Possibilities of application and limitations of this method are studied in further systematic investigations on local perturbations. It is shown that with the integrated code system developed in this paper a number of local perturbations may be checked requiring little computing time. With it flux perturbations in first approximation and perturbations of the multiplication constant in second approximation can be evaluated. (orig./RW) [de
International Nuclear Information System (INIS)
Claro, L.H.; Alvim, A.C.M.; Thome, Z.D.
1988-08-01
The objective of this work is to stydy the effect of intense perturbations, such as control rod insertion in the core of PWR reactors, through a perturbation approach consisting of a modified version of the pseudo-harmonics method. A typical one-dimensional PWR reactor model was used as a reference state, from which two perturbations were imposed, simulation gray and black control rod insertion. In the first case, eigenvalue convergence was achieved with the eighth order of approximation approximation and perturbed fluxes and eigenvalue estimates agreed very well with direct calculation results. The second case tested represents a very intense localized perturbation. Oscillation in keff were observed er of approximation increased and the method failed to converge. Results obtained indicate that the pseudo-harmonics method can be used to compute 2 group fluxes and fundamental eigenvalue of perturbated states resulting from gray control rod insertion in PWR reactors. The method is limited, however, by perturbation intensity, as other perturbation methods are. (author) [pt
Local perturbations perturb—exponentially–locally
International Nuclear Information System (INIS)
De Roeck, W.; Schütz, M.
2015-01-01
We elaborate on the principle that for gapped quantum spin systems with local interaction, “local perturbations [in the Hamiltonian] perturb locally [the groundstate].” This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835–871 (2012)], relying on the “spectral flow technique” or “quasi-adiabatic continuation” [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique “bulk ground state” or “topological quantum order.” We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate
Mode coupling of Schwarzschild perturbations: Ringdown frequencies
International Nuclear Information System (INIS)
Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel
2010-01-01
Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.
Supersymmetry restoration in superstring perturbation theory
International Nuclear Information System (INIS)
Sen, Ashoke
2015-01-01
Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.
Supersymmetry restoration in superstring perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Sen, Ashoke [Harish-Chandra Research Institute,Chhatnag Road, Jhusi, Allahabad 211019 (India)
2015-12-14
Superstring perturbation theory based on the 1PI effective theory approach has been useful for addressing the problem of mass renormalization and vacuum shift. We derive Ward identities associated with space-time supersymmetry transformation in this approach. This leads to a proof of the equality of renormalized masses of bosons and fermions and identities relating fermionic amplitudes to bosonic amplitudes after taking into account the effect of mass renormalization. This also relates unbroken supersymmetry to a given order in perturbation theory to absence of tadpoles of massless scalars to higher order. The results are valid at the perturbative vacuum as well as in the shifted vacuum when the latter describes the correct ground state of the theory. We apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but analysis of the low energy effective field theory indicates that there is a nearby vacuum where supersymmetry is restored. We explicitly prove that the perturbative amplitudes of this theory around the shifted vacuum indeed satisfy the Ward identities associated with unbroken supersymmetry. We also test the general arguments by explicitly verifying the equality of bosonic and fermionic masses at one loop order in the shifted vacuum, and the appearance of two loop dilaton tadpole in the perturbative vacuum where supersymmetry is expected to be broken.
Multigroup perturbation model for kinetic analysis of nuclear reactors
International Nuclear Information System (INIS)
Souza, G.M.
1989-01-01
The scope of this work is the development of a multigroup perturbation theory for the purpose of Kinetic and dynamic analysis of nuclear reactors. The equations that describe the reactor behavior were presented in all generality and written in the shorthand notation of matrices and vectors. In the derivation of those equations indetermined operators and discretizing factors were introduced and then determined by comparision with conventional equations. Fick's Law was developed in higher orders for neutron and importance current density. The solution of the direct and adjoint fields were represented by combination of the eigenfunctions of the B and B* operators and the eigenvalue modulus equality was established mathematically. In the derivation of the reactivity expression the B operator perturbation was split in two non coupled to the flux form and level. The prompt neutrons effective mean life was derived from reactor equations and importance conservation. The establishment of the Nordheim's equation, although modified, was based on Gandini. Finally, a mathematical interpretation of the flux-trap region was avented. (author)
DEFF Research Database (Denmark)
Sadegh, Payman; Spall, J. C.
1998-01-01
simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...
Utilization of the perturbation method for determination of the buckling heterogenous reactors
International Nuclear Information System (INIS)
Gheorghe, R.
1975-01-01
Evaluation of material buckling for heterogenous nulcear reactors is a key-problem for reactor people. In this direction several methods have been elaborated: bi-group method, heterogenous method and perturbation methods. Out of them, mostly employed is the perturbation method which is also presented in this paper and is applied in some parameter calculations of a new cell type for which fuel is positioned in the marginal area and the moderator is in the centre. It is based on the technique of progressive substitution. Advantages of the method: buckling comes out clearly, high level defects due to differences between O perturbated fluxes and the unperturbated flux Osub(o) can be corrected by an iterative procedure; using a modified bi-group theory, one can clearly describe effects of other parameters
Tension perturbations of black brane spacetimes
International Nuclear Information System (INIS)
Traschen, Jennie; Fox, Daniel
2004-01-01
We consider black brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension parameter is associated with spatial translations in much the same way that the ADM mass is associated with the time translation Killing field. In this work, we explore the implications of the spatial translation symmetry for small perturbations around a background black brane. For static-charged black branes we derive a law which relates the tension perturbation to the surface gravity times the change in the horizon area, plus terms that involve variations in the charges and currents. We find that as a black brane evaporates the tension decreases. We also give a simple derivation of a first law for black brane spacetimes. These constructions hold when the background stress-energy is governed by a Hamiltonian, and the results include arbitrary perturbative stress-energy sources
Perturbation measurement of waveguides for acoustic thermometry
Lin, H.; Feng, X. J.; Zhang, J. T.
2013-09-01
Acoustic thermometers normally embed small acoustic transducers in the wall bounding a gas-filled cavity resonator. At high temperature, insulators of transducers loss electrical insulation and degrade the signal-to-noise ratio. One essential solution to this technical trouble is to couple sound by acoustic waveguides between resonator and transducers. But waveguide will break the ideal acoustic surface and bring perturbations(Δf+ig) to the ideal resonance frequency. The perturbation model for waveguides was developed based on the first-order acoustic theory in this paper. The frequency shift Δf and half-width change g caused by the position, length and radius of waveguides were analyzed using this model. Six different length of waveguides (52˜1763 mm) were settled on the cylinder resonator and the perturbation (Δf+ig) were measured at T=332 K and p=250˜500 kPa. The experiment results agreed with the theoretical prediction very well.
Microfluidic mixing through oscillatory transverse perturbations
Wu, J. W.; Xia, H. M.; Zhang, Y. Y.; Zhu, P.
2018-05-01
Fluid mixing in miniaturized fluidic devices is a challenging task. In this work, the mixing enhancement through oscillatory transverse perturbations coupling with divergent circular chambers is studied. To simplify the design, an autonomous microfluidic oscillator is used to produce the oscillatory flow. It is then applied to four side-channels that intersect with a central channel of constant flow. The mixing performance is tested at high fluid viscosities of up to 16 cP. Results show that the oscillatory flow can cause strong transverse perturbations which effectively enhance the mixing. The influence of a fluidic capacitor in the central channel is also examined, which at low viscosities can intensify the perturbations and further improve the mixing.
