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.
NASA Astrophysics Data System (ADS)
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Series Expansion of Functions with He's Homotopy Perturbation Method
ERIC Educational Resources Information Center
Khattri, Sanjay Kumar
2012-01-01
Finding a series expansion, such as Taylor series, of functions is an important mathematical concept with many applications. Homotopy perturbation method (HPM) is a new, easy to use and effective tool for solving a variety of mathematical problems. In this study, we present how to apply HPM to obtain a series expansion of functions. Consequently,…
Application of the Homotopy Perturbation Method to the Nonlinear Pendulum
ERIC Educational Resources Information Center
Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.
2007-01-01
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…
Optimal homotopy perturbation method for solving a nonlinear problem in elasticity
NASA Astrophysics Data System (ADS)
Ene, R.-D.; Marinca, V.; Cãruntu, B.
2012-09-01
In this paper we present an analytical method - the Optimal Homotopy Perturbation Method (OHPM), and we apply it to find approximate solutions for a nonlinear problem related to the stress and deformation states of a thin elastic plate. OHPM combines the features of the homotopy approach with an efficient computational algorithm which provides a convenient way to control the convergence of the approximation series. The comparison of the results obtained by OHPM with results obtained by numerical integration show a very good agreement proving the effectiveness and accuracy of the method.
NASA Astrophysics Data System (ADS)
Marinca, Vasile; Ene, Remus-Daniel
2017-01-01
In this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.
Homotopy Perturbation Method-Based Analytical Solution for Tide-Induced Groundwater Fluctuations.
Munusamy, Selva Balaji; Dhar, Anirban
2016-05-01
The groundwater variations in unconfined aquifers are governed by the nonlinear Boussinesq's equation. Analytical solution for groundwater fluctuations in coastal aquifers under tidal forcing can be solved using perturbation methods. However, the perturbation parameters should be properly selected and predefined for traditional perturbation methods. In this study, a new dimensional, higher-order analytical solution for groundwater fluctuations is proposed by using the homotopy perturbation method with a virtual perturbation parameter. Parameter-expansion method is used to remove the secular terms generated during the solution process. The solution does not require any predefined perturbation parameter and valid for higher values of amplitude parameter A/D, where A is the amplitude of the tide and D is the aquifer thickness.
On the Application of Homotopy Perturbation Method for Solving Systems of Linear Equations
Edalatpanah, S. A.; Rashidi, M. M.
2014-01-01
The application of homotopy perturbation method (HPM) for solving systems of linear equations is further discussed and focused on a method for choosing an auxiliary matrix to improve the rate of convergence. Moreover, solving of convection-diffusion equations has been developed by HPM and the convergence properties of the proposed method have been analyzed in detail; the obtained results are compared with some other methods in the frame of HPM. Numerical experiment shows a good improvement on the convergence rate and the efficiency of this method. PMID:27350974
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.
Homotopy perturbation method for free vibration analysis of beams on elastic foundation
NASA Astrophysics Data System (ADS)
Ozturk, Baki; Bozkurt Coskun, Safa; Zahid Koc, Mehmet; Tarik Atay, Mehmet
2010-06-01
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, Nr. 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.
Reck, Kasper; Thomsen, Erik V; Hansen, Ole
2011-01-31
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. 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.
Calculation of the neutron diffusion equation by using Homotopy Perturbation Method
NASA Astrophysics Data System (ADS)
Koklu, H.; Ersoy, A.; Gulecyuz, M. C.; Ozer, O.
2016-03-01
The distribution of the neutrons in a nuclear fuel element in the nuclear reactor core can be calculated by the neutron diffusion theory. It is the basic and the simplest approximation for the neutron flux function in the reactor core. In this study, the neutron flux function is obtained by the Homotopy Perturbation Method (HPM) that is a new and convenient method in recent years. One-group time-independent neutron diffusion equation is examined for the most solved geometrical reactor core of spherical, cubic and cylindrical shapes, in the frame of the HPM. It is observed that the HPM produces excellent results consistent with the existing literature.
Vazquez-Leal, H; Jimenez-Fernandez, V M; Benhammouda, B; Filobello-Nino, U; Sarmiento-Reyes, A; Ramirez-Pinero, A; Marin-Hernandez, A; Huerta-Chua, J
2014-01-01
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.
Vazquez-Leal, H.; Jimenez-Fernandez, V. M.; Benhammouda, B.; Filobello-Nino, U.; Sarmiento-Reyes, A.; Ramirez-Pinero, A.; Marin-Hernandez, A.; Huerta-Chua, J.
2014-01-01
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. PMID:25184157
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.
Global optimization using homotopy with 2-step predictor-corrector method
NASA Astrophysics Data System (ADS)
Chang, Kerk Lee; Ahmad, Rohanin Bt.
2014-06-01
In this research, we suggest a new method for solving global optimization problem by improving Homotopy Optimization with Perturbations and Ensembles (HOPE) method. Our new method, named as Homotopy 2-Step Predictor-corrector Method (HSPM) is based on the intermediate Value Theorem (IVT) coupled with modified Predictor-Corrector Halley method (PCH) for solving global optimization problem. HSPM does not require a good initial guess since it contains the element of homotopy, which is a globally convergent method. This paper discusses the time complexity of the new algorithm, which makes it more efficient than HOPE.
NASA Astrophysics Data System (ADS)
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\
Density perturbations in general modified gravitational theories
De Felice, Antonio; Tsujikawa, Shinji; Mukohyama, Shinji
2010-07-15
We derive the equations of linear cosmological perturbations for the general Lagrangian density f(R,{phi},X)/2+L{sub c}, where R is a Ricci scalar, {phi} is a scalar field, and X=-{partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}/}2 is a field kinetic energy. We take into account a nonlinear self-interaction term L{sub c}={xi}({phi}) {open_square}{phi}({partial_derivative}{sup {mu}{phi}{partial_derivative}}{sub {mu}{phi}}) recently studied in the context of ''Galileon'' cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasistatic approximation on subhorizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature; and thus it is convenient to test the viability of such models from both theoretical and observational points of view.
NASA Astrophysics Data System (ADS)
Abdel Wahab, N. H.; Salah, Ahmed
2015-05-01
In this paper, the interaction of a three-level -configration atom and a one-mode quantized electromagnetic cavity field has been studied. The detuning parameters, the Kerr nonlinearity and the arbitrary form of both the field and intensity-dependent atom-field coupling have been taken into account. The wave function when the atom and the field are initially prepared in the excited state and coherent state, respectively, by using the Schrödinger equation has been given. The analytical approximation solution of this model has been obtained by using the modified homotopy analysis method (MHAM). The homotopy analysis method is mentioned summarily. MHAM can be obtained from the homotopy analysis method (HAM) applied to Laplace, inverse Laplace transform and Pade approximate. MHAM is used to increase the accuracy and accelerate the convergence rate of truncated series solution obtained by the HAM. The time-dependent parameters of the anti-bunching of photons, the amplitude-squared squeezing and the coherent properties have been calculated. The influence of the detuning parameters, Kerr nonlinearity and photon number operator on the temporal behavior of these phenomena have been analyzed. We noticed that the considered system is sensitive to variations in the presence of these parameters.
Homotopy optimization methods for global optimization.
Dunlavy, Daniel M.; O'Leary, Dianne P. (University of Maryland, College Park, MD)
2005-12-01
We define a new method for global optimization, the Homotopy Optimization Method (HOM). This method differs from previous homotopy and continuation methods in that its aim is to find a minimizer for each of a set of values of the homotopy parameter, rather than to follow a path of minimizers. We define a second method, called HOPE, by allowing HOM to follow an ensemble of points obtained by perturbation of previous ones. We relate this new method to standard methods such as simulated annealing and show under what circumstances it is superior. We present results of extensive numerical experiments demonstrating performance of HOM and HOPE.
Modified contour-improved perturbation theory
Cvetic, Gorazd; Loewe, Marcelo; Martinez, Cristian; Valenzuela, Cristian
2010-11-01
The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard ''contour-improved'' method based on a derivative expansion of the Adler function. The new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the renormalization scheme dependence remains approximately equal. The extracted QCD coupling at the tau mass scale is by 2% lower than the contour-improved value. We find {alpha}{sub s}(M{sub Z}{sup 2})=0.1211{+-}0.0010.
Analysis of seismo-ionospheric perturbations using modified covariance algorithm
NASA Astrophysics Data System (ADS)
Revathi, R.; Lakshminarayana, S.; Koteswara Rao, S.; Ramesh, K. S.; Kiran, K. Uday
2016-05-01
Earthquakes are the most vulnerable disasters in nature and are inevitable. Electromagnetic detection of earthquakes using Global Positioning System (GPS) has lead to better understanding of our planet earth and related atmospheric systems. In the present work an attempt is made to analyze seismo-ionospheric perturbations for an earthquake which has occurred in Indonesia on 15th January 2014 with a magnitude of 4.5 on Richter scale. Modified covariance algorithm is applied on the GPS vertical total electron content data taken from the International Global Navigation Satellite System Service station named BAKO It is clearly observed that there is an enhancement of energy in the ionosphere for every 15 minutes from the starting of perturbations.
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
HOPE: a homotopy optimization method for protein structure prediction.
Dunlavy, Daniel M; O'Leary, Dianne P; Klimov, Dmitri; Thirumalai, D
2005-12-01
We use a homotopy optimization method, HOPE, to minimize the potential energy associated with a protein model. The method uses the minimum energy conformation of one protein as a template to predict the lowest energy structure of a query sequence. This objective is achieved by following a path of conformations determined by a homotopy between the potential energy functions for the two proteins. Ensembles of solutions are produced by perturbing conformations along the path, increasing the likelihood of predicting correct structures. Successful results are presented for pairs of homologous proteins, where HOPE is compared to a variant of Newton's method and to simulated annealing.
Noncommutative geometry modified non-Gaussianities of cosmological perturbation
Fang Kejie; Xue Wei; Chen Bin
2008-03-15
We investigate the noncommutative effect on the non-Gaussianities of primordial cosmological perturbation. In the lowest order of string length and slow-roll parameter, we find that in the models with small speed of sound the noncommutative modifications could be observable if assuming a relatively low string scale. In particular, the dominant modification of the non-Gaussianity estimator f{sub NL} could reach O(1) in Dirac-Born-Infeld (DBI) inflation and K-inflation. The corrections are sensitive to the speed of sound and the choice of string length scale. Moreover the shapes of the corrected non-Gaussianities are distinct from that of ordinary ones.
Asymptotic invariants of homotopy groups
NASA Astrophysics Data System (ADS)
Manin, Fedor
We study the homotopy groups of a finite CW complex X via constraints on the geometry of representatives of their elements. For example, one can measure the "size" of alpha ∈ pi n (X) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in pin(X), analogously to the way that such functions are studied in asymptotic geometric group theory. We provide a number of examples and techniques for studying these invariants, with a special focus on spaces with few rational homotopy groups. Our main theorem characterizes those X in which all non-torsion homotopy classes are undistorted, that is, their volume distortion functions, and hence also their Lipschitz distortion functions, are linear.
Effective action approach to cosmological perturbations in dark energy and modified gravity
Battye, Richard A.; Pearson, Jonathan A. E-mail: jp@jb.man.ac.uk
2012-07-01
In light of upcoming observations modelling perturbations in dark energy and modified gravity models has become an important topic of research. We develop an effective action to construct the components of the perturbed dark energy momentum tensor which appears in the perturbed generalized gravitational field equations, δG{sup μν} = 8πGδT{sup μν}+δU{sup μν} for linearized perturbations. Our method does not require knowledge of the Lagrangian density of the dark sector to be provided, only its field content. The method is based on the fact that it is only necessary to specify the perturbed Lagrangian to quadratic order and couples this with the assumption of global statistical isotropy of spatial sections to show that the model can be specified completely in terms of a finite number of background dependent functions. We present our formalism in a coordinate independent fashion and provide explicit formulae for the perturbed conservation equation and the components of δU{sup μ}{sub ν} for two explicit generic examples: (i) the dark sector does not contain extra fields, L = L(g{sub μν}) and (ii) the dark sector contains a scalar field and its first derivative L = L(g{sub μν},φ,∇{sub μ}φ). We discuss how the formalism can be applied to modified gravity models containing derivatives of the metric, curvature tensors, higher derivatives of the scalar fields and vector fields.
Homotopy theory in toric topology
NASA Astrophysics Data System (ADS)
Grbić, J.; Theriault, S.
2016-04-01
In toric topology one associates with each simplicial complex K on m vertices two key spaces, the Davis-Januszkiewicz space DJK and the moment-angle complex \\mathscr{Z}K, which are related by a homotopy fibration \\mathscr{Z}K\\xrightarrow{\\tilde{w}}DJ_K\\to \\prodi=1m{C}P∞. A great deal of work has been done to study the properties of DJK and \\mathscr{Z}K, their generalizations to polyhedral products, and applications to algebra, combinatorics, and geometry. Chap. 1 surveys some of the main results in the homotopy theory of these spaces. Chap. 2 breaks new ground by initiating a study of the map \\tilde{w}. It is shown that, for a certain family of simplicial complexes K, the map \\tilde{w} is a sum of higher and iterated Whitehead products. Bibliography: 49 titles.
NASA Astrophysics Data System (ADS)
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
Comparative study of homotopy continuation methods for nonlinear algebraic equations
NASA Astrophysics Data System (ADS)
Nor, Hafizudin Mohamad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd.
2014-07-01
We compare some recent homotopy continuation methods to see which method has greater applicability and greater accuracy. We test the methods on systems of nonlinear algebraic equations. The results obtained indicate the superior accuracy of Newton Homotopy Continuation Method (NHCM).
Regular homotopy for immersions of graphs into surfaces
NASA Astrophysics Data System (ADS)
Permyakov, D. A.
2016-06-01
We study invariants of regular immersions of graphs into surfaces up to regular homotopy. The concept of the winding number is used to introduce a new simple combinatorial invariant of regular homotopy. Bibliography: 20 titles.
Magnetic Soliton, Homotopy and Higgs Theory,
1986-04-24
OD-AL67 366 NAGETIC SOLITON ONOTOPY ND HIGGS THEORY(U) FOREIGNI n1/ 1TECHNOLOGY D V NRIGHT-PATTERSON AFD ON Y LI ET AL. UNCLSSIIED24 APR 86 FTD-ID...MAGNETIC SOLITON, HOMOTOPY AND HIGGS THEORY by Li Yuanjie and Lei Shizu *. . * . .%..**% . . .-..C./ ~~~Approved for public release; -," Distribution...HOMOTOPY AND HIGGS THEORY By: Li Yuanjie and Lei Shizu English pages: 9 Source: Huazhong Gongxueyuan Xuebao, Vol. 11, Nr. 6, 1983, pp. 65-70 Country of
Hong, Baojian; Lu, Dianchen
2014-01-01
Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of the GFNLS are investigated. Furthermore, the approximate iterative series and numerical results show that the modified fractional variational iteration method is powerful, reliable, and effective when compared with some classic traditional methods such as homotopy analysis method, homotopy perturbation method, adomian decomposition method, and variational iteration method in searching for approximate solutions of the Schrödinger equations.
Power System Transient Stability Analysis through a Homotopy Analysis Method
Wang, Shaobu; Du, Pengwei; Zhou, Ning
2014-04-01
As an important function of energy management systems (EMSs), online contingency analysis plays an important role in providing power system security warnings of instability. At present, N-1 contingency analysis still relies on time-consuming numerical integration. To save computational cost, the paper proposes a quasi-analytical method to evaluate transient stability through time domain periodic solutions’ frequency sensitivities against initial values. First, dynamic systems described in classical models are modified into damping free systems whose solutions are either periodic or expanded (non-convergent). Second, because the sensitivities experience sharp changes when periodic solutions vanish and turn into expanded solutions, transient stability is assessed using the sensitivity. Third, homotopy analysis is introduced to extract frequency information and evaluate the sensitivities only from initial values so that time consuming numerical integration is avoided. Finally, a simple case is presented to demonstrate application of the proposed method, and simulation results show that the proposed method is promising.
Kobayashi, Tsutomu; Suzuki, Daichi; Tashiro, Hiroyuki
2010-03-15
A scalar-tensor theory of gravity can be made not only to account for the current cosmic acceleration, but also to satisfy solar-system and laboratory constraints, by introducing a nonlinear derivative interaction for the scalar field. Such an additional scalar degree of freedom is called 'Galileon'. The basic idea is inspired by the Dvali-Gabadadze-Porrati braneworld, but one can construct a ghost-free model that admits a self-accelerating solution. We perform a fully relativistic analysis of linear perturbations in Galileon cosmology. Although the Galileon model can mimic the background evolution of standard {Lambda}CDM cosmology, the behavior of perturbation is quite different. It is shown that there exists a superhorizon growing mode in the metric and Galileon perturbations at early times, suggesting that the background is unstable. A fine-tuning of the initial condition for the Galileon fluctuation is thus required in order to promote a desirable evolution of perturbations at early times. Assuming the safe initial condition, we then compute the late-time evolution of perturbations and discuss observational implications in Galileon cosmology. In particular, we find anticorrelations in the cross correlation of the integrated Sachs-Wolfe effect and large scale structure, similar to the normal branch of the Dvali-Gabadadze-Porrati model.
Probability-one homotopies in computational science
NASA Astrophysics Data System (ADS)
Watson, Layne T.
2002-03-01
Probability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that, under mild assumptions, are globally convergent for a wide range of problems in science and engineering. Convergence theory, robust numerical algorithms, and production quality mathematical software exist for general nonlinear systems of equations, and special cases such as Brouwer fixed point problems, polynomial systems, and nonlinear constrained optimization. Using a sample of challenging scientific problems as motivation, some pertinent homotopy theory and algorithms are presented. The problems considered are analog circuit simulation (for nonlinear systems), reconfigurable space trusses (for polynomial systems), and fuel-optimal orbital rendezvous (for nonlinear constrained optimization). The mathematical software packages HOMPACK90 and POLSYS_PLP are also briefly described.
Mochizuki, George; Boe, Shaun G; Marlin, Amanda; McIlroy, William E
2017-02-16
Preparation for postural instability engages cortical resources that serve to optimize compensatory balance responses. Engagement of these cortical resources in cognitive dual-task activities may impact the ability to appropriately prepare and optimize responses to instability. The purpose of this study was to determine whether cognitive dual-task activities influenced cortical activity preceding and following postural instability. Postural instability was induced using a lean-and-release paradigm in 10 healthy participants. Perturbations were either temporally predictable (PRED) or unpredictable (UNPRED) and presented with (COG) or without a cognitive dual-task, presented in blocks of trials. The electroencephalogram was recorded from multiple frontal electrode sites. EEG data were averaged over 25-35 trials across conditions. Area under the curve of pre-perturbation cortical activity and peak latency and amplitude of post-perturbation cortical activity were quantified at the Cz site and compared across conditions. Performance of the concurrent cognitive task reduced the mean (SE) magnitude of pre-perturbation cortical activity in advance of predictable bouts of postural instability (PRED: 18.7(3.0)mVms; PRED-COG; 14.0(2.3)mVms). While the level of cognitive load influenced the amplitude of the post-perturbation N1 potential in the predictable conditions, there were no changes in N1 with a cognitive dual task during unpredictable conditions (PRED: -32.1(3.2)µV; PRED-COG: -50.8(8.4)µV; UNPRED: -65.0(12.2)µV; UNPRED-COG: -64.2(12.7)µV). Performance of the cognitive task delayed and reduced the magnitude of the initial gastrocnemius response. The findings indicate that pre- and post-perturbation cortical activity is affected by a cognitive distractor when postural instability is temporally predictable. Distraction also influences associated muscle responses.
NASA Astrophysics Data System (ADS)
Pramod Chakravarthy, P.; Nageshwar Rao, R.
2012-01-01
In this paper a modified fourth order Numerov method is presented for singularly perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having positive shift. Similar boundary value problems are associated with expected first exit time problems of the membrane potential in the models for the neuron. To handle the negative and positive shift terms, we construct a special type of mesh, so that the terms containing shift lie on nodal points after discretization. The proposed finite difference method works nicely when the shift parameters are smaller or bigger to perturbation parameter. An extensive amount of computational work has been carried out to demonstrate the proposed method and to show the effect of shift parameters on the boundary layer behavior or oscillatory behavior of the solution of the problem.
Co-contraction modifies the stretch reflex elicited in muscles shortened by a joint perturbation
Lewis, Gwyn N.; MacKinnon, Colum D.; Trumbower, Randy; Perreault, Eric J.
2011-01-01
Simultaneous contraction of agonist and antagonist muscles acting about a joint influences joint stiffness and stability. Although several studies have shown that reflexes in the muscle lengthened by a joint perturbation are modulated during co-contraction, little attention has been given to reflex regulation in the antagonist (shortened) muscle. The goal of the present study was to determine whether co-contraction gives rise to altered reflex regulation across the joint by examining reflexes in the muscle shortened by a joint perturbation. Reflexes were recorded from electromyographic activity in elbow flexors and extensors while positional perturbations to the elbow joint were applied. Perturbations were delivered during isolated activation of the flexor or extensor muscles as well as during flexor and extensor co-contraction. Across the group, the shortening reflex in the elbow extensor switched from suppression during isolated extensor muscle activation to facilitation during co-contraction. The shortening reflex in the elbow flexor remained suppressive during co-contraction but was significantly smaller compared to the response obtained during isolated elbow flexor activation. This response in the shortened muscle was graded by the level of activation in the lengthened muscle. The lengthening reflex did not change during co-contraction. These results support the idea that reflexes are regulated across multiple muscles around a joint. We speculate that the facilitatory response in the shortened muscle arises through a fast-conducting oligosynaptic pathway involving Ib interneurons. PMID:20878148
Co-contraction modifies the stretch reflex elicited in muscles shortened by a joint perturbation.
Lewis, Gwyn N; MacKinnon, Colum D; Trumbower, Randy; Perreault, Eric J
2010-11-01
Simultaneous contraction of agonist and antagonist muscles acting about a joint influences joint stiffness and stability. Although several studies have shown that reflexes in the muscle lengthened by a joint perturbation are modulated during co-contraction, little attention has been given to reflex regulation in the antagonist (shortened) muscle. The goal of the present study was to determine whether co-contraction gives rise to altered reflex regulation across the joint by examining reflexes in the muscle shortened by a joint perturbation. Reflexes were recorded from electromyographic activity in elbow flexors and extensors while positional perturbations to the elbow joint were applied. Perturbations were delivered during isolated activation of the flexor or extensor muscles as well as during flexor and extensor co-contraction. Across the group, the shortening reflex in the elbow extensor switched from suppression during isolated extensor muscle activation to facilitation during co-contraction. The shortening reflex in the elbow flexor remained suppressive during co-contraction but was significantly smaller compared to the response obtained during isolated elbow flexor activation. This response in the shortened muscle was graded by the level of activation in the lengthened muscle. The lengthening reflex did not change during co-contraction. These results support the idea that reflexes are regulated across multiple muscles around a joint. We speculate that the facilitatory response in the shortened muscle arises through a fast-conducting oligosynaptic pathway involving Ib interneurons.
Wang, Hong; Wang, Xi-cheng
2014-02-21
Metabolism is a very important cellular process and its malfunction contributes to human disease. Therefore, building dynamic models for metabolic networks with experimental data in order to analyze biological process rationally has attracted a lot of attention. Owing to the technical limitations, some unknown parameters contained in models need to be estimated effectively by means of the computational method. Generally, problems of parameter estimation of nonlinear biological network are known to be ill condition and multimodal. In particular, with the increasing amount and enlarging the scope of parameters, many optimization algorithms often fail to find a global solution. In this paper, two-stage variable factor Bregman regularization homotopy method is proposed. Discrete homotopy is used to identify the possible extreme region and continuous homotopy is executed for the purpose of stability of path tracing in the special region. Meanwhile, Latin hypercube sampling is introduced to get the good initial guess value and a perturbation strategy is developed to jump out of the local optimum. Three metabolic network inverse problems are investigated to demonstrate the effectiveness of the proposed method.
NASA Astrophysics Data System (ADS)
Chattopadhyay, Surajit
In this work, we investigate the cosmological application of modified Chaplygin gas (MCG) interacting with pressureless dark matter (DM) in the f(T) modified gravity framework, where T is the torsion scalar in teleparallelism. The interaction term has been chosen proportional to the MCG density with positive coupling constant. In the Einstein general relativity (GR) framework, the interacting MCG has been found to have equation of state (EoS) parameter behaving like quintessence. However, the f(T) gravity reconstructed via the interacting MCG has been found to have EoS crossing the phantom boundary of ‑ 1. Thus, one can generate a quintom-like EoS from an interacting MCG model in flat universe in the modified gravity cosmology framework. The reconstructed f(T) model has been found to interpolate between dust and ΛCDM. Stability of the reconstructed f(T) has been investigated and it has been observed that the model is stable against gravitational perturbation. Cosmological evolution of primordial perturbations has also been investigated and the self-interacting potential has been found to increase with cosmic time and the squared speed of sound has been found to be non-negative.
Perturbative analysis in higher-spin theories
NASA Astrophysics Data System (ADS)
Didenko, V. E.; Misuna, N. G.; Vasiliev, M. A.
2016-07-01
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 higherspin 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.
NASA Astrophysics Data System (ADS)
Jain, Shekhar; Dominik, Aleksandra; Chapman, Walter G.
2007-12-01
A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.
ECE imaging of modified edge localized modes (ELMs) under n=1 magnetic perturbations in KSTAR
NASA Astrophysics Data System (ADS)
Lee, Jaehyun; Yun, G. S.; Kim, M.; Choi, M. J.; Lee, W.; Park, H. K.; Lee, J. H.; Jeon, Y. M.; Domier, C. W.; Luhmann, N. C., Jr.; Donné, A. J. H.
2012-10-01
In order to control the ELMs in KSTAR H-mode plasmas, magnetic perturbations (MPs) of toroidal mode number n=1 were introduced through three sets of field error correction (FEC) coils [1] during the 2011 campaign. The plasma response was studied in 2-D using electron cyclotron emission imaging (ECEI) diagnostic [2], which showed alteration of both the spatial structure and temporal dynamics of the ELMs. The characteristics of the ELMs such as the growth rate, filament size, and poloidal flow are compared before and after the n=1 MP for various configurations of the FEC coil currents. In particular, the ELM suppression by resonant MP condition is characterized by occasional (non-periodic) tiny transport events, which involve the appearance and crash of transient filament structure localized near the separatrix.[4pt] [1] Y. Jeon et al., accepted for publication in Phys. Rev. Lett.[0pt] [2] G.S. Yun et al., Phys. Rev. Lett., 107, 045004 (2011).
Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling
NASA Astrophysics Data System (ADS)
Arsenault, Louis-François; Sémon, Patrick; Tremblay, A.-M. S.
2012-08-01
The dynamical mean-field theory approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of noninteracting electrons. Iterated perturbation theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact continuous-time quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-D. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy, and specific heat on the fcc lattice are calculated with both IPT-D and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-D. Particle-hole asymmetry persists even at coupling twice the bandwidth. A generalization to the multiorbital case is suggested. Several algorithms that speed up the calculations are described in appendixes.
Efficient Homotopy Continuation Algorithms with Application to Computational Fluid Dynamics
NASA Astrophysics Data System (ADS)
Brown, David A.
New homotopy continuation algorithms are developed and applied to a parallel implicit finite-difference Newton-Krylov-Schur external aerodynamic flow solver for the compressible Euler, Navier-Stokes, and Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras one-equation turbulence model. Many new analysis tools, calculations, and numerical algorithms are presented for the study and design of efficient and robust homotopy continuation algorithms applicable to solving very large and sparse nonlinear systems of equations. Several specific homotopies are presented and studied and a methodology is presented for assessing the suitability of specific homotopies for homotopy continuation. . A new class of homotopy continuation algorithms, referred to as monolithic homotopy continuation algorithms, is developed. These algorithms differ from classical predictor-corrector algorithms by combining the predictor and corrector stages into a single update, significantly reducing the amount of computation and avoiding wasted computational effort resulting from over-solving in the corrector phase. The new algorithms are also simpler from a user perspective, with fewer input parameters, which also improves the user's ability to choose effective parameters on the first flow solve attempt. Conditional convergence is proved analytically and studied numerically for the new algorithms. The performance of a fully-implicit monolithic homotopy continuation algorithm is evaluated for several inviscid, laminar, and turbulent flows over NACA 0012 airfoils and ONERA M6 wings. The monolithic algorithm is demonstrated to be more efficient than the predictor-corrector algorithm for all applications investigated. It is also demonstrated to be more efficient than the widely-used pseudo-transient continuation algorithm for all inviscid and laminar cases investigated, and good performance scaling with grid refinement is demonstrated for the inviscid cases. Performance is also demonstrated
NASA Astrophysics Data System (ADS)
Belolipetskii, A. A.; Ter-Krikorov, A. M.
2016-11-01
The functional equation f( x,ɛ) = 0 containing a small parameter ɛ and admitting regular and singular degeneracy as ɛ → 0 is considered. By the methods of small parameter, a function x n 0(ɛ) satisfying this equation within a residual error of O(ɛ n+1) is found. A modified Newton's sequence starting from the element x n 0(ɛ) is constructed. The existence of the limit of Newton's sequence is based on the NK theorem proven in this work (a new variant of the proof of the Kantorovich theorem substantiating the convergence of Newton's iterative sequence). The deviation of the limit of Newton's sequence from the initial approximation x n 0(ɛ) has the order of O(ɛ n+1), which proves the asymptotic character of the approximation x n 0(ɛ). The method proposed is implemented in constructing an asymptotic approximation of a system of ordinary differential equations on a finite or infinite time interval with a small parameter multiplying the derivatives, but it can be applied to a wider class of functional equations with a small parameters.
Homotopy Algorithm for Optimal Control Problems with a Second-order State Constraint
Hermant, Audrey
2010-02-15
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.
An SN Application of Homotopy Continuation in Neutral Particle Transport
NASA Astrophysics Data System (ADS)
Myers, Nicholas T.
The objective of this dissertation is to investigate the usefulness of homotopy continuation applied in the context of neutral particle transport where traditional methods of acceleration degrade. This occurs in higher dimensional heterogeneous problems. We focus on utilizing homotopy continuation as a means of providing a better initial guess for difficult problems. We investigate various homotopy formulations for two primary difficult problems: a thick-diffusive fixed internal source, and a k-eigenvalue problem with high dominance ratio. We also investigate the usefulness of homotopy continuation for computationally intensive problems with 30-energy groups. We find that homotopy continuation exhibits usefulness in specific problem formulations. In the thick-diffusive problem it shows benefit when there is a strong internal source in thin materials. In the k-eigenvalue problem, homotopy continuation provides an improvement in convergence speed for fixed point iteration methods in high dominance ratio problems. We also show that one of our imbeddings successfully stabilizes the nonlinear formulation of the k-eigenvalue problem with a high dominance ratio.
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.
A Choice Reaction Time Index of Callosal Anatomical Homotopy
ERIC Educational Resources Information Center
Desjardins, Sameul; Braun, Claude M. J.; Achim, Andre; Roberge, Carl
2009-01-01
Tachistoscopically presented bilateral stimulus pairs not parallel to the meridian produced significantly longer RTs on a task requiring discrimination of shapes (Go/no-Go) than pairs emplaced symmetrically on each side of the meridian in Desjardins and Braun [Desjardins, S., & Braun, C. M. J. (2006). Homotopy and heterotopy and the bilateral…
2012-09-03
use of so-called probability-one methods [22]. The significant advantage of homotopy method to compute steady state solutions is free of Courant ...A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws Wenrui Hao∗ Jonathan D. Hauenstein† Chi...robustness of the new method . Keywords homotopy continuation, hyperbolic conservation laws, WENO scheme, steady state problems. ∗Department of Applied and
Splitting a simple homotopy equivalence along a submanifold with filtration
Bak, A; Muranov, Yu V
2008-06-30
A simple homotopy equivalence f:M{sup n}{yields}X{sup n} of manifolds splits along a submanifold Y subset of X if it is homotopic to a map that is a simple homotopy equivalence on the transversal preimage of the submanifold and on the complement of this preimage. The problem of splitting along a submanifold with filtration is a natural generalization of this problem. In this paper we define groups LSF{sub *} of obstructions to splitting along a submanifold with filtration and describe their properties. We apply the results obtained to the problem of the realization of surgery and splitting obstructions by maps of closed manifolds and consider several examples. Bibliography: 36 titles.
NASA Technical Reports Server (NTRS)
Stokan, E.; Campbell-Brown, M. D.
2011-01-01
This is a preliminary investigation of how perturbations to meteoroid shape or atmospheric density affect a meteor light curve. A simple equation of motion and ablation are simultaneously solved numerically to give emitted light intensity as a function of height. It is found that changing the meteoroid shape, by changing the relationship between the cross-section area and the mass, changes the curvature and symmetry of the light curve, while making a periodic oscillation in atmospheric density gives a small periodic oscillation in the light curve.
Yi, Xia; de Vries, Hilda I.; 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.
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 accumulation of this type of DNA damage that coincides with hampered DNA synthesis. Here, we report the identification of stonewall (stwl) as a novel hydroxyurea-hypersensitive mutant. We demonstrate that Stwl is required to prevent accumulation of DNA damage induced by hydroxyurea; yet, Stwl is not involved in S/M checkpoint regulation. We show that Stwl is a heterochromatin-associated protein with transcription-repressing capacities. In stwl mutants, levels of trimethylated H3K27 and H3K9 (two hallmarks of silent chromatin) are decreased. Our data provide evidence for a Stwl-dependent epigenetic mechanism that is involved in the maintenance of the normal balance between euchromatin and heterochromatin and that is required to prevent accumulation of DNA damage in the presence of DNA replication stress. PMID:19056684
NASA Astrophysics Data System (ADS)
Arsenault, Louis-François; Sémon, Patrick; Shastry, B. Sriram; Tremblay, A.-M. S.
2012-02-01
The Dynamical Mean-Field theory(DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory(IPT)[1] has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC)[2], here we show that the standard implementation of IPT fails when the interaction is much larger than the bandwidth. We propose a slight modification to the IPT algorithm by requiring that double occupancy calculated with IPT gives the correct value. We call this method IPT-D. We show how this approximate impurity solver compares with respect to CTQMC. We consider a face centered cubic lattice(FCC) in 3d for different physical properties. We also use IPT-D to study the thermopower using two recently proposed approximations[3]S^* and SKelvin that do not require analytical continuation and show how thermopower is essentially the entropy per particle in the incoherent regime but not in the coherent one.[1]H.Kajueter et al. Phys. Rev. Lett. 77, 131(1996)[2]P. Werner, et al. Phys. Rev. Lett. 97, 076405(2006)[3]B.S. Sriram Shastry Rep. Prog. Phys. 72 016501(2009)
Wen, Xiao-Yong; Yang, Yunqing; Yan, Zhenya
2015-07-01
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation (1,N-1)-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.
Wave propagation in nonlinear metamaterial multi-atomic chains based on homotopy method
NASA Astrophysics Data System (ADS)
Fang, Xin; Wen, Jihong; Yin, Jianfei; Yu, Dianlong
2016-12-01
This paper studies the dispersion properties and wave propagation in the tetratomic nonlinear acoustic metamaterial chain based on the homotopy analysis method (HAM). We perform a comparison between HAM and Perturbation approach, harmonic balance method (HBM) and equivalent method. Results indicate that HAM can filter the unstable multiple periodic solutions fined by HBM and be more accurate. The succinct equivalent formulas can estimate the bandgaps. There is a limit of the dispersion solution when the nonlinearity tends to infinity. Analyses demonstrate that the energy dispersion in spectrum replaces the linear energy localization because of the hyperchaos that is induced by period-doubling bifurcations. The hyper-chaotic phenomena are demonstrated with frequency spectra, bifurcation diagram and Lyapunov Exponents. This paper further proves the chaotic bands can significantly expand the bandwidth for wave suppression. Enhancing the nonlinearity will vary the behavior of nonlinear bandgaps from independent state to coupling state and then experience a transition. Approaches to manipulate bands are elucidated. The strong nonlinearity is beneficial to expand the total width about 6 times. Moreover, lightweight, low-frequency and broadband characteristics are compatible so can be achieved simultaneously for nonlinear acoustic metamaterial.
Sparse diffraction imaging method using an adaptive reweighting homotopy algorithm
NASA Astrophysics Data System (ADS)
Yu, Caixia; Zhao, Jingtao; Wang, Yanfei; Qiu, Zhen
2017-02-01
Seismic diffractions carry valuable information from subsurface small-scale geologic discontinuities, such as faults, cavities and other features associated with hydrocarbon reservoirs. However, seismic imaging methods mainly use reflection theory for constructing imaging models, which means a smooth constraint on imaging conditions. In fact, diffractors occupy a small account of distributions in an imaging model and possess discontinuous characteristics. In mathematics, this kind of phenomena can be described by the sparse optimization theory. Therefore, we propose a diffraction imaging method based on a sparsity-constraint model for studying diffractors. A reweighted L 2-norm and L 1-norm minimization model is investigated, where the L 2 term requests a least-square error between modeled diffractions and observed diffractions and the L 1 term imposes sparsity on the solution. In order to efficiently solve this model, we use an adaptive reweighting homotopy algorithm that updates the solutions by tracking a path along inexpensive homotopy steps. Numerical examples and field data application demonstrate the feasibility of the proposed method and show its significance for detecting small-scale discontinuities in a seismic section. The proposed method has an advantage in improving the focusing ability of diffractions and reducing the migration artifacts.
Homotopy method for inverse design of the bulbous bow of a container ship
NASA Astrophysics Data System (ADS)
Huang, Yu-jia; Feng, Bai-wei; Hou, Guo-xiang; Gao, Liang; Xiao, Mi
2017-03-01
The homotopy method is utilized in the present inverse hull design problem to minimize the wave-making coefficient of a 1300 TEU container ship with a bulbous bow. Moreover, in order to improve the computational efficiency of the algorithm, a properly smooth function is employed to update the homotopy parameter during iteration. Numerical results show that the homotopy method has been successfully applied in the inverse design of the ship hull. This method has an advantage of high performance on convergence and it is credible and valuable for engineering practice.
Stability of gradient semigroups under perturbations
NASA Astrophysics Data System (ADS)
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).
The order of a homotopy invariant in the stable case
NASA Astrophysics Data System (ADS)
Podkorytov, Semen S.