One dimensional systems with singular perturbations
International Nuclear Information System (INIS)
Alvarez, J J; Gadella, M; Nieto, L M; Glasser, L M; Lara, L P
2011-01-01
This paper discusses some one dimensional quantum models with singular perturbations. Eventually, a mass discontinuity is added at the points that support the singular perturbations. The simplest model includes an attractive singular potential with a mass jump both located at the origin. We study the form of the only bound state. Another model exhibits a hard core at the origin plus one or more repulsive deltas with mass jumps at the points supporting these deltas. We study the location and the multiplicity of these resonances for the case of one or two deltas and settle the basis for a generalization. Finally, we consider the harmonic oscillator and the infinite square well plus a singular potential at the origin. We see how the energy of bound states is affected by the singular perturbation.
Perturbations of higher-dimensional spacetimes
Energy Technology Data Exchange (ETDEWEB)
Durkee, Mark; Reall, Harvey S, E-mail: M.N.Durkee@damtp.cam.ac.uk, E-mail: H.S.Reall@damtp.cam.ac.uk [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2011-02-07
We discuss linearized gravitational perturbations of higher-dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher-dimensional generalizations of the 4D Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.
On the domain of string perturbation theory
International Nuclear Information System (INIS)
Davis, S.
1989-06-01
For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformized by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground states, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behavior of the perturbation series are discussed. (author). 20 refs, 6 figs
Perturbation theory for continuous stochastic equations
International Nuclear Information System (INIS)
Chechetkin, V.R.; Lutovinov, V.S.
1987-01-01
The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)
MCNP perturbation technique for criticality analysis
International Nuclear Information System (INIS)
McKinney, G.W.; Iverson, J.L.
1995-01-01
The differential operator perturbation technique has been incorporated into the Monte Carlo N-Particle transport code MCNP and will become a standard feature of future releases. This feature includes first and/or second order terms of the Taylor Series expansion for response perturbations related to cross-section data (i.e., density, composition, etc.). Criticality analyses can benefit from this technique in that predicted changes in the track-length tally estimator of K eff may be obtained for multiple perturbations in a single run. A key advantage of this method is that a precise estimate of a small change in response (i.e., < 1%) is easily obtained. This technique can also offer acceptable accuracy, to within a few percent, for up to 20-30% changes in a response
Gravitational perturbation theory and synchrotron radiation
Energy Technology Data Exchange (ETDEWEB)
Breuer, R A [Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (F.R. Germany). Inst. fuer Astrophysik
1975-01-01
This article presents methods and results for a gravitational perturbation theory which treats massless fields as linearized perturbations of an arbitrary gravitational vacuum background spacetime. The formalism is outlined for perturbations of type (22) spacetimes. As an application, high-frequency radiation emitted by particles moving approximately on relativistic circular geodesic orbits is computed. More precisely, the test particle assumption is made; throughout it is therefore assumed that the reaction of the radiation on the particle motion is negligible. In particular, these orbits are studied in the gravitational field of a spherically symmetric (Schwarzschild-) black hole as well as of a rotating (Kerr-) black hole. In this model, the outgoing radiation is highly focussed and of much higher fequency than the orbital frequency, i.e. one is dealing with 'gravitational synchrotron radiation'.
Gribov ambiguity, perturbation theory, and confinement
International Nuclear Information System (INIS)
Greensite, J.P.
1978-01-01
The generating functional proposed for gauge theories by Bender, Eguchi, and Pagels (BEP) is shown to be equivalent to a truncated form of the functional integral, in which only one field configuration from each gauge-equivalent Gribov set contributes to the functional integration. The standard perturbation technique provides a method of realizing this truncation condition. It is shown that any gauge-covariant quantity (such as the quark N-point functions), evaluated by perturbating around a field configuration gauge-equivalent to A = 0, is related by a gauge transformation to the same quantity evaluated perturbatively around the trivial vacuum. It follows that, contrary to the conclusion of BEP, the existence of degeneracies in the Coulomb gauge-fixing condition (the Gribov ambiguity) is not directly related to the physics of confinement
Non-Perturbative Quantum Geometry III
Krefl, Daniel
2016-08-02
The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stockes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stockes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.
Redshift-space distortions from vector perturbations
Bonvin, Camille; Durrer, Ruth; Khosravi, Nima; Kunz, Martin; Sawicki, Ignacy
2018-02-01
We compute a general expression for the contribution of vector perturbations to the redshift space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift space distortions, we show that the multipoles of the correlation function are sensitive to vorticity induced by non-linear clustering. Therefore future redshift surveys such as DESI or the SKA should be capable of measuring such vector modes, especially with the hexadecapole which appears to be the most sensitive to the presence of vorticity.
Operator Decomposition Framework for Perturbation Theory
Energy Technology Data Exchange (ETDEWEB)
Abdel-Khalik, Hany S.; Wang, Congjian; Bang, Young Suk [North Carolina State University, Raleigh (United States)
2012-05-15
This summary describes a new framework for perturbation theory intended to improve its performance, in terms of the associated computational cost and the complexity of implementation, for routine reactor calculations in support of design, analysis, and regulation. Since its first introduction in reactor analysis by Winger, perturbation theory has assumed an aura of sophistication with regard to its implementation and its capabilities. Only few reactor physicists, typically mathematically proficient, have contributed to its development, with the general body of the nuclear engineering community remaining unaware of its current status, capabilities, and challenges. Given its perceived sophistication and the small body of community users, the application of perturbation theory has been limited to investigatory analyses only. It is safe to say that the nuclear community is split into two groups, a small one which understands the theory and, and a much bigger group with the perceived notion that perturbation theory is nothing but a fancy mathematical approach that has very little use in practice. Over the past three years, research has demonstrated two goals. First, reduce the computational cost of perturbation theory in order to enable its use for routine reactor calculations. Second, expose some of the myth about perturbation theory and present it in a form that is simple and relatable in order to stimulate the interest of nuclear practitioners, especially those who are currently working on the development of next generation reactor design and analysis tools. The operator decomposition approach has its roots in linear algebra and can be easily understood by code developers, especially those involved in the design of iterative numerical solution strategies
Perturbation expansions generated by an approximate propagator
International Nuclear Information System (INIS)
Znojil, M.
1987-01-01
Starting from a knowledge of an approximate propagator R at some trial energy guess E 0 , a new perturbative prescription for p-plet of bound states and of their energies is proposed. It generalizes the Rayleigh-Schroedinger (RS) degenerate perturbation theory to the nondiagonal operators R (eliminates a RS need of their diagnolisation) and defines an approximate Hamiltonian T by mere inversion. The deviation V of T from the exact Hamiltonian H is assumed small only after a substraction of a further auxiliary Hartree-Fock-like separable ''selfconsistent'' potential U of rank p. The convergence is illustrated numerically on the anharmonic oscillator example
On algebraically special perturbations of black holes
International Nuclear Information System (INIS)
Chandrasekhar, S.
1984-01-01
Algebraically special perturbations of black holes excite gravitational waves that are either purely ingoing or purely outgoing. Solutions, appropriate to such perturbations of the Kerr, the Schwarzschild, and the Reissner-Nordstroem black-holes, are obtained in explicit forms by different methods. The different methods illustrate the remarkable inner relations among different facets of the mathematical theory. In the context of the Kerr black-hole they derive from the different ways in which the explicit value of the Starobinsky constant emerges, and in the context of the Schwarzschild and the Reissner-Nordstroem black-holes they derive from the potential barriers surrounding them belonging to a special class. (author)
Primordial perturbations with pre-inflationary bounce
Cai, Yong; Wang, Yu-Tong; Zhao, Jin-Yun; Piao, Yun-Song
2018-05-01
Based on the effective field theory (EFT) of nonsingular cosmologies, we build a stable model, without the ghost and gradient instabilities, of bounce-inflation (inflation is preceded by a cosmological bounce). We perform a full simulation for the evolution of scalar perturbation, and find that the perturbation spectrum has a large-scale suppression (as expected), which is consistent with the power deficit of the cosmic microwave background (CMB) TT-spectrum at low multipoles, but unexpectedly, it also shows itself one marked lower valley. The depth of valley is relevant with the physics around the bounce scale, which is model-dependent.
Perturbative evaluation of the Thermal Wilson Loop
International Nuclear Information System (INIS)
Gava, E.; Jengo, R.
1981-06-01
The Thermal Wilson Loop 0 sup(β) dtauA 0 (tau, x-vector)>, representing an order parameter for the gauge theory and expected to be zero in the confining phase, is perturbatively evaluated up to the O(g 4 ) included for an SU(N) pure Yang-Mills theory. This evaluation should be meaningful at high temperature, β → 0. Its behaviour is discussed and a possible need for non-perturbative instanton-like contributions is pointed out. (author)
A generalized perturbation program for CANDU reactor
Energy Technology Data Exchange (ETDEWEB)
Kim, Do Heon; Kim, Jong Kyung [Hanyang University, Seoul (Korea, Republic of); Choi, Hang Bok; Roh, Gyu Hong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Yang, Won Sik [Chosun University, Kwangju (Korea, Republic of)
1999-12-31
A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible. 2 refs., 1 figs., 1 tab. (Author)
Pre-inflation physics and scalar perturbations
International Nuclear Information System (INIS)
Hirai, Shiro
2005-01-01
The effect of pre-inflation physics on the power spectrum of scalar perturbations is investigated. Considering various pre-inflation models with radiation-dominated or matter-dominated periods before inflation, the power spectra of curvature perturbations for large scales are calculated, and the spectral index and running spectral index are derived. It is shown that pre-inflation models in which the length of inflation is near 60 e-folds may reproduce some key properties implied by the Wilkinson microwave anisotropy probe data
Non-perturbative QCD and hadron physics
International Nuclear Information System (INIS)
Cobos-Martínez, J J
2016-01-01
A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented. (paper)
Perturbative approach to Markovian open quantum systems.
Li, Andy C Y; Petruccione, F; Koch, Jens
2014-05-08
The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical.
Free-boundary perturbed MHD equilibria
International Nuclear Information System (INIS)
Nührenberg, C
2012-01-01
The concept of perturbed ideal MHD equilibria [Boozer A H and Nuhrenberg C 2006 Phys. Plasmas 13 102501] is employed to study the influence of external error-fields and of small plasma-pressure changes on toroidal plasma equilibria. In tokamak and stellarator free-boundary calculations, benchmarks were successful of the perturbed-equilibrium version of the CAS3D stability code [Nührenberg C et al. 2009 Phys. Rev. Lett. 102 235001] with the ideal MHD equilibrium code NEMEC [Hirshman S P et al. 1986 Comput. Phys. Commun. 43 143].
Death to perturbative QCD in exclusive processes?
Energy Technology Data Exchange (ETDEWEB)
Eckardt, R.; Hansper, J.; Gari, M.F. [Institut fuer Theoretische Physik, Bochum (Germany)
1994-04-01
The authors discuss the question of whether perturbative QCD is applicable in calculations of exclusive processes at available momentum transfers. They show that the currently used method of determining hadronic quark distribution amplitudes from QCD sum rules yields wave functions which are completely undetermined because the polynomial expansion diverges. Because of the indeterminacy of the wave functions no statement can be made at present as to whether perturbative QCD is valid. The authors emphasize the necessity of a rigorous discussion of the subject and the importance of experimental data in the range of interest.
Perturbative and nonperturbative renormalization in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)
2010-03-15
We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)
A generalized perturbation program for CANDU reactor
Energy Technology Data Exchange (ETDEWEB)
Kim, Do Heon; Kim, Jong Kyung [Hanyang University, Seoul (Korea, Republic of); Choi, Hang Bok; Roh, Gyu Hong [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of); Yang, Won Sik [Chosun University, Kwangju (Korea, Republic of)
1998-12-31
A generalized perturbation program has been developed for the purpose of estimating zonal power variation of a CANDU reactor upon refueling operation. The forward and adjoint calculation modules of RFSP code were used to construct the generalized perturbation program. The numerical algorithm for the generalized adjoint flux calculation was verified by comparing the zone power estimates upon refueling with those of forward calculation. It was, however, noticed that the truncation error from the iteration process of the generalized adjoint flux is not negligible. 2 refs., 1 figs., 1 tab. (Author)
Scaling violations and perturbative quantum chromodynamics
International Nuclear Information System (INIS)
Barbieri, R.; d'Emilio, E.; Caneschi, L.; Curci, G.
1979-01-01
The authors try to understand the meaning of the recent data on scaling violations of the moments of the structure function F 3 measured in γ and anti γ deep inelastic scattering, and their relevance as a test of QCD. This is done by reducing to the minimum the theoretical machinery and prejudices and stressing the perturbative nature of the problem. This leads to a definition of the perturbation coupling constant αsub(s) (Q = 2.5 GeV) = 0.61 +- 0.06, in terms of which the corrective terms for all quantities computed so far turn out to be relatively small. (Auth.)
Non-Gaussianity from isocurvature perturbations
Energy Technology Data Exchange (ETDEWEB)
Kawasaki, Masahiro; Nakayama, Kazunori; Sekiguchi, Toyokazu; Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582 (Japan); Takahashi, Fuminobu, E-mail: kawasaki@icrr.u-tokyo.ac.jp, E-mail: nakayama@icrr.u-tokyo.ac.jp, E-mail: sekiguti@icrr.u-tokyo.ac.jp, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Kashiwa 277-8568 (Japan)
2008-11-15
We develop a formalism for studying non-Gaussianity in both curvature and isocurvature perturbations. It is shown that non-Gaussianity in the isocurvature perturbation between dark matter and photons leaves distinct signatures in the cosmic microwave background temperature fluctuations, which may be confirmed in future experiments, or possibly even in the currently available observational data. As an explicit example, we consider the quantum chromodynamics axion and show that it can actually induce sizable non-Gaussianity for the inflationary scale, H{sub inf} = O(10{sup 9}-10{sup 11}) GeV.
A perturbative DFT approach for magnetic anisotropy
Energy Technology Data Exchange (ETDEWEB)
Khoo, Khoong Hong; Laskowski, Robert, E-mail: rolask@ihpc.a-star.edu.sg
2017-04-15
We develop a perturbative formalism for computing magnetocrystalline anisotropy within density functional theory and the magnetic force theorem. Instead of computing eigenvalues of the spin–orbit Hamiltonian for selected spin polarizations, as in the conventional “force theorem” approach, we show that the effect can be cast into a redefined form of the spin–orbit operator. This allows to separate the large eigenvalue shift due to spin-orbit interaction common for both polarizations from the much smaller magnetic anisotropy splitting. As a consequence the anisotropy splitting may by considered as a perturbation.
Gauge-invariant perturbations in a spatially flat anisotropic universe
International Nuclear Information System (INIS)
Den, Mitsue.