2011-08-01
Let X, Y be cell complexes, let U be an Abelian group, and let f\\colon \\lbrack X,Y \\rbrack \\to U be a homotopy invariant. By definition, the invariant f has order at most r if the characteristic function of the rth Cartesian power of the graph of a continuous map a\\colon X\\to Y determines the value f( \\lbrack a \\rbrack ) {Z}-linearly. It is proved that, in the stable case (that is, when \\operatorname{dim} X<2n-1, and Y is (n-1)-connected for some natural number n), for a finite cell complex X the order of the invariant f is equal to its degree with respect to the Curtis filtration of the group \\lbrack X,Y \\rbrack . Bibliography: 9 titles.
Demján, Tamás; Vörös, Márton; Palummo, Maurizia; Gali, Adam
2014-08-14
Diamondoids are small diamond nanoparticles (NPs) that are built up from diamond cages. Unlike usual semiconductor NPs, their atomic structure is exactly known, thus they are ideal test-beds for benchmarking quantum chemical calculations. Their usage in spintronics and bioimaging applications requires a detailed knowledge of their electronic structure and optical properties. In this paper, we apply density functional theory (DFT) based methods to understand the electronic and optical properties of a few selected pure and modified diamondoids for which accurate experimental data exist. In particular, we use many-body perturbation theory methods, in the G{sub 0}W{sub 0} and G{sub 0}W{sub 0}+BSE approximations, and time-dependent DFT in the adiabatic local density approximation. We find large quasiparticle gap corrections that can exceed thrice the DFT gap. The electron-hole binding energy can be as large as 4 eV but it is considerably smaller than the GW corrections and thus G{sub 0}W{sub 0}+BSE optical gaps are about 50% larger than the Kohn-Sham (KS) DFT gaps. We find significant differences between KS time-dependent DFT and GW+BSE optical spectra on the selected diamondoids. The calculated G{sub 0}W{sub 0} quasiparticle levels agree well with the corresponding experimental vertical ionization energies. We show that nuclei dynamics in the ionization process can be significant and its contribution may reach about 0.5 eV in the adiabatic ionization energies.
Mahowaldean families of elements in stable homotopy groups revisited
NASA Astrophysics Data System (ADS)
Hunter, David J.; Kuhn, Nicholas J.
1999-09-01
In the mid 1970s Mark Mahowald constructed a new infinite family of elements in the 2-component of the stable homotopy groups of spheres, [eta]j[set membership][pi]Sj2 (S0)(2) [M]. Using standard Adams spectral sequence terminology (which will be recalled in Section 3 below), [eta]j is detected by h1hj[set membership]Ext2,*[script A] (Z/2, Z/2). Thus he had found an infinite family of elements all having the same Adams filtration (in this case, 2), thus dooming the so-called Doomsday Conjecture. His constructions were ingenious: his elements were constructed as composites of pairs of maps, with the intermediate spaces having, on one hand, a geometric origin coming from double loopspace theory and, on the other hand, mod2 cohomology making them amenable to Adams Spectral Sequence analysis and suggesting that they were related to the new discovered Brown-Gitler spectra [BG].In the years that followed, various other related 2-primary infinite families were constructed, perhaps most notably (and correctly) Bruner's family detected by h2h2j[set membership] Ext3,*[script A](Z/2, Z/2) [B]. An odd prime version was studied by Cohen [C], leading to a family in [pi]S[low asterisk](S0)(p) detected by h0bj[set membership] Ext3,*[script A] (Z/p, Z/p) and a filtration 2 family in the stable homotopy groups of the odd prime Moore space. Cohen also initiated the development of odd primary Brown-Gitler spectra, completed in the mid 1980s, using a different approach, by Goerss [G], and given the ultimate ‘modern’ treatment by Goerss, Lannes and Morel in the 1993 paper [GLM]. Various papers in the late 1970s and early 1980s, e.g. [BP, C, BC], related some of these to loopspace constructions.Our project originated with two goals. One was to see if any of the later work on Brown-Gitler spectra led to clarification of the original constructions. The other was to see if taking advantage of post Segal Conjecture knowledge of the stable cohomotopy of the classifying space BZ/p would
A homotopy algorithm for digital optimal projection control GASD-HADOC
NASA Technical Reports Server (NTRS)
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.
Numerical Polynomial Homotopy Continuation Method and String Vacua
Mehta, Dhagash
2011-01-01
Finding vmore » acua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some simple toy models, it is, however, difficult to find all the vacua analytically. Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models. However, they suffer from serious algorithmic complexities and are limited to small system sizes. In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions. The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable , and hence its applicability goes way beyond the existing symbolic methods. We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work. We then show that all the vacua of a more complicated model of a compactified M theory model, which has an S U ( 3 ) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods. Finally, we compare the various technicalities between the two methods.« less
"Nonlinear pullbacks" of functions and L∞-morphisms for homotopy Poisson structures
NASA Astrophysics Data System (ADS)
Voronov, Theodore Th.
2017-01-01
We introduce mappings between spaces of functions on (super)manifolds that generalize pullbacks with respect to smooth maps but are, in general, nonlinear (actually, formal). The construction is based on canonical relations and generating functions. (The underlying structure is a formal category, which is a "thickening" of the usual category of supermanifolds; it is close to the category of symplectic micromanifolds and their micromorphisms considered recently by A. Weinstein and A. Cattaneo-B. Dherin-A. Weinstein.) There are two parallel settings, for even and odd functions. As an application, we show how such nonlinear pullbacks give L∞-morphisms for algebras of functions on homotopy Schouten or homotopy Poisson manifolds.
NASA Technical Reports Server (NTRS)
Garcia, F., Jr.
1974-01-01
A study of the solution problem of a complex entry optimization was studied. The problem was transformed into a two-point boundary value problem by using classical calculus of variation methods. Two perturbation methods were devised. These methods attempted to desensitize the contingency of the solution of this type of problem on the required initial co-state estimates. Also numerical results are presented for the optimal solution resulting from a number of different initial co-states estimates. The perturbation methods were compared. It is found that they are an improvement over existing methods.
Global Study of the Simple Pendulum by the Homotopy Analysis Method
ERIC Educational Resources Information Center
Bel, A.; Reartes, W.; Torresi, A.
2012-01-01
Techniques are developed to find all periodic solutions in the simple pendulum by means of the homotopy analysis method (HAM). This involves the solution of the equations of motion in two different coordinate representations. Expressions are obtained for the cycles and periods of oscillations with a high degree of accuracy in the whole range of…
REVIEWS OF TOPICAL PROBLEMS: Defects in liquid crystals: homotopy theory and experimental studies
NASA Astrophysics Data System (ADS)
Kurik, Mikhail V.; Lavrentovich, O. D.
1988-03-01
The fundamental concepts of the homotopy theory of defects in liquid crystals and the results of experimental studies in this field are presented. The concepts of degeneracy space, homotopy groups, and topological charge, which are used for classifying the topologically stable inhomogeneous distributions in different liquid-crystalline phases are examined (uni and biaxial nematics, cholesterics, smectics, and columnar phases). Experimental data are given for the different mesophases on the structure and properties of dislocations, disclinations, point defects in the volume (hedgehogs) and on the surface of the medium (boojums), monopoles, domain formations, and solitons. Special attention is paid to the results of studies of defects in closed volumes (spherical drops, cylindrical capillaries), and to the connection between the topological charges of these defects and the character of the orientation of the molecules of the liquid crystal at the surface. A set of fundamentally new effects that can occur in studying the topological properties of defects in liquid crystals is discussed.
Solving nonlinear or stiff differential equations by Laplace homotopy analysis method(LHAM)
NASA Astrophysics Data System (ADS)
Chong, Fook Seng; Lem, Kong Hoong; Wong, Hui Lin
2015-10-01
The initial value problems of nonlinear or stiff ordinary differential equation appear in many fields of engineering science, particularly in the studies of electrical circuits, chemical reactions, wave vibration and so on. In this research, the standard homotopy analysis method hybrids with Laplace transform method to solve nonlinear and stiff differential equations. Using this modification, the problems solved by LHAM successfully yield good solutions. Some examples are examined to highlight the convenience and effectiveness of LHAM.
Danko, Stefania; Yamasaki, Kazuo; Daiho, Takashi; Suzuki, Hiroshi
2017-01-01
Ca2+ transport by sarcoplasmic reticulum Ca2+-ATPase involves ATP-dependent phosphorylation of a catalytic aspartic acid residue. The key process, luminal Ca2+ release occurs upon phosphoenzyme isomerization, abbreviated as E1PCa2 (reactive to ADP regenerating ATP and with two occluded Ca2+ at transport sites) → E2P (insensitive to ADP and after Ca2+ release). The isomerization involves gathering of cytoplasmic actuator and phosphorylation domains with second transmembrane helix (M2), and is epitomized by protection of a Leu119-proteinase K (prtK) cleavage site on M2. Ca2+ binding to the luminal transport sites of E2P, producing E2PCa2 before Ca2+-release exposes the prtK-site. Here we explore E2P structure to further elucidate luminal gating mechanism and effect of membrane perturbation. We find that ground state E2P becomes cleavable at Leu119 in a non-solubilizing concentration of detergent C12E8 at pH 7.4, indicating a shift towards a more E2PCa2-like state. Cleavage is accelerated by Mg2+ binding to luminal transport sites and blocked by their protonation at pH 6.0. Results indicate that possible disruption of phospholipid-protein interactions strongly favors an E2P species with looser head domain interactions at M2 and responsive to specific ligand binding at the transport sites, likely an early flexible intermediate in the development towards ground state E2P. PMID:28117348
Shepherd, Louise V T; McNicol, James W; Razzo, Ruth; Taylor, Mark A; Davies, Howard V
2006-08-01
Targeted compositional analysis was carried out on transgenic potato tubers of either cultivar (cv.) Record or cv. Desirée to assess the potential for unintended effects caused by the genetic modification process. The range of transgenic lines analysed included those modified in primary carbohydrate metabolism, polyamine biosynthesis and glycoprotein processing. Controls included wildtype tubers, tubers produced from plants regenerated through tissue culture (including a callus phase) and tubers derived from transformation with the 'empty vector' i.e. no specific target gene included (with the exception of the kanamycin resistance gene as a selectable marker). Metabolite analysis included soluble carbohydrates, glycoalkaloids, vitamin C, total nitrogen and fatty acids. Trypsin inhibitor activity was also assayed. These cover the major compounds recommended by the OECD in their Consensus Document on Compositional Considerations for New Varieties of Potatoes: Key Food and Feed Nutrients, Anti-Nutrients and Toxicants (2002). Data was statistically analysed using analysis of variance (ANOVA) for individual compounds and, where applicable, principal component analysis (PCA). In general, targeted compositional analysis revealed no consistent differences between GM lines and respective controls. No construct specifically induced unintended effects. Statistically significant differences between wildtype controls and specific GM lines did occur but appeared to be random and not associated with any specific construct. Indeed such significant differences were also found between wildtypes and both tissue culture derived tubers and tubers derived from transformation with the empty vector. This raises the possibility that somaclonal variation (known to occur significantly in potato, depending on genotype) may be responsible for an unknown proportion of any differences observed between specific GM lines and the wildtype. The most obvious differences seen in GC-MS profiles were
Communication: Newton homotopies for sampling stationary points of potential energy landscapes
Mehta, Dhagash; Chen, Tianran; Hauenstein, Jonathan D.; Wales, David J.
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.
Homotopy Algorithm for Fixed Order Mixed H2/H(infinity) Design
NASA Technical Reports Server (NTRS)
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.
Development of homotopy algorithms for fixed-order mixed H2/H(infinity) controller synthesis
NASA Technical Reports Server (NTRS)
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.
A homotopy analysis method for the option pricing PDE in illiquid markets
NASA Astrophysics Data System (ADS)
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.
Optimal q-homotopy analysis method for time-space fractional gas dynamics equation
NASA Astrophysics Data System (ADS)
Saad, K. M.; AL-Shareef, E. H.; Mohamed, Mohamed S.; Yang, Xiao-Jun
2017-01-01
It is well known that the homotopy analysis method is one of the most efficient methods for obtaining analytical or approximate semi-analytical solutions of both linear and non-linear partial differential equations. A more general form of HAM is introduced in this paper, which is called Optimal q-Homotopy Analysis Method (Oq-HAM). It has better convergence properties as compared with the usual HAM, due to the presence of fraction factor associated with the solution. The convergence of q-HAM is studied in details elsewhere (M.A. El-Tawil, Int. J. Contemp. Math. Sci. 8, 481 (2013)). Oq-HAM is applied to the non-linear homogeneous and non-homogeneous time and space fractional gas dynamics equations with initial condition. An optimal convergence region is determined through the residual error. By minimizing the square residual error, the optimal convergence control parameters can be obtained. The accuracy and efficiency of the proposed method are verified by comparison with the exact solution of the fractional gas dynamics equation. Also, it is shown that the Oq-HAM for the fractional gas dynamics equation is equivalent to the exact solution. We obtain graphical representations of the solutions using MATHEMATICA.
Homotopy Particle Filter for Ground-Based Tracking of Satellites at GEO
NASA Astrophysics Data System (ADS)
Moshtagh, N.; Chan, J.; Chan, M.
2016-09-01
Ground telescopes enable low-cost tracking and characterization of meter-class space objects. Since a telescope may be tasked to observe multiple fields of the sky, the time between observations for each object may vary from several seconds to tens of minutes. Long propagation times with nonlinear dynamics are challenging for traditional filtering methods such as the Extended Kalman Filter (EKF). Sampling-based filters based on the Particle Filter (PF) are promising for this type of problem but typically require maintaining a large number of samples. In this work, we evaluate the Homotopy Particle Filter (HPF) which promises effective performance with orders of magnitude fewer particles. The performance of the HPF is evaluated against GEO satellite observations collected by a ground telescope at Lockheed Martin's Space Object Tracking (SPOT) facility.
NASA Technical Reports Server (NTRS)
Scheid, R. E.; Milman, M. H.; Salama, M.; Bruno, R.; Gibson, J. S.
1990-01-01
This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objectives of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to assist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further considerations, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose. Analytical and numerical examples are also presented.
Homotopy-Theoretic Study & Atomic-Scale Observation of Vortex Domains in Hexagonal Manganites
Li, Jun; Chiang, Fu-Kuo; Chen, Zhen; Ma, Chao; Chu, Ming-Wen; Chen, Cheng-Hsuan; Tian, Huanfang; Yang, Huaixin; Li, Jianqi
2016-01-01
Essential structural properties of the non-trivial “string-wall-bounded” topological defects in hexagonal manganites are studied through homotopy group theory and spherical aberration-corrected scanning transmission electron microscopy. The appearance of a “string-wall-bounded” configuration in RMnO3 is shown to be strongly linked with the transformation of the degeneracy space. The defect core regions (~50 Å) mainly adopt the continuous U(1) symmetry of the high-temperature phase, which is essential for the formation and proliferation of vortices. Direct visualization of vortex strings at atomic scale provides insight into the mechanisms and macro-behavior of topological defects in crystalline materials. PMID:27324701
Topological and geometrical quantum computation in cohesive Khovanov homotopy type theory
NASA Astrophysics Data System (ADS)
Ospina, Juan
2015-05-01
The recently proposed Cohesive Homotopy Type Theory is exploited as a formal foundation for central concepts in Topological and Geometrical Quantum Computation. Specifically the Cohesive Homotopy Type Theory provides a formal, logical approach to concepts like smoothness, cohomology and Khovanov homology; and such approach permits to clarify the quantum algorithms in the context of Topological and Geometrical Quantum Computation. In particular we consider the so-called "open-closed stringy topological quantum computer" which is a theoretical topological quantum computer that employs a system of open-closed strings whose worldsheets are open-closed cobordisms. The open-closed stringy topological computer is able to compute the Khovanov homology for tangles and for hence it is a universal quantum computer given than any quantum computation is reduced to an instance of computation of the Khovanov homology for tangles. The universal algebra in this case is the Frobenius Algebra and the possible open-closed stringy topological quantum computers are forming a symmetric monoidal category which is equivalent to the category of knowledgeable Frobenius algebras. Then the mathematical design of an open-closed stringy topological quantum computer is involved with computations and theorem proving for generalized Frobenius algebras. Such computations and theorem proving can be performed automatically using the Automated Theorem Provers with the TPTP language and the SMT-solver Z3 with the SMT-LIB language. Some examples of application of ATPs and SMT-solvers in the mathematical setup of an open-closed stringy topological quantum computer will be provided.
Palenik, Mark C.; Dunlap, Brett I.
2015-07-28
Despite the fundamental importance of electron density in density functional theory, perturbations are still usually dealt with using Hartree-Fock-like orbital equations known as coupled-perturbed Kohn-Sham (CPKS). As an alternative, we develop a perturbation theory that solves for the perturbed density directly, removing the need for CPKS. This replaces CPKS with a true Hohenberg-Kohn density perturbation theory. In CPKS, the perturbed density is found in the basis of products of occupied and virtual orbitals, which becomes ever more over-complete as the size of the orbital basis set increases. In our method, the perturbation to the density is expanded in terms of a series of density basis functions and found directly. It is possible to solve for the density in such a way that it makes the total energy stationary even if the density basis is incomplete.
Cosmological perturbations in unimodular gravity
Gao, Caixia; Brandenberger, Robert H.; Cai, Yifu; Chen, Pisin E-mail: rhb@hep.physics.mcgill.ca E-mail: chen@slac.stanford.edu
2014-09-01
We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.
NASA Astrophysics Data System (ADS)
Atangana, Abdon
2013-10-01
We exploit a relatively new analytical technique, the Homotopy Decomposition Method (HDM), for solving nonlinear fractional partial differential equations arising in prey-predator biological population dynamics system. Numerical solutions are provided and they have certain properties which exhibit biologically significant dependence on the parameter values. The fractional derivatives are described in the Caputo sense. The HDM is reliable and reduces the number of computations. This gives the HDM a wider applicability. In addition, the method is very easy to use.
Automated Lattice Perturbation Theory
Monahan, Christopher
2014-11-01
I review recent developments in automated lattice perturbation theory. Starting with an overview of lattice perturbation theory, I focus on the three automation packages currently "on the market": HiPPy/HPsrc, Pastor and PhySyCAl. I highlight some recent applications of these methods, particularly in B physics. In the final section I briefly discuss the related, but distinct, approach of numerical stochastic perturbation theory.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Discrete homotopy analysis for optimal trading execution with nonlinear transient market impact
NASA Astrophysics Data System (ADS)
Curato, Gianbiagio; Gatheral, Jim; Lillo, Fabrizio
2016-10-01
Optimal execution in financial markets is the problem of how to trade a large quantity of shares incrementally in time in order to minimize the expected cost. In this paper, we study the problem of the optimal execution in the presence of nonlinear transient market impact. Mathematically such problem is equivalent to solve a strongly nonlinear integral equation, which in our model is a weakly singular Urysohn equation of the first kind. We propose an approach based on Homotopy Analysis Method (HAM), whereby a well behaved initial trading strategy is continuously deformed to lower the expected execution cost. Specifically, we propose a discrete version of the HAM, i.e. the DHAM approach, in order to use the method when the integrals to compute have no closed form solution. We find that the optimal solution is front loaded for concave instantaneous impact even when the investor is risk neutral. More important we find that the expected cost of the DHAM strategy is significantly smaller than the cost of conventional strategies.
Wang, Tianyun; Lu, Xinfei; Yu, Xiaofei; Xi, Zhendong; Chen, Weidong
2014-03-26
In recent years, various applications regarding sparse continuous signal recovery such as source localization, radar imaging, communication channel estimation, etc., have been addressed from the perspective of compressive sensing (CS) theory. However, there are two major defects that need to be tackled when considering any practical utilization. The first issue is off-grid problem caused by the basis mismatch between arbitrary located unknowns and the pre-specified dictionary, which would make conventional CS reconstruction methods degrade considerably. The second important issue is the urgent demand for low-complexity algorithms, especially when faced with the requirement of real-time implementation. In this paper, to deal with these two problems, we have presented three fast and accurate sparse reconstruction algorithms, termed as HR-DCD, Hlog-DCD and Hlp-DCD, which are based on homotopy, dichotomous coordinate descent (DCD) iterations and non-convex regularizations, by combining with the grid refinement technique. Experimental results are provided to demonstrate the effectiveness of the proposed algorithms and related analysis.
Wang, Tianyun; Lu, Xinfei; Yu, Xiaofei; Xi, Zhendong; Chen, Weidong
2014-01-01
In recent years, various applications regarding sparse continuous signal recovery such as source localization, radar imaging, communication channel estimation, etc., have been addressed from the perspective of compressive sensing (CS) theory. However, there are two major defects that need to be tackled when considering any practical utilization. The first issue is off-grid problem caused by the basis mismatch between arbitrary located unknowns and the pre-specified dictionary, which would make conventional CS reconstruction methods degrade considerably. The second important issue is the urgent demand for low-complexity algorithms, especially when faced with the requirement of real-time implementation. In this paper, to deal with these two problems, we have presented three fast and accurate sparse reconstruction algorithms, termed as HR-DCD, Hlog-DCD and Hlp-DCD, which are based on homotopy, dichotomous coordinate descent (DCD) iterations and non-convex regularizations, by combining with the grid refinement technique. Experimental results are provided to demonstrate the effectiveness of the proposed algorithms and related analysis. PMID:24675758
NASA Astrophysics Data System (ADS)
Rong, Shu-Jun; Liu, Qiu-Yu
2012-04-01
The puma model on the basis of the Lorentz and CPT violation may bring an economical interpretation to the conventional neutrinos oscillation and part of the anomalous oscillations. We study the effect of the perturbation to the puma model. In the case of the first-order perturbation which keeps the (23) interchange symmetry, the mixing matrix element Ue3 is always zero. The nonzero mixing matrix element Ue3 is obtained in the second-order perturbation that breaks the (23) interchange symmetry.
Minimum-fuel station-change for geostationary satellites using low-thrust considering perturbations
NASA Astrophysics Data System (ADS)
Zhao, ShuGe; Zhang, JingRui
2016-10-01
The objective of this paper is to find the minimum-fuel station change for geostationary satellites with low-thrust while considering significant perturbation forces for geostationary Earth orbit (GEO). The effect of Earth's triaxiality, lunisolar perturbations, and solar radiation pressure on the terminal conditions of a long duration GEO transfer is derived and used for establishing the station change model with consideration of significant perturbation forces. A method is presented for analytically evaluating the effect of Earth's triaxiality on the semimajor axis and longitude during a station change. The minimum-fuel problem is solved by the indirect optimization method. The easier and related minimum-energy problem is first addressed and then the energy-to-fuel homotopy is employed to finally obtain the solution of the minimum-fuel problem. Several effective techniques are employed in solving the two-point boundary-value problem with a shooting method to overcome the problem of the small convergence radius and the sensitivity of the initial costate variables. These methods include normalization of the initial costate vector, computation of the analytic Jacobians matrix, and switching detection. The simulation results show that the solution of the minimum-fuel station change with low-thrust considering significant perturbation forces can be obtained by applying these preceding techniques.
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1974-01-01
For perturbed nonlinear systems, a norm, other than the supremum norm, is introduced on some spaces of continuous functions. This makes possible the study of new types of behavior. A study is presented on a perturbed nonlinear differential equation defined on a half line, and the existence of a family of solutions with special boundedness properties is established. The ideas developed are applied to the study of integral manifolds, and examples are given.
Evolution of dark energy perturbations in scalar-tensor cosmologies
Bueno Sanchez, J. C.; Perivolaropoulos, L.
2010-05-15
We solve analytically and numerically the generalized Einstein equations in scalar-tensor cosmologies to obtain the evolution of dark energy and matter linear perturbations. We compare our results with the corresponding results for minimally coupled quintessence perturbations. We find that scalar-tensor dark energy density perturbations are amplified by a factor of about 10{sup 4} compared to minimally coupled quintessence perturbations on scales less than about 1000 h{sup -1} Mpc (sub-Hubble scales). On these scales dark energy perturbations constitute a fraction of about 10% compared to matter density perturbations. Scalar-tensor dark energy density perturbations are anticorrelated with matter linear perturbations on sub-Hubble scales. This anticorrelation of matter with negative pressure perturbations induces a mild amplification of matter perturbations by about 10% on sub-Hubble scales. The evolution of scalar field perturbations on sub-Hubble scales is scale independent and therefore corresponds to a vanishing effective speed of sound (c{sub s{Phi}=}0). We briefly discuss the observational implications of our results, which may include predictions for galaxy and cluster halo profiles that are modified compared to {Lambda}CDM. The observed properties of these profiles are known to be in some tension with the predictions of {Lambda}CDM.
NASA Technical Reports Server (NTRS)
Criminale, W. O.; Lasseigne, D. G.; Jackson, T. L.
1995-01-01
An initial value approach is used to examine the dynamics of perturbations introduced into a vortex under strain. Both the basic vortex considered and the perturbations are taken as fully three-dimensional. An explicit solution for the time evolution of the vorticity perturbations is given for arbitrary initial vorticity. Analytical solutions for the resulting velocity components are found when the initial vorticity is assumed to be localized. For more general initial vorticity distributions, the velocity components are determined numerically. It is found that the variation in the radial direction of the initial vorticity disturbance is the most important factor influencing the qualitative behavior of the solutions. Transient growth in the magnitude of the velocity components is found to be directly attributable to the compactness of the initial vorticity.
Perturbations for transient acceleration
Vargas, Cristofher Zuñiga; Zimdahl, Winfried; Hipólito-Ricaldi, Wiliam S. E-mail: hipolito@ceunes.ufes.br
2012-04-01
According to the standard ΛCDM model, the accelerated expansion of the Universe will go on forever. Motivated by recent observational results, we explore the possibility of a finite phase of acceleration which asymptotically approaches another period of decelerated expansion. Extending an earlier study on a corresponding homogeneous and isotropic dynamics, in which interactions between dark matter and dark energy are crucial, the present paper also investigates the dynamics of the matter perturbations both on the Newtonian and General Relativistic (GR) levels and quantifies the potential relevance of perturbations of the dark-energy component. In the background, the model is tested against the Supernova type Ia (SNIa) data of the Constitution set and on the perturbative level against growth rate data, among them those of the WiggleZ survey, and the data of the 2dFGRS project. Our results indicate that a transient phase of accelerated expansion is not excluded by current observations.
NASA Astrophysics Data System (ADS)
Alizadeh-Pahlavan, Amir; Aliakbar, Vahid; Vakili-Farahani, Farzad; Sadeghy, Kayvan
2009-02-01
The performance of a two-auxiliary-parameter homotopy analysis method (HAM) is investigated in solving laminar MHD flow of an upper-convected Maxwell fluid (UCM) above a porous isothermal stretching sheet. The analysis is carried out up to the 20th-order of approximation, and the effect of parameters such as elasticity number, suction/injection velocity, and magnetic number are studied on the velocity field above the sheet. The results will be contrasted with those reported recently by Hayat et al. [Hayat T, Abbas Z, Sajid M. Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys Lett A 358;2006:396-403] obtained using a third-order one-auxiliary-parameter homotopy analysis method. It is concluded that the flow reversal phenomenon as predicted by Hayat et al. (2006) may have arisen because of the inadequacies of using just one-auxiliary-parameter in their analysis. That is, no flow reversal is predicted to occur if instead of using one-auxiliary-parameter use is made of two auxiliary parameters together with a more convenient set of base functions to assure the convergence of the series used to solve the highly nonlinear ODE governing the flow.
Perturbed nonlinear differential equations
NASA Technical Reports Server (NTRS)
Proctor, T. G.
1972-01-01
The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.
NASA Astrophysics Data System (ADS)
Kandasamy, R.; Muhaimin, I.
2010-03-01
Homotopy analysis method is used to analyze the effect of thermophoretic particle deposition on magnetohydrodynamic mixed convection flow with heat and mass transfer over a porous wedge. An explicit analytical solution is obtained which is valid throughout the solution domain and is consistent with numerical results.
Perturbing turbulence beyond collapse
NASA Astrophysics Data System (ADS)
Kühnen, Jakob; Scarselli, Davide; Hof, Björn; Nonlinear Dynamics; Turbulence Group Team
2016-11-01
Wall-bounded turbulent flows are considered to be in principle stable against perturbations and persist as long as the Reynolds number is sufficiently high. We show for the example of pipe flow that a specific perturbation of the turbulent flow field disrupts the genesis of new turbulence at the wall. This leads to an immediate collapse of the turbulent flow and causes complete relaminarisation further downstream. The annihilation of turbulence is effected by a steady manipulation of the streamwise velocity component only, greatly simplifying control efforts which usually require knowledge of the highly complex three dimensional and time dependent velocity fields. We present several different control schemes from laboratory experiments which achieve the required perturbation of the flow for total relaminarisation. Transient growth, a linear amplification mechanism measuring the efficiency of eddies in redistributing shear that quantifies the maximum perturbation energy amplification achievable over a finite time in a linearized framework, is shown to set a clear-cut threshold below which turbulence is impeded in its formation and thus permanently annihilated.
Cosmological perturbations in antigravity
NASA Astrophysics Data System (ADS)
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.
Testing gravity theories using tensor perturbations
NASA Astrophysics Data System (ADS)
Lin, Weikang; Ishak-Boushaki, Mustapha B.
2017-01-01
Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to tensor-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the tensor-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation. We find that, the tensor spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.
Cosmological perturbations in a family of deformations of general relativity
Krasnov, Kirill; Shtanov, Yuri E-mail: shtanov@bitp.kiev.ua
2010-06-01
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.
Renormalized Lie perturbation theory
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.
Covariant Bardeen perturbation formalism
NASA Astrophysics Data System (ADS)
Vitenti, S. D. P.; Falciano, F. T.; Pinto-Neto, N.
2014-05-01
In a previous work we obtained a set of necessary conditions for the linear approximation in cosmology. Here we discuss the relations of this approach with the so-called covariant perturbations. It is often argued in the literature that one of the main advantages of the covariant approach to describe cosmological perturbations is that the Bardeen formalism is coordinate dependent. In this paper we will reformulate the Bardeen approach in a completely covariant manner. For that, we introduce the notion of pure and mixed tensors, which yields an adequate language to treat both perturbative approaches in a common framework. We then stress that in the referred covariant approach, one necessarily introduces an additional hypersurface choice to the problem. Using our mixed and pure tensors approach, we are able to construct a one-to-one map relating the usual gauge dependence of the Bardeen formalism with the hypersurface dependence inherent to the covariant approach. Finally, through the use of this map, we define full nonlinear tensors that at first order correspond to the three known gauge invariant variables Φ, Ψ and Ξ, which are simultaneously foliation and gauge invariant. We then stress that the use of the proposed mixed tensors allows one to construct simultaneously gauge and hypersurface invariant variables at any order.
Amplitudes of Spiral Perturbations
NASA Astrophysics Data System (ADS)
Grosbol, P.; Patsis, P. A.
2014-03-01
It has proven very difficult to estimate the amplitudes of spiral perturbations in disk galaxies from observations due to the variation of mass-to-light ratio and extinction across spiral arms. Deep, near-infrared images of grand-design spiral galaxies obtained with HAWK-I/VLT were used to analyze the azimuthal amplitude and shape of arms, which, even in the K-band may, be significantly biased by the presence of young stellar populations. Several techniques were applied to evaluate the relative importance of young stars across the arms, such as surface brightness of the disk with light from clusters subtracted, number density of clusters detected, and texture of the disk. The modulation of the texture measurement, which correlates with the number density of faint clusters, yields amplitudes of the spiral perturbation in the range 0.1-0.2. This estimate gives a better estimate of the mass perturbation in the spiral arms, since it is dominated by old clusters.
Chiral perturbation theory with nucleons
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, {pi}N scattering and the {sigma}-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.
Perturbative theory for Brownian vortexes
NASA Astrophysics Data System (ADS)
Moyses, Henrique W.; Bauer, Ross O.; Grosberg, Alexander Y.; Grier, David G.
2015-06-01
Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.
Perturbative theory for Brownian vortexes.
Moyses, Henrique W; Bauer, Ross O; Grosberg, Alexander Y; Grier, David G
2015-06-01
Brownian vortexes are stochastic machines that use static nonconservative force fields to bias random thermal fluctuations into steadily circulating currents. The archetype for this class of systems is a colloidal sphere in an optical tweezer. Trapped near the focus of a strongly converging beam of light, the particle is displaced by random thermal kicks into the nonconservative part of the optical force field arising from radiation pressure, which then biases its diffusion. Assuming the particle remains localized within the trap, its time-averaged trajectory traces out a toroidal vortex. Unlike trivial Brownian vortexes, such as the biased Brownian pendulum, which circulate preferentially in the direction of the bias, the general Brownian vortex can change direction and even topology in response to temperature changes. Here we introduce a theory based on a perturbative expansion of the Fokker-Planck equation for weak nonconservative driving. The first-order solution takes the form of a modified Boltzmann relation and accounts for the rich phenomenology observed in experiments on micrometer-scale colloidal spheres in optical tweezers.
Basiri Parsa, A; Rashidi, M M; Anwar Bég, O; Sadri, S M
2013-09-01
In this paper, the semi-numerical techniques known as the optimal homotopy analysis method (HAM) and Differential Transform Method (DTM) are applied to study the magneto-hemodynamic laminar viscous flow of a conducting physiological fluid in a semi-porous channel under a transverse magnetic field. The two-dimensional momentum conservation partial differential equations are reduced to ordinary form incorporating Lorentizian magnetohydrodynamic body force terms. These ordinary differential equations are solved by the homotopy analysis method, the differential transform method and also a numerical method (fourth-order Runge-Kutta quadrature with a shooting method), under physically realistic boundary conditions. The homotopy analysis method contains the auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region of solution series. The differential transform method (DTM) does not require an auxiliary parameter and is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. The influence of Hartmann number (Ha) and transpiration Reynolds number (mass transfer parameter, Re) on the velocity profiles in the channel are studied in detail. Interesting fluid dynamic characteristics are revealed and addressed. The HAM and DTM solutions are shown to both correlate well with numerical quadrature solutions, testifying to the accuracy of both HAM and DTM in nonlinear magneto-hemodynamics problems. Both these semi-numerical techniques hold excellent potential in modeling nonlinear viscous flows in biological systems.
Testing gravity theories using tensor perturbations
NASA Astrophysics Data System (ADS)
Lin, Weikang; Ishak, Mustapha
2016-12-01
Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the tensor spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B
Perturbed effects at radiation physics
NASA Astrophysics Data System (ADS)
Külahcı, Fatih; Şen, Zekâi
2013-09-01
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.
Hamiltonian formalism for Perturbed Black Hole Spacetimes
NASA Astrophysics Data System (ADS)
Mihaylov, Deyan; Gair, Jonathan
2017-01-01
Present and future gravitational wave observations provide a new mechanism to probe the predictions of general relativity. Observations of extreme mass ratio inspirals with millihertz gravitational wave detectors such as LISA will provide exquisite constraints on the spacetime structure outside astrophysical black holes, enabling tests of the no-hair property that all general relativistic black holes are described by the Kerr metric. Previous work to understand what constraints LISA observations will be able to place has focussed on specific alternative theories of gravity, or generic deviations that preserve geodesic separability. We describe an alternative approach to this problem--a technique that employs canonical perturbations of the Hamiltonian function describing motion in the Kerr metric. We derive this new approach and demonstrate its application to the cases of a slowly rotating Kerr black hole which is viewed as a perturbation of a Schwarzschild black hole, of coupled perturbations of black holes in the second-order Chern-Simons modified gravity theory, and several more indicative scenarios. Deyan Mihaylov is funded by STFC.
Perturbation theory in electron diffraction
NASA Astrophysics Data System (ADS)
Bakken, L. N.; Marthinsen, K.; Hoeier, R.
1992-12-01
The Bloch-wave approach is used for discussing multiple inelastic electron scattering and higher-order perturbation theory in inelastic high-energy electron diffraction. In contrast to previous work, the present work describes three-dimensional diffraction so that higher-order Laue zone (HOLZ) effects are incorporated. Absorption is included and eigenvalues and eigenvectors are calculated from a structure matrix with the inclusion of an absorptive potential. Centrosymmetric as well as non-centrosymmetric crystal structures are allowed. An iteration method with a defined generalized propagation function for solving the inelastic coupling equations is described. It is shown that a similar iteration method with the same propagation function can be used for obtaining higher-order perturbation terms for the wave-function when a perturbation is added to the crystal potential. Finally, perturbation theory by matrix calculations when a general perturbation is added to the structure matrix is considered.
You, Peng; Liu, Zhen; Wang, Hongqiang; Wei, Xizhang; Li, Xiang
2014-05-08
Compressed sensing has been applied to achieve high resolution range profiles (HRRPs) using a stepped-frequency radar. In this new scheme, much fewer pulses are required to recover the target's strong scattering centers, which can greatly reduce the coherent processing interval (CPI) and improve the anti-jamming capability. For practical applications, however, the required number of pulses is difficult to determine in advance and any reduction of the transmitted pulses is attractive. In this paper, a dynamic compressed sensing strategy for HRRP generation is proposed, in which the estimated HRRP is updated with sequentially transmitted and received pulses until the proper stopping rules are satisfied. To efficiently implement the sequential update, a complex-valued fast sequential homotopy (CV-FSH) algorithm is developed based on group sparse recovery. This algorithm performs as an efficient recursive procedure of sparse recovery, thus avoiding solving a new optimization problem from scratch. Furthermore, the proper stopping rules are presented according to the special characteristics of HRRP. Therefore, the optimal number of pulses required in each CPI can be sought adapting to the echo signal. The results using simulated and real data show the effectiveness of the proposed approach and demonstrate that the established dynamic strategy is more suitable for uncooperative targets.
NASA Astrophysics Data System (ADS)
Jamali, Ali; Anton, François; Rahman, Alias Abdul; Mioc, Darka
2016-10-01
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.
NASA Technical Reports Server (NTRS)
Smith, R. L.; Huang, C.
1986-01-01
A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.
You, Peng; Liu, Zhen; Wang, Hongqiang; Wei, Xizhang; Li, Xiang
2014-01-01
Compressed sensing has been applied to achieve high resolution range profiles (HRRPs) using a stepped-frequency radar. In this new scheme, much fewer pulses are required to recover the target's strong scattering centers, which can greatly reduce the coherent processing interval (CPI) and improve the anti-jamming capability. For practical applications, however, the required number of pulses is difficult to determine in advance and any reduction of the transmitted pulses is attractive. In this paper, a dynamic compressed sensing strategy for HRRP generation is proposed, in which the estimated HRRP is updated with sequentially transmitted and received pulses until the proper stopping rules are satisfied. To efficiently implement the sequential update, a complex-valued fast sequential homotopy (CV-FSH) algorithm is developed based on group sparse recovery. This algorithm performs as an efficient recursive procedure of sparse recovery, thus avoiding solving a new optimization problem from scratch. Furthermore, the proper stopping rules are presented according to the special characteristics of HRRP. Therefore, the optimal number of pulses required in each CPI can be sought adapting to the echo signal. The results using simulated and real data show the effectiveness of the proposed approach and demonstrate that the established dynamic strategy is more suitable for uncooperative targets. PMID:24815679
Perturbative gadgets at arbitrary orders
NASA Astrophysics Data System (ADS)
Jordan, Stephen P.; Farhi, Edward
2008-06-01
Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k -body effective interactions from two-body Hamiltonians. These effective interactions arise from the k th order in perturbation theory.