1986-12-01
The gauge-invariant perturbations in a spatially flat anisotropic universe with an arbitrary dimension (= N) are studied. In a previous paper the equations for the perturbations with a wave vector k a in one of the axial directions were derived and their solutions were shown. In this paper the perturbations with k a in arbitrary directions are treated. The remarkable properties are that all three types (scalar, vector, and tensor) of perturbations are generally coupled, so that a density perturbation can be produced also by vector or tensor perturbations. The formulation is quite general, but the behavior of the perturbations is discussed in a simple case such that N = 4 and k a is orthogonal to one of the axial directions. In this case, the perturbations are divided into two groups which are dynamically decoupled from each other. The asymptotic behavior of the perturbations in the group containing the density perturbation is discussed. (author)
Gauge invariance properties and singularity cancellations in a modified PQCD
Cabo-Montes de Oca, Alejandro; Cabo, Alejandro; Rigol, Marcos
2006-01-01
The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works, are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter $\\alpha $. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the $\\alpha$-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge invariance-properties.
Reduction of some perturbed Keplerian problems
Energy Technology Data Exchange (ETDEWEB)
Inarrea, Manuel [Universidad de La Rioja, Area de Fisica, 26006 Logrono (Spain); Lanchares, Victor [Universidad de La Rioja, Departamento de Matematicas y Computacion, 26004 Logrono (Spain)] e-mail: vlancha@dmc.unirioja.es; Palacian, Jesus F. [Universidad Publica de Navarra, Departamento de Matematica e Informatica, 31006 Pamplona (Spain); Pascual, Ana I. [Universidad de La Rioja, Departamento de Matematicas y Computacion, 26004 Logrono (Spain); Salas, J. Pablo [Universidad de La Rioja, Area de Fisica, 26006 Logrono (Spain); Yanguas, Patricia [Universidad Publica de Navarra, Departamento de Matematica e Informatica, 31006 Pamplona (Spain)
2006-01-01
Perturbed Hamiltonian Keplerian systems enjoying some discrete and continuous symmetries can be brought to a one degree of freedom system containing the main qualitative features of the original one. This reduced system is defined in a compact set of the plane where the qualitative dynamics can be studied in a systematic way.
CIRCUMSTELLAR DEBRIS DISKS: DIAGNOSING THE UNSEEN PERTURBER
Energy Technology Data Exchange (ETDEWEB)
Nesvold, Erika R. [Department of Terrestrial Magnetism, Carnegie Institution for Science, 5241 Broad Branch Rd., Washington, DC 20015 (United States); Naoz, Smadar; Vican, Laura [Department of Physics and Astronomy, UCLA, 475 Portola Plaza, Los Angeles, CA 90095 (United States); Farr, Will M. [School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT (United Kingdom)
2016-07-20
The first indication of the presence of a circumstellar debris disk is usually the detection of excess infrared emission from the population of small dust grains orbiting the star. This dust is short-lived, requiring continual replenishment, and indicating that the disk must be excited by an unseen perturber. Previous theoretical studies have demonstrated that an eccentric planet orbiting interior to the disk will stir the larger bodies in the belt and produce dust via interparticle collisions. However, motivated by recent observations, we explore another possible mechanism for heating a debris disk: a stellar-mass perturber orbiting exterior to and inclined to the disk and exciting the disk particles’ eccentricities and inclinations via the Kozai–Lidov mechanism. We explore the consequences of an exterior perturber on the evolution of a debris disk using secular analysis and collisional N -body simulations. We demonstrate that a Kozai–Lidov excited disk can generate a dust disk via collisions and we compare the results of the Kozai–Lidov excited disk with a simulated disk perturbed by an interior eccentric planet. Finally, we propose two observational tests of a dust disk that can distinguish whether the dust was produced by an exterior brown dwarf or stellar companion or an interior eccentric planet.
Perturbative renormalization of QED via flow equations
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1991-01-01
We prove the perturbative renormalizability of euclidean QED 4 with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.)
Perturbative renormalization of QED via flow equations
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany)); Kopper, C. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany) Inst. fuer Theoretische Physik, Univ. Goettingen (Germany))
1991-12-19
We prove the perturbative renormalizability of euclidean QED{sub 4} with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.).
Perturbation of operators and approximation of spectrum
Indian Academy of Sciences (India)
outside the bounds of essential spectrum of A(x) can be approximated ... some perturbed discrete Schrödinger operators treating them as block ...... particular, one may think of estimating the spectrum and spectral gaps of Schrödinger.
On the divergences of inflationary superhorizon perturbations
Energy Technology Data Exchange (ETDEWEB)
Enqvist, K; Nurmi, S [Physics Department, University of Helsinki, PO Box 64, Helsinki, FIN-00014 (Finland); Podolsky, D; Rigopoulos, G I, E-mail: kari.enqvist@helsinki.fi, E-mail: sami.nurmi@helsinki.fi, E-mail: dmitry.podolsky@helsinki.fi, E-mail: gerasimos.rigopoulos@helsinki.fi [Helsinki Institute of Physics, University of Helsinki, PO Box 64, Helsinki, FIN-00014 (Finland)
2008-04-15
We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that, within the stochastic framework, they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the {Delta}N formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two-and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would, of course, be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization-group-invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point-independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.
Effective field theory of cosmological perturbations
International Nuclear Information System (INIS)
Piazza, Federico; Vernizzi, Filippo
2013-01-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu–Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy. (paper)
Modification of the perturbative QCD towards confinement
International Nuclear Information System (INIS)
Arodz, H.
1981-01-01
Modification of the low momentum behaviour of the perturbative SU(2) gauge theory is proposed. The modification is closely related (although not equivalent) to a nonstandard choice of boundary condition for the Euclidean 2-point gluonic Green function. In the resulting theory already single graphs lead to the confining potential between heavy, static quarks, V(r) = ar 2 for r → infinity. (author)
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations
Many body perturbation calculations of photoionization
International Nuclear Information System (INIS)
Kelly, H.P.
1979-01-01
The application of many body perturbation theory to the calculation of atomic photoionization cross sections is reviewed. The choice of appropriate potential for the single-particle state is discussed and results are presented for several atoms including resonance structure. In addition to single photoionization, the process of double photoionization is considered and is found to be significant. (Auth.)
Quenched Chiral Perturbation Theory to one loop
Colangelo, G.; Pallante, E.
The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral
Reduction of some perturbed Keplerian problems
International Nuclear Information System (INIS)
Inarrea, Manuel; Lanchares, Victor; Palacian, Jesus F.; Pascual, Ana I.; Salas, J. Pablo; Yanguas, Patricia
2006-01-01
Perturbed Hamiltonian Keplerian systems enjoying some discrete and continuous symmetries can be brought to a one degree of freedom system containing the main qualitative features of the original one. This reduced system is defined in a compact set of the plane where the qualitative dynamics can be studied in a systematic way
Perturbation theory for arbitrary coupling strength?
Mahapatra, Bimal P.; Pradhan, Noubihary
2018-03-01
We present a new formulation of perturbation theory for quantum systems, designated here as: “mean field perturbation theory” (MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of arbitrary strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the “standard formulation of perturbation theory” (SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the nonlinearity and the analytic structure (in the coupling strength) of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since “renormalon”-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case.
Higher order corrections in perturbative quantum chromodynamics
Indian Academy of Sciences (India)
Since the discovery of asymptotic freedom in non-abelian gauge field theories, like quan- tum chromodynamics (QCD), many perturbative calculations have been performed to ..... The integral above appears in the partial integration with respect to the momentum. &½ of the expression below (see figure 2). ¼. Т&½. ґѕπµТ.
Stratospheric HTO perturbations 1980-1983
Mason, A. S.
1985-02-01
Three perturbations of the stratospheric tritiated water burden have occurred. An atmospheric nuclear detonation in 1980 injected about 2.1 MCi. The massive eruptions of the volcano El Chichon may have contributed to a doubling of the removal rate in 1982. An unusually large wintertime exchange with the upper stratosphere may have occurred between 1982 and 1983.
Perturbed soliton excitations in inhomogeneous DNA
International Nuclear Information System (INIS)
Daniel, M.; Vasumathi, V.
2005-05-01
We study nonlinear dynamics of inhomogeneous DNA double helical chain under dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation when taking into account the interstrand hydrogen bonding energy and intrastrand inhomogeneous stacking energy and making an analogy with the Heisenberg model of the Hamiltonian for an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagentic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of open state configuration in DNA double helix. The effect of inhomogeneity in stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple scale soliton perturbation theory by solving the associated linear eigen value problem and constructing the complete set of eigen functions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of inhomogeneity. Also it introduces fluctuations in the form of train of pulses or periodic oscillation in the open state configuration (author)
Where does cosmological perturbation theory break down?
International Nuclear Information System (INIS)
Armendariz-Picon, Cristian; Fontanini, Michele; Penco, Riccardo; Trodden, Mark
2009-01-01
It is often assumed that initial conditions for the evolution of a cosmological mode should be set at the time its physical wavelength reaches a cut-off of the order of the Planck length. Beyond that scale, trans-Planckian corrections to the dispersion relation are supposed to become dominant, leading to the breakdown of cosmological perturbation theory. In this paper, we apply the effective field theory approach to the coupled metric-inflaton system in order to calculate the corrections to the power spectrum of scalar and tensor perturbations induced by higher-dimension operators at short wavelengths. These corrections can be interpreted as modifications of the dispersion relation, and thus open a window to probe the validity of cosmological perturbation theory. Both for scalars and tensors, the modifications become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length at which such a breakdown occurs is finite, but much smaller than the Planck length.
Analytic continuation and perturbative expansions in QCD
Czech Academy of Sciences Publication Activity Database
Caprini, I.; Fischer, Jan
2002-01-01
Roč. 24, - (2002), s. 127-135 ISSN 1434-6044 R&D Projects: GA MPO RP-4210/69 Institutional research plan: CEZ:AV0Z1010920 Keywords : perturbative expansion * quantum chromodynamics * infrared ambiguity * essential singularities Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 6.162, year: 2002
Privacy Is Become with, Data Perturbation
Singh, Er. Niranjan; Singhai, Niky
2011-06-01
Privacy is becoming an increasingly important issue in many data mining applications that deal with health care, security, finance, behavior and other types of sensitive data. Is particularly becoming important in counterterrorism and homeland security-related applications. We touch upon several techniques of masking the data, namely random distortion, including the uniform and Gaussian noise, applied to the data in order to protect it. These perturbation schemes are equivalent to additive perturbation after the logarithmic Transformation. Due to the large volume of research in deriving private information from the additive noise perturbed data, the security of these perturbation schemes is questionable Many artificial intelligence and statistical methods exist for data analysis interpretation, Identifying and measuring the interestingness of patterns and rules discovered, or to be discovered is essential for the evaluation of the mined knowledge and the KDD process as a whole. While some concrete measurements exist, assessing the interestingness of discovered knowledge is still an important research issue. As the tool for the algorithm implementations we chose the language of choice in industrial world MATLAB.
Characterizing heterogeneous cellular responses to perturbations.
Slack, Michael D; Martinez, Elisabeth D; Wu, Lani F; Altschuler, Steven J
2008-12-09
Cellular populations have been widely observed to respond heterogeneously to perturbation. However, interpreting the observed heterogeneity is an extremely challenging problem because of the complexity of possible cellular phenotypes, the large dimension of potential perturbations, and the lack of methods for separating meaningful biological information from noise. Here, we develop an image-based approach to characterize cellular phenotypes based on patterns of signaling marker colocalization. Heterogeneous cellular populations are characterized as mixtures of phenotypically distinct subpopulations, and responses to perturbations are summarized succinctly as probabilistic redistributions of these mixtures. We apply our method to characterize the heterogeneous responses of cancer cells to a panel of drugs. We find that cells treated with drugs of (dis-)similar mechanism exhibit (dis-)similar patterns of heterogeneity. Despite the observed phenotypic diversity of cells observed within our data, low-complexity models of heterogeneity were sufficient to distinguish most classes of drug mechanism. Our approach offers a computational framework for assessing the complexity of cellular heterogeneity, investigating the degree to which perturbations induce redistributions of a limited, but nontrivial, repertoire of underlying states and revealing functional significance contained within distinct patterns of heterogeneous responses.
Perturbations of normally solvable nonlinear operators, I
Directory of Open Access Journals (Sweden)
William O. Ray
1985-01-01
Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
Transport perturbation theory in nuclear reactor analysis
International Nuclear Information System (INIS)
Nishigori, Takeo; Takeda, Toshikazu; Selvi, S.
1985-01-01
Perturbation theory is formulated on the basis of transport theory to obtain a formula for the reactivity changes due to possible variations of cross sections. Useful applications to cell homogenization are presented for the whole core calculation in transport and in diffusion theories. (author)
Mechanical perturbation control of cardiac alternans
Hazim, Azzam; Belhamadia, Youssef; Dubljevic, Stevan
2018-05-01
Cardiac alternans is a disturbance in heart rhythm that is linked to the onset of lethal cardiac arrhythmias. Mechanical perturbation control has been recently used to suppress alternans in cardiac tissue of relevant size. In this control strategy, cardiac tissue mechanics are perturbed via active tension generated by the heart's electrical activity, which alters the tissue's electric wave profile through mechanoelectric coupling. We analyze the effects of mechanical perturbation on the dynamics of a map model that couples the membrane voltage and active tension systems at the cellular level. Therefore, a two-dimensional iterative map of the heart beat-to-beat dynamics is introduced, and a stability analysis of the system of coupled maps is performed in the presence of a mechanical perturbation algorithm. To this end, a bidirectional coupling between the membrane voltage and active tension systems in a single cardiac cell is provided, and a discrete form of the proposed control algorithm, that can be incorporated in the coupled maps, is derived. In addition, a realistic electromechanical model of cardiac tissue is employed to explore the feasibility of suppressing alternans at cellular and tissue levels. Electrical activity is represented in two detailed ionic models, the Luo-Rudy 1 and the Fox models, while two active contractile tension models, namely a smooth variant of the Nash-Panfilov model and the Niederer-Hunter-Smith model, are used to represent mechanical activity in the heart. The Mooney-Rivlin passive elasticity model is employed to describe passive mechanical behavior of the myocardium.
Non-perturbative Heavy Quark Effective Theory
DEFF Research Database (Denmark)
Della Morte, Michele; Heitger, Jochen; Simma, Hubert
2015-01-01
We review a lattice strategy how to non-perturbatively determine the coefficients in the HQET expansion of all components of the heavy-light axial and vector currents, including 1/m_h-corrections. We also discuss recent preliminary results on the form factors parameterizing semi-leptonic B...
A perturbed martingale approach to global optimization
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Saikat [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Roy, Debasish, E-mail: royd@civil.iisc.ernet.in [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Vasu, Ram Mohan [Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012 (India)
2014-08-01
A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization. - Highlights: • Evolutionary global optimization is posed as a perturbed martingale problem. • Resulting search via additive updates is a generalization over Gateaux derivatives. • Additional layers of random perturbation help avoid trapping at local extrema. • The approach ensures efficient design space exploration and high accuracy. • The method is numerically assessed via parameter recovery of chaotic oscillators.
Proprioceptive perturbations of stability during gait
Duysens, J.; Beerepoot, V.P.; Veltink, Petrus H.; Weerdesteyn, V.; Smits-Engelsman, B.C.M.