Inflationary perturbations in bimetric gravity
Cusin, Giulia; Durrer, Ruth; Guarato, Pietro; Motta, Mariele E-mail: ruth.durrer@unige.ch E-mail: mariele.motta@unige.ch
2015-09-01
In this paper we study the generation of primordial perturbations in a cosmological setting of bigravity during inflation. We consider a model of bigravity which can reproduce the ΛCDM background and large scale structure and a simple model of inflation with a single scalar field and a quadratic potential. Reheating is implemented with a toy-model in which the energy density of the inflaton is entirely dissipated into radiation. We present analytic and numerical results for the evolution of primordial perturbations in this cosmological setting. We find that the amplitude of tensor perturbations generated during inflation is sufficiently suppressed to avoid the effects of the tensor instability discovered in refs. [1,2] which develops during the cosmological evolution in the physical sector. We argue that from a pure analysis of the tensor perturbations this bigravity model is compatible with present observations. However, we derive rather stringent limits on inflation from the vector and scalar sectors.
Causal compensated perturbations in cosmology
NASA Technical Reports Server (NTRS)
Veeraraghavan, Shoba; Stebbins, Albert
1990-01-01
A theoretical framework is developed to calculate linear perturbations in the gravitational and matter fields which arise causally in response to the presence of stiff matter sources in a FRW cosmology. It is shown that, in order to satisfy energy and momentum conservation, the gravitational fields of the source must be compensated by perturbations in the matter and gravitational fields, and the role of such compensation in containing the initial inhomogeneities in their subsequent evolution is discussed. A complete formal solution is derived in terms of Green functions for the perturbations produced by an arbitrary source in a flat universe containing cold dark matter. Approximate Green function solutions are derived for the late-time density perturbations and late-time gravitational waves in a universe containing a radiation fluid. A cosmological energy-momentum pseudotensor is defined to clarify the nature of energy and momentum conservation in the expanding universe.
Robust stability under additive perturbations
NASA Technical Reports Server (NTRS)
Bhaya, A.; Desoer, C. A.
1985-01-01
A MIMO linear time-invariant feedback system 1S(P,C) is considered which is assumed to be U-stable. The plant P is subjected to an additive perturbation Delta P which is proper but not necessarily stable. It is proved that the perturbed system is U-stable if and only if Delta P(I + Q x Delta P) exp -1 is U-stable.
Non-adiabatic perturbations in Ricci dark energy model
Karwan, Khamphee; Thitapura, Thiti E-mail: nanodsci2523@hotmail.com
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.
NASA Astrophysics Data System (ADS)
Jeffrey, Lisa C.; Ramras, Daniel A.; Weitsman, Jonathan
2017-03-01
We show that the prequantum line bundle on the moduli space of flat SU(2) connections on a closed Riemann surface of positive genus has degree 1. It then follows from work of Lawton and the second author that the classifying map for this line bundle induces a homotopy equivalence between the stable moduli space of flat SU(n) connections, in the limit as n tends to infinity, and CP^∞. Applications to the stable moduli space of flat unitary connections are also discussed.
NASA Technical Reports Server (NTRS)
Vaughan, William W.; Friedman, Mark J.; Monteiro, Anand C.
1993-01-01
In earlier papers, Doedel and the authors have developed a numerical method and derived error estimates for the computation of branches of heteroclinic orbits for a system of autonomous ordinary differential equations in R(exp n). The idea of the method is to reduce a boundary value problem on the real line to a boundary value problem on a finite interval by using a local (linear or higher order) approximation of the stable and unstable manifolds. A practical limitation for the computation of homoclinic and heteroclinic orbits has been the difficulty in obtaining starting orbits. Typically these were obtained from a closed form solution or via a homotopy from a known solution. Here we consider extensions of our algorithm which allow us to obtain starting orbits on the continuation branch in a more systematic way as well as make the continuation algorithm more flexible. In applications, we use the continuation software package AUTO in combination with some initial value software. The examples considered include computation of homoclinic orbits in a singular perturbation problem and in a turbulent fluid boundary layer in the wall region problem.
Shock wave perturbation decay in granular materials
Vogler, Tracy J.
2015-11-05
A technique in which the evolution of a perturbation in a shock wave front is monitored as it travels through a sample is applied to granular materials. Although the approach was originally conceived as a way to measure the viscosity of the sample, here it is utilized as a means to probe the deviatoric strength of the material. Initial results for a tungsten carbide powder are presented that demonstrate the approach is viable. Simulations of the experiments using continuum and mesoscale modeling approaches are used to better understand the experiments. The best agreement with the limited experimental data is obtained for the mesoscale model, which has previously been shown to give good agreement with planar impact results. The continuum simulations indicate that the decay of the perturbation is controlled by material strength but is insensitive to the compaction response. Other sensitivities are assessed using the two modeling approaches. The simulations indicate that the configuration used in the preliminary experiments suffers from certain artifacts and should be modified to remove them. As a result, the limitations of the current instrumentation are discussed, and possible approaches to improve it are suggested.
Shock wave perturbation decay in granular materials
Vogler, Tracy J.
2015-11-05
A technique in which the evolution of a perturbation in a shock wave front is monitored as it travels through a sample is applied to granular materials. Although the approach was originally conceived as a way to measure the viscosity of the sample, here it is utilized as a means to probe the deviatoric strength of the material. Initial results for a tungsten carbide powder are presented that demonstrate the approach is viable. Simulations of the experiments using continuum and mesoscale modeling approaches are used to better understand the experiments. The best agreement with the limited experimental data is obtainedmore » for the mesoscale model, which has previously been shown to give good agreement with planar impact results. The continuum simulations indicate that the decay of the perturbation is controlled by material strength but is insensitive to the compaction response. Other sensitivities are assessed using the two modeling approaches. The simulations indicate that the configuration used in the preliminary experiments suffers from certain artifacts and should be modified to remove them. As a result, the limitations of the current instrumentation are discussed, and possible approaches to improve it are suggested.« less
Perturbative stability of SFT-based cosmological models
Galli, Federico; Koshelev, Alexey S. E-mail: alexey.koshelev@vub.ac.be
2011-05-01
We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numerically that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.
Poulsen, P; Kuklo, R M
2001-03-01
We have previously reported the degree of attenuation and perturbation by a Cu jet passing through Comp B explosive. Similar tests have now been performed with high explosive (HE) targets having CJ pressures higher than and lower than the CJ pressure of Comp B. The explosives were LX-14 and TNT, respectively. We found that the measured exit velocity of the jet where it transitions from perturbed to solid did not vary significantly as a function of HE type for each HE thickness. The radial momentum imparted to the perturbed jet segment did vary as a function of HE type, however, and we report the radial spreading of the jet and the penetration of a downstream target as a function of HE type and thickness.
Multi-field inflation and cosmological perturbations
NASA Astrophysics Data System (ADS)
Gong, Jinn-Ouk
We provide a concise review on multi-field inflation and cosmological perturbations. We discuss convenient and physically meaningful bases in terms of which perturbations can be systematically studied. We give formal accounts on the gauge fixing conditions and present the perturbation action in two gauges. We also briefly review nonlinear perturbations.
Thermal perturbation of the Sun
NASA Technical Reports Server (NTRS)
Twigg, L. W.; Endal, A. S.
1981-01-01
An investigation of thermal perturbations of the solar convective zone via changes in the mixing length parameter were carried out, with a view toward understanding the possible solar radius and luminosity changes cited in the literature. The results show that: (a) a single perturbation of alpha is probably not the cause of the solar radius change and (b) the parameter W = d lambda nR./d lambda nL. can not be characterized by a single value, as implied in recent work.
Effects of thermal inflation on small scale density perturbations
Hong, Sungwook E.; Lee, Hyung-Joo; Lee, Young Jae; Stewart, Ewan D.; Zoe, Heeseung E-mail: ohsk111@kaist.ac.kr E-mail: jcap@profstewart.org
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.
Constraining dark sector perturbations II: ISW and CMB lensing tomography
NASA Astrophysics Data System (ADS)
Soergel, B.; Giannantonio, T.; Weller, J.; Battye, R. A.
2015-02-01
Any Dark Energy (DE) or Modified Gravity (MG) model that deviates from a cosmological constant requires a consistent treatment of its perturbations, which can be described in terms of an effective entropy perturbation and an anisotropic stress. We have considered a recently proposed generic parameterisation of DE/MG perturbations and compared it to data from the Planck satellite and six galaxy catalogues, including temperature-galaxy (Tg), CMB lensing-galaxy (varphi g) and galaxy-galaxy (gg) correlations. Combining these observables of structure formation with tests of the background expansion allows us to investigate the properties of DE/MG both at the background and the perturbative level. Our constraints on DE/MG are mostly in agreement with the cosmological constant paradigm, while we also find that the constraint on the equation of state w (assumed to be constant) depends on the model assumed for the perturbation evolution. We obtain w=-0.92+0.20-0.16 (95% CL; CMB+gg+Tg) in the entropy perturbation scenario; in the anisotropic stress case the result is w=-0.86+0.17-0.16. Including the lensing correlations shifts the results towards higher values of w. If we include a prior on the expansion history from recent Baryon Acoustic Oscillations (BAO) measurements, we find that the constraints tighten closely around w=-1, making it impossible to measure any DE/MG perturbation evolution parameters. If, however, upcoming observations from surveys like DES, Euclid or LSST show indications for a deviation from a cosmological constant, our formalism will be a useful tool towards model selection in the dark sector.
VHS Movies: Perturbations for Morphogenesis.
ERIC Educational Resources Information Center
Holmes, Danny L.
This paper discusses the concept of a family system in terms of an interactive system of interrelated, interdependent parts and suggests that VHS movies can act as perturbations, i.e., change promoting agents, for certain dysfunctional family systems. Several distinct characteristics of a family system are defined with particular emphasis on…
Recent Developments in Perturbative QCD
Dixon, Lance J.; /SLAC
2005-07-11
I review recent progress in perturbative QCD on two fronts: extending next-to-next-to-leading order QCD corrections to a broader range of collider processes, and applying twistor-space methods (and related spinoffs) to computations of multi-parton scattering amplitudes.
Adaptation Strategies in Perturbed /s/
ERIC Educational Resources Information Center
Brunner, Jana; Hoole, Phil; Perrier, Pascal
2011-01-01
The purpose of this work is to investigate the role of three articulatory parameters (tongue position, jaw position and tongue grooving) in the production of /s/. Six normal speakers' speech was perturbed by a palatal prosthesis. The fricative was recorded acoustically and through electromagnetic articulography in four conditions: (1) unperturbed,…
Disformal invariance of curvature perturbation
Motohashi, Hayato; White, Jonathan E-mail: jwhite@post.kek.jp
2016-02-01
We show that under a general disformal transformation the linear comoving curvature perturbation is not identically invariant, but is invariant on superhorizon scales for any theory that is disformally related to Horndeski's theory. The difference between disformally related curvature perturbations is found to be given in terms of the comoving density perturbation associated with a single canonical scalar field. In General Relativity it is well-known that this quantity vanishes on superhorizon scales through the Poisson equation that is obtained on combining the Hamiltonian and momentum constraints, and we confirm that a similar result holds for any theory that is disformally related to Horndeski's scalar-tensor theory so long as the invertibility condition for the disformal transformation is satisfied. We also consider the curvature perturbation at full nonlinear order in the unitary gauge, and find that it is invariant under a general disformal transformation if we assume that an attractor regime has been reached. Finally, we also discuss the counting of degrees of freedom in theories disformally related to Horndeski's.
Basics of QCD perturbation theory
Soper, D.E.
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.
New results in perturbative QCD
Ellis, R.K.
1985-11-01
Three topics in perturbative QCD important for Super-collider physics are reviewed. The topics are: (2 2) jet phenomena calculated in O( sT); new techniques for the calculation of tree graphs; and colour coherence in jet phenomena. 31 refs., 6 figs.
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.
The natural and perturbed troposphere
NASA Technical Reports Server (NTRS)
Stewart, R. W.; Hameed, S.; Pinto, J.
1978-01-01
A quantitative assessment of the chemical and climatic effects of industrial emissions into the atmosphere requires an understanding of the complex interactions of species within the atmosphere and of the atmosphere with other physical systems such as the oceans, lithosphere, and biosphere. The concentration of a particular species is determined by competition between various production and loss processes. The abundances of tropospheric gases are examined. The reactions of the members of the oxygen group are considered along with the models which have been developed to describe the involved relationships. Attention is also given to the natural carbon cycle, perturbations to the carbon cycle, the natural nitrogen cycle, perturbations to the nitrogen cycle, the hydrogen group, the sulfur group, and the halogen group.
BRST quantization of cosmological perturbations
NASA Astrophysics Data System (ADS)
Armendariz-Picon, Cristian; Şengör, Gizem
2016-11-01
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas Dirac quantization, which amounts to quantization in synchronous gauge, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.
BRST quantization of cosmological perturbations
Armendariz-Picon, Cristian; Şengör, Gizem
2016-11-08
BRST quantization is an elegant and powerful method to quantize theories with local symmetries. In this article we study the Hamiltonian BRST quantization of cosmological perturbations in a universe dominated by a scalar field, along with the closely related quantization method of Dirac. We describe how both formalisms apply to perturbations in a time-dependent background, and how expectation values of gauge-invariant operators can be calculated in the in-in formalism. Our analysis focuses mostly on the free theory. By appropriate canonical transformations we simplify and diagonalize the free Hamiltonian. BRST quantization in derivative gauges allows us to dramatically simplify the structure of the propagators, whereas Dirac quantization, which amounts to quantization in synchronous gauge, dispenses with the need to introduce ghosts and preserves the locality of the gauge-fixed action.
R evolution: Improving perturbative QCD
Hoang, Andre H.; Jain, Ambar; Stewart, Iain W.; Scimemi, Ignazio
2010-07-01
Perturbative QCD results in the MS scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the ''MSR scheme'' which achieves this in a Lorentz and gauge invariant way and has a very simple relation to MS. Results in MSR depend on a cutoff parameter R, in addition to the {mu} of MS. R variations can be used to independently estimate (i.) the size of power corrections, and (ii.) higher-order perturbative corrections (much like {mu} in MS). We give two examples at three-loop order, the ratio of mass splittings in the B*-B and D*-D systems, and the Ellis-Jaffe sum rule as a function of momentum transfer Q in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for Q{approx}1 GeV, and power corrections are reduced compared to MS.
Perturbation growth in accreting filaments
NASA Astrophysics Data System (ADS)
Clarke, S. D.; Whitworth, A. P.; Hubber, D. A.
2016-05-01
We use smoothed particle hydrodynamic simulations to investigate the growth of perturbations in infinitely long filaments as they form and grow by accretion. The growth of these perturbations leads to filament fragmentation and the formation of cores. Most previous work on this subject has been confined to the growth and fragmentation of equilibrium filaments and has found that there exists a preferential fragmentation length-scale which is roughly four times the filament's diameter. Our results show a more complicated dispersion relation with a series of peaks linking perturbation wavelength and growth rate. These are due to gravo-acoustic oscillations along the longitudinal axis during the sub-critical phase of growth. The positions of the peaks in growth rate have a strong dependence on both the mass accretion rate onto the filament and the temperature of the gas. When seeded with a multiwavelength density power spectrum, there exists a clear preferred core separation equal to the largest peak in the dispersion relation. Our results allow one to estimate a minimum age for a filament which is breaking up into regularly spaced fragments, as well as an average accretion rate. We apply the model to observations of filaments in Taurus by Tafalla & Hacar and find accretion rates consistent with those estimated by Palmeirim et al.
NASA Astrophysics Data System (ADS)
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
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.
Mabood, Fazle; Khan, Waqar A.; Ismail, Ahmad Izani
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. PMID:24376722
NASA Astrophysics Data System (ADS)
Kandasamy, R.; Muhaimin, I.; Puvi Arasu, P.; Loganathan, P.
2011-05-01
An analytical technique, namely, the homotopy analysis method, is applied to analyze the effect of chemical reaction and thermophoresis particle deposition on the MHD mixed convective heat and mass transfer for a Hiemenz flow over a porous wedge in the presence of heat radiation. The fluid is assumed to be viscous and incompressible. Analytical and numerical calculations are carried out for different values of dimensionless parameters, and an analysis of the results obtained shows that the flow field is influenced appreciably by the buoyancy ratio as well as by the thermal diffusion and suction/injection parameters. The effects of these parameters on the process characteristics are investigated methodically, and typical results are illustrated. An explicit, totally analytical, and uniformly valid solution is derived which agrees well with numerical results.
Geometric Hamiltonian structures and perturbation theory
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.
Gyrokinetic Theory and Computational Methods for Electromagnetic Perturbations in Tokamaks
NASA Astrophysics Data System (ADS)
Qin, H.; Tang, W. M.; Rewoldt, G.
1998-11-01
A general gyrokinetic formalism and computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and the associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both MHD instabilities and electromagnetic drift waves(H. Qin, W. M. Tang, and G. Rewoldt, Phys. Plasmas 5), 1035 (1998). The gyrokinetic system of equations is derived by phase-space Lagrangian Lie perturbation methods. An important component missing from previous gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed. The corresponding numerical code, KIN-2DEM, has been systematically benchmarked against the high-n FULL code, the PEST code, and the NOVA-K code for kinetic ballooning modes, internal kink modes, and TAEs, respectively. For the internal kink mode, it is found that kinetic effects due to trapped ions can significantly modify the γ vs. q0 curve. For the destabilization of the TAEs by energetic particles, comparisons have been made between the non-perturbative, fully kinetic KIN-2DEM results and the perturbative hybrid NOVA-K results.
Anisotropic Heat Transport in the Presence of Resonant Magnetic Perturbations
NASA Astrophysics Data System (ADS)
Held, Eric; Kruger, Scott
2009-05-01
Heat transport in the H-mode tokamak edge is significantly modified by the presence of resonant magnetic perturbations. Application of collisional transport models to this problem ignores the fact that temperatures at the top of the edge pedestal may be several keV. Here, we compare the effective radial heat transport predicted by local (diffusive) and nonlocal (integral) forms for the parallel heat flux. Accurately predicting this effective radial heat transport becomes important when significant magnetic field line stochasticity is present, as in the case of overlapping magnetic perturbations. For such cases, the integral form for the parallel heat transport correctly assesses the effects of temperature perturbations all along the magnetic field line and yields predictions that vary substantially from the diffusive closure, which relies only on the local temperature gradient. Quantitative comparisons of effective radial transport are given for single helicity and multiple helicity magnetic perturbations in cylindrical and toroidal geometry, with emphasis given to a toroidal case with a narrow pedestal width and a high temperature at the top of the pedestal. E. D. Held, J. D. Callen, C. C. Hegna, C. R. Sovinec, T. A. Gianakon,and S. E. Kruger, Phys Plasmas, 11, 2419 (2004).
Anisotropic Heat Transport in the Presence of Resonant Magnetic Perturbations
NASA Astrophysics Data System (ADS)
Kruger, Scott; Held, Eric
2008-11-01
Heat transport in the H-mode tokamak edge is significantly modified by the presence of resonant magnetic perturbations. Application of collisional transport models to this problem ignores the fact that temperatures at the top of the edge pedestal may be several keV. Here, we compare the effective radial heat transport predicted by local (diffusive) and nonlocal [1] (integral) forms for the parallel heat flux. Accurately predicting this effective radial heat transport becomes important when significant magnetic field line stochasticity is present, as in the case of overlapping magnetic perturbations. For such cases, the integral form for the parallel heat transport correctly assesses the effects of temperature perturbations all along the magnetic field line and yields predictions that vary substantially from the diffusive closure, which relies only on the local temperature gradient. Quantitative comparisons of effective radial transport are given for single helicity and multiple helicity magnetic perturbations in cylindrical and toroidal geometry, with emphasis given to a toroidal case with a narrow pedestal width and a high temperature at the top of the pedestal. [0pt] [1] E. D. Held, J. D. Callen, C. C. Hegna, C. R. Sovinec, T. A. Gianakon, and S. E. Kruger, Phys Plasmas, 11, 2419 (2004).
Cosmological perturbations and quasistatic assumption in f (R ) theories
NASA Astrophysics Data System (ADS)
Chiu, Mu-Chen; Taylor, Andy; Shu, Chenggang; Tu, Hong
2015-11-01
f (R ) gravity is one of the simplest theories of modified gravity to explain the accelerated cosmic expansion. Although it is usually assumed that the quasi-Newtonian approach (a combination of the quasistatic approximation and sub-Hubble limit) for cosmic perturbations is good enough to describe the evolution of large scale structure in f (R ) models, some studies have suggested that this method is not valid for all f (R ) models. Here, we show that in the matter-dominated era, the pressure and shear equations alone, which can be recast into four first-order equations to solve for cosmological perturbations exactly, are sufficient to solve for the Newtonian potential, Ψ , and the curvature potential, Φ . Based on these two equations, we are able to clarify how the exact linear perturbations fit into different limits. We find that the Compton length controls the quasistatic behaviors in f (R ) gravity. In addition, regardless the validity of quasistatic approximation, a strong version of the sub-Hubble limit alone is sufficient to reduce the exact linear perturbations in any viable f (R ) gravity to second order. Our findings disagree with some previous studies where we find little difference between our exact and quasi-Newtonian solutions even up to k =10 c-1H0.
Semi-dynamical perturbations of unified dark energy
Lombriser, Lucas; Taylor, Andy E-mail: ant@roe.ac.uk
2015-11-01
Linear cosmological perturbations of a large class of modified gravity and dark energy models can be unified in the effective field theory of cosmic acceleration, encompassing Horndeski scalar-tensor theories and beyond. The fully available model space inherent to this formalism cannot be constrained by measurements in the quasistatic small-scale regime alone. To facilitate the analysis of modifications from the concordance model beyond this limit, we introduce a semi-dynamical treatment extrapolated from the evolution of perturbations at a pivot scale of choice. At small scales, and for Horndeski theories, the resulting modifications recover a quasistatic approximation but account for corrections to it near the Hubble scale. For models beyond Horndeski gravity, we find that the velocity field and time derivative of the spatial metric potential can generally not be neglected, even in the small-scale limit. We test the semi-dynamical approximation against the linear perturbations of a range of dark energy and modified gravity models, finding good agreement between the two.
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.
NASA Astrophysics Data System (ADS)
Kanno, Ryutaro; Nunami, Masanori; Satake, Shinsuke; Takamaru, Hisanori; Okamoto, Masao
2013-06-01
We investigate how the neoclassical thermal diffusivity of an axisymmetric toroidal plasma is modified by the effect of resonant magnetic perturbations (RMPs), using a drift-kinetic simulation code for calculating the radial thermal diffusivity of ion in the perturbed region under an assumption of zero electric field. Here, the perturbed region is assumed to be generated on and near the resonance surfaces, and is wedged in between the regular closed magnetic surfaces. We find that the dependence of the radial thermal diffusivity on parameters of the toroidal plasma is represented as \\chi_r=\\chi_r^{(0)} \\{1+ c_0\\,(\\omega_b/\
Generalized perturbation theory using two-dimensional, discrete ordinates transport theory
Childs, R.L.
1980-06-01
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 GAMMA and GAMMA*. 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.
A new approach to cosmological perturbations in f(R) models
Bertacca, Daniele; Bartolo, Nicola; Matarrese, Sabino E-mail: nicola.bartolo@pd.infn.it
2012-08-01
We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a ΛCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called 'quasi-static' approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.
Identifying Network Perturbation in Cancer
Logsdon, Benjamin A.; Gentles, Andrew J.; Lee, Su-In
2016-01-01
We present a computational framework, called DISCERN (DIfferential SparsE Regulatory Network), to identify informative topological changes in gene-regulator dependence networks inferred on the basis of mRNA expression datasets within distinct biological states. DISCERN takes two expression datasets as input: an expression dataset of diseased tissues from patients with a disease of interest and another expression dataset from matching normal tissues. DISCERN estimates the extent to which each gene is perturbed—having distinct regulator connectivity in the inferred gene-regulator dependencies between the disease and normal conditions. This approach has distinct advantages over existing methods. First, DISCERN infers conditional dependencies between candidate regulators and genes, where conditional dependence relationships discriminate the evidence for direct interactions from indirect interactions more precisely than pairwise correlation. Second, DISCERN uses a new likelihood-based scoring function to alleviate concerns about accuracy of the specific edges inferred in a particular network. DISCERN identifies perturbed genes more accurately in synthetic data than existing methods to identify perturbed genes between distinct states. In expression datasets from patients with acute myeloid leukemia (AML), breast cancer and lung cancer, genes with high DISCERN scores in each cancer are enriched for known tumor drivers, genes associated with the biological processes known to be important in the disease, and genes associated with patient prognosis, in the respective cancer. Finally, we show that DISCERN can uncover potential mechanisms underlying network perturbation by explaining observed epigenomic activity patterns in cancer and normal tissue types more accurately than alternative methods, based on the available epigenomic data from the ENCODE project. PMID:27145341
Perturbation analyses of intermolecular interactions
NASA Astrophysics Data System (ADS)
Koyama, Yohei M.; Kobayashi, Tetsuya J.; Ueda, Hiroki R.
2011-08-01
Conformational fluctuations of a protein molecule are important to its function, and it is known that environmental molecules, such as water molecules, ions, and ligand molecules, significantly affect the function by changing the conformational fluctuations. However, it is difficult to systematically understand the role of environmental molecules because intermolecular interactions related to the conformational fluctuations are complicated. To identify important intermolecular interactions with regard to the conformational fluctuations, we develop herein (i) distance-independent and (ii) distance-dependent perturbation analyses of the intermolecular interactions. We show that these perturbation analyses can be realized by performing (i) a principal component analysis using conditional expectations of truncated and shifted intermolecular potential energy terms and (ii) a functional principal component analysis using products of intermolecular forces and conditional cumulative densities. We refer to these analyses as intermolecular perturbation analysis (IPA) and distance-dependent intermolecular perturbation analysis (DIPA), respectively. For comparison of the IPA and the DIPA, we apply them to the alanine dipeptide isomerization in explicit water. Although the first IPA principal components discriminate two states (the α state and PPII (polyproline II) + β states) for larger cutoff length, the separation between the PPII state and the β state is unclear in the second IPA principal components. On the other hand, in the large cutoff value, DIPA eigenvalues converge faster than that for IPA and the top two DIPA principal components clearly identify the three states. By using the DIPA biplot, the contributions of the dipeptide-water interactions to each state are analyzed systematically. Since the DIPA improves the state identification and the convergence rate with retaining distance information, we conclude that the DIPA is a more practical method compared with the
Phase perturbation measurements through a heated ionosphere
NASA Technical Reports Server (NTRS)
Frey, A.; Gordon, W. E.
1982-01-01
High frequency radiowaves incident on an overdense (i.e., HF-frequency penetration frequency) ionosphere produce electron density irregularities. The effect of such ionospheric irregularities on the phase of UHF-radiowaves was determined. For that purpose the phase of radiowaves originating from celestial radio sources was observed with two antennas. The radiosources were chosen such that the line of sight to at least one of the antennas (usually both) passed through the modified volume of the ionosphere. Observations at 430 MHz and at 2380 MHz indicate that natural irregularities have a much stronger effect on the UHF phase fluctuations than the HF-induced irregularities for presently achieved HF-power densities of 20-80 uW/sq m. It is not clear whether some of the effects observed are the result of HF-modification of the ionosphere. Upper limits on the phase perturbations produced by HF-modification are 10 deg at 2380 MHz and 80 deg at 430 MHz.
A Schwarz alternating procedure for singular perturbation problems
Garbey, M.; Kaper, H.G.
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.
A generalized stochastic perturbation technique for plasticity problems
NASA Astrophysics Data System (ADS)
Kamiński, Marcin Marek
2010-03-01
The main aim of this paper is to present an algorithm and the solution to the nonlinear plasticity problems with random parameters. This methodology is based on the finite element method covering physical and geometrical nonlinearities and, on the other hand, on the generalized nth order stochastic perturbation method. The perturbation approach resulting from the Taylor series expansion with uncertain parameters is provided in two different ways: (i) via the straightforward differentiation of the initial incremental equation and (ii) using the modified response surface method. This methodology is illustrated with the analysis of the elasto-plastic plane truss with random Young’s modulus leading to the determination of the probabilistic moments by the hybrid stochastic symbolic-finite element method computations.
'Constraint consistency' at all orders in cosmological perturbation theory
Nandi, Debottam; Shankaranarayanan, S. E-mail: shanki@iisertvm.ac.in
2015-08-01
We study the equivalence of two—order-by-order Einstein's equation and Reduced action—approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we refer to as 'Constraint consistency' condition that needs to be satisfied in order for the two approaches to lead to identical single variable equation of motion. The method we propose here is quick and efficient to check the consistency for any model including modified gravity models. Our analysis points out an important feature which is crucial for inflationary model building i.e., all 'constraint' inconsistent models have higher order Ostrogradsky's instabilities but the reverse is not true. In other words, one can have models with constraint Lapse function and Shift vector, though it may have Ostrogradsky's instabilities. We also obtain single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.
Dark matter perturbations and viscosity: A causal approach
NASA Astrophysics Data System (ADS)
Acquaviva, Giovanni; John, Anslyn; Pénin, Aurélie
2016-08-01
The inclusion of dissipative effects in cosmic fluids modifies their clustering properties and could have observable effects on the formation of large-scale structures. We analyze the evolution of density perturbations of cold dark matter endowed with causal bulk viscosity. The perturbative analysis is carried out in the Newtonian approximation and the bulk viscosity is described by the causal Israel-Stewart (IS) theory. In contrast to the noncausal Eckart theory, we obtain a third-order evolution equation for the density contrast that depends on three free parameters. For certain parameter values, the density contrast and growth factor in IS mimic their behavior in Λ CDM when z ≥1 . Interestingly, and contrary to intuition, certain sets of parameters lead to an increase of the clustering.
"Phonon" scattering beyond perturbation theory
NASA Astrophysics Data System (ADS)
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.
Perturbative Methods in Path Integration
NASA Astrophysics Data System (ADS)
Johnson-Freyd, Theodore Paul
This dissertation addresses a number of related questions concerning perturbative "path" integrals. Perturbative methods are one of the few successful ways physicists have worked with (or even defined) these infinite-dimensional integrals, and it is important as mathematicians to check that they are correct. Chapter 0 provides a detailed introduction. We take a classical approach to path integrals in Chapter 1. Following standard arguments, we posit a Feynman-diagrammatic description of the asymptotics of the time-evolution operator for the quantum mechanics of a charged particle moving nonrelativistically through a curved manifold under the influence of an external electromagnetic field. We check that our sum of Feynman diagrams has all desired properties: it is coordinate-independent and well-defined without ultraviolet divergences, it satisfies the correct composition law, and it satisfies Schrodinger's equation thought of as a boundary-value problem in PDE. Path integrals in quantum mechanics and elsewhere in quantum field theory are almost always of the shape ∫ f es for some functions f (the "observable") and s (the "action"). In Chapter 2 we step back to analyze integrals of this type more generally. Integration by parts provides algebraic relations between the values of ∫ (-) es for different inputs, which can be packaged into a Batalin--Vilkovisky-type chain complex. Using some simple homological perturbation theory, we study the version of this complex that arises when f and s are taken to be polynomial functions, and power series are banished. We find that in such cases, the entire scheme-theoretic critical locus (complex points included) of s plays an important role, and that one can uniformly (but noncanonically) integrate out in a purely algebraic way the contributions to the integral from all "higher modes," reducing ∫ f es to an integral over the critical locus. This may help explain the presence of analytic continuation in questions like the
Phytochemicals Perturb Membranes and Promiscuously Alter Protein Function
2015-01-01
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. PMID:24901212
Accuracy of perturbative master equations.
Fleming, C H; Cummings, N I
2011-03-01
We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
Initial conditions for cosmological perturbations
NASA Astrophysics Data System (ADS)
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.
Robust control with structured perturbations
NASA Technical Reports Server (NTRS)
Keel, Leehyun
1988-01-01
Two important problems in the area of control systems design and analysis are discussed. The first is the robust stability using characteristic polynomial, which is treated first in characteristic polynomial coefficient space with respect to perturbations in the coefficients of the characteristic polynomial, and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l(sup 2) stability margin for both monic and non-monic cases. Following this, a method is extended to reveal much larger stability region. This result has been extended to the parameter space so that one can determine the stability margin, in terms of ranges of parameter variations, of the closed loop system when the nominal stabilizing controller is given. The stability margin can be enlarged by a choice of better stabilizing controller. The second problem describes the lower order stabilization problem, the motivation of the problem is as follows. Even though the wide range of stabilizing controller design methodologies is available in both the state space and transfer function domains, all of these methods produce unnecessarily high order controllers. In practice, the stabilization is only one of many requirements to be satisfied. Therefore, if the order of a stabilizing controller is excessively high, one can normally expect to have a even higher order controller on the completion of design such as inclusion of dynamic response requirements, etc. Therefore, it is reasonable to have a lowest possible order stabilizing controller first and then adjust the controller to meet additional requirements. The algorithm for designing a lower order stabilizing controller is given. The algorithm does not necessarily produce the minimum order controller; however, the algorithm is theoretically logical and some simulation results show that the algorithm works in general.
Perturbation propagation in random and evolved Boolean networks
NASA Astrophysics Data System (ADS)
Fretter, Christoph; Szejka, Agnes; Drossel, Barbara
2009-03-01
In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.
Perturbed Radius of Geosynchronous-Satellite Orbit
NASA Astrophysics Data System (ADS)
Kawase, Sei-Ichiro
We analyze theoretically how the radius of geosynchronous orbits would vary owing to the perturbations due to the sun/moon gravity, solar radiation pressure, and the oblate earth. The analysis is simple, as it uses a diagrammatic method to solve near-circular orbital motions. Results are obtained in seven terms of corrections to the radius of non-perturbed ideal orbits. Each correction term is derived, with clear physical meaning, from each component of the perturbing forces.
Singularity perturbed zero dynamics of nonlinear systems
NASA Technical Reports Server (NTRS)
Isidori, A.; Sastry, S. S.; Kokotovic, P. V.; Byrnes, C. I.
1992-01-01
Stability properties of zero dynamics are among the crucial input-output properties of both linear and nonlinear systems. Unstable, or 'nonminimum phase', zero dynamics are a major obstacle to input-output linearization and high-gain designs. An analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system's relative degree, it manifests itself as a singular perturbation of zero dynamics. Conditions are given under which the zero dynamics evolve in two timescales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics.
Kato expansion in quantum canonical perturbation theory
NASA Astrophysics Data System (ADS)
Nikolaev, Andrey
2016-06-01
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.
Simple Theory of Geosynchronous-Orbit Perturbations
NASA Astrophysics Data System (ADS)
Kawase, Sei-Ichiro
A simple perturbation theory is introduced for modeling geosynchronous orbits. The theory uses diagrammatic representations of orbits, and derives the perturbations in a direct manner without using differential equations. Perturbations of major importance are derived, including satellite-longitude changes due to the earth’s asymmetric shape, orbital eccentricity increase due to the sun-radiation pressure, and orbital plane inclination due to the sun/moon attraction. The theory clarifies the physical/geometrical meaning of the perturbations while using minimal mathematical analysis.
Generic perturbations of linear integrable Hamiltonian systems
NASA Astrophysics Data System (ADS)
Bounemoura, Abed
2016-11-01
In this paper, we investigate perturbations of linear integrable Hamiltonian systems, with the aim of establishing results in the spirit of the KAM theorem (preservation of invariant tori), the Nekhoroshev theorem (stability of the action variables for a finite but long interval of time) and Arnold diffusion (instability of the action variables). Whether the frequency of the integrable system is resonant or not, it is known that the KAM theorem does not hold true for all perturbations; when the frequency is resonant, it is the Nekhoroshev theorem that does not hold true for all perturbations. Our first result deals with the resonant case: we prove a result of instability for a generic perturbation, which implies that the KAM and the Nekhoroshev theorem do not hold true even for a generic perturbation. The case where the frequency is nonresonant is more subtle. Our second result shows that for a generic perturbation the KAM theorem holds true. Concerning the Nekhrosohev theorem, it is known that one has stability over an exponentially long (with respect to some function of ɛ -1) interval of time and that this cannot be improved for all perturbations. Our third result shows that for a generic perturbation one has stability for a doubly exponentially long interval of time. The only question left unanswered is whether one has instability for a generic perturbation (necessarily after this very long interval of time).
Schettino, Luis F; Adamovich, Sergei V; Tunik, Eugene
2017-03-22
Our understanding of reach-to-grasp movements has evolved from the original formulation of the movement as two semi-independent visuomotor channels to one of interdependence. In spite of a number of important contributions involving perturbations of the reach or the grasp, some of the features of the movement, such as the presence or absence of coordination between the digits during the pincer grasp and the extent of spatio-temporal interdependence between the transport and the grasp are still unclear. In this study, we physically perturbed the index finger into extension during grasping closure, on a minority of trials, to test whether modifying the movement of one digit would affect the movement of the opposite digit, suggestive of an overarching coordinative process. Furthermore, we tested whether the disruption of the grasp results in the modification of kinematic parameters of the transport. Our results showed that a continuous perturbation to the index finger affected wrist velocity but not lateral displacement. Moreover, we found that the typical flexion of the thumb observed in non-perturbed trials was delayed until the index finger counteracted the extension force. These results suggest that physically perturbing the grasp modifies the kinematics of the transport component, indicating a two-way interdependence of the reach and the grasp. Further, a perturbation to one digit affects the kinematics of the other, supporting a model of grasping wherein the digits are coordinated by a higher level process rather than being independently controlled.
Perturbation theory in light-cone quantization
Langnau, A.
1992-01-01
A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory.