2008-01-01
Through recent studies, the role of proprioceptors in reactions to perturbations during gait has been finally somewhat better understood. The input from spindle afferents has been investigated with tendon taps, vibration and other forms of muscle stretches, including some resembling natural
Acoustic anisotropic wavefields through perturbation theory
Alkhalifah, Tariq Ali
2013-01-01
these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing
Gravitational clustering to all perturbative orders
International Nuclear Information System (INIS)
Abdalla, E.; Mohayaee, R.
1999-04-01
We derive the time evolution of the density contrast to all orders of perturbation theory, by solving the Einstein equation for scale-invariant fluctuations. These fluctuations are represented by an infinite series in inverse powers of the radial parameter. In addition to the standard growing modes, we find infinitely many more new growing modes for open and closed universes. (author)
Effective field theory of cosmological perturbations
Piazza, Federico; Vernizzi, Filippo
2013-11-01
The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry—that allows us to write down the most general Lagrangian—and of the Stückelberg ‘trick’—that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
C-semigroup S(·) may not be densely defined and the perturbation operator B is a ... rems for local C-semigroups on X with densely defined generators. ...... [8] Shaw S-Y and Kuo C-C, Generation of local C-semigroups and solvability of the ...
On-Shell Methods in Perturbative QCD
International Nuclear Information System (INIS)
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-01-01
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider
Non-hard sphere thermodynamic perturbation theory.
Zhou, Shiqi
2011-08-21
A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. © 2011 American Institute of Physics
Spontaneous breaking of Lorentz symmetry by ghost condensation in perturbative quantum gravity
Faizal, Mir
2011-10-01
In this paper, we will study the spontaneous breakdown of the Lorentz symmetry by ghost condensation in perturbative quantum gravity. Our analysis will be done in the Curci-Ferrari gauge. We will also analyse the modification of the BRST and anti-BRST transformations by the formation of this ghost condensate. It will be shown that even though the modified BRST and anti-BRST transformations are not nilpotent, their nilpotency is restored on-shell.
A robust computational technique for a system of singularly perturbed reaction–diffusion equations
Directory of Open Access Journals (Sweden)
Kumar Vinod
2014-06-01
Full Text Available In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor. Numerical results are presented which are in agreement with the theoretical results.
Cosmological perturbations on the phantom brane
Energy Technology Data Exchange (ETDEWEB)
Bag, Satadru; Sahni, Varun [Inter-University Centre for Astronomy and Astrophysics, Pune (India); Viznyuk, Alexander; Shtanov, Yuri, E-mail: satadru@iucaa.in, E-mail: viznyuk@bitp.kiev.ua, E-mail: shtanov@bitp.kiev.ua, E-mail: varun@iucaa.in [Bogolyubov Institute for Theoretical Physics, Kiev 03680 (Ukraine)
2016-07-01
We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, w {sub eff} < −1, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom—the 'Weyl fluid' or 'dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in ΛCDM. Additionally, the gravitational potentials Φ and Ψ evolve differently on the brane than in ΛCDM, for which Φ = Ψ. On the brane, by contrast, the ratio Φ/Ψ exceeds unity during the late matter-dominated epoch ( z ∼< 50). These features emerge as smoking gun tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.
Growth of matter perturbation in quintessence cosmology
Mulki, Fargiza A. M.; Wulandari, Hesti R. T.
2017-01-01
Big bang theory states that universe emerged from singularity with very high temperature and density, then expands homogeneously and isotropically. This theory gives rise standard cosmological principle which declares that universe is homogeneous and isotropic on large scales. However, universe is not perfectly homogeneous and isotropic on small scales. There exist structures starting from clusters, galaxies even to stars and planetary system scales. Cosmological perturbation theory is a fundamental theory that explains the origin of structures. According to this theory, the structures can be regarded as small perturbations in the early universe, which evolves as the universe expands. In addition to the problem of inhomogeneities of the universe, observations of supernovae Ia suggest that our universe is being accelerated. Various models of dark energy have been proposed to explain cosmic acceleration, one of them is cosmological constant. Because of several problems arise from cosmological constant, the alternative models have been proposed, one of these models is quintessence. We reconstruct growth of structure model following quintessence scenario at several epochs of the universe, which is specified by the effective equation of state parameters for each stage. Discussion begins with the dynamics of quintessence, in which exponential potential is analytically derived, which leads to various conditions of the universe. We then focus on scaling and quintessence dominated solutions. Subsequently, we review the basics of cosmological perturbation theory and derive formulas to investigate how matter perturbation evolves with time in subhorizon scales which leads to structure formation, and also analyze the influence of quintessence to the structure formation. From analytical exploration, we obtain the growth rate of matter perturbation and the existence of quintessence as a dark energy that slows down the growth of structure formation of the universe.
Unique Fock quantization of scalar cosmological perturbations
Fernández-Méndez, Mikel; Mena Marugán, Guillermo A.; Olmedo, Javier; Velhinho, José M.
2012-05-01
We investigate the ambiguities in the Fock quantization of the scalar perturbations of a Friedmann-Lemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a three-sphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter-field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.
Regularization and computational methods for precise solution of perturbed orbit transfer problems
Woollands, Robyn Michele
The author has developed a suite of algorithms for solving the perturbed Lambert's problem in celestial mechanics. These algorithms have been implemented as a parallel computation tool that has broad applicability. This tool is composed of four component algorithms and each provides unique benefits for solving a particular type of orbit transfer problem. The first one utilizes a Keplerian solver (a-iteration) for solving the unperturbed Lambert's problem. This algorithm not only provides a "warm start" for solving the perturbed problem but is also used to identify which of several perturbed solvers is best suited for the job. The second algorithm solves the perturbed Lambert's problem using a variant of the modified Chebyshev-Picard iteration initial value solver that solves two-point boundary value problems. This method converges over about one third of an orbit and does not require a Newton-type shooting method and thus no state transition matrix needs to be computed. The third algorithm makes use of regularization of the differential equations through the Kustaanheimo-Stiefel transformation and extends the domain of convergence over which the modified Chebyshev-Picard iteration two-point boundary value solver will converge, from about one third of an orbit to almost a full orbit. This algorithm also does not require a Newton-type shooting method. The fourth algorithm uses the method of particular solutions and the modified Chebyshev-Picard iteration initial value solver to solve the perturbed two-impulse Lambert problem over multiple revolutions. The method of particular solutions is a shooting method but differs from the Newton-type shooting methods in that it does not require integration of the state transition matrix. The mathematical developments that underlie these four algorithms are derived in the chapters of this dissertation. For each of the algorithms, some orbit transfer test cases are included to provide insight on accuracy and efficiency of these
DEFF Research Database (Denmark)
Mackeprang, Kasper; Kjærgaard, Henrik Grum
2017-01-01
The local mode perturbation theory (LMPT) model was developed to improve the description of hydrogen bonded XH-stretching transitions, where X is typically O or N. We present a modified version of the LMPT model to extend its application from hydrated bimolecular complexes to hydrogen bonded...
Evolution of the curvature perturbations during warm inflation
International Nuclear Information System (INIS)
Matsuda, Tomohiro
2009-01-01
This paper considers warm inflation as an interesting application of multi-field inflation. Delta-N formalism is used for the calculation of the evolution of the curvature perturbations during warm inflation. Although the perturbations considered in this paper are decaying after the horizon exit, the corrections to the curvature perturbations sourced by these perturbations can remain and dominate the curvature perturbations at large scales. In addition to the typical evolution of the curvature perturbations, inhomogeneous diffusion rate is considered for warm inflation, which may lead to significant non-Gaussianity of the spectrum
Non-adiabatic perturbations in multi-component perfect fluids
Energy Technology Data Exchange (ETDEWEB)
Koshelev, N.A., E-mail: koshna71@inbox.ru [Ulyanovsk State University, Leo Tolstoy str 42, 432970 (Russian Federation)
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Non-adiabatic perturbations in multi-component perfect fluids
International Nuclear Information System (INIS)
Koshelev, N.A.