Non-perturbative approach for curvature perturbations in stochastic δ N formalism
Fujita, Tomohiro; Kawasaki, Masahiro; Tada, Yuichiro E-mail: kawasaki@icrr.u-tokyo.ac.jp
2014-10-01
In our previous paper [1], we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the perturbative expansion with respect to the inflaton fields on super-horizon scale, it works even in highly stochastic cases. For example, when the curvature perturbations are very large or the non-Gaussianities of the curvature perturbations are sizable, the perturbative expansion may break down but our algorithm enables to calculate the curvature perturbations. We apply it to two well-known inflation models, chaotic and hybrid inflation, in this paper. Especially for hybrid inflation, while the potential is very flat around the critical point and the standard perturbative computation is problematic, we successfully calculate the curvature perturbations.
Laine, T A; Friberg, A T
2000-06-01
We investigate electromagnetic wave reflection and propagation in layered Kerr structures by introducing a method based on the application of canonical perturbation theory to fields in nonlinear media. Via the Hamilton-Jacobi formalism of classical mechanics, the waves in linear layers are expressed with constant canonical variables. The nonlinearity is treated as a small perturbation that modifies the constant invariants. We explicitly evaluate the nonlinear fields correct to first order by perturbation and compare the results to a rigorous nonlinear thin-layer model. Both polarizations, TE and TM, are considered separately. An exact quadrature solution of the nonlinear field in TM polarization is derived. We show that with weak nonlinearities the perturbative technique yields simple and accurate analytical expressions for the nonlinear fields. The results give physical insight into the use of nonlinear media for controlling the scattered fields in layered structures.
Full linear perturbations and localization of gravity on f( R, T) brane
NASA Astrophysics Data System (ADS)
Gu, Bao-Min; Zhang, Yu-Peng; Yu, Hao; Liu, Yu-Xiao
2017-02-01
We study the thick brane world system constructed in the recently proposed f( R, T) theories of gravity, with R the Ricci scalar and T the trace of the energy-momentum tensor. We try to get the analytic background solutions and discuss the full linear perturbations, especially the scalar perturbations. We compare how the brane world model is modified with that of general relativity coupled to a canonical scalar field. It is found that some more interesting background solutions are allowed, and only the scalar perturbation mode is modified. There is no tachyon state existing in this model and only the massless tensor mode can be localized on the brane, which recovers the effective four-dimensional gravity. These conclusions hold provided that two constraints on the original formalism of the action are satisfied.
Importance of Plasma Response to Non-axisymmetric Perturbations in Tokamaks
Jong-kyu Park, Allen H. Boozer, Jonathan E. Menard, Andrea M. Garofalo, Michael J. Schaffer, Richard J. Hawryluk, Stanley M. Kaye, Stefan P. Gerhardt, Steve A. Sabbagh, and the NSTX Team
2009-04-22
Tokamaks are sensitive to deviations from axisymmetry as small as δB=B0 ~ 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 equiva- lently 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 suffciently 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.
Lensing signals from spin-2 perturbations
Adamek, Julian; Durrer, Ruth; Tansella, Vittorio E-mail: ruth.durrer@unige.ch
2016-01-01
We compute the angular power spectra of the E-type and B-type lensing potentials for gravitational waves from inflation and for tensor perturbations induced by scalar perturbations. We derive the tensor-lensed CMB power spectra for both cases. We also apply our formalism to determine the linear lensing potential for a Bianchi I spacetime with small anisotropy.
Scalar Quantum Electrodynamics: Perturbation Theory and Beyond
Bashir, A.; Gutierrez-Guerrero, L. X.; Concha-Sanchez, Y.
2006-09-25
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.
Speech Compensation for Time-Scale-Modified Auditory Feedback
ERIC Educational Resources Information Center
Ogane, Rintaro; Honda, Masaaki
2014-01-01
Purpose: The purpose of this study was to examine speech compensation in response to time-scale-modified auditory feedback during the transition of the semivowel for a target utterance of /ija/. Method: Each utterance session consisted of 10 control trials in the normal feedback condition followed by 20 perturbed trials in the modified auditory…
NASA Astrophysics Data System (ADS)
Kirschner, S. M.; Samii, M. V.; Broaddus, S. R.; Doll, C. E.
1988-09-01
The Preliminary Orbit Determination System (PODS) provides early orbit determination capability in the Trajectory Computation and Orbital Products System (TCOPS) for a Tracking and Data Relay Satellite System (TDRSS)-tracked spacecraft. PODS computes a set of orbit states from an a priori estimate and six tracking measurements, consisting of any combination of TDRSS range and Doppler tracking measurements. PODS uses the homotopy continuation method to solve a set of nonlinear equations, and it is particularly effective for the case when the a priori estimate is not well known. Since range and Doppler measurements produce multiple states in PODS, a screening technique selects the desired state. PODS is executed in the TCOPS environment and can directly access all operational data sets. At the completion of the preliminary orbit determination, the PODS-generated state, along with additional tracking measurements, can be directly input to the differential correction (DC) process to generate an improved state. To validate the computational and operational capabilities of PODS, tests were performed using simulated TDRSS tracking measurements for the Cosmic Background Explorer (COBE) satellite and using real TDRSS measurements for the Earth Radiation Budget Satellite (ERBS) and the Solar Mesosphere Explorer (SME) spacecraft. The effects of various measurement combinations, varying arc lengths, and levels of degradation of the a priori state vector on the PODS solutions were considered.
NASA Technical Reports Server (NTRS)
Kirschner, S. M.; Samii, M. V.; Broaddus, S. R.; Doll, C. E.
1988-01-01
The Preliminary Orbit Determination System (PODS) provides early orbit determination capability in the Trajectory Computation and Orbital Products System (TCOPS) for a Tracking and Data Relay Satellite System (TDRSS)-tracked spacecraft. PODS computes a set of orbit states from an a priori estimate and six tracking measurements, consisting of any combination of TDRSS range and Doppler tracking measurements. PODS uses the homotopy continuation method to solve a set of nonlinear equations, and it is particularly effective for the case when the a priori estimate is not well known. Since range and Doppler measurements produce multiple states in PODS, a screening technique selects the desired state. PODS is executed in the TCOPS environment and can directly access all operational data sets. At the completion of the preliminary orbit determination, the PODS-generated state, along with additional tracking measurements, can be directly input to the differential correction (DC) process to generate an improved state. To validate the computational and operational capabilities of PODS, tests were performed using simulated TDRSS tracking measurements for the Cosmic Background Explorer (COBE) satellite and using real TDRSS measurements for the Earth Radiation Budget Satellite (ERBS) and the Solar Mesosphere Explorer (SME) spacecraft. The effects of various measurement combinations, varying arc lengths, and levels of degradation of the a priori state vector on the PODS solutions were considered.
Perturbative stability of catenoidal soap films
NASA Astrophysics Data System (ADS)
Jana, Soumya; Kar, Sayan
2013-09-01
The perturbative stability of catenoidal soap films formed between parallel, equal radii, coaxial rings is studied using analytical and semi-analytical methods. Using a theorem on the nature of eigenvalues for a class of Sturm-Liouville operators, we show that, for the given boundary conditions, azimuthally asymmetric perturbations are stable, while symmetric perturbations lead to an instability --a result demonstrated in Ben Amar et al. (Eur. Phys. J. B 3, 197 (1998)) using numerics and experiment. Further, we show how to obtain the lowest real eigenvalue of perturbations, using the semi-analytical Asymptotic Iteration Method (AIM). Conclusions using AIM support the analytically obtained result as well as the results by Ben Amar et al.. Finally, we compute the eigenfunctions and show, pictorially, how the perturbed soap film evolves in time.
The recursion relation in Lagrangian perturbation theory
Rampf, Cornelius
2012-12-01
We derive a recursion relation in the framework of Lagrangian perturbation theory, appropriate for studying the inhomogeneities of the large scale structure of the universe. We use the fact that the perturbative expansion of the matter density contrast is in one-to-one correspondence with standard perturbation theory (SPT) at any order. This correspondence has been recently shown to be valid up to fourth order for a non-relativistic, irrotational and dust-like component. Assuming it to be valid at arbitrary (higher) order, we express the Lagrangian displacement field in terms of the perturbative kernels of SPT, which are itself given by their own and well-known recursion relation. We argue that the Lagrangian solution always contains more non-linear information in comparison with the SPT solution, (mainly) if the non-perturbative density contrast is restored after the displacement field is obtained.
Covariant generalization of cosmological perturbation theory
Enqvist, Kari; Hoegdahl, Janne; Nurmi, Sami; Vernizzi, Filippo
2007-01-15
We present an approach to cosmological perturbations based on a covariant perturbative expansion between two worldlines in the real inhomogeneous universe. As an application, at an arbitrary order we define an exact scalar quantity which describes the inhomogeneities in the number of e-folds on uniform density hypersurfaces and which is conserved on all scales for a barotropic ideal fluid. We derive a compact form for its conservation equation at all orders and assign it a simple physical interpretation. To make a comparison with the standard perturbation theory, we develop a method to construct gauge-invariant quantities in a coordinate system at arbitrary order, which we apply to derive the form of the nth order perturbation in the number of e-folds on uniform density hypersurfaces and its exact evolution equation. On large scales, this provides the gauge-invariant expression for the curvature perturbation on uniform density hypersurfaces and its evolution equation at any order.
Cosmological perturbations in Hořava-Lifshitz gravity
NASA Astrophysics Data System (ADS)
Gao, Xian; Wang, Yi; Brandenberger, R.; Riotto, A.
2010-04-01
λ=1, the equation of motion for cosmological perturbations in the far UV takes the same form as in general relativity. However, in general the equation of motion is characterized by a modified dispersion relation.
Building a non-perturbative quark-gluon vertex from a perturbative one
NASA Astrophysics Data System (ADS)
Bermudez, Rocio
2016-10-01
The quark-gluon vertex describes the electromagnetic and the strong interaction among these particles. The description of this interaction at high precision in both regimes, perturbative and non-perturbative, continues being a matter of interest in the context of QCD and Hadron Physics. There exist very helpful models in the literature that explain perturbative aspects of the theory but they fail describing non-perturbative phenomena, as confinement and dynamic chiral symmetry breaking. In this work we study the structure of the quark-gluon vertex in a non-perturbative regime examining QCD, checking results with QED, and working in the Schwinger-Dyson formalism.
Anderson, C.; Macrae, P.; Taylor-Kamara, I.; Serel, S.; Vose, A.
2015-01-01
Traditional motor learning studies focus on highly goal-oriented, volitional tasks that often do not readily generalize to real-world movements. The goal of this study was to investigate how different perturbation paradigms alter error-based learning outcomes in a highly automated task. Swallowing was perturbed with neck surface electrical stimulation that opposes hyo-laryngeal elevation in 25 healthy adults (30 swallows: 10 preperturbation, 10 perturbation, and 10 postperturbation). The four study conditions were gradual-masked, gradual-unmasked, abrupt-masked, and abrupt-unmasked. Gradual perturbations increasingly intensified overtime, while abrupt perturbations were sustained at the same high intensity. The masked conditions reduced cues about the presence/absence of the perturbation (pre- and postperturbation periods had low stimulation), but unmasked conditions did not (pre- and postperturbation periods had no stimulation). Only hyo-laryngeal range of motion measures had significant outcomes; no timing measure demonstrated learning. Systematic-error reduction occurred only during the abrupt-masked and abrupt-unmasked perturbations. Only the abrupt-masked perturbation caused aftereffects. In this highly automated task, gradual perturbations did not induce learning similarly to findings of some volitional, goal-oriented adaptation task studies. Furthermore, our subtle and brief adjustment of the stimulation paradigm (masked vs. unmasked) determined whether aftereffects were present. This suggests that, in the unmasked group, sensory predictions of a motor plan were quickly and efficiently modified to disengage error-based learning behaviors. PMID:26023226
Dziekan, P; Lemarchand, A; Nowakowski, B
2012-02-01
We present a modified master equation for a homogeneous gaseous reactive system which includes nonequilibrium corrections due to the reaction-induced perturbation of the particle velocity distribution function. For the Schlögl model, the modified stochastic approach predicts nonequilibrium-induced transitions between different dynamical regimes, including the transformation of a monostable system into a bistable one, and vice versa. These predictions are confirmed by the comparison with microscopic simulations using the direct simulation Monte Carlo method. Compared to microscopic simulations of the particle dynamics, the modified master equation approach proves to be much more efficient.
Perturbative quantization of two-dimensional space-time noncommutative QED
Ghasemkhani, M.; Sadooghi, N.
2010-02-15
Using the method of perturbative quantization in the first order approximation, we quantize a nonlocal QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e{sup 2},{theta}{sup 3}), where e is the NC-QED coupling constant and {theta} is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e{sup 2},{theta}{sup 3}). Using these commutation relations, the canonical current algebra of the modified theory is also derived.
Vector perturbations in a contracting Universe
Battefeld, T.J.; Brandenberger, R.
2004-12-15
In this note we show that vector perturbations exhibit growing mode solutions in a contracting Universe, such as the contracting phase of the pre big bang or the cyclic/ekpyrotic models of the Universe. This is not a gauge artifact and will in general lead to the breakdown of perturbation theory--a severe problem that has to be addressed in any bouncing model. We also comment on the possibility of explaining, by means of primordial vector perturbations, the existence of the observed large-scale magnetic fields. This is possible since they can be seeded by vorticity.
Asymptotic stability of singularly perturbed differential equations
NASA Astrophysics Data System (ADS)
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Perturbation calculation of thermodynamic density of states
Brown, Greg; Schulthess, Thomas C; Nicholson, Don M; Eisenbach, Markus; Stocks, George Malcolm
2011-01-01
The density of states g( ) is frequently used to calculate the temperature-dependent properties of a thermodynamic system. Here a derivation is given for calculating the warped density of states g ( ) resulting from the addition of a perturbation. The method is validated for a classical Heisenberg model of bcc Fe and the errors in the free energy are shown to be second order in the perturbation. Taking the perturbation to be the difference between a first-principles quantum-mechanical energy and a corresponding classical energy, this method can significantly reduce the computational effort required to calculate g( ) for quantum systems using the Wang-Landau approach.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
Perturbing macroscopic magnetohydrodynamic stability for toroidal plasmas
NASA Astrophysics Data System (ADS)
Comer, Kathryn J.
We have introduced a new perturbative technique to rapidly explore the dependence of long wavelength ideal magnetohydrodynamic (MHD) instabilities on equilibrium profiles, shaping properties, and wall parameters. Traditionally, these relations are studied with numerical parameter scans using computationally intensive stability codes. Our perturbative technique first finds the equilibrium and stability using traditional methods. Subsequent small changes in the original equilibrium parameters change the stability. We quickly find the new stability with an expansion of the energy principle, rather than with another run of the stability codes. We first semi-analytically apply the technique to the screw pinch after eliminating compressional Alfven wave effects. The screw pinch results validate the approach, but also indicate that allowable perturbations to equilibria with certain features may be restricted. Next, we extend the approach to toroidal geometry using experimental equilibria and a simple constructed equilibrium, with the ideal MHD stability code GATO. Stability properties are successfully predicted from perturbed toroidal equilibria when only the vacuum beyond the plasma is perturbed (through wall parameter variations), rather than the plasma itself. Small plasma equilibrium perturbations to both experimental and simple equilibria result in very large errors to the predicted stability, and valid results are found only over a narrow range of most perturbations. Despite the large errors produced when changing plasma parameters, the wall perturbations revealed two useful applications of this technique. Because the calculations are non-iterative matrix multiplications, the convergence issues that can disrupt a full MHD stability code are absent. Marginal stability, therefore, is much easier to find with the perturbative technique. Also, the perturbed results can be input as the initial guess for the eigenvalue for a full stability code, and improve subsequent
Quantitative methods in classical perturbation theory.
NASA Astrophysics Data System (ADS)
Giorgilli, A.
Poincaré proved that the series commonly used in Celestial mechanics are typically non convergent, although their usefulness is generally evident. Recent work in perturbation theory has enlightened this conjecture of Poincaré, bringing into evidence that the series of perturbation theory, although non convergent in general, furnish nevertheless valuable approximations to the true orbits for a very large time, which in some practical cases could be comparable with the age of the universe. The aim of the author's paper is to introduce the quantitative methods of perturbation theory which allow to obtain such powerful results.
Stellar oscillations in modified gravity
NASA Astrophysics Data System (ADS)
Sakstein, Jeremy
2013-12-01
Starting from the equations of modified gravity hydrodynamics, we derive the equations of motion governing linear, adiabatic, radial perturbations of stars in scalar-tensor theories. There are two new features: first, the eigenvalue equation for the period of stellar oscillations is modified such that the eigenfrequencies are always larger than predicted by general relativity. Second, the general relativity condition for stellar instability is altered so that the adiabatic index can fall below 4/3 before unstable modes appear. Stars are more stable in modified gravity theories. Specializing to the case of chameleonlike theories, we investigate these effects numerically using both polytropic Lane-Emden stars and models coming from modified gravity stellar structure simulations. We find that the change in the oscillation period of Cepheid star models can be as large as 30% for order-one matter couplings and the change in the inferred distance using the period-luminosity relation can be up to three times larger than if one had only considered the modified equilibrium structure. We discuss the implications of these results for recent and upcoming astrophysical tests and estimate that previous methods can produce new constraints such that the modifications are screened in regions of Newtonian potential of O(10-8).
Expansion of Perturbation Theory Applied to Shim Rotation Automation of the Advanced Test Reactor
NASA Astrophysics Data System (ADS)
Peterson, Joshua Loren
In 2007, the Department of Energy (DOE) declared the Advanced Test Reactor (ATR) a National Scientific User Facility (NSUF). This declaration expanded the focus of the ATR to include diversified classes of academic and industrial experiments. An essential part of the new suite of more accurate and flexible codes being deployed to support the NSUF is their ability to predict reactor behavior at startup, particularly the position of the outer shim control cylinders (OSCC). The current method used for calculating the OSCC positions during a cycle startup utilizes a heuristic trial and error approach that is impractical with the computationally intensive reactor physics tools, such as NEWT. It is therefore desirable that shim rotation prediction for startup be automated. Shim rotation prediction with perturbation theory was chosen to be investigated as one method for use with startup calculation automation. A modified form of first order perturbation theory, called phase space interpolated perturbation theory, was developed to more accurately model shim rotation prediction. Shim rotation prediction is just one application for this new modified form of perturbation theory. Phase space interpolated perturbation theory can be used on any application where the range of change to the system is known a priori, but the magnitude of change is not known. A cubic regression method was also developed to automate shim rotation prediction by using only forward solutions to the transport equation.
Perturbations of black p-branes
Abdalla, Elcio; Fernandez Piedra, Owen Pavel; Oliveira, Jeferson de; Molina, C.
2010-03-15
We consider black p-brane solutions of the low-energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a AdS{sub (p+2)}xS{sup (8-p)} space which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a (p+1)-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.
The Perturbational MO Method for Saturated Systems.
ERIC Educational Resources Information Center
Herndon, William C.
1979-01-01
Summarizes a theoretical approach using nonbonding MO's and perturbation theory to correlate properties of saturated hydrocarbons. Discussion is limited to correctly predicted using this method. Suggests calculations can be carried out quickly in organic chemistry. (Author/SA)
Simple Perturbation Example for Quantum Chemistry.
ERIC Educational Resources Information Center
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)
Controlling roll perturbations in fruit flies
Beatus, Tsevi; Guckenheimer, John M.; Cohen, Itai
2015-01-01
Owing to aerodynamic instabilities, stable flapping flight requires ever-present fast corrective actions. Here, we investigate how flies control perturbations along their body roll angle, which is unstable and their most sensitive degree of freedom. We glue a magnet to each fly and apply a short magnetic pulse that rolls it in mid-air. Fast video shows flies correct perturbations up to 100° within 30 ± 7 ms by applying a stroke-amplitude asymmetry that is well described by a linear proportional–integral controller. For more aggressive perturbations, we show evidence for nonlinear and hierarchical control mechanisms. Flies respond to roll perturbations within 5 ms, making this correction reflex one of the fastest in the animal kingdom. PMID:25762650
Singular Perturbation for Discontinuous Ordinary Differential Equations
NASA Astrophysics Data System (ADS)
Teixeira, M. A.; da Silva, P. R.
In this article some qualitative aspects of non-smooth systems on ℝn are studied through methods of Geometric Singular Perturbation Theory (GSP-Theory). We present some results that generalize some settings in low dimension, that bridge the space between such systems and singularly perturbed smooth systems. We analyze the local behavior around typical singularities and prove that the dynamics of the so called Sliding Vector Field is determined by the reduced problem on the center manifold.
Local gravitomagnetic perturbations of the lunar orbit
NASA Technical Reports Server (NTRS)
Shahid-Saless, Bahman
1992-01-01
Using the metric in the local inertial frame of the Earth, we calculate relativistic effects on the lunar orbit with the synodic month period. It is shown that such perturbations arise entirely from the gravitomagnetic components of the local metric which exist because of the relative motion of the sun with respect to the Earth. In the case of general relativity, the net perturbation has an amplitude of 3 cm for the lunar range.
A Perturbation Mechanism for Investigations of Phase-Dependent Behavior in Human Locomotion
Villarreal, Dario J.; Quintero, David; Gregg, Robert D.
2016-01-01
Bipedal locomotion is a popular area of study across multiple fields (e.g., biomechanics, neuroscience and robotics). Different hypotheses and models have tried explaining how humans achieve stable locomotion. Perturbations that produce shifts in the nominal periodic orbit of the joint kinematics during locomotion could inform about the manner in which the human neuromechanics represent the phase of gait. Ideally, this type of perturbation would modify the progression of the human subject through the gait cycle without deviating from the nominal kinematic orbits of the leg joints. However, there is a lack of publicly available experimental data with this type of perturbation. This paper presents the design and validation of a perturbation mechanism and an experimental protocol capable of producing phase-shifting perturbations of the gait cycle. The effects of this type of perturbation on the gait cycle are statistically quantified and analyzed in order to show that a clean phase shift in the gait cycle was achieved. The data collected during these experiments will be publicly available for the scientific community to test different hypotheses and models of human locomotion. PMID:27570719
NASA Astrophysics Data System (ADS)
Gavryuseva, E.; Kroussanova, N.
2002-12-01
The relationship between the state of human body and the external factors such as the different phenomena of solar activity, geomagnetic perturbations and local atmospheric characteristics is studied. The monitoring of blood pressure and electro-conductivity of human body in acupuncture points for a group fo 28 people over the period of 1.5 year has been performed daily from February 2001 to August 2002 in Capodimonte Observatory in Naples, Italy. The modified Voll method of electropuncture diagnostics was used. The strong correlation between the human body state and meteo conditions is found and the probable correlation with geomagnetic perturbations is discussed.
Perturbations of the Robertson-Walker space
NASA Astrophysics Data System (ADS)
Hwang, Jai Chan
This dissertation contains three parts consisting of thirteen chapters. Each chapter is self-contained, and can be read independently. In chapter 1, we have presented a complete set of cosmological perturbation equations using the covariant equations. We also present an explicit solution for the evolution of large scale cosmological density perturbations assuming a perfect fluid. In chapter 2, two independent gauge-invariant variables are derived which are continuous at any transition where there is a discontinuous change in pressure. In chapter 3, we present a Newtonian counterpart to the general relativistic covariant approach to cosmological perturbations. In chapter 4, we present a simple way of deriving cosmological perturbation equations in generalized gravity theories which accounts for metric perturbations in gauge-invariant way. We apply this approach to the f(phi,R)-omega(phi)phi, cphi;c Lagrangian. In chapter 5, we have derived second order differential equations for cosmological perturbations in a Robertson-Walker space, for each of the following gravity theories: f(R) gravity, generalized scalar-tensor gravity, gravity with non-minimally coupled scalar field, and induced gravity. Asymptotic solutions are derived for the large and small scale limits. In chapter 6, classical evolution of density perturbations in the large scale limit is clarified in the generalized gravity theories. In chapter 7, we apply our method to a theory with the Lagrangian L approximately f(R) + gamma RR;c;c. In chapter 8, T(M)ab;b equals 0 is shown in a general ground. In chapter 9, the origin of the Friedmann-like behavior of the perturbed model in the large scale limit is clarified in a comoving gauge. Thus, when the imperfect fluid contributions are negligible, the large scale perturbations in a nearly flat background evolve like separate Friedmann models. In chapter 10, we generalize the perturbation equations applicable to a class of generalized gravity theories with multi
Perturbations of ultralight vector field dark matter
NASA Astrophysics Data System (ADS)
Cembranos, J. A. R.; Maroto, A. L.; Núñez Jareño, S. J.
2017-02-01
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}^2≪ Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with {k}^2≫ Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c s 2 ≃ k 2/ m 2 a 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 s 2 . Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/ Φ ˜ c s 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.
Non-parametric reconstruction of cosmological matter perturbations
González, J.E.; Alcaniz, J.S.; Carvalho, J.C. E-mail: alcaniz@on.br
2016-04-01
Perturbative quantities, such as the growth rate (f) and index (γ), are powerful tools to distinguish different dark energy models or modified gravity theories even if they produce the same cosmic expansion history. In this work, without any assumption about the dynamics of the Universe, we apply a non-parametric method to current measurements of the expansion rate H(z) from cosmic chronometers and high-z quasar data and reconstruct the growth factor and rate of linearised density perturbations in the non-relativistic matter component. Assuming realistic values for the matter density parameter Ω{sub m0}, as provided by current CMB experiments, we also reconstruct the evolution of the growth index γ with redshift. We show that the reconstruction of current H(z) data constrains the growth index to γ=0.56 ± 0.12 (2σ) at z = 0.09, which is in full agreement with the prediction of the ΛCDM model and some of its extensions.
Solving Sturm-Liouville problems by piecewise perturbation methods, revisited
NASA Astrophysics Data System (ADS)
Ledoux, V.; Van Daele, M.
2010-08-01
We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the original CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability of the CPM to a wider variety of problems and allows a more efficient solution of many problems. The CPMs are closely related to the second-order coefficient approximation method underlying the SLEDGE software package, but provide for higher order approximations. These higher order approximations can also be obtained by applying a modified Neumann method. The CPM approach, however, leads to simpler formulae in a more convenient form.
Perturbed Energy Metabolism and Neuronal Circuit Dysfunction in Cognitive Impairment
Kapogiannis, Dimitrios; Mattson, Mark P.
2010-01-01
Summary Epidemiological, neuropathological and functional neuroimaging evidence implicates global and regional derangements in brain metabolism and energetics in the pathogenesis of cognitive impairment. Nerve cell microcircuits are modified adaptively by excitatory and inhibitory synaptic activity and neurotrophic factors. Aging and Alzheimer’s disease (AD) cause perturbations in cellular energy metabolism, level of excitation/inhibition and neurotrophic factor release that overwhelm compensatory mechanisms and result in neuronal microcircuit and brain network dysfunction. A prolonged positive energy balance impairs the ability of neurons to respond adaptively to oxidative and metabolic stress. Experimental studies in animals demonstrate how derangements related to chronic positive energy balance, such as diabetes, set the stage for accelerated cognitive aging and AD. Therapeutic interventions to allay cognitive dysfunction that target energy metabolism and adaptive stress responses (such as neurotrophin signaling) have shown efficacy in animal models and preliminary studies in humans. PMID:21147038
A perturbative density functional theory for square-well fluids.
Jin, Zhehui; Tang, Yiping; Wu, Jianzhong
2011-05-07
We report a perturbative density functional theory for quantitative description of the structural and thermodynamic properties of square-well fluids in the bulk or at inhomogeneous conditions. The free-energy functional combines a modified fundamental measure theory to account for the short-range repulsion and a quadratic density expansion for the long-range attraction. The long-correlation effects are taken into account by using analytical expressions of the direct correlation functions of bulk fluids recently obtained from the first-order mean-spherical approximation. The density functional theory has been calibrated by extensive comparison with simulation data from this work and from the literature. The theory yields good agreement with simulation results for the radial distribution function of bulk systems and for the density profiles of square-well fluids near the surfaces of spherical cavities or in slit pores over a broad range of the parameter space and thermodynamic conditions.
Consistent perturbations in an imperfect fluid
Sawicki, Ignacy; Amendola, Luca; Saltas, Ippocratis D.; Kunz, Martin E-mail: i.saltas@sussex.ac.uk E-mail: martin.kunz@unige.ch
2013-01-01
We present a new prescription for analysing cosmological perturbations in a more-general class of scalar-field dark-energy models where the energy-momentum tensor has an imperfect-fluid form. This class includes Brans-Dicke models, f(R) gravity, theories with kinetic gravity braiding and generalised galileons. We employ the intuitive language of fluids, allowing us to explicitly maintain a dependence on physical and potentially measurable properties. We demonstrate that hydrodynamics is not always a valid description for describing cosmological perturbations in general scalar-field theories and present a consistent alternative that nonetheless utilises the fluid language. We apply this approach explicitly to a worked example: k-essence non-minimally coupled to gravity. This is the simplest case which captures the essential new features of these imperfect-fluid models. We demonstrate the generic existence of a new scale separating regimes where the fluid is perfect and imperfect. We obtain the equations for the evolution of dark-energy density perturbations in both these regimes. The model also features two other known scales: the Compton scale related to the breaking of shift symmetry and the Jeans scale which we show is determined by the speed of propagation of small scalar-field perturbations, i.e. causality, as opposed to the frequently used definition of the ratio of the pressure and energy-density perturbations.
Local perturbations perturb—exponentially–locally
De Roeck, W. Schütz, M.
2015-06-15
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.
Compensation to whole body active rotation perturbation.
Rossi, S; Gazzellini, S; Petrarca, M; Patanè, F; Salfa, I; Castelli, E; Cappa, P
2014-01-01
The aim of the present study is the exploration of the compensation mechanisms in healthy adults elicited by superimposing a horizontal perturbation, through a rotation of the support base, during a whole body active rotation around the participant's own vertical body axis. Eight healthy participants stood on a rotating platform while executing 90° whole body rotations under three conditions: no concurrent platform rotation (NP), support surface rotation of ± 45° in the same (45-S) and opposite (45-O) directions. Participants' kinematics and CoP displacements were analyzed with an optoelectronic system and a force platform. In both 45-S and 45-O conditions, there was a tendency for the head to be affected by the external perturbation and to be the last and least perturbed segment while the pelvis was the most perturbed. The observed reduced head perturbation in 45-S and 45-O trials is consistent with a goal-oriented strategy mediated by vision and vestibular information, whereas the tuning of lumbar rotation is consistent with control mechanisms mediated by somato-sensory information.
Second order density perturbations for dust cosmologies
NASA Astrophysics Data System (ADS)
Uggla, Claes; Wainwright, John
2014-08-01
We present simple expressions for the relativistic first and second order fractional density perturbations for Friedmann-Lemaître cosmologies with dust, in four different gauges: the Poisson, uniform curvature, total matter and synchronous-comoving gauges. We include a cosmological constant and arbitrary spatial curvature in the background. A distinctive feature of our approach is our description of the spatial dependence of the perturbations using a canonical set of quadratic differential expressions involving an arbitrary spatial function that arises as a conserved quantity. This enables us to unify, simplify and extend previous seemingly disparate results. We use the primordial matter and metric perturbations that emerge at the end of the inflationary epoch to determine the additional arbitrary spatial function that arises when integrating the second order perturbation equations. This introduces a non-Gaussianity parameter into the expressions for the second order density perturbation. In the special case of zero spatial curvature we show that the time evolution simplifies significantly, and requires the use of only two nonelementary functions, the so-called growth suppression factor at the linear level, and one new function at the second order level. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the Universe.
Perturbed kernel approximation on homogeneous manifolds
NASA Astrophysics Data System (ADS)
Levesley, J.; Sun, X.
2007-02-01
Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.
Mode coupling of Schwarzschild perturbations: Ringdown frequencies
NASA Astrophysics Data System (ADS)
Pazos, Enrique; Brizuela, David; Martín-García, José M.; Tiglio, Manuel
2010-11-01
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.
Cosmological perturbations during the Bose-Einstein condensation of dark matter
Freitas, R.C.; Gonçalves, S.V.B. E-mail: sergio.vitorino@pq.cnpq.br
2013-04-01
In the present work, we analyze the evolution of the scalar and tensorial perturbations and the quantities relevant for the physical description of the Universe, as the density contrast of the scalar perturbations and the gravitational waves energy density during the Bose-Einstein condensation of dark matter. The behavior of these parameters during the Bose-Einstein phase transition of dark matter is analyzed in details. To study the cosmological dynamics and evolution of scalar and tensorial perturbations in a Universe with and without cosmological constant we use both analytical and numerical methods. The Bose-Einstein phase transition modifies the evolution of gravitational waves of cosmological origin, as well as the process of large-scale structure formation.
Analytic description of Dvali-Gabadadze-Porrati perturbations on all scales
NASA Astrophysics Data System (ADS)
Seahra, Sanjeev S.; Hu, Wayne
2010-12-01
We develop analytic solutions for the linear evolution of metric perturbations in the Dvali-Gabadadze-Porrati braneworld modified gravity scenario including near-horizon and superhorizon modes where solutions in the bulk are required. These solutions apply to both the self-accelerating and normal branch and elucidate the nature of coordinate singularities and initial data in the bulk as well as their effect on perturbation evolution on the brane. Even on superhorizon scales, the evolution of metric perturbations is no longer necessarily scale free due to multiple resonances in the bulk. Based on these analytic solutions, we devise convenient fitting functions for the evolutions that bridge the various spatial and temporal regimes. Compared with a direct numerical integration of the bulk equations, the fits are accurate at the percent level and are sufficient for current and upcoming observational tests.
Perturbation analysis of electromagnetic geodesic acoustic modes
Ren, Haijun
2014-06-15
Lagrangian displacement and magnetic field perturbation response to the geodesic acoustic mode is analyzed by using the ideal magnetohydrodynamic equations in a large-aspect-ratio tokamak. δB{sub θ}, the poloidal component of magnetic field perturbation, has poloidal wave number m = 2 created by the poloidal displacement ξ{sub θ}. The parallel perturbation of magnetic field, δB{sub ∥}, has a poloidally asymmetric structure with m = 1 and is on the same order of magnitude with δB{sub θ} to the leading order. The radial displacement ξ{sub r} is of order O(βϵξ{sub θ}) but plays a significant role in determining δB{sub ∥}, where β is the plasma/magnetic pressure ratio and ϵ is the inverse aspect ratio.
Note on the semiclassicality of cosmological perturbations
NASA Astrophysics Data System (ADS)
Donà, Pietro; Marcianò, Antonino
2016-12-01
Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to convince readers that cosmological perturbations must be addressed in term of the semiclassical limit of the expectation value of quantum fields. We first take into account cosmological perturbations originated by a quantum scalar field, and then extend our treatment in order to account for the expectation values of bilinears of Dirac fermion fields. The latter can indeed transform as scalar quantities under diffeomorphisms, as well as all the other bilinear of the Dirac fields that belong to the Clifford algebra. This is the first of a series of works that is intended to prove that cosmological quantum perturbations can actually be accounted for in terms of Dirac fermion fields, which must be treated as fundamental quantum objects, and their dynamics.
Perturbations in a regular bouncing universe
Battefeld, T.J.; Geshnizjani, G.
2006-03-15
We consider a simple toy model of a regular bouncing universe. The bounce is caused by an extra timelike dimension, which leads to a sign flip of the {rho}{sup 2} term in the effective four dimensional Randall Sundrum-like description. We find a wide class of possible bounces: big bang avoiding ones for regular matter content, and big rip avoiding ones for phantom matter. Focusing on radiation as the matter content, we discuss the evolution of scalar, vector and tensor perturbations. We compute a spectral index of n{sub s}=-1 for scalar perturbations and a deep blue index for tensor perturbations after invoking vacuum initial conditions, ruling out such a model as a realistic one. We also find that the spectrum (evaluated at Hubble crossing) is sensitive to the bounce. We conclude that it is challenging, but not impossible, for cyclic/ekpyrotic models to succeed, if one can find a regularized version.
The non-perturbative unquenched quark model
NASA Astrophysics Data System (ADS)
Entern, D. R.; Ortega, P. G.; Fernández, F.
2017-03-01
In recent years states in the quarkonium spectrum not expected in the naive quark model have appeared and created a lot of interest. In the theoretical side the study of the effect of meson-meson thresholds in the spectrum have been performed in different approximations. In a quark model framework, and in the spirit of the Cornell model, when a meson-meson threshold is included, the coupling to all the quark-antiquark states have to be considered. In practice only the closest states are included perturbatively. In this contribution we will present a framework in which we couple quark-antiquark states with meson-meson states non-perturbatively, taking into account effectively the coupling to all quark-antiquark states. The method will be applied to the study of the X(3872) and a comparison with the perturbative calculation will be performed.
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
Non-gravitational perturbations and satellite geodesy
Milani, A.; Nobill, A.M.; Farinella, P.
1987-01-01
This book presents the basic ideas of the physics of non-gravitational perturbations and the mathematics required to compute their orbital effects. It conveys the relevance of the different problems that must be solved to achieve a given level of accuracy in orbit determination and in recovery of geophysically significant parameters. Selected Contents are: Orders of Magnitude of the Perturbing Forces, Tides and Apparent Forces, Tools from Celestial Mechanics, Solar Radiation Pressure-Direct Effects: Satellite-Solar Radiation Interaction, Long-Term Effects on Semi-Major Axis, Radiation Pressure-Indirect Effects: Earth-Reflected Radiation Pressure, Anisotropic Thermal Emission, Drag: Orbital Perturbations by a Drag-Like Force, and Charged Particle Drag.
Instability of charged Lovelock black holes: Vector perturbations and scalar perturbations
NASA Astrophysics Data System (ADS)
Takahashi, Tomohiro
2013-01-01
We examine the stability of charged Lovelock black hole solutions under vector-type and scalar-type perturbations. We find suitable master variables for the stability analysis; the equations for these variables are Schrödinger-type equations with two components, and these Schrödinger operators are symmetric. By these master equations, we show that charged Lovelock black holes are stable under vector-type perturbations. For scalar-type perturbations, we show the criteria for instability and check these numerically. In our previous paper [T. Takahashi, Prog. Theor. Phys. 125, 1289 (2011)], we have shown that nearly extreme black holes show instability under tensor-type perturbations. In this paper, we find that black holes with a small charge show instability under scalar-type perturbations even if they have a relatively large mass.
A perturbative DFT approach for magnetic anisotropy
NASA Astrophysics Data System (ADS)
Khoo, Khoong Hong; Laskowski, Robert
2017-04-01
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.
Death to perturbative QCD in exclusive processes?
Eckardt, R.; Hansper, J.; Gari, M.F.
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.
Evolution of perturbations in an inflationary universe
NASA Technical Reports Server (NTRS)
Frieman, J. A.; Will, C. M.