2011-01-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models
Perturbation Theory for Open Two-Level Nonlinear Quantum Systems
International Nuclear Information System (INIS)
Zhang Zhijie; Jiang Dongguang; Wang Wei
2011-01-01
Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)
Perturbative QCD and electromagnetic form factors
International Nuclear Information System (INIS)
Carlson, C.E.; Gross, F.
1987-01-01
We calculate nucleon magnetic form factors using perturbative QCD for several distribution amplitudes including a general one given in terms of Appell polynomials. We find that the magnitude and sign of both nucleon magnetic form factors can be explained within perturbative QCD. The observed normalization of G/sub Mp/ requires that the distribution amplitude be broader than its superhigh momentum transfer limit, and the G/sub Mn//G/sub Mp/ data may require the distribution amplitude to be asymmetric, in accord with distribution amplitudes derived from QCD sum rules. Some speculation as to how an asymmetric distribution amplitude can come about is offered. Finally, we show that the soft contributions corresponding to the particular distribution amplitudes we use need not be bigger than the data. 16 refs., 6 figs
Cosmological perturbations in transient phantom inflation scenarios
Energy Technology Data Exchange (ETDEWEB)
Richarte, Martin G. [Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba (Brazil); Universidad de Buenos Aires, Ciudad Universitaria 1428, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Kremer, Gilberto M. [Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba (Brazil)
2017-01-15
We present a model of inflation where the inflaton is accommodated as a phantom field which exhibits an initial transient pole behavior and then decays into a quintessence field which is responsible for a radiation era. We must stress that the present unified model only deals with a single field and that the transition between the two eras is achieved in a smooth way, so the model does not suffer from the eternal inflation issue. We explore the conditions for the crossing of the phantom divide line within the inflationary era along with the structural stability of several critical points. We study the behavior of the phantom field within the slow-climb approximation along with the necessary conditions to have sufficient inflation. We also examine the model at the level of classical perturbations within the Newtonian gauge and determine the behavior of the gravitational potential, contrast density and perturbed field near the inflation stage and the subsequent radiation era. (orig.)
Perturbative search for dead-end CFTs
International Nuclear Information System (INIS)
Nakayama, Yu
2015-01-01
To explore the possibility of self-organized criticality, we look for CFTs without any relevant scalar deformations (a.k.a. dead-end CFTs) within power-counting renormalizable quantum field theories with a weakly coupled Lagrangian description. In three dimensions, the only candidates are pure (Abelian) gauge theories, which may be further deformed by Chern-Simons terms. In four dimensions, we show that there are infinitely many non-trivial candidates based on chiral gauge theories. Using the three-loop beta functions, we compute the gap of scaling dimensions above the marginal value, and it can be as small as O(10"−"5) and robust against the perturbative corrections. These classes of candidates are very weakly coupled and our perturbative conclusion seems difficult to refute. Thus, the hypothesis that non-trivial dead-end CFTs do not exist is likely to be false in four dimensions.
Theory of cosmological perturbations with cuscuton
Energy Technology Data Exchange (ETDEWEB)
Boruah, Supranta S.; Kim, Hyung J.; Geshnizjani, Ghazal, E-mail: ssarmabo@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca, E-mail: ggeshniz@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo, 200 University Ave W., Waterloo, ON N2L 3G1 (Canada)
2017-07-01
This paper presents the first derivation of the quadratic action for curvature perturbations, ζ, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify ζ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potential development of other instabilities in cuscuton models. We find that in a large class of these models, there is no generic instability problem. However, depending on the details of slow-roll parameters, specific models may display gradient instabilities.
Perturbative Universality in Soft Particle Production
Khoze, V A; Ochs, Wolfgang; Khoze, Valery A.; Lupia, Sergio; Ochs, Wolfgang
1998-01-01
The spectrum of partons in a QCD jet becomes independent of the primary energy in the low momentum limit. This follows within the perturbative QCD from the colour coherence in soft gluon branching. Remarkably, the hadrons follow such behaviour closely, suggesting the parton hadron duality picture to be appropriate also for the low momentum particles. More generally, this scaling property holds for particles of low transverse and arbitrary longitudinal momentum, which explains an old experimental observation (``fan invariance''). Further tests of the perturbatively based picture for soft particle production are proposed for three-jet events in e+e- annihilation and di-jet production events in gamma p, gamma-gamma and p\\bar p collisions. They are based upon the difference in the intensity of the soft radiation from primary q\\bar q and gg antennae.
Small-sample-worth perturbation methods
International Nuclear Information System (INIS)
1985-01-01
It has been assumed that the perturbed region, R/sub p/, is large enough so that: (1) even without a great deal of biasing there is a substantial probability that an average source-neutron will enter it; and (2) once having entered, the neutron is likely to make several collisions in R/sub p/ during its lifetime. Unfortunately neither assumption is valid for the typical configurations one encounters in small-sample-worth experiments. In such experiments one measures the reactivity change which is induced when a very small void in a critical assembly is filled with a sample of some test-material. Only a minute fraction of the fission-source neutrons ever gets into the sample and, of those neutrons that do, most emerge uncollided. Monte Carlo small-sample perturbations computations are described
A primer for Chiral Perturbative Theory
International Nuclear Information System (INIS)
Scherer, Stefan; Schindler, Matthias R.; George Washington Univ., Washington, DC
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)
Infrared problems in field perturbation theory
International Nuclear Information System (INIS)
David, Francois.
1982-12-01
The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr
A non-perturbative operator product expansion
International Nuclear Information System (INIS)
Bietenholz, W.; Cundy, N.; Goeckeler, M.
2009-10-01
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of electromagnetic currents (with large photonmomenta) between quark states (of low momenta). By means of an Operator Product Expansion the structure function can be decomposed into matrix elements of local operators, and Wilson coefficients. For consistency both have to be computed non-perturbatively. Here we present precision results for a set of Wilson coefficients. They are evaluated from propagators for numerous quark momenta on the lattice, where the use of chiral fermions suppresses undesired operator mixing. This overdetermines the Wilson coefficients, but reliable results can be extracted by means of a Singular Value Decomposition. (orig.)
A primer for chiral perturbation theory
Scherer, Stefan
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.
Renormalization of the inflationary perturbations revisited
Markkanen, Tommi
2018-05-01
In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.
Nonderivative Modified Gravity: a Classification
Comelli, Denis; Pilo, Luigi
2014-01-01
We analyze the theories of gravity modified by a generic nonderivative potential built from the metric, under the minimal requirement of unbroken spatial rotations. Using the canonical analysis, we classify the potentials $V$ according to the number of degrees of freedom (DoF) that propagate at the nonperturbative level. We then compare the nonperturbative results with the perturbative DoF propagating around Minkowski and FRW backgrounds. A generic $V$ implies 6 propagating DoF at the non-perturbative level, with a ghost on Minkowski background. There exist potentials which propagate 5 DoF, as already studied in previous works. Here, no $V$ with unbroken rotational invariance admitting 4 DoF is found. Theories with 3 DoF turn out to be strongly coupled on Minkowski background. Finally, potentials with only the 2 DoF of a massive graviton exist. Their effect on cosmology is simply equivalent to a cosmological constant. Potentials with 2 or 5 DoF and explicit time dependence appear to be a further viable possib...