1982-01-01
The evolution of inhomogeneous density perturbations in a model of the very early universe that is dominated for a time by a constant energy density of a false quantum-mechanical vacuum is analyzed. During this period, the universe inflates exponentially and supercools exponentially, until a phase transition back to the true vacuum reheats the matter and radiation. Focus is on the physically measurable, coordinate-independent modes of inhomogeneous perturbations of this model and it is found that all modes either are constant or are exponentially damped during the inflationary era.
Non-perturbative QCD and hadron physics
NASA Astrophysics Data System (ADS)
Cobos-Martínez, J. J.
2016-10-01
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.
Bayesian model selection and isocurvature perturbations
NASA Astrophysics Data System (ADS)
Beltrán, María; García-Bellido, Juan; Lesgourgues, Julien; Liddle, Andrew R.; Slosar, Anže
2005-03-01
Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the performance of cosmological models including isocurvature modes with the purely adiabatic case; this framework automatically and consistently penalizes models which use more parameters to fit the data. We compute the Bayesian evidence for fits to a data set comprised of WMAP and other microwave anisotropy data, the galaxy power spectrum from 2dFGRS and SDSS, and Type Ia supernovae luminosity distances. We find that Bayesian model selection favors the purely adiabatic models, but so far only at low significance.
Continuum methods in lattice perturbation theory
Becher, Thomas G
2002-11-15
We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Using integration-by-parts relations all of these can be expressed in terms of a small number of master integrals. Four master integrals are needed for bosonic one loop integrals, sixteen in QCD with Wilson or staggered fermions.
Conservative perturbation theory for nonconservative systems
NASA Astrophysics Data System (ADS)
Shah, Tirth; Chattopadhyay, Rohitashwa; Vaidya, Kedar; Chakraborty, Sagar
2015-12-01
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit-cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz., Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system—a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass an even wider range of nonconservative systems.
Poynting-Robertson effect. II - Perturbation equations
NASA Astrophysics Data System (ADS)
Klacka, J.
1992-12-01
The paper addresses the problem of the complete set of perturbation equations of celestial mechanics as applied to the Poynting-Robertson effect. Differential equations and initial conditions for them are justified. The sudden beginning of the operation of the Poynting-Robertson effect (e.g., sudden release of dust particles from a comet) is taken into account. Two sets of differential equations and initial conditions for them are obtained. Both of them are completely equivalent to Newton's equation of motion. It is stressed that the transformation mu yields mu(1-beta) must be made in perturbation equations of celestial mechanics.
Galilean invariant resummation schemes of cosmological perturbations
NASA Astrophysics Data System (ADS)
Peloso, Marco; Pietroni, Massimo
2017-01-01
Many of the methods proposed so far to go beyond Standard Perturbation Theory break invariance under time-dependent boosts (denoted here as extended Galilean Invariance, or GI). This gives rise to spurious large scale effects which spoil the small scale predictions of these approximation schemes. By using consistency relations we derive fully non-perturbative constraints that GI imposes on correlation functions. We then introduce a method to quantify the amount of GI breaking of a given scheme, and to correct it by properly tailored counterterms. Finally, we formulate resummation schemes which are manifestly GI, discuss their general features, and implement them in the so called Time-Flow, or TRG, equations.
Perturbative approach to Markovian open quantum systems
Li, Andy C. Y.; Petruccione, F.; Koch, Jens
2014-01-01
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. PMID:24811607
Spontaneous breaking of Lorentz symmetry by ghost condensation in perturbative quantum gravity
NASA Astrophysics Data System (ADS)
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.
On-Shell Methods in Perturbative QCD
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-04-25
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.
Staggered heavy baryon chiral perturbation theory
Bailey, Jon A.
2008-03-01
Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms of O(m{sub {pi}}{sup 3}), which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms of O(a{sup 2}). The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.
Revealing global regulatory perturbations across human cancers
Goodarzi, Hani; Elemento, Olivier; Tavazoie, Saeed
2010-01-01
Summary The discovery of pathways and regulatory networks whose perturbation contributes to neoplastic transformation remains a fundamental challenge for cancer biology. We show that such pathway perturbations, and the cis-regulatory elements through which they operate, can be efficiently extracted from global gene-expression profiles. Our approach utilizes information-theoretic analysis of expression levels, pathways, and genomic sequences. Analysis across a diverse set of human cancers reveals the majority of previously known cancer pathways. Through de novo motif discovery we associate these pathways with transcription-factor binding sites and miRNA targets, including those of E2F, NF-Y, p53, and let-7. Follow-up experiments confirmed that these predictions correspond to functional in vivo regulatory interactions. Strikingly, the majority of the perturbations, associated with putative cis-regulatory elements, fall outside of known cancer pathways. Our study provides a systems-level dissection of regulatory perturbations in cancer—an essential component of a rational strategy for therapeutic intervention and drug-target discovery. PMID:20005852
What Perturbs the ggrdgr Rings of Uranus?
French, R G; Kangas, J A; Elliot, J L
1986-01-31
The gamma and delta rings have by far the largest radial perturbations of any of the nine known Uranian rings. These two rings deviate from Keplerian orbits, having typical root-mean-square residuals of about 3 kilometers (compared to a few hundred meters for the other seven known rings). Possible causes for the perturbations include nearby shepherd satellites and Lindblad resonances. If shepherd satellites are responsible, they could be as large as several tens of kilometers in diameter. The perturbation patterns of the gamma and delta rings have been examined for evidence of Lindblad resonances of azimuthal wave number m = 0, 1, 2, 3, and 4. The beta ring radial residuals are well matched by a 2:1 Lindblad resonance. If this represents a real physical phenomenon and is not an artifact of undersampling, then the most plausible interpretation is that there is an undiscovered satellite orbiting 76,522 +/- 8 kilometers from Uranus, with an orbital period of 15.3595 +/- 0.0001 hours and a radius of 75 to 100 kilometers. Such a satellite would be easily detected by the Voyager spacecraft when it encounters Uranus. The 2:1 resonance location is 41 +/- 9 kilometers inside the delta ring, which makes it unlikely that the resonance is due to a viscous instability within the ring. In contrast, no low-order Lindblad resonance matches the gamma ring perturbations, which are probably caused by one or more shepherd satellites large enough to be clearly visible in Voyager images.
On the divergences of inflationary superhorizon perturbations
Enqvist, K; Nurmi, S; Podolsky, D; Rigopoulos, G I E-mail: sami.nurmi@helsinki.fi E-mail: gerasimos.rigopoulos@helsinki.fi
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.
Cosmological perturbations and classical change of signature
NASA Astrophysics Data System (ADS)
Martin, Jérôme
1995-12-01
Cosmological perturbations on a manifold admitting signature change are studied. The background solution consists in a Friedmann-Lemaître-Robertson-Walker universe filled by a constant scalar field playing the role of a cosmological constant. It is shown that no regular solution exists satisfying the junction conditions at the surface of change. The comparison with similar studies in quantum cosmology is made.
Aharonov-Bohm Effect in Perturbation Theory.
ERIC Educational Resources Information Center
Purcell, Kay M.; Henneberger, Walter C.
1978-01-01
The Aharonov-Bohn effect is obtained in first-order perturbation theory. It is shown that the effect occurs only when the initial state is a superposition of eigenstates of Lz corresponding to eigenvalues having opposite sign. (Author/GA)
Privacy Is Become with, Data Perturbation
NASA Astrophysics Data System (ADS)
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.
Doubly perturbed neutral stochastic functional equations
NASA Astrophysics Data System (ADS)
Hu, Lanying; Ren, Yong
2009-09-01
In this paper, we prove the existence and uniqueness of the solution to a class of doubly perturbed neutral stochastic functional equations (DPNSFEs in short) under some non-Lipschitz conditions. The solution is constructed by successive approximation. Furthermore, we give the continuous dependence of the solution on the initial value by means of the corollary of Bihari inequality.
NASA Astrophysics Data System (ADS)
Enea Romano, Antonio; Sanes Negrete, Sergio; Sasaki, Misao; Starobinsky, Alexei A.
2014-06-01
We study effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations of the type predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local underdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of a cosmological constant of the order of 0.6{%},1{%},1.5{%} , respectively. These effects cannot be neglected in the precision cosmology era in which we are entering. Our results can be considered an upper bound for the effect of the monopole component of the local non-linear structure which can arise from primordial curvature perturbations and requires a fully non-perturbative relativistic treatment.
Nonderivative modified gravity: a classification
Comelli, D.; Nesti, F.; Pilo, L. E-mail: fabrizio.nesti@irb.hr
2014-11-01
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 possibility.
Conformal invariant cosmological perturbations via the covariant approach
Li, Mingzhe; Mou, Yicen E-mail: moinch@mail.ustc.edu.cn
2015-10-01
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it is possible to do equivalent analysis in a certain frame in which the perturbation equations are simpler. In this paper we revisit the problem of conformal invariances of cosmological perturbations in terms of the covariant approach in which the perturbation variables have clear geometric and physical meanings. We show that with this approach the conformal invariant perturbations are easily identified.
Uniqueness of static photon surfaces: Perturbative approach
NASA Astrophysics Data System (ADS)
Yoshino, Hirotaka
2017-02-01
A photon surface S is defined as a three-dimensional timelike hypersurface such that any null geodesic initially tangent to S continues to be included in S , like r =3 M of the Schwarzschild spacetime. Using analytic solutions to static perturbations of a Schwarzschild spacetime, we examine whether a nonspherical spacetime can possess a distorted static photon surface. It is shown that if the region outside of r =3 M is vacuum, no distorted photon surface can be present. Therefore, we establish the perturbative uniqueness for an asymptotically flat vacuum spacetime with a static photon surface. It is also pointed out that if matter is present in the outside region, there is a possibility that a distorted photon surface could form.
Control of asymmetric magnetic perturbations in tokamaks.
Park, Jong-Kyu; Schaffer, Michael J; Menard, Jonathan E; Boozer, Allen H
2007-11-09
The sensitivity of tokamak plasmas to very small deviations from the axisymmetry of the magnetic field |deltaB/B| approximately 10{-4} is well known. What was not understood until very recently is the importance of the perturbation to the plasma equilibrium in assessing the effects of externally produced asymmetries in the magnetic field, even far from a stability limit. DIII-D and NSTX experiments find that when the deleterious effects of asymmetries are mitigated, the external asymmetric field was often made stronger and had an increased interaction with the magnetic field of the unperturbed equilibrium. This Letter explains these counterintuitive results. The explanation using ideal perturbed equilibria has important implications for the control of field errors in all toroidal plasmas.
Revisiting perturbations in extended quasidilaton massive gravity
Heisenberg, Lavinia
2015-04-01
In this work we study the theory of extended quasidilaton massive gravity together with the presence of matter fields. After discussing the homogeneous and isotropic fully dynamical background equations, which governs the exact expansion history of the universe, we consider small cosmological perturbations around these general FLRW solutions. The stability of tensor, vector and scalar perturbations on top of these general background solutions give rise to slightly different constraints on the parameters of the theory than those obtained in the approximative assumption of the late-time asymptotic form of the expansion history, which does not correspond to our current epoch. This opens up the possibility of stable FLRW solutions to be compared with current data on cosmic expansion with the restricted parameter space based on theoretical ground.
Four-loop screened perturbation theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Kyllingstad, Lars
2008-10-01
We study the thermodynamics of massless ϕ4-theory using screened perturbation theory. In this method, the perturbative expansion is reorganized by adding and subtracting a thermal mass term in the Lagrangian. We calculate the free energy through four loops expanding in a double power expansion in m/T and g2, where m is the thermal mass and g is the coupling constant. The expansion is truncated at order g7 and the loop expansion is shown to have better convergence properties than the weak-coupling expansion. The free energy at order g6 involves the four-loop triangle sum-integral evaluated by Gynther, Laine, Schröder, Torrero, and Vuorinen using the methods developed by Arnold and Zhai. The evaluation of the free energy at order g7 requires the evaluation of a nontrivial three-loop sum-integral, which we calculate by the same methods.
Perturbation theory for asymmetric deformed microdisk cavities
NASA Astrophysics Data System (ADS)
Kullig, Julius; Wiersig, Jan
2016-10-01
In an article by Dubertrand et al. [Phys. Rev. A 77, 013804 (2008), 10.1103/PhysRevA.77.013804] the perturbation theory for slightly deformed optical microcavities with a mirror-reflection symmetry was developed. However, in real experiments such a mirror-reflection symmetry is often not present either intended or unintended via production tolerances. In this paper we therefore extended the perturbation theory to asymmetric boundary deformations. Consequently, we are able to describe interesting non-Hermitian phenomena like copropagation of optical modes in the (counter-)clockwise direction inside the cavity. The derived analytic formulas are demonstrated at two generic boundary shapes, the spiral and the double-notched circle where a good agreement to the numerical boundary element method is observed.
Random matter density perturbations and LMA
NASA Astrophysics Data System (ADS)
Reggiani, N.; Guzzo, M. M.; de Holanda, P. C.
There are reasons to believe that mechanisms exist in the solar interior which lead to random density perturbations in the resonant region of the Large Mixing Angle solution to the solar neutrino problem. We find that, in the presence of these density perturbations, the best fit point in the (sin 2 2θ , Δ m2) parameter space moves to smaller values, compared with the values obtained for the standard LMA solution. Combining solar data with KamLAND results, we find a new compatibility region, which we call VERY-LOW LMA, where sin 2 2θ ~ 0.6 and Δm2 2× 10-5 eV2, for random density fluctuations of order 5% < ξ < 8%. We argue that such values of density fluctuations are still allowed by helioseismological observations at small scales of order 10 - 1000 km deep inside the solar core. PACS: 26.65 - 90.60J - 96.60.H
Confinement with Perturbation Theory, After All?
NASA Astrophysics Data System (ADS)
Hoyer, Paul
2015-09-01
I call attention to the possibility that QCD bound states (hadrons) could be derived using rigorous Hamiltonian, perturbative methods. Solving Gauss' law for A 0 with a non-vanishing boundary condition at spatial infinity gives an linear potential for color singlet and qqq states. These states are Poincaré and gauge covariant and thus can serve as initial states of a perturbative expansion, replacing the conventional free in and out states. The coupling freezes at , allowing reasonable convergence. The bound states have a sea of pairs, while transverse gluons contribute only at . Pair creation in the linear A 0 potential leads to string breaking and hadron loop corrections. These corrections give finite widths to excited states, as required by unitarity. Several of these features have been verified analytically in D = 1 + 1 dimensions, and some in D = 3 + 1.
Cosmological perturbations in transient phantom inflation scenarios
NASA Astrophysics Data System (ADS)
Richarte, Martín G.; Kremer, Gilberto M.
2017-01-01
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.
Thermostat-Like Perturbations of an Oscillator
NASA Astrophysics Data System (ADS)
Freidlin, Mark
2016-07-01
We consider an oscillator with one degree of freedom perturbed by a deterministic thermostat-like perturbation and another system, in particular, another oscillator, coupled with the first one. If the Hamiltonian of the first system has saddle points, the whole system has, in a sense, a stochastic behavior on long time intervals. Under certain conditions, one can introduce the relative entropy and describe metastability and other large deviation effects in this deterministic system. If the coupled system is also an oscillator, the long time evolution of the energy of this oscillator has a diffusion approximation. To get these results one has to regularize the system. But the results are, to some extent, independent of the regularization: the stochasticity is due to instabilities at saddle points of the original system.
Intelligent perturbation algorithms for space scheduling optimization
NASA Technical Reports Server (NTRS)
Kurtzman, Clifford R.
1990-01-01
The optimization of space operations is examined in the light of optimization heuristics for computer algorithms and iterative search techniques. Specific attention is given to the search concepts known collectively as intelligent perturbation algorithms (IPAs) and their application to crew/resource allocation problems. IPAs iteratively examine successive schedules which become progressively more efficient, and the characteristics of good perturbation operators are listed. IPAs can be applied to aerospace systems to efficiently utilize crews, payloads, and resources in the context of systems such as Space-Station scheduling. A program is presented called the MFIVE Space Station Scheduling Worksheet which generates task assignments and resource usage structures. The IPAs can be used to develop flexible manifesting and scheduling for the Industrial Space Facility.
Constraining compensated isocurvature perturbations using the CMB
NASA Astrophysics Data System (ADS)
Smith, Tristan L.; Rhiannon Smith, Kyle Yee, Julian Munoz, Daniel Grin
2017-01-01
Compensated isocurvature perturbations (CIPs) are variations in the cosmic baryon fraction which leave the total non-relativistic matter (and radiation) density unchanged. They are predicted by models of inflation which involve more than one scalar field, such as the curvaton scenario. At linear order, they leave the CMB two-point correlation function nearly unchanged: this is why existing constraints to CIPs are so much more permissive than constraints to typical isocurvature perturbations. Recent work articulated an efficient way to calculate the second order CIP effects on the CMB two-point correlation. We have implemented this method in order to explore constraints to the CIP amplitude using current Planck temperature and polarization data. In addition, we have computed the contribution of CIPs to the CMB lensing estimator which provides us with a novel method to use CMB data to place constraints on CIPs. We find that Planck data places a constraint to the CIP amplitude which is competitive with other methods.
Perturbational analysis of plasmon decay in jellium
NASA Astrophysics Data System (ADS)
Bachlechner, Martina E.; Macke, Wilhelm; Miesenböck, Helga M.; Schinner, Andreas
1991-02-01
Plasmon damping in the three-dimensional homogeneous electron gas is investigated within second order perturbation theory for the density-density response function. The equivalence of several existing approaches that take into account lowest order two-pair excitations is shown explicitly. Finally, a complete Monte-Carlo analysis of the multi-dimensional integrals for the dielectric function is made for arbitrary densities.
Geometric perturbation theory and plasma physics
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.
A chiral perturbation expansion for gravity
NASA Astrophysics Data System (ADS)
Abou-Zeid, Mohab; Hull, Christopher M.
2006-02-01
A formulation of Einstein gravity, analogous to that for gauge theory arising from the Chalmers-Siegel action, leads to a perturbation theory about an asymmetric weak coupling limit that treats positive and negative helicities differently. We find power counting rules for amplitudes that suggest the theory could find a natural interpretation in terms of a twistor-string theory for gravity with amplitudes supported on holomorphic curves in twistor space.
Multiple scattering by deep perturbed gratings
Knotts, M.E.; O`Donnell, K.A.
1994-11-01
We present measurements of the far-field scattered intensity for gratings consisting of uniform, regularly spaced, wavelength-scale grooves that have randomly fluctuating depths. The complete polarization dependence of the scattering is determined, and particular attention is given to measurements that isolate multiple scattering. For both perturbed and unperturbed gratings, effects similar to backscattering enhancement seen for randomly rough surfaces are observed, and these effects are linked to the coherent interference of reciprocal pairs of waves multiply scattered within the grooves.
Intelligent perturbation algorithms to space scheduling optimization
NASA Technical Reports Server (NTRS)
Kurtzman, Clifford R.
1991-01-01
The limited availability and high cost of crew time and scarce resources make optimization of space operations critical. Advances in computer technology coupled with new iterative search techniques permit the near optimization of complex scheduling problems that were previously considered computationally intractable. Described here is a class of search techniques called Intelligent Perturbation Algorithms. Several scheduling systems which use these algorithms to optimize the scheduling of space crew, payload, and resource operations are also discussed.
Study of the spectrum of inflaton perturbations
NASA Astrophysics Data System (ADS)
Glenz, Matthew M.; Parker, Leonard
2009-09-01
We examine the spectrum of inflaton fluctuations resulting from any given long period of exponential inflation. Infrared and ultraviolet divergences in the inflaton dispersion summed over all modes do not appear in our approach. We show how the scale invariance of the perturbation spectrum arises. We also examine the spectrum of scalar perturbations of the metric that is created by the inflaton fluctuations that have left the Hubble sphere during inflation and the spectrum of density perturbations that they produce at reentry after inflation has ended. When the inflaton dispersion spectrum is renormalized during the expansion, we show (for the case of the quadratic inflaton potential) that the density perturbation spectrum approaches a mass-independent limit as the inflaton mass approaches zero, and remains near that limiting value for masses less than about 1/4 of the inflationary Hubble constant. We show that this limiting behavior does not occur if one only makes the Minkowski space subtraction, without the further adiabatic subtractions that involve time derivatives of the expansion scale factor a(t). We also find a parametrized expression for the energy density produced by the change in a(t) as inflation ends. If the end of inflation were sufficiently abrupt, then the temperature corresponding to this energy density could be very significant. We also show that fluctuations of the inflaton field that are present before inflation starts are not dissipated during inflation and could have a significant observational effect today. The mechanism for this is caused by the initial fluctuations through stimulated emission from the vacuum.
Study of the spectrum of inflaton perturbations
Glenz, Matthew M.; Parker, Leonard
2009-09-15
We examine the spectrum of inflaton fluctuations resulting from any given long period of exponential inflation. Infrared and ultraviolet divergences in the inflaton dispersion summed over all modes do not appear in our approach. We show how the scale invariance of the perturbation spectrum arises. We also examine the spectrum of scalar perturbations of the metric that is created by the inflaton fluctuations that have left the Hubble sphere during inflation and the spectrum of density perturbations that they produce at reentry after inflation has ended. When the inflaton dispersion spectrum is renormalized during the expansion, we show (for the case of the quadratic inflaton potential) that the density perturbation spectrum approaches a mass-independent limit as the inflaton mass approaches zero, and remains near that limiting value for masses less than about 1/4 of the inflationary Hubble constant. We show that this limiting behavior does not occur if one only makes the Minkowski space subtraction, without the further adiabatic subtractions that involve time derivatives of the expansion scale factor a(t). We also find a parametrized expression for the energy density produced by the change in a(t) as inflation ends. If the end of inflation were sufficiently abrupt, then the temperature corresponding to this energy density could be very significant. We also show that fluctuations of the inflaton field that are present before inflation starts are not dissipated during inflation and could have a significant observational effect today. The mechanism for this is caused by the initial fluctuations through stimulated emission from the vacuum.
(Perturbed angular correlations in zirconia ceramics)
Not Available
1990-01-01
This is the progress report for the first year of the currently-approved three year funding cycle. We have carried on a vigorous program of experimental and theoretical research on microscopic properties of zirconia and ceria using the Perturbed Angular Correlation (PAC) experimental technique. The experimental method was described in the original proposal and in a number of references as well as several of the technical reports that accompany this progress report.
Perturbations of nested branes with induced gravity
Sbisà, Fulvio; Koyama, Kazuya E-mail: kazuya.koyama@port.ac.uk
2014-06-01
We study the behaviour of weak gravitational fields in models where a 4D brane is embedded inside a 5D brane equipped with induced gravity, which in turn is embedded in a 6D spacetime. We consider a specific regularization of the branes internal structures where the 5D brane can be considered thin with respect to the 4D one. We find exact solutions corresponding to pure tension source configurations on the thick 4D brane, and study perturbations at first order around these background solutions. To perform the perturbative analysis, we adopt a bulk-based approach and we express the equations in terms of gauge invariant and master variables using a 4D scalar-vector-tensor decomposition. We then propose an ansatz on the behaviour of the perturbation fields when the thickness of the 4D brane goes to zero, which corresponds to configurations where gravity remains finite everywhere in the thin limit of the 4D brane. We study the equations of motion using this ansatz, and show that they give rise to a consistent set of differential equations in the thin limit, from which the details of the internal structure of the 4D brane disappear. We conclude that the thin limit of the ''ribbon'' 4D brane inside the (already thin) 5D brane is well defined (at least when considering first order perturbations around pure tension configurations), and that the gravitational field on the 4D brane remains finite in the thin limit. We comment on the crucial role of the induced gravity term on the 5D brane.
RECONSTRUCTING COSMOLOGICAL MATTER PERTURBATIONS USING STANDARD CANDLES AND RULERS
Alam, Ujjaini; Sahni, Varun; Starobinsky, Alexei A. E-mail: varun@iucaa.ernet.i
2009-10-20
For a large class of dark energy (DE) models, for which the effective gravitational constant is a constant and there is no direct exchange of energy between DE and dark matter (DM), knowledge of the expansion history suffices to reconstruct the growth factor of linearized density perturbations in the non-relativistic matter component on scales much smaller than the Hubble distance. In this paper, we develop a non-parametric method for extracting information about the perturbative growth factor from data pertaining to the luminosity or angular size distances. A comparison of the reconstructed density contrast with observations of large-scale structure and gravitational lensing can help distinguish DE models such as the cosmological constant and quintessence from models based on modified gravity theories as well as models in which DE and DM are either unified or interact directly. We show that for current supernovae (SNe) data, the linear growth factor at z = 0.3 can be constrained to 5% and the linear growth rate to 6%. With future SNe data, such as expected from the Joint Dark Energy Mission, we may be able to constrain the growth factor to 2%-3% and the growth rate to 3%-4% at z = 0.3 with this unbiased, model-independent reconstruction method. For future baryon acoustic oscillation data which would deliver measurements of both the angular diameter distance and the Hubble parameter, it should be possible to constrain the growth factor at z = 2.5%-9%. These constraints grow tighter with the errors on the data sets. With a large quantity of data expected in the next few years, this method can emerge as a competitive tool for distinguishing between different models of dark energy.
Reconstructing cosmological matter perturbations using standard candles and rulers
Alam, Ujjaini; Sahni, Varun; Starobinsky, Alexei A
2008-01-01
For a large class of dark energy (DE) models, for which the effective gravitational constant is a constant and there is no direct exchange of energy between DE and dark matter (DM), knowledge of the expansion history suffices to reconstruct the growth factor of linearized density perturbations in the non-relativistic matter component on scales much smaller than the Hubble distance. In this paper, we develop a non-parametric method for extracting information about the perturbative growth factor from data pertaining to the luminosity or angular size distances. A comparison of the reconstructed density contrast with observations of large-scale structure and gravitational lensing can help distinguish DE models such as the cosmological constant and quintessence from models based on modified gravity theories as well as models in which DE and DM are either unified or interact directly. We show that for current supernovae (SNe) data, the linear growth factor at z = 0.3 can be constrained to 5% and the linear growth rate to 6%. With future SNe data, such as expected from the Joint Dark Energy Mission, we may be able to constrain the growth factor to 2%-3% and the growth rate to 3%-4% at z = 0.3 with this unbiased, model-independent reconstruction method. For future baryon acoustic oscillation data which would deliver measurements of both the angular diameter distance and the Hubble parameter, it should be possible to constrain the growth factor at z = 2.5%-9%. These constraints grow tighter with the errors on the data sets. With a large quantity of data expected in the next few years, this method can emerge as a competitive tool for distinguishing between different models of dark energy.
Perturbative gravity in the causal approach
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2010-01-01
Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory in the causal approach. We emphasize the use of cohomology methods in this framework. After describing in detail the mathematical structure of the cohomology method we apply it in three different situations: (a) the determination of the most general expression of the interaction Lagrangian; (b) the proof of gauge invariance in the second order of perturbation theory for the pure gravity system—massless and massive; (c) the investigation of the arbitrariness of the second-order chronological products compatible with renormalization principles and gauge invariance (i.e. the renormalization problem in the second order of perturbation theory). In case (a) we investigate pure gravity systems and the interaction of massless gravity with matter (described by scalars and spinors) and massless Yang-Mills fields. We obtain a difference with respect to the classical field theory due to the fact that in quantum field theory one cannot enforce the divergenceless property on the vector potential and this spoils the divergenceless property of the usual energy-momentum tensor. To correct this one needs a supplementary ghost term in the interaction Lagrangian. In all three case, the computations are more simple than by the usual methods.
Noninflationary model with scale invariant cosmological perturbations
Peter, Patrick; Pinho, Emanuel J. C.; Pinto-Neto, Nelson
2007-01-15
We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-DeWitt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum (n{sub S}-1>0). Taking into account the spectral index constraint as well as the cosmic microwave background normalization measure yields an equation of state that should be less than {omega} < or approx. 8x10{sup -4}, implying n{sub S}-1{approx}O(10{sup -4}), and that the characteristic curvature scale of the Universe at the bounce is L{sub 0}{approx}10{sup 3}l{sub Pl}, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects. We have also obtained a consistency relation between the tensor-to-scalar ratio T/S and the scalar spectral index as T/S{approx}4.6x10{sup -2}{radical}(n{sub S}-1), leading to potentially measurable differences with inflationary predictions.
Quantum inflaton, primordial perturbations, and CMB fluctuations
Cao, F.J.; Vega, H.J. de; Sanchez, N.G.
2004-10-15
We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. Quantum field inflation (under conditions that are the quantum analog of slow-roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant quantum effects into account. The results for the scalar, vector and tensor primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current Wilkinson Microwave Anisotropy Probe observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of (m{sup 2}/NH{sup 2}), where m is the inflaton mass and H the Hubble constant at the moment of horizon crossing. An upper estimate turns to be about 4% for the cosmologically relevant scales. This quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it.
Non-perturbative effects in spin glasses
Castellana, Michele; Parisi, Giorgio
2015-01-01
We present a numerical study of an Ising spin glass with hierarchical interactions—the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d ≥ 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the -expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects. PMID:25733337
Cosmic perturbations through the cyclic ages
Erickson, Joel K.; Gratton, Steven; Steinhardt, Paul J.; Turok, Neil
2007-06-15
We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an epoch of gentle contraction with equation of state w>>1 preceding the hot big bang, makes the universe homogeneous, isotropic and flat within any given observer's horizon; and (3) although the universe is uniform within each observer's horizon, the structure of the cyclic universe on very large scales is more complex, owing to the effects of superhorizon length perturbations, and cannot be described globally as a Friedmann-Robertson-Walker cosmology. In particular, we show that the ekpyrotic contraction phase is so effective in smoothing, flattening and isotropizing the universe within the horizon that this phase alone suffices to solve the horizon and flatness problems even without an extended period of dark energy domination (a kind of low energy inflation). Instead, the cyclic model rests on a genuinely novel, noninflationary mechanism (ekpyrotic contraction) for resolving the classic cosmological conundrums.
Topological quantum order: Stability under local perturbations
Bravyi, Sergey; Hastings, Matthew B.; Michalakis, Spyridon
2010-09-15
We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrically local commuting projectors on a D-dimensional lattice with certain topological order conditions. Given such a Hamiltonian H{sub 0}, we prove that there exists a constant threshold {epsilon}>0 such that for any perturbation V representable as a sum of short-range bounded-norm interactions, the perturbed Hamiltonian H=H{sub 0}+{epsilon}V has well-defined spectral bands originating from low-lying eigenvalues of H{sub 0}. These bands are separated from the rest of the spectra and from each other by a constant gap. The band originating from the smallest eigenvalue of H{sub 0} has exponentially small width (as a function of the lattice size). Our proof exploits a discrete version of Hamiltonian flow equations, the theory of relatively bounded operators, and the Lieb-Robinson bound.
Relativistic Positioning System in perturbed spacetime
NASA Astrophysics Data System (ADS)
Kostić, Uroš; Horvat, Martin; Gomboc, Andreja
2015-11-01
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a spacetime around Earth, described by a perturbed Schwarzschild metric, where we included the perturbations due to Earth multipoles (up to the 6th), the Moon, the Sun, Venus, Jupiter, solid tide, ocean tide, and Kerr rotation effect. The exchange of signals between the satellites and a user was calculated using a ray-tracing method in the Schwarzschild spacetime. We find that positioning in a perturbed spacetime is feasible and is highly accurate already with standard numerical procedures: the positioning algorithms used to transform between the emission and the Schwarzschild coordinates of the user are very accurate and time efficient—on a laptop it takes 0.04 s to determine the user’s spatial and time coordinates with a relative accuracy of {10}-28-{10}-26 and {10}-32-{10}-30, respectively.
Perturbative Critical Behavior from Spacetime Dependent Couplings
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo
2012-08-03
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-{epsilon} Wilson-Fisher fixed point. Rather than considering 4-{epsilon} dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form {lambda}x{sup {kappa}}{mu}{sup {kappa}}, with a small parameter {kappa} playing a role analogous to {epsilon}. We show, in {phi}{sup 4} theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions x. The exact fixed point coupling {lambda}{sub *}(x) in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by 1/x. Similar statements hold for three-dimensional {phi}{sup 6} theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.
Multifrequency perturbations in matter-wave interferometry
NASA Astrophysics Data System (ADS)
Günther, A.; Rembold, A.; Schütz, G.; Stibor, A.
2015-11-01
High-contrast matter-wave interferometry is essential in various fundamental quantum mechanical experiments as well as for technical applications. Thereby, contrast and sensitivity are typically reduced by decoherence and dephasing effects. While decoherence accounts for a general loss of quantum information in a system due to entanglement with the environment, dephasing is due to collective time-dependent external phase shifts, which can be related to temperature drifts, mechanical vibrations, and electromagnetic oscillations. In contrast to decoherence, dephasing can, in principle, be reversed. Here, we demonstrate in experiment and theory a method for the analysis and reduction of the influence of dephasing noise and perturbations consisting of several external frequencies in an electron interferometer. This technique uses the high spatial and temporal resolution of a delay-line detector to reveal and remove dephasing perturbations by second-order correlation analysis. It allows matter-wave experiments under perturbing laboratory conditions and can be applied, in principle, to electron, atom, ion, neutron, and molecule interferometers.
Non-perturbative effects in spin glasses
NASA Astrophysics Data System (ADS)
Castellana, Michele; Parisi, Giorgio
2015-03-01
We present a numerical study of an Ising spin glass with hierarchical interactions--the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to d >= 4 and d < 4 for the d-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the -expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent ν in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only ~2% from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.
Baryonic matter perturbations in decaying vacuum cosmology
Marttens, R.F. vom; Zimdahl, W.; Hipólito-Ricaldi, W.S. E-mail: wiliam.ricaldi@ufes.br
2014-08-01
We consider the perturbation dynamics for the cosmic baryon fluid and determine the corresponding power spectrum for a Λ(t)CDM model in which a cosmological term decays into dark matter linearly with the Hubble rate. The model is tested by a joint analysis of data from supernovae of type Ia (SNIa) (Constitution and Union 2.1), baryonic acoustic oscillations (BAO), the position of the first peak of the anisotropy spectrum of the cosmic microwave background (CMB) and large-scale-structure (LSS) data (SDSS DR7). While the homogeneous and isotropic background dynamics is only marginally influenced by the baryons, there are modifications on the perturbative level if a separately conserved baryon fluid is included. Considering the present baryon fraction as a free parameter, we reproduce the observed abundance of the order of 5% independently of the dark-matter abundance which is of the order of 32% for this model. Generally, the concordance between background and perturbation dynamics is improved if baryons are explicitly taken into account.
Using Lagrangian perturbation theory for precision cosmology
Sugiyama, Naonori S.
2014-06-10
We explore the Lagrangian perturbation theory (LPT) at one-loop order with Gaussian initial conditions. We present an expansion method to approximately compute the power spectrum LPT. Our approximate solution has good convergence in the series expansion and enables us to compute the power spectrum in LPT accurately and quickly. Non-linear corrections in this theory naturally satisfy the law of conservation of mass because the relation between matter density and the displacement vector of dark matter corresponds to the conservation of mass. By matching the one-loop solution in LPT to the two-loop solution in standard perturbation theory, we present an approximate solution of the power spectrum which has higher order corrections than the two-loop order in standard perturbation theory with the conservation of mass satisfied. With this approximation, we can use LPT to compute a non-linear power spectrum without any free parameters, and this solution agrees with numerical simulations at k = 0.2 h Mpc{sup –1} and z = 0.35 to better than 2%.
Convergence of coupled cluster perturbation theory
NASA Astrophysics Data System (ADS)
Eriksen, Janus J.; Kristensen, Kasper; Matthews, Devin A.; Jørgensen, Poul; Olsen, Jeppe
2016-12-01
The convergence of a recently proposed coupled cluster (CC) family of perturbation series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between two CC models—a low-level parent and a high-level target model—is expanded in orders of the Møller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet CH2, distorted HF, and F-) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii have been determined by probing for possible front- and back-door intruder states, the existence of which would make the series divergent. In summary, we conclude how it is primarily the choice of the target state, and not the choice of the parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series which target the full configuration interaction limit, such as the standard MP series. Furthermore, we find that whereas a CC perturbation series might converge within standard correlation consistent basis sets, it may start to diverge whenever these become augmented by diffuse functions, similar to the MP case. However, unlike for the MP case, such potential divergences are not found to invalidate the practical use of the low-order corrections of the CC perturbation series.
NASA Astrophysics Data System (ADS)
Shaban, M.; Shivanian, E.; Abbasbandy, S.
2013-11-01
In this paper an algorithm based on the homotopy analysis method (HAM) is introduced to study the magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid in the presence of an applied magnetic field. The continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation via similarity transformations. In addition, by using the Tau method the problem converts to the algebraic equations to obtain the solution iteratively. The combined effect of inertia, electromagnetic forces for both suction and blowing cases is discussed. Additionally, the convergence of the obtained series solutions is explicitly studied and a proper discussion is given for the obtained results. The applicability, accuracy and efficiency of this new Tau modification of the HAM is demonstrated via the accomplished comparison.
Neutron stars in a perturbative f(R) gravity model with strong magnetic fields
Cheoun, Myung-Ki; Deliduman, Cemsinan; Güngör, Can; Keleş, Vildan; Ryu, C.Y.; Kajino, Toshitaka; Mathews, Grant J. E-mail: cemsinan@msgsu.edu.tr E-mail: kelesvi@itu.edu.tr E-mail: kajino@nao.ac.jp
2013-10-01
In Kaluza-Klein electromagnetism it is natural to associate modified gravity with strong electromagnetic fields. Hence, in this paper we investigate the combined effects of a strong magnetic field and perturbative f(R) gravity on the structure of neutron stars. The effect of an interior strong magnetic field of about 10{sup 17−18} G on the equation of state is derived in the context of a quantum hadrodynamics (QHD) equation of state (EoS) including effects of the magnetic pressure and energy along with occupied Landau levels. Adopting a random orientation of interior field domains, we solve the modified spherically symmetric hydrostatic equilibrium equations derived for a gravity model with f(R) = R+αR{sup 2}. Effects of both the finite magnetic field and the modified gravity are detailed for various values of the magnetic field and the perturbation parameter α along with a discussion of their physical implications. We show that there exists a parameter space of the modified gravity and the magnetic field strength, in which even a soft equation of state can accommodate a large ( > 2 M{sub s}un) maximum neutron star mass.
Perturbative and gauge invariant treatment of gravitational wave memory
NASA Astrophysics Data System (ADS)
Bieri, Lydia; Garfinkle, David
2014-04-01
We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.
Homotopy Solutions of Kepler's Equations
NASA Technical Reports Server (NTRS)
Fitz-Coy, Norman; Jang, Jiann-Woei
1996-01-01
Kepler's Equation is solved using an integrative algorithm developed using homotropy theory. The solution approach is applicable to both elliptic and hyperbolic forms of Kepler's Equation. The results from the proposed algorithm compare quite favorably with those from existing iterative schemes.
On spectral perturbation caused by bounded variation of potential
NASA Astrophysics Data System (ADS)
Ismagilov, R. S.
2014-01-01
The harmonic oscillator operator is perturbed by an arbitrary bounded continuous term. This results in the perturbation of the spectrum. The map sending the first of these perturbations into the second is examined. Its approximation by a linear map is studied. Bibliography: 2 titles.
On spectral perturbation caused by bounded variation of potential
Ismagilov, R S
2014-01-31
The harmonic oscillator operator is perturbed by an arbitrary bounded continuous term. This results in the perturbation of the spectrum. The map sending the first of these perturbations into the second is examined. Its approximation by a linear map is studied. Bibliography: 2 titles.
Exact Controllability and Perturbation Analysis for Elastic Beams
Moreles, Miguel Angel
2004-05-15
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials.
Perturbations of matter fields in the second-order gauge-invariant cosmological perturbation theory
NASA Astrophysics Data System (ADS)
Nakamura, Kouji
2009-12-01
To show that the general framework of the second-order gauge-invariant perturbation theory developed by K. Nakamura [Prog. Theor. Phys. 110, 723 (2003)PTPKAV0033-068X10.1143/PTP.110.723; Prog. Theor. Phys. 113, 481 (2005)PTPKAV0033-068X10.1143/PTP.113.481] is applicable to a wide class of cosmological situations, some formulas for the perturbations of the matter fields are summarized within the framework of the second-order gauge-invariant cosmological perturbation theory in a four-dimensional homogeneous isotropic universe, which is developed in Prog. Theor. Phys. 117, 17 (2007)PTPKAV0033-068X10.1143/PTP.117.17. We derive the formulas for the perturbations of the energy-momentum tensors and equations of motion for a perfect fluid, an imperfect fluid, and a single scalar field, and show that all equations are derived in terms of gauge-invariant variables without any gauge fixing. Through these formulas, we may say that the decomposition formulas for the perturbations of any tensor field into gauge-invariant and gauge-variant parts, which are proposed in the above papers, are universal.
NASA Technical Reports Server (NTRS)
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Modified Betatron Accelerator Studies.
1983-12-01
velocity equation can be derived in many ways, using the single particle energy formula seems simplest. Er S3 69e 6E9 + vr 6r (4) The perturbed...azimuthal angle 6e of a beam disk is related to 6Ve by S6V 0 * R 66 + Vr 6r (5) Perturbed beam currents resulting from the centroid displacements...and Vr , Ve are the beam velocity components. The second term in Eq. (1) shows that a rigid transverse (m - 1) displacement contributes to the perturbed
Master equation for a chemical wave front with perturbation of local equilibrium.
Dziekan, P; Lemarchand, A; Nowakowski, B
2011-08-28
In order to develop a stochastic description of gaseous reaction-diffusion systems, which includes a reaction-induced departure from local equilibrium, we derive a modified expression of the master equation from analytical calculations based on the Boltzmann equation. We apply the method to a chemical wave front of Fisher-Kolmogorov-Petrovsky-Piskunov type, whose propagation speed is known to be sensitive to small perturbations. The results of the modified master equation are compared successfully with microscopic simulations of the particle dynamics using the direct simulation Monte Carlo method. The modified master equation constitutes an efficient tool at the mesoscopic scale, which incorporates the nonequilibrium effect without need of determining the particle velocity distribution function.
Nonlinear electromagnetic perturbations in a degenerate ultrarelativistic electron-positron plasma.
El-Taibany, W F; Mamun, A A
2012-02-01
Nonlinear propagation of fast and slow magnetosonic perturbation modes in an ultrarelativistic, ultracold, degenerate (extremely dense) electron positron (EP) plasma (containing ultrarelativistic, ultracold, degenerate electron and positron fluids) has been investigated by the reductive perturbation method. The Alfvén wave velocity is modified due to the presence of the enthalpy correction in the fluid equations of motion. The degenerate EP plasma system (under consideration) supports the Korteweg-de Vries (KdV) solitons, which are associated with either fast or slow magnetosonic perturbation modes. It is found that the ultrarelativistic model leads to compressive (rarefactive) electromagnetic solitons corresponding to the fast (slow) wave mode. There are certain critical angles, θ(c), at which no soliton solution is found corresponding to the fast wave mode. For the slow mode, the magnetic-field intensity affects both the soliton amplitude and width. It is also illustrated that the basic features of the electromagnetic solitary structures, which are found to exist in such a degenerate EP plasma, are significantly modified by the effects of enthalpy correction, electron and positron degeneracy, magnetic-field strength, and the relativistic effect. The applications of the results in a pair-plasma medium, which occurs in many astrophysical objects (e.g., pulsars, white dwarfs, and neutron stars) are briefly discussed.
Belov, A. S.
2015-10-15
Results of numerical simulations of the near-Earth plasma perturbations induced by powerful HF radio waves from the SURA heating facility are presented. The simulations were performed using a modified version of the SAMI2 ionospheric model for the input parameters corresponding to the series of in-situ SURA–DEMETER experiments. The spatial structure and developmental dynamics of large-scale plasma temperature and density perturbations have been investigated. The characteristic formation and relaxation times of the induced large-scale plasma perturbations at the altitudes of the Earth’s outer ionosphere have been determined.
Dynamics of a single ion in a perturbed Penning trap: octupolar perturbation.
Lara, Martín; Salas, J Pablo
2004-09-01
Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincaré surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior.
Anomaly freedom in perturbative loop quantum gravity
Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.
2008-09-15
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, nontrivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.
Sidelobe Sector Nulling with Minimized Phase Perturbations.
1985-03-01
Sciences Division FOR THE COMMANDER: ~t~4iq JOHN A. RITZ Acting Chief, Plans Office If your address has changed or if you wish to be removed from the...Perturbations for Arrays of 11, 21, and 41 Elements W~41 z~ 21 7N II -2. 4.0 -J.0 -2.0 -11.6 0.0 1.!0 2.0 3.0 4.0 5.0 LOGI 0 (42141) Figure 3. Look...Trans. Antennas Propag. AP-20:432 -436. 4. Baird , C. A., and Rassweiler, G. G. (1976) Adaptive sidelobe nulling using digitally controlled phase
Cosmological explosions from cold dark matter perturbations
NASA Technical Reports Server (NTRS)
Scherrer, Robert J.
1992-01-01
The cosmological-explosion model is examined for a universe dominated by cold dark matter in which explosion seeds are produced from the growth of initial density perturbations of a given form. Fragmentation of the exploding shells is dominated by the dark-matter potential wells rather than the self-gravity of the shells, and particular conditions are required for the explosions to bootstrap up to very large scales. The final distribution of dark matter is strongly correlated with the baryons on small scales, but uncorrelated on large scales.
Transport studies in fusion plasmas: Perturbative experiments
Cardozo, N.J.L.
1996-03-01
By subjecting a plasma in steady state to small perturbations and measuring the response, it is possible to determine elements of the matrix of transport coefficients. Experimentally this is difficult, and results are mainly limited to transport driven by the pressure and temperature gradients. Importantly, off-diagonal elements in the transport matrix appear to be important. This has also implications for the interpretation of the so-called `power balance` diffusivity, determined from the steady state fluxes and gradients. Experimental techniques, analysis techniques, basic formulas, etc., are briefly reviewed. Experimental results are summarized. The fundamental question whether the fluxes are linear functions of the gradients or not is discussed. 31 refs.
Exciton dynamics in perturbed vibronic molecular aggregates
Brüning, C.; Wehner, J.; Hausner, J.; Wenzel, M.; Engel, V.
2015-01-01
A site specific perturbation of a photo-excited molecular aggregate can lead to a localization of excitonic energy. We investigate this localization dynamics for laser-prepared excited states. Changing the parameters of the electric field significantly influences the exciton localization which offers the possibility for a selective control of this process. This is demonstrated for aggregates possessing a single vibrational degree of freedom per monomer unit. It is shown that the effects identified for the molecular dimer can be generalized to larger aggregates with a high density of vibronic states. PMID:26798840
Light-Front Perturbation Without Spurious Singularities
NASA Astrophysics Data System (ADS)
Przeszowski, Jerzy A.; Dzimida-Chmielewska, Elżbieta; Żochowski, Jan
2016-07-01
A new form of the light front Feynman propagators is proposed. It contains no energy denominators. Instead the dependence on the longitudinal subinterval x^2_L = 2 x+ x- is explicit and a new formalism for doing the perturbative calculations is invented. These novel propagators are implemented for the one-loop effective potential and various 1-loop 2-point functions for a massive scalar field. The consistency with results for the standard covariant Feynman diagrams is obtained and no spurious singularities are encountered at all. Some remarks on the calculations with fermion and gauge fields in QED and QCD are added.
Geometric Perturbation Theory and Plasma Physics
NASA Astrophysics Data System (ADS)
Omohundro, Stephen Malvern
1985-12-01
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 ad hoc 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. 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
Growth rate, population entropy, and perturbation theory.
Demetrius, L
1989-04-01
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 the notion of environmental intensity. The intensity function, expressed in terms of the entropy parameters, is applied to give a comparative study of the effect of environmental factors on the dynamics of Swedish and French populations.
Bonding charge density from atomic perturbations.
Wang, Yi; Wang, William Yi; Chen, Long-Qing; Liu, Zi-Kui
2015-05-15
Charge transfer among individual atoms is the key concept in modern electronic theory of chemical bonding. In this work, we present a first-principles approach to calculating the charge transfer. Based on the effects of perturbations of an individual atom or a group of atoms on the electron charge density, we determine unambiguously the amount of electron charge associated with a particular atom or a group of atoms. We computed the topological electron loss versus gain using ethylene, graphene, MgO, and SrTiO3 as examples. Our results verify the nature of chemical bonds in these materials at the atomic level.
Theoretical priors on modified growth parametrisations
Song, Yong-Seon; Hollenstein, Lukas; Caldera-Cabral, Gabriela; Koyama, Kazuya E-mail: Lukas.Hollenstein@unige.ch E-mail: Kazuya.Koyama@port.ac.uk
2010-04-01
Next generation surveys will observe the large-scale structure of the Universe with unprecedented accuracy. This will enable us to test the relationships between matter over-densities, the curvature perturbation and the Newtonian potential. Any large-distance modification of gravity or exotic nature of dark energy modifies these relationships as compared to those predicted in the standard smooth dark energy model based on General Relativity. In linear theory of structure growth such modifications are often parameterised by virtue of two functions of space and time that enter the relation of the curvature perturbation to, first, the matter over- density, and second, the Newtonian potential. We investigate the predictions for these functions in Brans-Dicke theory, clustering dark energy models and interacting dark energy models. We find that each theory has a distinct path in the parameter space of modified growth. Understanding these theoretical priors on the parameterisations of modified growth is essential to reveal the nature of cosmic acceleration with the help of upcoming observations of structure formation.
Comparison of electroglottographic and acoustic analysis of pitch perturbation.
LaBlance, G R; Maves, M D; Scialfa, T M; Eitnier, C M; Steckol, K F
1992-11-01
Pitch perturbation is a measure of the cycle-to-cycle variation in vocal fold vibration. Perturbation can be assessed by means of electroglottographic or acoustic signals. The purpose of this study was to determine if these two analysis techniques are equivalent measures. The Laryngograph, an electroglottograph, and the Visi-Pitch, an acoustic analyzer, were used to measure pitch perturbation in 80 dysphonic subjects. Both instruments use Koike's formula to calculate relative average perturbation. While intra-subject variability appeared erratic, statistical analysis of intersubject data indicated that the two instruments provided an equivalent measure of pitch perturbation.
The spectrum of density perturbations in an expanding universe
NASA Technical Reports Server (NTRS)
Silk, J.
1974-01-01
The basic dynamic equations that govern the evolution of perturbations in a Friedmann-Lemaitre universe are derived. General solutions describing the evolution of adiabatic perturbations in the density of matter are obtained, and the choice of the appropriate initial conditions is examined. The various perturbation modes are compared, and the effects of decoupling on the perturbation spectrum are studied. The scheme used to follow the evolution of density perturbations through decoupling is based on an extension of the Eddington approximation to the radiative transfer equation, and is strictly valid in both optically thick and thin limits.
H(infinity) filtering for fuzzy singularly perturbed systems.
Yang, Guang-Hong; Dong, Jiuxiang
2008-10-01
This paper considers the problem of designing H(infinity) filters for fuzzy singularly perturbed systems with the consideration of improving the bound of singular-perturbation parameter epsilon. First, a linear-matrix-inequality (LMI)-based approach is presented for simultaneously designing the bound of the singularly perturbed parameter epsilon, and H(infinity) filters for a fuzzy singularly perturbed system. When the bound of singularly perturbed parameter epsilon is not under consideration, the result reduces to an LMI-based design method for H(infinity) filtering of fuzzy singularly perturbed systems. Furthermore, a method is given for evaluating the upper bound of singularly perturbed parameter subject to the constraint that the considered system is to be with a prescribed H(infinity) performance bound, and the upper bound can be obtained by solving a generalized eigenvalue problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.
Perturbation Theory for Parent Hamiltonians of Matrix Product States
NASA Astrophysics Data System (ADS)
Szehr, Oleg; Wolf, Michael M.
2015-05-01
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by Yarotsky that develops a perturbation theory for relatively bounded quantum perturbations of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltonian of a Matrix product state into a classical Hamiltonian plus some perturbation. We can thus extend Yarotsky's results to provide a perturbation theory for parent Hamiltonians of Matrix product states and recover some of the findings of the independent contributions (Cirac et al in Phys Rev B 8(11):115108, 2013) and (Michalakis and Pytel in Comm Math Phys 322(2):277-302, 2013).
Inferring propagation paths for sparsely observed perturbations on complex networks
Massucci, Francesco Alessandro; Wheeler, Jonathan; Beltrán-Debón, Raúl; Joven, Jorge; Sales-Pardo, Marta; Guimerà, Roger
2016-01-01
In a complex system, perturbations propagate by following paths on the network of interactions among the system’s units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very sparse in time (there is a single observation of the perturbed system) and in “space” (only a few perturbed and unperturbed units are observed). A major challenge in many areas, from biology to the social sciences, is to infer the propagation paths from observations of the effects of perturbation under these sparsity conditions. We address this problem and show that it is possible to go beyond the usual approach of using the shortest paths connecting the known perturbed nodes. Specifically, we show that a simple and general probabilistic model, which we solved using belief propagation, provides fast and accurate estimates of the probabilities of nodes being perturbed. PMID:27819038
Measurement and Perturbation of Morphogen Lifetime: Effects on Gradient Shape
Drocco, Jeffrey A.; Grimm, Oliver; Tank, David W.; Wieschaus, Eric
2011-01-01
Protein lifetime is of critical importance for most biological processes and plays a central role in cell signaling and embryonic development, where it impacts the absolute concentration of signaling molecules and, potentially, the shape of morphogen gradients. Early conceptual and mathematical models of gradient formation proposed that steady-state gradients are established by an equilibration between the lifetime of a morphogen and its rates of synthesis and diffusion, though whether gradients in fact reach steady state before being read out is a matter of controversy. In any case, this class of models predicts that protein lifetime is a key determinant of both the time to steady state and the spatial extent of a gradient. Using a method that employs repeated photoswitching of a fusion of the morphogen Bicoid (Bcd) and the photoconvertible fluorescent protein Dronpa, we measure and modify the lifetime of Dronpa-Bcd in living Drosophila embryos. We find that the lifetime of Bcd is dynamic, changing from 50 min before mitotic cycle 14 to 15 min during cellularization. Moreover, by measuring total quantities of Bcd over time, we find that the gradient does not reach steady state. Finally, using a nearly continuous low-level conversion to the dark state of Dronpa-Bcd to mimic the effect of increased degradation, we demonstrate that perturbation of protein lifetime changes the characteristic length of the gradient, providing direct support for a mechanism based on synthesis, diffusion, and degradation. PMID:22004733
Converging perturbed microvasculature and microglial clusters characterize Alzheimer disease brain.
Jantaratnotai, N; Schwab, C; Ryu, J K; McGeer, P L; McLarnon, J G
2010-11-01
We have investigated physical properties of microvasculature and vessel association with microglial clusters in cortical tissue from Alzheimer disease individuals, classified as severe (ADsev) or mild (ADmild), and nondemented controls (ND). Immunostaining with laminin or von Willerbrand factor demonstrated numbers of microvessels and microvascular density were significantly higher in ADsev cases compared with levels in ADmild or ND cases suggesting proangiogenic activity in ADsev brain. Evidence for extravascular laminin immunoreactivity was found in ADsev tissue and was largely absent in ADmild and ND cases suggesting vascular remodeling in ADsev brain included abnormalities in blood vessels. Microgliosis was progressively increased from ND to ADmild to ADsev with the latter demonstrating areas of clustered microglia (groupings of three or more cells) rarely observed in ADmild or ND cases. Microglial clusters in ADsev brain were in close proximity with extravascular laminin and also plasma protein, fibrinogen, implicating vascular perturbation as a component of inflammatory reactivity. ADsev brain also exhibited elevated levels of the pro-inflammatory/angiogenic factors tumor necrosis factor-α (TNF-α) and vascular endothelial growth factor (VEGF) in association, relative to non-association, with microglial clusters. The presence of extravascular laminin and fibrinogen and the vascular modifying factors, TNF-α and VEGF in localization with clusters of activated microglia, is consistent with microglial-induced vascular remodeling in ADsev brain. Microglial-vascular reciprocal interactions could serve a critical role in the amplification and perpetuation of inflammatory reactivity in AD brain.
GATO Code Modification to Compute Plasma Response to External Perturbations
NASA Astrophysics Data System (ADS)
Turnbull, A. D.; Chu, M. S.; Ng, E.; Li, X. S.; James, A.
2006-10-01
It has become increasingly clear that the plasma response to an external nonaxiymmetric magnetic perturbation cannot be neglected in many situations of interest. This response can be described as a linear combination of the eigenmodes of the ideal MHD operator. The eigenmodes of the system can be obtained numerically with the GATO ideal MHD stability code, which has been modified for this purpose. A key requirement is the removal of inadmissible continuum modes. For Finite Hybrid Element codes such as GATO, a prerequisite for this is their numerical restabilization by addition of small numerical terms to δ,to cancel the analytic numerical destabilization. In addition, robustness of the code was improved and the solution method speeded up by use of the SuperLU package to facilitate calculation of the full set of eigenmodes in a reasonable time. To treat resonant plasma responses, the finite element basis has been extended to include eigenfunctions with finite jumps at rational surfaces. Some preliminary numerical results for DIII-D equilibria will be given.
An Experimental Device for Generating High Frequency Perturbations in Supersonic Wind Tunnels
NASA Technical Reports Server (NTRS)
Melcher, Kevin J.; Ibrahim, Mounir B.
1996-01-01
This paper describes the analytical study of a device that has been proposed as a mechanism for generating gust-like perturbations in supersonic wind tunnels. The device is envisioned as a means to experimentally validate dynamic models and control systems designed for high-speed inlets. The proposed gust generator is composed of two flat trapezoidal plates that modify the properties of the flow ingested by the inlet. One plate may be oscillated to generate small perturbations in the flow. The other plate is held stationary to maintain a constant angle-of-attack. Using an idealized approach, design equations and performance maps for the new device were developed from the compressible flow relations. A two-dimensional CFD code was used to confirm the correctness of these results. The idealized approach was then used to design and evaluate a new gust generator for a 3.05-meter by 3.05-meter (10-foot by 10-foot) supersonic wind tunnel.
Analysis of a Leslie-Gower-type prey-predator model with periodic impulsive perturbations
NASA Astrophysics Data System (ADS)
Chen, Yiping; Liu, Zhijun; Haque, Mainul
2009-08-01
A modified Leslie-Gower-type prey-predator model with periodic impulsive perturbations is proposed and investigated. It is proved that there exists an asymptotically stable prey-free periodic solution when the impulsive period is less than some critical value. Otherwise, the above system can be permanent. And then the numerical simulations are carried out to study the effects of the impulsive varying parameters of the system. The results of simulations show that the model we consider, under the effects of impulsive perturbations for biologically feasible parametric values, has more complex dynamics including cycle, period adding, 3 T -period oscillation, chaos, period-doubling bifurcation, period-halving bifurcation, period windows, symmetry-breaking pitchfork bifurcation, and non-unique dynamics, meaning that several attractors coexist.
Kim, Kimin; Ahn, J. -W.; Scotti, F.; Park, J. -K.; Menard, J. E.
2015-09-03
Ideal plasma shielding and amplification of resonant magnetic perturbations in non-axisymmetric tokamak is presented by field line tracing simulation with full ideal plasma response, compared to measurements of divertor lobe structures. Magnetic field line tracing simulations in NSTX with toroidal non-axisymmetry indicate the ideal plasma response can significantly shield/amplify and phase shift the vacuum resonant magnetic perturbations. Ideal plasma shielding for n = 3 mode is found to prevent magnetic islands from opening as consistently shown in the field line connection length profile and magnetic footprints on the divertor target. It is also found that the ideal plasma shielding modifies the degree of stochasticity but does not change the overall helical lobe structures of the vacuum field for n = 3. Furthermore, amplification of vacuum fields by the ideal plasma response is predicted for low toroidal mode n = 1, better reproducing measurements of strong striation of the field lines on the divertor plate in NSTX.
Cosmological density perturbations with a scale-dependent Newton's constant G
Hamber, Herbert W.; Toriumi, Reiko
2010-08-15
We explore possible cosmological consequences of a running Newton's constant G({open_square}), as suggested by the nontrivial ultraviolet fixed point scenario in the quantum field-theoretic treatment of Einstein gravity with a cosmological constant term. In particular, we focus here on what possible effects the scale-dependent coupling might have on large scale cosmological density perturbations. Starting from a set of manifestly covariant effective field equations derived earlier, we systematically develop the linear theory of density perturbations for a nonrelativistic, pressureless fluid. The result is a modified equation for the matter density contrast, which can be solved and thus provides an estimate for the growth index parameter {gamma} in the presence of a running G. We complete our analysis by comparing the fully relativistic treatment with the corresponding results for the nonrelativistic (Newtonian) case, the latter also with a weakly scale-dependent G.
Hormonal Perturbations in Occupationally Exposed Nickel Workers
Beshir, Safia; Ibrahim, Khadiga Salah; Shaheen, Weam; Shahy, Eman M.
2016-01-01
BACKGROUND: Nickel exposure is recognized as an endocrine disruptor because of its adverse effects on reproduction. AIM: This study was designed to investigate the possible testiculo-hormonal perturbations on workers occupationally exposed to nickel and to assess its effects on human male sexual function. METHODS: Cross-sectional comparative study, comprising 105 electroplating male non-smoker, non-alcoholic workers exposed to soluble nickel and 60 controls was done. Serum luteinizing hormone, follicle stimulating hormone, testosterone levels and urinary nickel concentrations were determined for the studied groups. RESULTS: Serum luteinizing hormone, follicle stimulating hormone, urinary nickel and the simultaneous incidence of more than one sexual disorder were significantly higher in the exposed workers compared to controls. The occurrence of various types of sexual disorders (decreased libido, impotence and premature ejaculation) in the exposed workers was 9.5, 5.1 and 4.4 folds respectively than the controls. CONCLUSIONS: Exposure to nickel produces possible testiculo-hormonal perturbations in those exposed workers. PMID:27335607
Newtonian perturbations on models with matter creation
NASA Astrophysics Data System (ADS)
Jesus, J. F.; Oliveira, F. A.; Basilakos, S.; Lima, J. A. S.
2011-09-01
Creation of cold dark matter (CCDM) can macroscopically be described by a negative pressure, and, therefore, the mechanism is capable to accelerate the Universe, without the need of an additional dark energy component. In this framework, we discuss the evolution of perturbations by considering a Neo-Newtonian approach where, unlike in the standard Newtonian cosmology, the fluid pressure is taken into account even in the homogeneous and isotropic background equations (Lima, Zanchin, and Brandenberger, MNRAS 291, L1, 1997). The evolution of the density contrast is calculated in the linear approximation and compared to the one predicted by the ΛCDM model. The difference between the CCDM and ΛCDM predictions at the perturbative level is quantified by using three different statistical methods, namely: a simple χ2-analysis in the relevant space parameter, a Bayesian statistical inference, and, finally, a Kolmogorov-Smirnov test. We find that under certain circumstances, the CCDM scenario analyzed here predicts an overall dynamics (including Hubble flow and matter fluctuation field) which fully recovers that of the traditional cosmic concordance model. Our basic conclusion is that such a reduction of the dark sector provides a viable alternative description to the accelerating ΛCDM cosmology.
Consonantal perturbations of pitch in Halkomelem Salish
NASA Astrophysics Data System (ADS)
Brown, Jason; Thompson, James J.
2005-04-01
It has long been noted that consonants have an effect on the pitch of a following vowel: voiceless stops tend to raise F0, while voiced stops lower it. It has also been suggested that the duration of such perturbations is shorter in tone languages than in non-tone languages [Hombert, Studies in African Linguistics (1977)]. This study compares the effects that consonants have on F0 in two closely related Salish languages: Island Halkomelem, a non-tone language, and Upriver Halkomelem, a language that has reportedly undergone some limited tonogenesis but offers no clear prosodic clues regarding tonality. The effects of the voiceless and ejective stop series were observed, and measurements of F0 were taken at the onset of voicing for the vowel, then at 20 msec. intervals up to 100 msec. Preliminary results indicate that i) Island Halkomelem shows a greater magnitude of difference in F0 at vowel onset between the voiceless and ejective stops than Upriver Halkomelem, and ii) Island Halkomelem shows greater durations of consonantal perturbations of F0 than does Upriver Halkomelem. This suggests that Upriver Halkomelem may have become more sensitive to pitch than the Island dialect, supporting the interpretation of this language as tonal. [Work supported by Phillips Fund.
Membrane Perturbation Induced by Interfacially Adsorbed Peptides
Zemel, Assaf; Ben-Shaul, Avinoam; May, Sylvio
2004-01-01
The structural and energetic characteristics of the interaction between interfacially adsorbed (partially inserted) α-helical, amphipathic peptides and the lipid bilayer substrate are studied using a molecular level theory of lipid chain packing in membranes. The peptides are modeled as “amphipathic cylinders” characterized by a well-defined polar angle. Assuming two-dimensional nematic order of the adsorbed peptides, the membrane perturbation free energy is evaluated using a cell-like model; the peptide axes are parallel to the membrane plane. The elastic and interfacial contributions to the perturbation free energy of the “peptide-dressed” membrane are evaluated as a function of: the peptide penetration depth into the bilayer's hydrophobic core, the membrane thickness, the polar angle, and the lipid/peptide ratio. The structural properties calculated include the shape and extent of the distorted (stretched and bent) lipid chains surrounding the adsorbed peptide, and their orientational (C-H) bond order parameter profiles. The changes in bond order parameters attendant upon peptide adsorption are in good agreement with magnetic resonance measurements. Also consistent with experiment, our model predicts that peptide adsorption results in membrane thinning. Our calculations reveal pronounced, membrane-mediated, attractive interactions between the adsorbed peptides, suggesting a possible mechanism for lateral aggregation of membrane-bound peptides. As a special case of interest, we have also investigated completely hydrophobic peptides, for which we find a strong energetic preference for the transmembrane (inserted) orientation over the horizontal (adsorbed) orientation. PMID:15189858
Perturbation of physiological systems by nanoparticles.
Zhang, Yi; Bai, Yuhong; Jia, Jianbo; Gao, Ningning; Li, Yang; Zhang, Ruinan; Jiang, Guibin; Yan, Bing
2014-05-21
Nanotechnology is having a tremendous impact on our society. However, societal concerns about human safety under nanoparticle exposure may derail the broad application of this promising technology. Nanoparticles may enter the human body via various routes, including respiratory pathways, the digestive tract, skin contact, intravenous injection, and implantation. After absorption, nanoparticles are carried to distal organs by the bloodstream and the lymphatic system. During this process, they interact with biological molecules and perturb physiological systems. Although some ingested or absorbed nanoparticles are eliminated, others remain in the body for a long time. The human body is composed of multiple systems that work together to maintain physiological homeostasis. The unexpected invasion of these systems by nanoparticles disturbs normal cell signaling, impairs cell and organ functions, and may even cause pathological disorders. This review examines the comprehensive health risks of exposure to nanoparticles by discussing how nanoparticles perturb various physiological systems as revealed by animal studies. The potential toxicity of nanoparticles to each physiological system and the implications of disrupting the balance among systems are emphasized.
Approaches to the Treatment of Equilibrium Perturbations
NASA Astrophysics Data System (ADS)
Canagaratna, Sebastian G.
2003-10-01
Perturbations from equilibrium are treated in the textbooks by a combination of Le Châtelier's principle, the comparison of the equilibrium constant K with the reaction quotient Q,and the kinetic approach. Each of these methods is briefly reviewed. This is followed by derivations of the variation of the equilibrium value of the extent of reaction, ξeq, with various parameters on which it depends. Near equilibrium this relationship can be represented by a straight line. The equilibrium system can be regarded as moving on this line as the parameter is varied. The slope of the line depends on quantities like enthalpy of reaction, volume of reaction and so forth. The derivation shows that these quantities pertain to the equilibrium system, not the standard state. Also, the derivation makes clear what kind of assumptions underlie our conclusions. The derivation of these relations involves knowledge of thermodynamics that is well within the grasp of junior level physical chemistry students. The conclusions that follow from the derived relations are given as subsidiary rules in the form of the slope of ξeq, with T, p, et cetera. The rules are used to develop a visual way of predicting the direction of shift of a perturbed system. This method can be used to supplement one of the other methods even at the introductory level.
Bounded relative motion under zonal harmonics perturbations
NASA Astrophysics Data System (ADS)
Baresi, Nicola; Scheeres, Daniel J.
2017-04-01
The problem of finding natural bounded relative trajectories between the different units of a distributed space system is of great interest to the astrodynamics community. This is because most popular initialization methods still fail to establish long-term bounded relative motion when gravitational perturbations are involved. Recent numerical searches based on dynamical systems theory and ergodic maps have demonstrated that bounded relative trajectories not only exist but may extend up to hundreds of kilometers, i.e., well beyond the reach of currently available techniques. To remedy this, we introduce a novel approach that relies on neither linearized equations nor mean-to-osculating orbit element mappings. The proposed algorithm applies to rotationally symmetric bodies and is based on a numerical method for computing quasi-periodic invariant tori via stroboscopic maps, including extra constraints to fix the average of the nodal period and RAAN drift between two consecutive equatorial plane crossings of the quasi-periodic solutions. In this way, bounded relative trajectories of arbitrary size can be found with great accuracy as long as these are allowed by the natural dynamics and the physical constraints of the system (e.g., the surface of the gravitational attractor). This holds under any number of zonal harmonics perturbations and for arbitrary time intervals as demonstrated by numerical simulations about an Earth-like planet and the highly oblate primary of the binary asteroid (66391) 1999 KW4.
BICEP2, the curvature perturbation and supersymmetry
Lyth, David H.
2014-11-01
The tensor fraction r ≅ 0.16 found by BICEP2 corresponds to a Hubble parameter H ≅ 1.0 × 10{sup 14} GeV during inflation. This has two implications for the (single-field) slow-roll inflation hypothesis. First, the inflaton perturbation must account for much more than 10% of the curvature perturbation ζ, which barring fine-tuning means that it accounts for practically all of it. It follows that a curvaton-like mechanism for generating ζ requires an alternative to slow roll such as k-inflation. Second, accepting slow-roll inflation, the excursion of the inflaton field is at least of order Planck scale. As a result, the flatness of the inflaton presumably requires a shift symmetry. I point out that if such is the case, the resulting potential is likely to have at least approximately the quadratic form suggested in 1983 by Linde, which is known to be compatible with the observed r as well as the observed spectral index n{sub s}. The shift symmetry does not require supersymmetry. Also, the big H may rule out a GUT by restoring the symmetry and producing fatal cosmic strings. The absence of a GUT would correspond to the absence of superpartners for the Standard Model particles, which indeed have yet to be found at the LHC.
Covariant perturbations in a multifluid cosmological medium
NASA Astrophysics Data System (ADS)
Dunsby, Peter K. S.; Bruni, Marco; Ellis, George F. R.
1992-08-01
In a series of recent papers, a new covariant formalism was introduced to treat inhomogeneities in any spacetime. The variables introduced in these papers are gauge-invariant with respect to a Robertson-Walker background spacetime because they vanish identically in such models, and they have a transparent physical meaning. Exact evolution equations were found for these variables, and the linearized form of these equations were obtained, showing that they give the standard results for a barotropic perfect fluid. In this paper we extend this formalism to the general case of multicomponent fluid sources with interactions between them. We show, using the tilted formalism of King and Ellis, (1973) that choosing either the energy frame or the particle frame gives rise to a set of physically well-defined covariant and gauge-invariant variables which describe density and velocity perturbations, both for the total fluid and its constituent components. We then derive a complete set of equations for these variables and show, through harmonic analysis, that they are equivalent to those of Bardeen (1980) and of Kodama and Sasaki (1984). We discuss a number of interesting applications, including the case where the universe is filled with a mixture of baryons and radiation, coupled through Thomson scattering, and we derive solutions for the density and velocity perturbations in the large-scale limit. We also correct a number of errors in the previous literature.
Localized Perturbations in Saturn's C Ring
NASA Astrophysics Data System (ADS)
Spitale, Joseph N.; Tiscareno, Matthew S.
2016-10-01
Years of high-resolution imaging of Saturn's rings have revealed many examples of perturbations arising from local causes. For example, the presence of 100-m-scale and smaller moonlets is inferred in the A ring based on the propeller-shaped disturbances that they create (Tiscareno et al. 2006, 2010); the F ring is shaped by regular collisions with its shepherd Prometheus, as well as with other smaller bodies orbiting in the vicinity (Murray et al. 2005, 2008); the "wisps" on the outer edge of the Keeler gap (Porco et al. 2005) may mark the locations of small moonlets that have emerged from the A ring (Tiscareno and Arnault 2015); wakes in the Huygens ringlet imply the presence of two multi-km bodies, and the irregular shape of its inner edge suggests the presence of many smaller bodies (Spitale and Hahn 2016); based on shadow measurements, the B ring contains an embedded 300-m object that produces a small propeller-shaped disturbance (Spitale and Porco 2010; Spitale and Tiscareno 2012).Here, we present evidence for localized perturbations in the C ring. The ringlet embedded in the Bond gap, near 1.470 Saturn radii, shows discrete clumps orbiting at the Keplerian rate in images spanning about eight years. The clumps are not detected in all image sequences at the expected longitudes. The Dawes ringlet, near 1.495 Saturn radii, has an irregular edge that does not appear as a simple superposition of low-wavenumber normal modes.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Perceived timing of a postural perturbation.
Lupo, Julian; Barnett-Cowan, Michael
2017-02-03
Falling down is a common event that threatens the survival of an organism. Simple, yet sophisticated neural mechanisms allow for rapid detection of a fall as well as the generation of compensatory reflexes designed to prevent a fall. Fall awareness and preventative alerting devices could potentially mitigate the likelihood of a fall, however, relatively little is known about the perceived timing of a fall. Common anecdotal reports suggest that humans often describe distortions in their perception of time with very little recollection of what occurred during the fall. Previous research has also found that the vestibular system is perceptually slow compared to the other senses (45-160ms delay), indicating that vestibular stimuli must occur prior to other sensory stimuli in order for it to be perceived as synchronous. Here we examine whether fall perception is similarly slow. Participants made temporal order judgments identifying whether fall or sound onset came first to measure the point of subjective simultaneity. Results show that fall perception is slow, where the onset of a perturbation has to precede an auditory stimulus by ∼44 ms to appear coincident with the fall. We suggest that the central nervous system's rapid detection and response capabilities are restricted to reflexive behaviour, with conscious awareness of a fall being prioritized less. The additional lead times for detecting perturbation onset constrain possible fall detection and alert systems that have been proposed to inform a user to prevent falls and may also help explain the increased likelihood for fall incidence in the elderly.
Quantum cosmological perturbations of multiple fluids
NASA Astrophysics Data System (ADS)
Peter, Patrick; Pinto-Neto, N.; Vitenti, Sandro D. P.
2016-01-01
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and momenta leading to the quadratic Hamiltonian describing linear perturbations. The final Hamiltonian is obtained without assuming any equations of motions for the background variables. This general formalism is applied to the special case of two fluids, having in mind the usual radiation and matter mix which made most of our current Universe history. Quantization is achieved using an adiabatic expansion of the basis functions. This allows for an unambiguous definition of a vacuum state up to the given adiabatic order. Using this basis, we show that particle creation is well defined for a suitable choice of vacuum and canonical variables, so that the time evolution of the corresponding quantum fields is unitary. This provides constraints for setting initial conditions for an arbitrary number of fluids and background time evolution. We also show that the common choice of variables for quantization can lead to an ill-defined vacuum definition. Our formalism is not restricted to the case where the coupling between fields is small, but is only required to vary adiabatically with respect to the ultraviolet modes, thus paving the way to consistent descriptions of general models not restricted to single-field (or fluid).
Aircraft Range Optimization Using Singular Perturbations
NASA Technical Reports Server (NTRS)
Oconnor, Joseph Taffe
1973-01-01
An approximate analytic solution is developed for the problem of maximizing the range of an aircraft for a fixed end state. The problem is formulated as a singular perturbation and solved by matched inner and outer asymptotic expansions and the minimum principle of Pontryagin. Cruise in the stratosphere, and on transition to and from cruise at constant Mach number are discussed. The state vector includes altitude, flight path angle, and mass. Specific fuel consumption becomes a linear function of power approximating that of the cruise values. Cruise represents the outer solution; altitude and flight path angle are constants, and only mass changes. Transitions between cruise and the specified initial and final conditions correspond to the inner solutions. The mass is constant and altitude and velocity vary. A solution is developed which is valid for cruise but which is not for the initial and final conditions. Transforming of the independent variable near the initial and final conditions result in solutions which are valid for the two inner solutions but not for cruise. The inner solutions can not be obtained without simplifying the state equations. The singular perturbation approach overcomes this difficulty. A quadratic approximation of the state equations is made. The resulting problem is solved analytically, and the two inner solutions are matched to the outer solution.