Perturbative and global anomalies in supergravity theories
International Nuclear Information System (INIS)
Sezgin, E.
1986-09-01
Perturbative and global anomalies in supergravity theories are reviewed. The existence of a matter and gauge coupled supergravity theory in six dimensions with E 6 xE 7 xU(1) symmetry and highly nontrivial anomaly cancellations is emphasised. The possible string origin of this theory is posed as an open problem, study of which may lead to discovery of new ways to construct/compactify heterotic superstrings. (author)
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Geometric perturbation theory and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Understanding Theoretical Uncertainties in Perturbative QCD Computations
DEFF Research Database (Denmark)
Jenniches, Laura Katharina
effective field theories and perturbative QCD to predict the effect of New Physics on measurements at the LHC and at other future colliders. We use heavy-quark, heavy-scalar and soft-collinear effective theory to calculate a three-body cascade decay at NLO QCD in the expansion-by-regions formalism...... discuss an extension of the Cacciari-Houdeau approach to observables with hadrons in the initial state....
Inclusive central region in perturbative Reggeon calculus
International Nuclear Information System (INIS)
Pajares, C.; Pascual, R.
1976-01-01
The single-particle inclusive cross section and the correlation function are studied in the perturbative approach to Gribov's Reggeon calculus; the leading contributions to both functions are evaluated. The large energy rise of the inclusive cross section appears as a consequence of the Pomerons having an intercept larger than 1. The same set of parameters which describes correctly the cross-section data and the triple-Regge region also describes the inclusive data in the central region
Word Embedding Perturbation for Sentence Classification
Zhang, Dongxu; Yang, Zhichao
2018-01-01
In this technique report, we aim to mitigate the overfitting problem of natural language by applying data augmentation methods. Specifically, we attempt several types of noise to perturb the input word embedding, such as Gaussian noise, Bernoulli noise, and adversarial noise, etc. We also apply several constraints on different types of noise. By implementing these proposed data augmentation methods, the baseline models can gain improvements on several sentence classification tasks.
Growth rate, population entropy, and perturbation theory.
Demetrius, L.
1989-01-01
This paper is concerned with the connection between two classes of population variables: measures of population growth rate—the Malthusian parameter, the net reproduction rate, the gross reproduction rate, and the mean life expectancy; and measures of demographic heterogeneity—population entropy. It is shown that the entropy functions predict the response of the growth rate parameters to perturbations in the age-specific fecundity and mortality schedule. These results are invoked to introduce...
Baryon form factors in chiral perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Kubis, B.; Meissner, U.G. [Forschungszentrum Juelich GmbH (Germany). Inst. fuer Kernphysik
2001-01-01
We analyze the electromagnetic form factors of the ground state baryon octet to fourth order in relativistic baryon chiral perturbation theory. Predictions for the {sigma}{sup -} charge radius and the {lambda}-{sigma}{sup 0} transition moment are found to be in excellent agreement with the available experimental information. Furthermore, the convergence behavior of the hyperon charge radii is shown to be more than satisfactory. (orig.)
Geometric perturbation theory and plasma physics
International Nuclear Information System (INIS)
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism
Capillary and viscous perturbations to Helmholtz flows
Moore, M. R.; Ockendon, H.; Ockendon, J. R.; Oliver, J. M.
2014-01-01
Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p.Â 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in steady Helmholtz flows. In particular, we identify the regimes in which appreciable vorticity can be shed from the boundary layer to the bulk flow. © 2014 Cambridge University Press.
Capillary and viscous perturbations to Helmholtz flows
Moore, M. R.
2014-02-21
Inspired by recent calculations by Thoraval et al. (Phys. Rev. Lett., vol. 108, 2012, p.Â 264506) relating to droplet impact, this paper presents an analysis of the perturbations to the free surface caused by small surface tension and viscosity in steady Helmholtz flows. In particular, we identify the regimes in which appreciable vorticity can be shed from the boundary layer to the bulk flow. © 2014 Cambridge University Press.
Recent progress on perturbative QCD fragmentation functions
International Nuclear Information System (INIS)
Cheung, K.
1995-05-01
The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize B c meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous J/ψ and ψ' production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons
Excitation and propagation of modified fluctuation in a toroidal plasma in KT-5C device
International Nuclear Information System (INIS)
Sun Xuan; Wang Zhijiang; Lu Ronghua; Wen Yizhi; Wan Shude; Yu Changxuan; Liu Wandong; Wang Cheng; Pan Gesheng; Wang Wenhao; Wang Jun
2002-01-01
Understanding the propagation of the turbulent perturbation in the tokamak edge plasma is an important issue to actively modify or control the turbulence, reduce the anomalous transport and improve plasma confinement. To realize active modification of the edge perturbation, a high dynamic output, broad-band, low-cost power amplifier is set up, and used to drive the active probes in the experiments on KT-5C Tokamak. By using small-size magnetic probes together with Langmiur probes. It is observed that the modified perturbation by the active probes with sufficiently driving power may spread with electrostatic mode, and electromagnetic mode as well
Inflationary perturbations in no-scale theories
Energy Technology Data Exchange (ETDEWEB)
Salvio, Alberto [CERN, Theoretical Physics Department, Geneva (Switzerland)
2017-04-15
We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index n{sub s} and the tensor-to-scalar ratio r. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantisation is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formulae are then applied to a concrete no-scale model, which includes the Higgs and a scalar, ''the planckion'', whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but it may be detectable with future experiments. (orig.)
Methods and applications of analytical perturbation theory
International Nuclear Information System (INIS)
Kirchgraber, U.; Stiefel, E.
1978-01-01
This monograph on perturbation theory is based on various courses and lectures held by the authors at the ETH, Zurich and at the University of Texas, Austin. Its principal intention is to inform application-minded mathematicians, physicists and engineers about recent developments in this field. The reader is not assumed to have mathematical knowledge beyond what is presented in standard courses on analysis and linear algebra. Chapter I treats the transformations of systems of differential equations and the integration of perturbed systems in a formal way. These tools are applied in Chapter II to celestial mechanics and to the theory of tops and gyroscopic motion. Chapter III is devoted to the discussion of Hamiltonian systems of differential equations and exposes the algebraic aspects of perturbation theory showing also the necessary modifications of the theory in case of singularities. The last chapter gives the mathematical justification for the methods developed in the previous chapters and investigates important questions such as error estimations for the solutions and asymptotic stability. Each chapter ends with useful comments and an extensive reference to the original literature. (HJ) [de
Non-perturbative materialization of ghosts
International Nuclear Information System (INIS)
Emparan, Roberto; Garriga, Jaume
2006-01-01
In theories with a hidden ghost sector that couples to visible matter through gravity only, empty space can decay into ghosts and ordinary matter by graviton exchange. Perturbatively, such processes can be very slow provided that the gravity sector violates Lorentz invariance above some cut-off scale. Here, we investigate non-perturbative decay processes involving ghosts, such as the spontaneous creation of self-gravitating lumps of ghost matter, as well as pairs of Bondi dipoles (i.e. lumps of ghost matter chasing after positive energy objects). We find the corresponding instantons and calculate their Euclidean action. In some cases, the instantons induce topology change or have negative Euclidean action. To shed some light on the meaning of such peculiarities, we also consider the nucleation of concentrical domain walls of ordinary and ghost matter, where the Euclidean calculation can be compared with the canonical (Lorentzian) description of tunneling. We conclude that non-perturbative ghost nucleation processes can be safely suppressed in phenomenological scenarios