Gradient expansion, curvature perturbations, and magnetized plasmas
Giovannini, Massimo; Rezaei, Zahra
2011-04-15
The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative description prior to photon decoupling. The latter assumption is hereby relaxed and predecoupling plasmas are described within a suitable expansion where the inhomogeneities are treated to a given order in the spatial gradients. It is argued that the (general relativistic) gradient expansion shares the same features of the drift approximation, customarily employed in the description of cold plasmas, so that the two schemes are physically complementary in the large-scale limit and for the low-frequency branch of the spectrum of plasma modes. The two-fluid description, as well as the magnetohydrodynamical reduction, is derived and studied in the presence of the spatial gradients of the geometry. Various solutions of the coupled system of evolution equations in the anti-Newtonian regime and in the quasi-isotropic approximation are presented. The relation of this analysis to the so-called separate universe paradigm is outlined. The evolution of the magnetized curvature perturbations in the nonlinear regime is addressed for the magnetized adiabatic mode in the plasma frame.
Cosmological tests of modified gravity
NASA Astrophysics Data System (ADS)
Koyama, Kazuya
2016-04-01
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein’s theory of general relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including f(R) gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard Λ CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars. The last decade has seen a number of new constraints placed on gravity from astrophysical to cosmological scales. Thanks to on-going and future surveys, cosmological tests of gravity will enjoy another, possibly even more, exciting ten years.
Cosmological tests of modified gravity.
Koyama, Kazuya
2016-04-01
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of general relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including f(R) gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard [Formula: see text]CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars. The last decade has seen a number of new constraints placed on gravity from astrophysical to cosmological scales. Thanks to on-going and future surveys, cosmological tests of gravity will enjoy another, possibly even more, exciting ten years.
A hybrid-perturbation-Galerkin technique which combines multiple expansions
NASA Technical Reports Server (NTRS)
Geer, James F.; Andersen, Carl M.
1989-01-01
A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.
Ergodicity in randomly perturbed quantum systems
NASA Astrophysics Data System (ADS)
Gherardini, Stefano; Lovecchio, Cosimo; Müller, Matthias M.; Lombardi, Pietro; Caruso, Filippo; Saverio Cataliotti, Francesco
2017-03-01
The theoretical cornerstone of statistical mechanics is the ergodic assumption, i.e. the assumption that the time average of an observable equals its ensemble average. Here, we show how such a property is present when an open quantum system is continuously perturbed by an external environment effectively observing the system at random times while the system dynamics approaches the quantum Zeno regime. In this context, by large deviation theory we analytically show how the most probable value of the probability for the system to be in a given state eventually deviates from the non-stochastic case when the Zeno condition is not satisfied. We experimentally test our results with ultra-cold atoms prepared on an atom chip.
Perturbative High Harmonic Wave Front Control
NASA Astrophysics Data System (ADS)
Li, Zhengyan; Brown, Graham; Ko, Dong Hyuk; Kong, Fanqi; Arissian, Ladan; Corkum, P. B.
2017-01-01
We pattern the wave front of a high harmonic beam by intersecting the intense driving laser pulse that generates the high harmonic with a weak control pulse. To illustrate the potential of wave-front control, we imprint a Fresnel zone plate pattern on a harmonic beam, causing the harmonics to focus and defocus. The quality of the focus that we achieve is measured using the spectral wave-front optical reconstruction by diffraction method. We will show that it is possible to enhance the peak intensity by orders of magnitude without a physical optical element in the path of the extreme ultraviolet (XUV) beam. Through perturbative wave-front control, XUV beams can be created with a flexibility approaching what technology allows for visible and infrared light.
Profiling DNA damage response following mitotic perturbations
S. Pedersen, Ronni; Karemore, Gopal; Gudjonsson, Thorkell; Rask, Maj-Britt; Neumann, Beate; Hériché, Jean-Karim; Pepperkok, Rainer; Ellenberg, Jan; Gerlich, Daniel W.; Lukas, Jiri; Lukas, Claudia
2016-01-01
Genome integrity relies on precise coordination between DNA replication and chromosome segregation. Whereas replication stress attracted much attention, the consequences of mitotic perturbations for genome integrity are less understood. Here, we knockdown 47 validated mitotic regulators to show that a broad spectrum of mitotic errors correlates with increased DNA breakage in daughter cells. Unexpectedly, we find that only a subset of these correlations are functionally linked. We identify the genuine mitosis-born DNA damage events and sub-classify them according to penetrance of the observed phenotypes. To demonstrate the potential of this resource, we show that DNA breakage after cytokinesis failure is preceded by replication stress, which mounts during consecutive cell cycles and coincides with decreased proliferation. Together, our results provide a resource to gauge the magnitude and dynamics of DNA breakage associated with mitotic aberrations and suggest that replication stress might limit propagation of cells with abnormal karyotypes. PMID:27976684
Systematic analysis of endocytosis by cellular perturbations.
Kühling, Lena; Schelhaas, Mario
2014-01-01
Endocytosis is an essential process of eukaryotic cells that facilitates numerous cellular and organismal functions. The formation of vesicles from the plasma membrane serves the internalization of ligands and receptors and leads to their degradation or recycling. A number of distinct mechanisms have been described over the years, several of which are only partially characterized in terms of mechanism and function. These are often referred to as novel endocytic pathways. The pathways differ in their mode of uptake and in their intracellular destination. Here, an overview of the set of cellular proteins that facilitate the different pathways is provided. Further, the approaches to distinguish between the pathways by different modes of perturbation are critically discussed, emphasizing the use of genetic tools such as dominant negative mutant proteins.
Pressure perturbation calorimetry of unfolded proteins.
Tsamaloukas, Alekos D; Pyzocha, Neena K; Makhatadze, George I
2010-12-16
We report the application of pressure perturbation calorimetry (PPC) to study unfolded proteins. Using PPC we have measured the temperature dependence of the thermal expansion coefficient, α(T), in the unfolded state of apocytochrome C and reduced BPTI. We have shown that α(T) is a nonlinear function and decreases with increasing temperature. The decrease is most significant in the low (2-55 °C) temperature range. We have also tested an empirical additivity approach to predict α(T) of unfolded state from the amino acid sequence using α(T) values for individual amino acids. A comparison of the experimental and calculated functions shows a very good agreement, both in absolute values of α(T) and in its temperature dependence. Such an agreement suggests the applicability of using empirical calculations to predict α(T) of any unfolded protein.
Degenerate R-S perturbation theory
NASA Technical Reports Server (NTRS)
Hirschfelder, J. O.; Certain, P. R.
1973-01-01
A concise, systematic procedure is given for determining the Rayleigh-Schrodinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n+1)st order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite order operators which are determined by the successive resolution of the space of the zeroth order functions.
Plasma Braking Due to External Magnetic Perturbations
NASA Astrophysics Data System (ADS)
Frassinetti, L.; Olofsson, Kejo; Brunsell, P. R.; Khan, M. W. M.; Drake, J. R.
2010-11-01
The RFP EXTRAP T2R is equipped with a comprehensive active feedback system (128 active saddle coils in the full-coverage array) and active control of both resonant and non-resonant MHD modes has been demonstrated. The feedback algorithms, based on modern control methodology such as reference mode tracking (both amplitude and phase), are a useful tool to improve the ``state of the art'' of the MHD mode control. But this tool can be used also to improve the understanding and the characterization of other phenomena such as the ELM mitigation with a resonant magnetic perturbation or the plasma viscosity. The present work studies plasma and mode braking due to static RMPs. Results show that a static RMP produces a global braking of the flow profile. The study of the effect of RMPs characterized by different helicities will also give information on the plasma viscosity profile. Experimental results are finally compared to theoretical models.
Applications of partially quenched chiral perturbation theory
Golterman, M.F.; Leung, K.C.
1998-05-01
Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B{sub K}, and the K{sup +}{r_arrow}{pi}{sup +}{pi}{sup 0} decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B{sub K} and the K{sup +} decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta, are also considered. We find that typical one-loop corrections can be substantial. {copyright} {ital 1998} {ital The American Physical Society}
Chiral nontopological solitons with perturbative quantum pions
NASA Astrophysics Data System (ADS)
Williams, A. G.; Dodd, L. R.
1988-04-01
We investigate chiral extensions of a broad class of nontopological soliton bag models. Chiral symmetry is restored in a nonlinear realization through the introduction of an elementary pion field. We show in particular that it is consistent to treat the pions as a perturbative quantum field, as is done in the cloudy-bag model. The cloudy-bag model is recovered as a limiting case. A careful comparison is made between predictions of chiral extensions of the Friedberg-Lee and the Nielsen-Patkos color-dielectric nontopological soliton models and the cloudy-bag model. Once the overall distance scale is fixed we find relative insensitivity to the detailed choice of nontopological soliton parameters. We investigate two versions of chiral nontopological solitons, analogous to the surface- and volume-coupled cloudy-bag model, and discuss their relation to current algebra.
Singular perturbations in the state regulator problem
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1972-01-01
Most of the results of singular perturbation theory have been concerned with initial value problems whereas optimal control problems are of two-point boundary value type. The portions of this theory applicable to the open loop state regulator problem are reviewed. For obtaining approximate solutions to the state regulator problem the method of matched asymptotic expansions is employed. This method has been developed in connection with certain fluid mechanics problems and is applicable to nonlinear as well as linear problems. It has been found in the past to be advantageous not to formulate this method generally but to apply it to each individual problem and this approach is adopted here. A general recipe for the method is given and its application is illustrated by using the method to obtain an approximate solution to a simple, specific state regulator problem.
Formation of Voids from Negative Density Perturbations
NASA Astrophysics Data System (ADS)
de Araujo, J. C. N.; Opher, R.
1990-11-01
RESUMEN. Se estudia la formaci6n de huecos a partir de un espectro negativo de perturbaciones, tomando en cuenta la expansi6n del Universo, arrastre por fotones, enfriamiento por fotones, fotoionizaci6n, ioniza- ci6n colisional, enfriamiento Lyman a y la formaci6n y enfriamiento de moleculas H2. Nuestros resultados predicen la existencia de regiones 1/10 de Ia densidad promedio para regiones de masa lO - 1O10M . ABSTRACT. In the present paer we study the formation of voids from a negative spectrum of perturbations taking into account the expansion of the Universe, photon-drag, photon-cooling, photoionization, collisional ionization, Lyman a cooling and the formation and cooling of 112 molecules. Our results predict the existence of regions 1/10 the average density for regions of mass 1O - 1O10M@ : CLUSTERS-GALAXIES - COSMOLOGY
Relativistic Lagrangian displacement field and tensor perturbations
NASA Astrophysics Data System (ADS)
Rampf, Cornelius; Wiegand, Alexander
2014-12-01
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully nonperturbative approach based on the Arnowitt-Deser-Misner (ADM) split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the nonperturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious nonpropagating tensor artifacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the nonlinear frame dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a Λ CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.
Chemical Approaches To Perturb, Profile, and Perceive Glycans
2009-01-01
Glycosylation is an essential form of post-translational modification that regulates intracellular and extracellular processes. Regrettably, conventional biochemical and genetic methods often fall short for the study of glycans, because their structures are often not precisely defined at the genetic level. To address this deficiency, chemists have developed technologies to perturb glycan biosynthesis, profile their presentation at the systems level, and perceive their spatial distribution. These tools have identified potential disease biomarkers and ways to monitor dynamic changes to the glycome in living organisms. Still, glycosylation remains the underexplored frontier of many biological systems. In this Account, we focus on research in our laboratory that seeks to transform the study of glycan function from a challenge to routine practice. In studies of proteins and nucleic acids, functional studies have often relied on genetic manipulations to perturb structure. Though not directly subject to mutation, we can determine glycan structure−function relationships by synthesizing defined glycoconjugates or by altering natural glycosylation pathways. Chemical syntheses of uniform glycoproteins and polymeric glycoprotein mimics have facilitated the study of individual glycoconjugates in the absence of glycan microheterogeneity. Alternatively, selective inhibition or activation of glycosyltransferases or glycosidases can define the biological roles of the corresponding glycans. Investigators have developed tools including small molecule inhibitors, decoy substrates, and engineered proteins to modify cellular glycans. Current approaches offer a precision approaching that of genetic control. Genomic and proteomic profiling form a basis for biological discovery. Glycans also present a rich matrix of information that adapts rapidly to changing environs. Glycomic and glycoproteomic analyses via microarrays and mass spectrometry are beginning to characterize alterations in
Electrons fortement correles: Une approche perturbative a couplage fort
NASA Astrophysics Data System (ADS)
Pairault, Stephane
Nous présentons une nouvelle méthode perturbative à couplage fort, reposant sur un analogue fermionique de la transformation de Hubbard- Stratonovitch, et susceptible d'être appliquée à plusieurs hamiltoniens de la physique du solide. Nous établissons une théorie diagrammatique, gouvernée par des règles de Feynman modifiées, et montrons que, pour mener à un poids spectral physiquement acceptable, le développement de la fonction de Green doit être paramétré sous la forme dune fraction continue. Appliquée à l'ordre trois au modèle de Hubbard à demi-remplissage, cette méthode permet d'établir un diagramme de crossover dans lequel on peut distinguer trois régions de comportements différents: conducteur, isolant paramagnétique, et isolant à fortes corrélations antiferromagnétiques. Le rôle des ordres plus élevés de la théorie des perturbations, et les limites de fiabilité de la solution, notamment à basse température, sont ensuite débattus. Nos conclusions sont confrontées avec succès aux résultats de simulations Monte-Carlo. On calcule le facteur d'occupation double et la susceptibilité magnétique dynamique non uniforme, avant d'examiner la transition métal- isolant induite par le dopage. Finalement, deux solutions partiellement autocohérentes sont analysées. Puis, on incorpore le désordre dans le modèle de Hubbard afin d'étudier la transition métal-isolant en présence d'impuretés. Deux schémas d'approximation (à fort et faible désordre) sont discutés.
Alkaline Phosphatase Assay for Freshwater Sediments: Application to Perturbed Sediment Systems
Sayler, Gary S.; Puziss, Marla; Silver, Martin
1979-01-01
The p-nitrophenyl phosphate hydrolysis-phosphatase assay was modified for use in freshwater sediment. Laboratory studies indicated that the recovery of purified alkaline phosphatase activity was 100% efficient in sterile freshwater sediments when optimized incubation and sonication conditions were used. Field studies of diverse freshwater sediments demonstrated the potential use of this assay for determining stream perturbation. Significant correlations between phosphatase and total viable cell counts, as well as adenosine triphosphate biomass, suggested that alkaline phosphatase activity has utility as an indicator of microbial population density and biomass in freshwater sediments. PMID:16345464
Converting entropy to curvature perturbations after a cosmic bounce
Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno; Wilson-Ewing, Edward
2016-10-04
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Non-perturbative String Theory from Water Waves
Iyer, Ramakrishnan; Johnson, Clifford V.; Pennington, Jeffrey S.; /SLAC
2012-06-14
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.
Adiabatic and isocurvature perturbation projections in multi-field inflation
Gordon, Chris; Saffin, Paul M. E-mail: Paul.Saffin@nottingham.ac.uk
2013-08-01
Current data are in good agreement with the predictions of single field inflation. However, the hemispherical asymmetry, seen in the cosmic microwave background data, may hint at a potential problem. Generalizing to multi-field models may provide one possible explanation. A useful way of modeling perturbations in multi-field inflation is to investigate the projection of the perturbation along and perpendicular to the background fields' trajectory. These correspond to the adiabatic and isocurvature perturbations. However, it is important to note that in general there are no corresponding adiabatic and isocurvature fields. The purpose of this article is to highlight the distinction between a field redefinition and a perturbation projection. We provide a detailed derivation of the evolution of the isocurvature perturbation to show that no assumption of an adiabatic or isocurvature field is needed. We also show how this evolution equation is consistent with the field covariant evolution equations for the adiabatic perturbation in the flat field space limit.
Intersegmental coupling and recovery from perturbations in freely running cockroaches.
Couzin-Fuchs, Einat; Kiemel, Tim; Gal, Omer; Ayali, Amir; Holmes, Philip
2015-01-15
Cockroaches are remarkably stable runners, exhibiting rapid recovery from external perturbations. To uncover the mechanisms behind this important behavioral trait, we recorded leg kinematics of freely running animals in both undisturbed and perturbed trials. Functional coupling underlying inter-leg coordination was monitored before and during localized perturbations, which were applied to single legs via magnetic impulses. The resulting transient effects on all legs and the recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architecture and strength by fitting experimental data to a six-leg-unit phase oscillator model. Using maximum-likelihood techniques, we found that a network with nearest-neighbor inter-leg coupling best fitted the data and that, although coupling strengths vary among preparations, the overall inputs entering each leg are approximately balanced and consistent. Simulations of models with different coupling strengths encountering perturbations suggest that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations.
Delta-Measure Perturbations of a Contact Discontinuity
NASA Astrophysics Data System (ADS)
Baty, Roy
2012-11-01
In this presentation, nonstandard analysis is applied to study generalized function perturbations of contact discontinuities in compressible, inviscid fluids. Nonstandard analysis is an area of modern mathematics that studies extensions of the real number system to nonstandard number systems that contain infinitely large and infinitely small numbers. Perturbations of a contact discontinuity are considered that represent one-dimensional analogs of the two-dimensional perturbations observed in the initial evolution of a Richtmyer-Meshkov instability on a density interface. Nonstandard predistributions of the Dirac delta measure and its derivatives are applied as the perturbations of a contact discontinuity. The one-dimensional Euler equations are used to model the flow field of a fluid containing a perturbed density interface and generalized solutions are constructed for the perturbed flow field.
Investigations of Probe Induced Perturbations in a Hall Thruster
D. Staack; Y. Raitses; N.J. Fisch
2002-08-12
An electrostatic probe used to measure spatial plasma parameters in a Hall thruster generates perturbations of the plasma. These perturbations are examined by varying the probe material, penetration distance, residence time, and the nominal thruster conditions. The study leads us to recommendations for probe design and thruster operating conditions to reduce discharge perturbations, including metal shielding of the probe insulator and operation of the thruster at lower densities.
Anomaly-free cosmological perturbations in effective canonical quantum gravity
Barrau, Aurelien; Calcagni, Gianluca; Grain, Julien E-mail: bojowald@gravity.psu.edu E-mail: julien.grain@ias.u-psud.fr
2015-05-01
This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of space-time, the classical perturbative treatment must be rethought carefully. The present discussion provides a unified picture of several previous works, together with new treatments of higher-order perturbations and the specification of initial states.
Quark Matter Equation of State from Perturbative QCD
NASA Astrophysics Data System (ADS)
Vuorinen, Aleksi
2017-03-01
In this proceedings contribution, we discuss recent developments in the perturbative determination of the Equation of State of dense quark matter, relevant for the microscopic description of neutron star cores. First, we introduce the current state of the art in the problem, both at zero and small temperatures, and then present results from two recent perturbative studies that pave the way towards extending the EoS to higher orders in perturbation theory.
Density Perturbations in the Universe from Massive Vector Fields
Dimopoulos, K.
2007-11-20
I discuss the possibility of using a massive vector field to generate the density perturbation in the Universe. I find that a scale-invariant superhorizon spectrum of vector field perturbations is possible to generate during inflation. The associated curvature perturbation is imprinted onto the Universe following the curvaton scenario. The mechanism does not generate a long-range anisotropy because an oscillating massive vector field behaves as a pressureless isotropic fluid.
Equation-of-motion coupled cluster perturbation theory revisited.
Eriksen, Janus J; Jørgensen, Poul; Olsen, Jeppe; Gauss, Jürgen
2014-05-07
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally converges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby remedying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz.
Constraints on primordial density perturbations from induced gravitational waves
Assadullahi, Hooshyar; Wands, David
2010-01-15
We consider the stochastic background of gravitational waves produced during the radiation-dominated hot big bang as a constraint on the primordial density perturbation on comoving length scales much smaller than those directly probed by the cosmic microwave background or large-scale structure. We place weak upper bounds on the primordial density perturbation from current data. Future detectors such as BBO and DECIGO will place much stronger constraints on the primordial density perturbation on small scales.
Nondimensional forms for singular perturbation analyses of aircraft energy climbs
NASA Technical Reports Server (NTRS)
Calise, A. J.; Markopoulos, N.; Corban, J. E.
1991-01-01
This paper proposes a systematic approach for identifying the perturbation parameter in singular perturbation analysis of aircraft optimal guidance, and in particular considers a family of problems related to aircraft energy climbs. The approach, which is based on a nondimensionalization of the equations of motion, is used to evaluatae the appropriateness of forced singular perturbation formulations used in the past for transport and fighter aircraft, and to assess the applicability of energy state approximations and singular perturbation analysis for airbreathing transatmospheric vehicles with hypersonic cruise and orbital capabilities.
Perturbation Monte Carlo methods for tissue structure alterations.
Nguyen, Jennifer; Hayakawa, Carole K; Mourant, Judith R; Spanier, Jerome
2013-01-01
This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15-25% of the scattering parameters.
The study of effects of small perturbations on chaotic systems
Grebogi, C. . Lab. for Plasma Research); Yorke, J.A. . Inst. for Physical Science and Technology)
1990-12-01
This report discusses the following topics on small perturbations on chaotic systems: controlling chaos; shadowing and noise reduction; chaotic scattering; random maps; magnetic dynamo; and aids transmission. (LSP)
Non-linear isocurvature perturbations and non-Gaussianities
Langlois, David; Vernizzi, Filippo; Wands, David E-mail: filippo.vernizzi@cea.fr
2008-12-15
We study non-linear primordial adiabatic and isocurvature perturbations and their non-Gaussianity. After giving a general formulation in the context of an extended {delta}N formalism, we analyse in detail two illustrative examples. The first is a mixed curvaton-inflaton scenario in which fluctuations of both the inflaton and a curvaton (a light isocurvature field during inflation) contribute to the primordial density perturbation. The second example is that of double inflation involving two decoupled massive scalar fields during inflation. In the mixed curvaton-inflaton scenario we find that the bispectrum of primordial isocurvature perturbations may be large and comparable to the bispectrum of adiabatic curvature perturbations.
A new method to compute lunisolar perturbations in satellite motions
NASA Technical Reports Server (NTRS)
Kozai, Y.
1973-01-01
A new method to compute lunisolar perturbations in satellite motion is proposed. The disturbing function is expressed by the orbital elements of the satellite and the geocentric polar coordinates of the moon and the sun. The secular and long periodic perturbations are derived by numerical integrations, and the short periodic perturbations are derived analytically. The perturbations due to the tides can be included in the same way. In the Appendix, the motion of the orbital plane for a synchronous satellite is discussed; it is concluded that the inclination cannot stay below 7 deg.
Some topics on scale-invariant perturbations from noninflationary universe
NASA Astrophysics Data System (ADS)
Li, Mingzhe
In this paper, we review some topics on generations of scale-invariant primordial scalar and tensor perturbations in the early universe models different from inflation. The content includes generation of scale-invariant and Gaussian scalar perturbation in the ekpyrotic/cyclic universe, and production scale-invariant tensor perturbation in contracting universe. The main property of the models reviewed in this paper is the nonminimal couplings, include nonminimal couplings between the scalar fields and those to the gravity. By introducing these couplings, it is not difficult to achieve scale-invariances for the perturbations in the early universe models alternative to inflation.
Multifield cosmological perturbations at third order and the ekpyrotic trispectrum
Lehners, Jean-Luc; Renaux-Petel, Sebastien
2009-09-15
Using the covariant formalism, we derive the equations of motion for adiabatic and entropy perturbations at third order in perturbation theory for cosmological models involving two scalar fields. We use these equations to calculate the trispectrum of ekpyrotic and cyclic models in which the density perturbations are generated via the entropic mechanism. In these models, the conversion of entropy into curvature perturbations occurs just before the big bang, either during the ekpyrotic phase or during the subsequent kinetic energy dominated phase. In both cases, we find that the nonlinearity parameters f{sub NL} and g{sub NL} combine to leave a very distinct observational imprint.
Quaternion regularization and stabilization of perturbed central motion. II
NASA Astrophysics Data System (ADS)
Chelnokov, Yu. N.
1993-04-01
Generalized regular quaternion equations for the three-dimensional two-body problem in terms of Kustaanheimo-Stiefel variables are obtained within the framework of the quaternion theory of regularizing and stabilizing transformations of the Newtonian equations for perturbed central motion. Regular quaternion equations for perturbed central motion of a material point in a central field with a certain potential Pi are also derived in oscillatory and normal forms. In addition, systems of perturbed central motion equations are obtained which include quaternion equations of perturbed orbit orientations in oscillatory or normal form, and a generalized Binet equation is derived. A comparative analysis of the equations is carried out.
Moleriu, Radu Dumitru; Zaharie, Daniela; Moatar-Moleriu, Lavinia Cristina; Gruia, Alexandra Teodora; Mic, Ani Aurora; Mic, Felix Aurel
2014-05-07
T-cells develop in the thymus and based on CD4 and CD8 expressions there are four main thymocyte populations in a normal mouse thymus. Currently, there are several mathematical models that describe the dynamics of thymocyte populations in a normal thymus, but only a few of them model the transient perturbation of their homeostasis. Our aim is to model the perturbation in the dynamics of each thymocyte population which is induced by the administration of a glucocorticoid, i.e. dexamethasone. The proposed approach relies on extending a four compartment thymus model based on differential equations by adding perturbation terms either globally (at the level of each equation) or locally (at the level of proliferation, death, and transfer rates). By fitting the perturbed model with experimental data on mice thymi collected before and after the administration of dexamethasone, it was possible to estimate the relevant parameters using a population-based stochastic search method. The fitted model is further used to conduct a quantitative analysis on the differentiated impact of dexamethasone on each T-cell population and on proliferation, death, and transfer processes. The obtained quantitative information on the perturbation could be used to explore and modify the flow of thymocytes between thymus compartments in order to elucidate the mechanisms of thymus involution and its subsequent regeneration. Since glucocorticoids are raised in many pathological situations, such a model could be useful in evaluating the impact of diseases on thymocyte dynamics in the thymus.
NASA Astrophysics Data System (ADS)
Tang, Zhanqi; Jiang, Nan; Zheng, Xiaobo; Wu, Yanhua
2016-05-01
Hot-wire measurements on a turbulent boundary layer flow perturbed by a wall-mounted cylinder roughness element (CRE) are carried out in this study. The cylindrical element protrudes into the logarithmic layer, which is similar to those employed in turbulent boundary layers by Ryan et al. (AIAA J 49:2210-2220, 2011. doi: 10.2514/1.j051012) and Zheng and Longmire (J Fluid Mech 748:368-398, 2014. doi: 10.1017/jfm.2014.185) and in turbulent channel flow by Pathikonda and Christensen (AIAA J 53:1-10, 2014. doi: 10.2514/1.j053407). The similar effects on both the mean velocity and Reynolds stress are observed downstream of the CRE perturbation. The series of hot-wire data are decomposed into large- and small-scale fluctuations, and the characteristics of large- and small-scale bursting process are observed, by comparing the bursting duration, period and frequency between CRE-perturbed case and unperturbed case. It is indicated that the CRE perturbation performs the significant impact on the large- and small-scale structures, but within the different impact scenario. Moreover, the large-scale bursting process imposes a modulation on the bursting events of small-scale fluctuations and the overall trend of modulation is not essentially sensitive to the present CRE perturbation, even the modulation extent is modified. The conditionally averaging fluctuations are also plotted, which further confirms the robustness of the bursting modulation in the present experiments.
Perturbative and non-perturbative aspects of the two-dimensional string/Yang-Mills correspondence
NASA Astrophysics Data System (ADS)
Lelli, Simone; Maggiore, Michele; Rissone, Anna
2003-04-01
It is known that YM 2 with gauge group SU( N) is equivalent to a string theory with coupling gs=1/ N, order by order in the 1/ N expansion. We show how this result can be obtained from the bosonization of the fermionic formulation of YM 2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM 2 partition function of order exp{- kA/( πα' gs)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead strictly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM 2 is described by a perturbative string theory separated from a region where it is described by a topological string theory.
Solitary magnetic perturbations at the ELM onset
NASA Astrophysics Data System (ADS)
Wenninger, R. P.; Zohm, H.; Boom, J. E.; Burckhart, A.; Dunne, M. G.; Dux, R.; Eich, T.; Fischer, R.; Fuchs, C.; Garcia-Munoz, M.; Igochine, V.; Hölzl, M.; Luhmann N., C., Jr.; Lunt, T.; Maraschek, M.; Müller, H. W.; Park, H. K.; Schneider, P. A.; Sommer, F.; Suttrop, W.; Viezzer, E.; the ASDEX Upgrade Team
2012-11-01
Tokamak H-mode plasmas frequently exhibit edge-localized modes (ELMs). ELMs allow maintaining sufficient plasma purity and thus enable stationary H-mode. On the other hand in a future device ELMs may cause divertor power flux densities far in excess of tolerable material limits. The size of the energy loss per ELM is determined by saturation effects in the non-linear phase of the ELM, which at present is hardly understood. ASDEX Upgrade is now equipped with a set of fast sampling diagnostics, which is well suited to investigate the chain of events around the ELM crash with appropriate temporal resolution (⩽10 µs). Solitary magnetic perturbations (SMPs) are identified as dominant features in the radial magnetic fluctuations below 100 kHz. They are typically observed close (±100 µs) to the onset of pedestal erosion. SMPs are field aligned structures rotating in the electron diamagnetic drift direction with perpendicular velocities of about 10 km s-1. A comparison of perpendicular velocities suggests that the perturbation evoking SMPs is located at or inside the separatrix. Analysis of very pronounced examples showed that the number of peaks per toroidal turn is 1 or 2, which is clearly lower than the corresponding numbers in linear stability calculations. In combination with strong peaking of the magnetic signals this results in a solitary appearance resembling modes like palm tree modes, edge snakes or outer modes. This behaviour has been quantified as solitariness and correlated with main plasma parameters. SMPs may be considered as a signature of the non-linear ELM phase originating at the separatrix or further inside. Thus they provide a handle to investigate the transition from linear to non-linear ELM phase. By comparison with data from gas puff imaging processes in the non-linear phase at or inside the separatrix and in the scrape-off layer (SOL) can be correlated. A connection between the passing of an SMP and the onset of radial filament propagation has
NASA Astrophysics Data System (ADS)
Shenavar, Hossein
2016-03-01
We impose Neumann boundary condition to solve cosmological perturbation equations and we derive a modified Friedmann equation and a new lensing equation. To check the new lensing equation and the value of Neumann constant, a sample that contains ten strong lensing systems is surveyed. Except for one lens, masses of the other lenses are found to be within the constrains of the observational data. Furthermore, we argue that by using the concept of geometrodynamic clocks it is possible to modify the equation of motion of massive particles too. Also, a sample that includes 101 HSB and LSB galaxies is used to re-estimate the value of the Neumann constant and we found that this value is consistent with the prior evaluation from Friedmann and lensing equations. Finally, the growth of structure is studied by a Newtonian approach which resulted in a more rapid rate of the structure formation in matter dominated era.
A perturbative approach to the redshift space power spectrum: beyond the Standard Model
NASA Astrophysics Data System (ADS)
Bose, Benjamin; Koyama, Kazuya
2016-08-01
We develop a code to produce the power spectrum in redshift space based on standard perturbation theory (SPT) at 1-loop order. The code can be applied to a wide range of modified gravity and dark energy models using a recently proposed numerical method by A.Taruya to find the SPT kernels. This includes Horndeski's theory with a general potential, which accommodates both chameleon and Vainshtein screening mechanisms and provides a non-linear extension of the effective theory of dark energy up to the third order. Focus is on a recent non-linear model of the redshift space power spectrum which has been shown to model the anisotropy very well at relevant scales for the SPT framework, as well as capturing relevant non-linear effects typical of modified gravity theories. We provide consistency checks of the code against established results and elucidate its application within the light of upcoming high precision RSD data.
Tewari, Muneesh; Hu, Patrick J; Ahn, Jin Sook; Ayivi-Guedehoussou, Nono; Vidalain, Pierre-Olivier; Li, Siming; Milstein, Stuart; Armstrong, Chris M; Boxem, Mike; Butler, Maurice D; Busiguina, Svetlana; Rual, Jean-François; Ibarrola, Nieves; Chaklos, Sabrina T; Bertin, Nicolas; Vaglio, Philippe; Edgley, Mark L; King, Kevin V; Albert, Patrice S; Vandenhaute, Jean; Pandey, Akhilesh; Riddle, Donald L; Ruvkun, Gary; Vidal, Marc
2004-02-27
To initiate a system-level analysis of C. elegans DAF-7/TGF-beta signaling, we combined interactome mapping with single and double genetic perturbations. Yeast two-hybrid (Y2H) screens starting with known DAF-7/TGF-beta pathway components defined a network of 71 interactions among 59 proteins. Coaffinity purification (co-AP) assays in mammalian cells confirmed the overall quality of this network. Systematic perturbations of the network using RNAi, both in wild-type and daf-7/TGF-beta pathway mutant animals, identified nine DAF-7/TGF-beta signaling modifiers, seven of which are conserved in humans. We show that one of these has functional homology to human SNO/SKI oncoproteins and that mutations at the corresponding genetic locus daf-5 confer defects in DAF-7/TGF-beta signaling. Our results reveal substantial molecular complexity in DAF-7/TGF-beta signal transduction. Integrating interactome maps with systematic genetic perturbations may be useful for developing a systems biology approach to this and other signaling modules.
Applications of the Kustaanheimo-Stieffel transformation of the perturbed two-body problem
NASA Technical Reports Server (NTRS)
Bond, V. R.
1973-01-01
The Newtonian differential equations of motion for the two-body problem can be transformed into four linear harmonic-oscillator equations by simultaneously applying the regularization step dt/ds = r and the Kustaanheimo-Stieffel (KS) transformation. The regularization step changes the independent variable from time to a new variable s, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. A derivation of a uniform, regular solution for the perturbed two-body problem in the four-dimensional space is presented. The variation-of-parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. This ten-element solution has mixed secular terms that degrade the long-term accuracy during numerical integration. Therefore, to eliminate these terms, the solution is modified by introducing two additional elements.
Roberson, B. Race; Winglee, Robert; Prager, James
2011-05-15
The high power helicon (HPH) is capable of producing a high density plasma (10{sup 17}-10{sup 18} m{sup -3}) and directed ion energies greater than 20 eV that continue to increase tens of centimeters downstream of the thruster. In order to understand the coupling mechanism between the helicon antenna and the plasma outside the immediate source region, measurements were made in the plasma plume downstream from the thruster of the propagating wave magnetic field and the perturbation of the axial bulk field using a type 'R' helicon antenna. This magnetic field perturbation ({Delta}B) peaks at more than 15 G in strength downstream of the plasma source, and is 3-5 times larger than those previously reported from HPH. Taking the curl of this measured magnetic perturbation and assuming azimuthal symmetry suggests that this magnetic field is generated by a (predominantly) azimuthal current ring with a current density on the order of tens of kA m{sup -2}. At this current density the diamagnetic field is intense enough to cancel out the B{sub 0} axial magnetic field near the source region. The presence of the diamagnetic current is important as it demonstrates modification of the vacuum fields well beyond the source region and signifies the presence of a high density, collimated plasma stream. This diamagnetic current also modifies the propagation of the helicon wave, which facilitates a better understanding of coupling between the helicon wave and the resultant plasma acceleration.
Randomized perturbed posturography: methodology and effects of midazolam sedation.
Ledin, T; Gupta, A; Larsen, L E; Odkvist, L M
1993-05-01
To study quiescent stance without applying external disturbances is not a theoretically appealing way to unveil the dynamic properties of human equilibrium. Methods to disturb equilibrium range from standing on foam surface, attaching vibrators to the calves to interfere with somatosensation, and exposure to body-position tracking environments, as in dynamic posturography (EquiTest). The EquiTest apparatus was modified by a menu-driven software to allow arbitrary movements of the support surface and visual surround, and force data were recorded for subsequent analysis. The support surface was randomly moved in the antero-posterior direction. First equilibrium was studied on the stable support surface, then low (RMS 1.3 cm) and high (RMS 2.6 cm) amplitude movements were used. Vision was either present or absent at all test amplitudes. Equilibrium was evaluated by the confidence (61%) ellipse sway area and average sway velocity during 45 s. Eleven healthy subjects aged 23-36 years (mean 29) were sedated with a short acting sedative, midazolam 0.1 mg/kg. Randomized perturbed posturography was conducted at baseline, and at about 60, 120 and 180 min after injection. Psychomotor tests were conducted at baseline, and at 30, 90, 150 and 210 min. Large interindividual variations were found. One subject could not be tested at all at 60 min due to sleepiness, whereas some subjects felt nearly full awake at 30 min. Sway areas were larger at 60 min, but not subsequently. At 60 min, sway velocities with open eyes were higher, just as when vision was absent and low amplitude movements were used. Later no effects could be shown.(ABSTRACT TRUNCATED AT 250 WORDS)
Stabilization of perturbed Boolean network attractors through compensatory interactions
2014-01-01
Background Understanding and ameliorating the effects of network damage are of significant interest, due in part to the variety of applications in which network damage is relevant. For example, the effects of genetic mutations can cascade through within-cell signaling and regulatory networks and alter the behavior of cells, possibly leading to a wide variety of diseases. The typical approach to mitigating network perturbations is to consider the compensatory activation or deactivation of system components. Here, we propose a complementary approach wherein interactions are instead modified to alter key regulatory functions and prevent the network damage from triggering a deregulatory cascade. Results We implement this approach in a Boolean dynamic framework, which has been shown to effectively model the behavior of biological regulatory and signaling networks. We show that the method can stabilize any single state (e.g., fixed point attractors or time-averaged representations of multi-state attractors) to be an attractor of the repaired network. We show that the approach is minimalistic in that few modifications are required to provide stability to a chosen attractor and specific in that interventions do not have undesired effects on the attractor. We apply the approach to random Boolean networks, and further show that the method can in some cases successfully repair synchronous limit cycles. We also apply the methodology to case studies from drought-induced signaling in plants and T-LGL leukemia and find that it is successful in both stabilizing desired behavior and in eliminating undesired outcomes. Code is made freely available through the software package BooleanNet. Conclusions The methodology introduced in this report offers a complementary way to manipulating node expression levels. A comprehensive approach to evaluating network manipulation should take an "all of the above" perspective; we anticipate that theoretical studies of interaction modification
Perturbing Streaming in Dictyostelium discoidium Aggregation
NASA Astrophysics Data System (ADS)
Rericha, Erin; Garcia, Gene; Parent, Carole; Losert, Wolfgang
2009-03-01
The ability of cells to move towards environmental cues is a critical process allowing the destruction of intruders by the immune system, the formation of the vascular system and the whole scale remodeling of tissues during embryo development. We examine the initial transition from single cell to group migration in the social amoeba Dictyostelium discoidium. Upon starvation, D. discoidium cells enter into a developmental program that triggers solitary cells to aggregate into a multicellular structure. The aggregation is mediated by the small molecule, cyclic-AMP, that cells sense, synthesize, secrete and migrate towards often in a head-to-tail fashion called a stream. Using experiment and numerical simulation, we study the sensitivity of streams to perturbations in the cyclic-AMP concentration field. We find the stability of the streams requires cells to shape the cyclic-AMP field through localized secretion and degradation. In addition, we find the streaming phenotype is sensitive to changes in the substrate properties, with slicker surfaces leading to longer more branched streams that yield large initial aggregates.
Computation of solar perturbations with Poisson series
NASA Technical Reports Server (NTRS)
Broucke, R.
1974-01-01
Description of a project for computing first-order perturbations of natural or artificial satellites by integrating the equations of motion on a computer with automatic Poisson series expansions. A basic feature of the method of solution is that the classical variation-of-parameters formulation is used rather than rectangular coordinates. However, the variation-of-parameters formulation uses the three rectangular components of the disturbing force rather than the classical disturbing function, so that there is no problem in expanding the disturbing function in series. Another characteristic of the variation-of-parameters formulation employed is that six rather unusual variables are used in order to avoid singularities at the zero eccentricity and zero (or 90 deg) inclination. The integration process starts by assuming that all the orbit elements present on the right-hand sides of the equations of motion are constants. These right-hand sides are then simple Poisson series which can be obtained with the use of the Bessel expansions of the two-body problem in conjunction with certain interation methods. These Poisson series can then be integrated term by term, and a first-order solution is obtained.
Hadronic Lorentz violation in chiral perturbation theory
NASA Astrophysics Data System (ADS)
Kamand, Rasha; Altschul, Brett; Schindler, Matthias R.
2017-03-01
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-4 Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz-violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, one can compare the sensitivity of different types of experiments. Our analysis shows that atomic physics experiments currently provide constraints on the quark parameters that are stronger by about 10 orders of magnitude than astrophysical experiments with relativistic pions. Alternatively, it is possible to place approximate bounds on pion Lorentz violation using only proton and neutron observations. Under the assumption that the Lorentz-violating operators considered here are the only ones contributing to the relevant observables and taking the currently unknown hadronic low-energy constants to be of natural size, the resulting estimated bounds on four pion parameters are at the 10-23 level, representing improvements of 10 orders of magnitude.
Perturbation theory for multipolar discrete fluids.
Benavides, Ana L; Gámez, Francisco
2011-10-07
An analytical expression for the Helmholtz free energy of discrete multipolar potentials as a function of density, temperature, and intermolecular parameters is obtained as an extension of the multipolar square-well perturbation theory [A. L. Benavides, Y. Guevara, and F. del Río, Physica A 202, 420 (1994)]. The presented procedure is suitable for the description of a more general intermolecular potential model taking into account the overlap and dispersion forces through a discrete potential represented by a sequence of square-shoulders and wells, as well as electrostatic interactions. The main advantage of this approach is that since the Helmholtz free energy is given as an explicit expression in terms of the intermolecular parameters characterizing the interaction, the properties of interest can be easily obtained through usual thermodynamic relations. Besides, since a great variety of discretized potentials can be used with this equation of state, its applicability is very vast. By varying the intermolecular parameters, some illustrative cases are considered, and their phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the vapor-liquid equilibrium of the chosen potentials with different multipole moment of varied strengths, except in the critical region.
Perturbative quantum gravity with the Immirzi parameter
NASA Astrophysics Data System (ADS)
Benedetti, Dario; Speziale, Simone
2011-06-01
We study perturbative quantum gravity in the first-order tetrad formalism. The lowest order action corresponds to Einstein-Cartan plus a parity-odd term, and is known in the literature as the Holst action. The coupling constant of the parity-odd term can be identified with the Immirzi parameter γ of loop quantum gravity. We compute the quantum effective action in the one-loop expansion. As in the metric second-order formulation, we find that in the case of pure gravity the theory is on-shell finite, and the running of Newton's constant and the Immirzi parameter is inessential. In the presence of fermions, the situation changes in two fundamental aspects. First, non-renormalizable logarithmic divergences appear, as usual. Second, the Immirzi parameter becomes a priori observable, and we find that it is renormalized by a four-fermion interaction generated by radiative corrections. We compute its beta function and discuss possible implications. The sign of the beta function depends on whether the Immirzi parameter is larger or smaller than one in absolute value, and γ2 = 1 is a UV fixed-point (we work in Euclidean signature). Finally, we find that the Holst action is stable with respect to radiative corrections in the case of minimal coupling, up to higher order non-renormalizable interactions.
A perturbative framework for jet quenching
NASA Astrophysics Data System (ADS)
Zapp, Korinna C.; Krauss, Frank; Wiedemann, Urs A.
2013-03-01
We present a conceptually new framework for describing jet evolution in the dense medium produced in ultra-relativistic nucleus-nucleus collisions using perturbative QCD and its implementation into the Monte Carlo event generator Jewel. The rescattering of hard partons in the medium is modelled by infrared continued pQCD matrix elements supplemented with parton showers. The latter approximate higher order real-emission matrix elements and thus generate medium-induced gluon emissions. The interplay between different emissions is governed by their formation times. The destructive interference between subsequent scattering processes, the non-Abelian version of the Landau-Pomeranchuk-Migdal effect, is also taken into account. In this way the complete radiation pattern is consistently treated in a uniform way. Results obtained within this minimal and theoretically well constrained framework are compared with a variety of experimental data susceptible to jet-quenching effects at both RHIC and the LHC. Overall, a good agreement between data and simulation is found. This new framework also allows to identify and quantify the dominant uncertainties in the simulation, and we show some relevant examples for this.
Perturbation theory for multipolar discrete fluids
NASA Astrophysics Data System (ADS)
Benavides, Ana L.; Gámez, Francisco
2011-10-01
An analytical expression for the Helmholtz free energy of discrete multipolar potentials as a function of density, temperature, and intermolecular parameters is obtained as an extension of the multipolar square-well perturbation theory [A. L. Benavides, Y. Guevara, and F. del Río, Physica A 202, 420 (1994), 10.1016/0378-4371(94)90469-3]. The presented procedure is suitable for the description of a more general intermolecular potential model taking into account the overlap and dispersion forces through a discrete potential represented by a sequence of square-shoulders and wells, as well as electrostatic interactions. The main advantage of this approach is that since the Helmholtz free energy is given as an explicit expression in terms of the intermolecular parameters characterizing the interaction, the properties of interest can be easily obtained through usual thermodynamic relations. Besides, since a great variety of discretized potentials can be used with this equation of state, its applicability is very vast. By varying the intermolecular parameters, some illustrative cases are considered, and their phase diagrams are tested against available simulation data. It is found that this theoretical approach is able to reproduce qualitatively and quantitatively well the vapor-liquid equilibrium of the chosen potentials with different multipole moment of varied strengths, except in the critical region.
Cosmological perturbations across an S-brane
Brandenberger, Robert H.; Kounnas, Costas; Partouche, Hervé; Patil, Subodh P.; Toumbas, Nicolaos E-mail: kounnas@lpt.ens.fr E-mail: subodh.patil@cern.ch
2014-03-01
Space-filling S-branes can mediate a transition between a contracting and an expanding universe in the Einstein frame. Following up on previous work that uncovered such bouncing solutions in the context of weakly coupled thermal configurations of a certain class of type II superstrings, we set up here the formalism in which we can study the evolution of metric fluctuations across such an S-brane. Our work shows that the specific nature of the S-brane, which is sourced by non-trivial massless thermal string states and appears when the universe reaches a maximal critical temperature, allows for a scale invariant spectrum of curvature fluctuations to manifest at late times via a stringy realization of the matter bounce scenario. The finite energy density at the transition from contraction to expansion provides calculational control over the propagation of the curvature perturbations through the bounce, furnishing a working proof of concept that such a stringy universe can result in viable late time cosmology.
Carbon content on perturbed wetlands of Yucatan
NASA Astrophysics Data System (ADS)
Morales Ojeda, S. M.; Orellana, R.; Herrera Silveira, J.
2013-05-01
The north coast of Yucatan Peninsula is a karstic scenario where the water flows mainly underground through the so called "cenotes"-ring system ("sink holes") toward the coast. This underground water system enhances the connection between watershed condition and coastal ecosystem health. Inland activities such as livestock, agriculture and urban development produce changes in the landscape, hydrological connectivity and in the water quality that can decrease wetland coverage specially mangroves and seagrasses. We conducted studies on the description of structure, biomass and carbon content of the soil, above and below ground of four different types of wetland in a perturbed region. The wetland ecological types were freshwater (Typha domingensis), dwarf mangroves (Avicenia germinans), grassland (Cyperacea) and Seagrasses. Due to the area is mainly covered by mangroves, they represent the most important carbon storage nevertheless the condition of the structure determine the carbon content in soil. Through GIS tools we explore the relationships between land use and costal condition in order to determine priority areas for conservation within the watershed that could be efficient to preserve the carbon storage of this area.
Previrialization: Perturbative and N-Body Results
NASA Astrophysics Data System (ADS)
Lokas, E. L.; Juszkiewicz, R.; Bouchet, F. R.; Hivon, E.
1996-08-01
We present a series of N-body experiments which confirm the reality of the previrialization effect. We use also a weakly nonlinear perturbative approach to study the phenomenon. These two approaches agree when the rms density contrast, σ, is small; more surprisingly, they remain in agreement when σ ~ 1. When the slope of the initial power spectrum is n > -1, nonlinear tidal interactions slow down the growth of density fluctuations, and the magnitude of the suppression increases when n (i.e., the relative amount of small-scale power) is increased. For n < -1, we see an opposite effect: the fluctuations grow more rapidly than in linear theory. The transition occurs at n = -1 when the weakly nonlinear correction to σ is close to zero and the growth rate is close to linear. Our results resolve recent controversy between two N- body studies of previrialization. Peebles assumed n = 0 and found strong evidence in support of previrialization, while Evrard & Crone, who assumed n = -1, reached opposite conclusions. As we show here, the initial conditions with n = -1 are rather special because the nonlinear effects nearly cancel out for that particular spectrum. In addition to our calculations for scale-free initial spectra, we show results for a more realistic spectrum of Peacock & Dodds. Its slope near the scale usually adopted for normalization is close to -1, so σ is close to linear. Our results retroactively justify linear normalization at 8 h^-1^ Mpc while also demonstrating the danger and limitations of this practice.
Suppression of Spiral Wave in Modified Orengonator Model
NASA Astrophysics Data System (ADS)
Ma, Jun; Jin, Wu-Yin; Yi, Ming; Wang, Chun-Ni
2008-08-01
In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Φ is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Φ changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the spiral turbulence.
Variational Perturbation Treatment of the Confined Hydrogen Atom
ERIC Educational Resources Information Center
Montgomery, H. E., Jr.
2011-01-01
The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…
Density perturbations in a finite scale factor singularity universe
NASA Astrophysics Data System (ADS)
Balcerzak, Adam; Denkiewicz, Tomasz
2012-07-01
We discuss evolution of density perturbations in cosmological models which admit finite scale factor singularities. After solving the matter perturbations equations we find that there exists a set of parameters which admits a finite scale factor singularity in future and instantaneously recover matter density evolution history which is indistinguishable from the standard ΛCDM scenario.
Investigation of Fano resonance in planar metamaterial with perturbed periodicity.
Pu, Mingbo; Hu, Chenggang; Huang, Cheng; Wang, Changtao; Zhao, Zeyu; Wang, Yanqin; Luo, Xiangang
2013-01-14
In this paper, we report the formation of sharp Fano resonance in planar metamaterial array with perturbed periodicity. Rigorous sheet impedance theory is given to analyze the electric-magnetic and magnetic-magnetic coupling effects. It is found that periodicity perturbation can provide a general approach for Fano resonance with ultra-strong local field enhancement.
TOPICAL REVIEW: A concise introduction to perturbation theory in cosmology
NASA Astrophysics Data System (ADS)
Malik, Karim A.; Matravers, David R.
2008-10-01
We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second orders, striking a balance between mathematical rigour and usability. In particular, we discuss gauge issues and the active and passive approaches to calculating gauge transformations. We also construct gauge-invariant variables, including the second-order tensor perturbation on uniform curvature hypersurfaces.
Plasma-satellite interaction driven magnetic field perturbations
Saeed-ur-Rehman; Marchand, Richard
2014-09-15
We report the first fully kinetic quantitative estimate of magnetic field perturbations caused by the interaction of a spacecraft with space environment. Such perturbations could affect measurements of geophysical magnetic fields made with very sensitive magnetometers on-board satellites. Our approach is illustrated with a calculation of perturbed magnetic fields near the recently launched Swarm satellites. In this case, magnetic field perturbations do not exceed 20 pT, and they are below the sensitivity threshold of the on-board magnetometers. Anticipating future missions in which satellites and instruments would be subject to more intense solar UV radiation, however, it appears that magnetic field perturbations associated with satellite interaction with space environment, might approach or exceed instruments' sensitivity thresholds.
A new model for realistic random perturbations of stochastic oscillators
NASA Astrophysics Data System (ADS)
Dieci, Luca; Li, Wuchen; Zhou, Haomin
2016-08-01
Classical theories predict that solutions of differential equations will leave any neighborhood of a stable limit cycle, if white noise is added to the system. In reality, many engineering systems modeled by second order differential equations, like the van der Pol oscillator, show incredible robustness against noise perturbations, and the perturbed trajectories remain in the neighborhood of a stable limit cycle for all times of practical interest. In this paper, we propose a new model of noise to bridge this apparent discrepancy between theory and practice. Restricting to perturbations from within this new class of noise, we consider stochastic perturbations of second order differential systems that -in the unperturbed case- admit asymptotically stable limit cycles. We show that the perturbed solutions are globally bounded and remain in a tubular neighborhood of the underlying deterministic periodic orbit. We also define stochastic Poincaré map(s), and further derive partial differential equations for the transition density function.
Reducing Plasma Perturbations with Segmented Metal Shielding on Electrostatic Probes
Staack, D.; Raitses, Y.; Fisch N.J.
2002-10-02
Electrostatic probes are widely used to measure spatial plasma parameters in the quasi-neutral plasma created in Hall thrusters and similar E x B electric discharge devices. Significant perturbations of the plasma, induced by such probes, can mask the actual physics involved in operation of these devices. In an attempt to reduce these perturbations in Hall thrusters, the perturbations were examined by varying the component material, penetration distance, and residence time of various probe designs. This study leads us to a conclusion that secondary electron emission from insulator ceramic tubes of the probe can affect local changes of the plasma parameters causing plasma perturbations. A probe design, which consists of a segmented metal shielding of the probe insulator, is suggested to reduce these perturbations. This new probe design can be useful for plasma applications in which the electron temperature is sufficient to produce secondary electron emission by interaction of plasma electrons with dielectric materials.
A hybrid variational-perturbational nuclear motion algorithm
NASA Astrophysics Data System (ADS)
Fábri, Csaba; Furtenbacher, Tibor; Császár, Attila G.
2014-09-01
A hybrid variational-perturbational nuclear motion algorithm based on the perturbative treatment of the Coriolis coupling terms of the Eckart-Watson kinetic energy operator following a variational treatment of the rest of the operator is described. The algorithm has been implemented in the quantum chemical code DEWE. Performance of the hybrid treatment is assessed by comparing selected numerically exact variational vibration-only and rovibrational energy levels of the C2H4, C2D4, and CH4 molecules with their perturbatively corrected counterparts. For many of the rotational-vibrational states examined, numerical tests reveal excellent agreement between the variational and even the first-order perturbative energy levels, whilst the perturbative approach is able to reduce the computational cost of the matrix-vector product evaluations, needed by the iterative Lanczos eigensolver, by almost an order of magnitude.
CMB constraint on non-Gaussianity in isocurvature perturbations
Hikage, Chiaki; Kawasaki, Masahiro; Sekiguchi, Toyokazu; Takahashi, Tomo E-mail: kawasaki@icrr.u-tokyo.ac.jp E-mail: tomot@cc.saga-u.ac.jp
2013-07-01
We study the CMB constraints on non-Gaussianity in CDM isocurvature perturbations. Non-Gaussian isocurvature perturbations can be produced in various models at the very early stage of the Universe. Since the isocurvature perturbations little affect the structure formation at late times, CMB is the best probe of isocurvature non-Gaussianity at least in the near future. In this paper, we focus on non-Gaussian curvature and isocurvature perturbations of the local-type, which are uncorrelated and in the form ζ = ζ{sub G}+(3/5)f{sub NL}(ζ{sub G}{sup 2}−(ζ{sub G}{sup 2})) and S = S{sub G}+f{sub NL}{sup (ISO)}(S{sub G}−(S{sub G}{sup 2})), and constrain the non-linearity parameter of isocurvature perturbations, f{sub NL}{sup (ISO)}, as well as the curvature one f{sub NL}. For this purpose, we employ several state-of-art techniques for the analysis of CMB data and simulation. Assuming that isocurvature perturbations are subdominant, we apply our method to the WMAP 7-year data of temperature anisotropy and obtain constraints on a combination α{sup 2}f{sub NL}{sup (ISO)}, where α is the ratio of the power spectrum of isocurvature perturbations to that of the adiabatic ones. When the adiabatic perturbations are assumed to be Gaussian, we obtained a constraint α{sup 2}f{sub NL}{sup (ISO)} = 40±66 assuming the power spectrum of isocurvature perturbations is scale-invariant. When we assume that the adiabatic perturbations can also be non-Gaussian, we obtain f{sub NL} = 38±24 and α{sup 2}f{sub NL}{sup (ISO)} = −8±72. We also discuss implications of our results for the axion CDM isocurvature model.
Covariant Hořava-like and mimetic Horndeski gravity: cosmological solutions and perturbations
NASA Astrophysics Data System (ADS)
Cognola, Guido; Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-11-01
We consider a variant of the Nojiri-Odintsov covariant Hořava-like gravitational model, where diffeomorphism invariance is broken dynamically via a non-standard coupling to a perfect fluid. The theory allows one to address some of the potential instability problems present in Hořava-Lifshitz gravity due to explicit diffeomorphism invariance breaking. The fluid is instead constructed from a scalar field constrained by a Lagrange multiplier. In fact, the Lagrange multiplier construction allows for an extension of the Hořava-like model to include the scalar field of mimetic gravity, an extension which we thoroughly explore. By adding a potential for the scalar field, we show how one can reproduce a number of interesting cosmological scenarios. We then turn to the study of perturbations around a flat FLRW background, showing that the fluid in question behaves as an irrotational fluid, with zero sound speed. To address this problem, we consider a modified version of the theory, adding higher derivative terms in a way which brings us beyond the Horndeski framework. We compute the sound speed in this modified higher order mimetic Hořava-like model and show that it is non-zero, which means that perturbations therein can be sensibly defined. Caveats to our analysis, as well as comparisons to projectable Hořava-Lifshitz gravity, are also discussed. In conclusion, we present a theory of gravity which preserves diffeomorphism invariance at the level of the action but breaks it dynamically in the UV, reduces to General Relativity (GR) in the IR, allows the realization of a number of interesting cosmological scenarios, is well defined when considering perturbations around a flat FLRW background, and features cosmological dark matter emerging as an integration constant.
Experimental verification of modified command shaping using a flexible manipulator
NASA Technical Reports Server (NTRS)
Magee, David P.; Book, Wayne J.
1991-01-01
A brief discussion introduces the original input shaping method applied to a system with varying parameters. A change in parameters causes a vibration in the system and a modified command shaping technique is created to eliminate this unwanted motion. Using a two degree of freedom (DOF) flexible manipulator, experiments are conducted by varying perturbations to input trajectories to compare the modified method to a previously used adaptive proportional plus derivative (P.D.) control method. The control scheme that produces the smaller magnitude of resonant vibration at the first natural frequency of the robot is considered the more effective control method.
Challenges in the extraction of TMDs from SIDIS data: perturbative vs non-perturbative aspects
Boglione, Mariaelena; Gonzalez Hernandez, Jose O.; Melis, Stefano; Prokudin, Alexey
2015-09-01
We present our recent results on the study of the Semi-Inclusive Deep Inelastic Scattering (SIDIS) cross section as a function of the transverse momentum, q_{T}. Using the Collins-Soper-Sterman (CSS) formalism, we study the matching between the region where fixed-order perturbative QCD can successfully be applied and the region where soft gluon resummation is necessary. We find that the commonly used prescription of matching through the so-called Y-factor cannot be applied in the SIDIS kinematical configurations we examine. We comment on the impact that the nonperturbative component has even at relatively high energies.
Detection of perturbed quantization class stego images based on possible change modes
NASA Astrophysics Data System (ADS)
Zhang, Yi; Liu, Fenlin; Yang, Chunfang; Luo, Xiangyang; Song, Xiaofeng
2015-11-01
To improve the detection performance for perturbed quantization (PQ) class [PQ, energy-adaptive PQ (PQe), and texture-adaptive PQ (PQt)] stego images, a detection method based on possible change modes is proposed. First, by using the relationship between the changeable coefficients used for carrying secret messages and the second quantization steps, the modes having even second quantization steps are identified as possible change modes. Second, by referencing the existing features, the modified features that can accurately capture the embedding changes based on possible change modes are extracted. Next, feature sensitivity analyses based on the modifications performed before and after the embedding are carried out. These analyses show that the modified features are more sensitive to the original features. Experimental results indicate that detection performance of the modified features is better than that of the corresponding original features for three typical feature models [Cartesian calibrated PEVny (ccPEV), Cartesian calibrated co-occurrence matrix features (CF), and JPEG rich model (JRM)], and the integrated feature consisting of enhanced histogram features (EHF) and the modified JRM outperforms two current state-of-the-art feature models, namely, phase aware projection model (PHARM) and Gabor rich model (GRM).
Transport of energetic ions by low-n magnetic perturbations
Mynick, H.E.
1992-10-01
The stochastic transport of MeV ions induced by low-n magnetic perturbations is studied, focussing chiefly on the stochastic mechanism operative for passing particles in low frequency perturbations. Beginning with a single-harmonic form for the perturbing field, it iii first shown numerically and analytically that the stochastic threshold of energetic particles can be much lower than that of the magnetic field, contrary to earlier expectations, so that MHD perturbations could cause appreciable loss of energetic ions without destroying the bulk confinement. The analytic theory is then extended in a number of directions, to darity the relation of the present stochaistic mechanism to instances already found, to allow for more complex perturbations, and to consider the more general relationship between the stochasticity of magnetic fields, and that of particles of differing energies (and pitch angles) moving in those fields. It is shown that the stochastic threshold is in general a nonmonotonic function of energy, whose form can to some extent be tailored to achieve desired goals (e.g., burn control or ash removal) by a judicious choice of the perturbation. Illustrative perturbations are exhibited which are stochastic for low but not for high-energy ions, for high but not for low-energy ions, and for intermediate-energy ions, but not for low or high energy. The second possibility is the behavior needed for burn control; the third provides a possible mechanism for ash removal.
Boundary Layer Instabilities Generated by Freestream Laser Perturbations
NASA Technical Reports Server (NTRS)
Chou, Amanda; Schneider, Steven P.
2015-01-01
A controlled, laser-generated, freestream perturbation was created in the freestream of the Boeing/AFOSR Mach-6 Quiet Tunnel (BAM6QT). The freestream perturbation convected downstream in the Mach-6 wind tunnel to interact with a flared cone model. The geometry of the flared cone is a body of revolution bounded by a circular arc with a 3-meter radius. Fourteen PCB 132A31 pressure transducers were used to measure a wave packet generated in the cone boundary layer by the freestream perturbation. This wave packet grew large and became nonlinear before experiencing natural transition in quiet flow. Breakdown of this wave packet occurred when the amplitude of the pressure fluctuations was approximately 10% of the surface pressure for a nominally sharp nosetip. The initial amplitude of the second mode instability on the blunt flared cone is estimated to be on the order of 10 -6 times the freestream static pressure. The freestream laser-generated perturbation was positioned upstream of the model in three different configurations: on the centerline, offset from the centerline by 1.5 mm, and offset from the centerline by 3.0 mm. When the perturbation was offset from the centerline of a blunt flared cone, a larger wave packet was generated on the side toward which the perturbation was offset. The offset perturbation did not show as much of an effect on the wave packet on a sharp flared cone as it did on a blunt flared cone.
Transient responses to spatial perturbations in advective systems.
Anderson, Kurt E; Nisbet, Roger M; McCauley, Edward
2008-07-01
We study the transient dynamics, following a spatially-extended perturbation of models describing populations residing in advective media such as streams and rivers. Our analyses emphasize metrics that are independent of initial perturbations-resilience, reactivity, and the amplification envelope-and relate them to component spatial wavelengths of the perturbation using spatial Fourier transforms of the state variables. This approach offers a powerful way of understanding the influence of spatial scale on the initial dynamics of a population following a spatially variable environmental perturbation, an important property in determining the ecological implications of transient dynamics in advective systems. We find that asymptotically stable systems may exhibit transient amplification of perturbations (i.e., have positive reactivity) for some spatial wavelengths and not others. Furthermore, the degree and duration of amplification varies strongly with spatial wavelength. For two single-population models, there is a relationship between transient dynamics and the response length that characterizes the steady state response to spatial perturbations: a long response length implies that peak amplification of perturbations is small and occurs fast. This relationship holds less generally in a specialist consumer-resource model, likely due to the model's tendency for flow-induced instabilities at an alternative characteristic spatial scale.
Perturbation solution of the shape of a nonaxisymmetric sessile drop.
Prabhala, Bharadwaj; Panchagnula, Mahesh; Subramanian, Venkat R; Vedantam, Srikanth
2010-07-06
We develop an approximate analytical solution for the shape of a nonaxisymmetric sessile drop using regular perturbation methods and ignoring gravity. We assume that the pinned, contorted triple-line shape is known and is a small perturbation of the circular footprint of a spherical cap. We obtain an analytical solution using regular perturbation methods that we validate by comparing to the numerical solution of the Young-Laplace equation obtained using publicly available Surface Evolver software. In this process, we also show that the pressure inside the perturbed drop is unchanged and relate this to the curvature of the drop using the Young-Laplace equation. The rms error between the perturbation and Evolver solutions is calculated for a range of contact angles and amplitudes of triple-line perturbations. We show that the perturbation solution matches the numerical results well for a wide range of contact angles. In addition, we calculate the extent to which the drop surface is affected by triple-line contortions. We discuss the applicability of this solution to the possibility of real time hybrid experimental/computational characterization of the 3D sessile drop shapes, including obtaining local contact angle information.
Postural responses to unexpected perturbations of balance during reaching
Trivedi, Hari; Leonard, Julia A.; Ting, Lena H.; Stapley, Paul J.
2014-01-01
To study the interaction between feedforward and feedback modes of postural control, we investigated postural responses during unexpected perturbations of the support surface that occurred during forward reaching in a standing position. We examined postural responses in lower limb muscles of 9 human subjects. Baseline measures were obtained when subjects executed reaching movements to a target placed in front of them (R condition) and during postural responses to forward and backward support-surface perturbations (no reaching, P condition) during quiet stance. Perturbations were also given at different delays after the onset of reaching movements (RP conditions) as well as with the arm extended in the direction of the target, but not reaching (P/AE condition). Results showed that during perturbations to reaching (RP), the initial automatic postural response, occurring around 100 ms after the onset of perturbations, was relatively unchanged in latency or amplitude compared to control conditions (P and P/AE). However, longer latency postural responses were modulated to aid in the reaching movements during forward perturbations but not during backward perturbations. Our results suggest that the nervous system prioritizes the maintenance of a stable postural base during reaching, and that later components of the postural responses can be modulated to ensure the performance of the voluntary task. PMID:20035321
Development of a perturbation generator for vortex stability studies
NASA Technical Reports Server (NTRS)
Riester, J. E.; Ash, Robert L.
1991-01-01
Theory predicts vortex instability when subjected to certain types of disturbances. It was desired to build a device which could introduce controlled velocity perturbations into a trailing line vortex in order to study the effects on stability. A perturbation generator was designed and manufactured which can be attached to the centerbody of an airfoil type vortex generator. Details of design tests and manufacturing of the perturbation generator are presented. The device produced controlled perturbation with frequencies in excess of 250 Hz. Preliminary testing and evaluation of the perturbation generator performance was conducted in a 4 inch cylindrical pipe. Observations of vortex shedding frequencies from a centerbody were measured. Further evaluation with the perturbation generator attached to the vortex generator in a 2 x 3 foot wind tunnel were also conducted. Hot-wire anemometry was used to confirm the perturbation generator's ability to introduce controlled frequency fluctuations. Comparison of the energy levels of the disturbances in the vortex core was made between locations 42 chord lengths and 15 chord lengths downstream.
Black hole perturbation theory in a light cone gauge
NASA Astrophysics Data System (ADS)
Preston, Brent
The metric of a Schwarzschild black hole immersed in a uniform magnetic field is studied using black hole perturbation theory in a light crone coordinate system that penetrates the event horizon and possesses a clear geometrical meaning. The magnetic field, which is distorted due to the presence of the black hole, has strength B which is assumed to be small compared to the curvature of the spacetime which allows the perturbed metric to be calculated to order B 2 only. The coordinates allow for an easy identification of the event horizon and the properties of the perturbed black hole are studied. To interpret this perturbed metric, the advanced coordinates are decomposed into irreducible parts which yields the metric of a perturbed black hole in the limit r >> 2 M . Finally we compare our perturbed solution to an exact solution. We show that our perturbed solution is able to match the exact solution but has the freedom to describe a larger class of physically relevant solutions.
Evolution equation for non-linear cosmological perturbations
Brustein, Ram; Riotto, Antonio E-mail: Antonio.Riotto@cern.ch
2011-11-01
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
Dynamics of strongly perturbed planetary rings
NASA Astrophysics Data System (ADS)
Lewis, Mark Christopher
2001-08-01
This thesis looks at the dynamics of regions of rings that are located close to a small moon so that they receive a significant eccentricity from every pass by that moon. All investigations were performed with highly optimized, large N-body numerical simulations that use new boundary conditions specifically designed for this type of system. The first system explored is the Encke gap region where the small moon Pan has cleared out a 325 km region of Saturn's rings. Simulations indicate that the behavior of this system is significantly more complex than what is found by standard fluid models of ring dynamics due largely to the fact that the particles epicyclic phases are aligned. The wake peaks decline exponentially at the end of the simulations and the dependence of this rate of this decline was examined as a function of optical depth, particle size, and coefficient of restitution. The variations are non-monotonical with optical depth and coefficient of restitution. The alignment of epicyclic phases in the wakes enables the guiding centers of the particles to undergo efficient radial migration. This process allows the particle guiding centers to group at the edges of the simulation region and in some cases is seen to result in ringlet formation. For regions more distant from the perturber than the edge of the Encke gap, the synodic periods are shorter and as a result, the forced eccentricities do not damp out completely in a synodic period. When this occurs, the presence of Lindblad resonances is seen. These resonances are observed to induce periodic structures in regions far from the Encke gap and speed narrow ringlet formation in systems resembling Saturn's F-ring. However, the narrow rings do not have to be located in resonances to be maintained, as the standard theory of shepherding would imply. Simulations including size distributions exhibited a buildup of small particles at the boundaries, in agreement with Voyager observations. Simulations involving self
Second-order perturbation on a SDCI calculation
NASA Astrophysics Data System (ADS)
Maynau, Daniel; Heully, Jean-Louis
1993-08-01
Starting from a SDCI calculation the SD eigenvector is perturbed by all triply and quadruply excited determinants. Efficiency is promoted through direct CI techniques, however, some flexibility has been kept, making possible the use of various perturbational schemes (here: Epstein—Nesbet and M∅ller—Plesset). The SDCI starting point avoids divergence problems posed by CCSD(T) and also by purely perturbative methods such as MP4. Several calculations on the potential curves of some molecules (H 2O, N 2, F 2, Ne 2) show that the present method is at least as good as the MP4 or CCSD(T) methods at comparable computational cost.
Characterizing regulatory path motifs in integrated networks using perturbational data
2010-01-01
We introduce Pathicular http://bioinformatics.psb.ugent.be/software/details/Pathicular, a Cytoscape plugin for studying the cellular response to perturbations of transcription factors by integrating perturbational expression data with transcriptional, protein-protein and phosphorylation networks. Pathicular searches for 'regulatory path motifs', short paths in the integrated physical networks which occur significantly more often than expected between transcription factors and their targets in the perturbational data. A case study in Saccharomyces cerevisiae identifies eight regulatory path motifs and demonstrates their biological significance. PMID:20230615
Axion inflation with cross-correlated axion isocurvature perturbations
Kadota, Kenji; Kobayashi, Tatsuo; Otsuka, Hajime E-mail: kobayashi@particle.sci.hokudai.ac.jp
2016-01-01
We study the inflation scenarios, in the framework of superstring theory, where the inflaton is an axion producing the adiabatic curvature perturbations while there exists another light axion producing the isocurvature perturbations. We discuss how the non-trivial couplings among string axions can generically arise, and calculate the consequent cross-correlations between the adiabatic and isocurvature modes through concrete examples. Based on the Planck analysis on the generally correlated isocurvature perturbations, we show that there is a preference for the existence of the correlated isocurvature modes for the axion monodromy inflation while the natural inflation disfavors such isocurvature modes.
Stability of coflowing capillary jets under nonaxisymmetric perturbations.
Montanero, J M; Gañán-Calvo, A M
2008-04-01
In this paper, linear hydrodynamic stability analysis is used to study the response of a capillary jet and a coflowing fluid to both axisymmetric and nonaxisymmetric perturbations. The temporal analysis revealed that nonaxisymmetric perturbations were damped (or overdamped) within the region of parameter space explored, which involved equal velocities for the jet and focusing fluid. It is explained how an extension to a spatiotemporal analysis implies that those perturbations can yield no transition from convective (jetting) to absolute (whipping) instability for that parameter region. This result provides a theoretical explanation for the absence of that kind of transition in most experimental results in the literature.
Current Density and Plasma Displacement Near Perturbed Rational Surface
A.H. Boozer and N. Pomphrey
2010-10-10
The current density in the vicinity of a rational surface of a force-free magnetic field subjected to an ideal perturbation is shown to be the sum of both a smooth and a delta-function distribution, which give comparable currents. The maximum perturbation to the smooth current density is comparable to a typical equilibrium current density and the width of the layer in which the current flows is shown to be proportional to the perturbation amplitude. In the standard linearized theory, the plasma displacement has an unphysical jump across the rational surface, but the full theory gives a continuous displacement.
Gauge invariant perturbations of Petrov type D space-times
NASA Astrophysics Data System (ADS)
Whiting, Bernard; Shah, Abhay
2016-03-01
The Regge-Wheeler and Zerilli equations are satisfied by gauge invariant perturbations of the Schwarzschild black hole geometry. Both the perturbation of the imaginary part of Ψ2 (a component of the Weyl curvature), and its time derivative, are gauge invariant and solve the Regge-Wheeler equation with different sources. The Ψ0 and Ψ4 perturbations of the Weyl curvature are not only gauge, but also tetrad, invariant. We explore the framework in which these results hold, and consider what generalizations may extend to the Kerr geometry, and presumably to Petrov type D space-times in general. NSF Grants PHY 1205906 and 1314529, ERC (EU) FP7 Grant 304978.
Secular perturbations of the Uranian satellites - Theory and practice
NASA Astrophysics Data System (ADS)
Malhotra, R.; Fox, K.; Murray, C. D.; Nicholson, P. D.
1989-09-01
A simple revised secular perturbation theory which incorporates the averaged secular effect of first-order near-resonances is derived. By including the effects of these near-resonances, the largest error in the secular frequencies is reduced from 16 percent to less than 3 percent. It is concluded that the revised secular perturbation theory is adequate for the quantitative modeling of the long-term perturbations in the Uranian satellite system. If incorporated within the general theory of Laskar (1986), this theory would lead to completely analytic theory.
Axion inflation with cross-correlated axion isocurvature perturbations
Kadota, Kenji; Kobayashi, Tatsuo; Otsuka, Hajime
2016-01-25
We study the inflation scenarios, in the framework of superstring theory, where the inflaton is an axion producing the adiabatic curvature perturbations while there exists another light axion producing the isocurvature perturbations. We discuss how the non-trivial couplings among string axions can generically arise, and calculate the consequent cross-correlations between the adiabatic and isocurvature modes through concrete examples. Based on the Planck analysis on the generally correlated isocurvature perturbations, we show that there is a preference for the existence of the correlated isocurvature modes for the axion monodromy inflation while the natural inflation disfavors such isocurvature modes.
Cosmological perturbations of a perfect fluid and noncommutative variables
De Felice, Antonio; Gerard, Jean-Marc; Suyama, Teruaki
2010-03-15
We describe the linear cosmological perturbations of a perfect fluid at the level of an action, providing thus an alternative to the standard approach based only on the equations of motion. This action is suited not only to perfect fluids with a barotropic equation of state, but also to those for which the pressure depends on two thermodynamical variables. By quantizing the system we find that (1) some perturbation fields exhibit a noncommutativity quite analogous to the one observed for a charged particle moving in a strong magnetic field, (2) local curvature and pressure perturbations cannot be measured simultaneously, (3) ghosts appear if the null energy condition is violated.
Extreme Value Analysis of Tidal Stream Velocity Perturbations
Harding, Samuel; Thomson, Jim; Polagye, Brian; Richmond, Marshall C.; Durgesh, Vibhav; Bryden, Ian
2011-04-26
This paper presents a statistical extreme value analysis of maximum velocity perturbations from the mean flow speed in a tidal stream. This study was performed using tidal velocity data measured using both an Acoustic Doppler Velocimeter (ADV) and an Acoustic Doppler Current Profiler (ADCP) at the same location which allows for direct comparison of predictions. The extreme value analysis implements of a Peak-Over-Threshold method to explore the effect of perturbation length and time scale on the magnitude of a 50-year perturbation.
Milosevic, Matija; Shinya, Masahiro; Masani, Kei; Patel, Kramay; McConville, Kristiina M V; Nakazawa, Kimitaka; Popovic, Milos R
2016-02-01
Trunk muscles are responsible for maintaining trunk stability during sitting. However, the effects of anticipation of perturbation on trunk muscle responses are not well understood. The objectives of this study were to identify the responses of trunk muscles to sudden support surface translations and quantify the effects of anticipation of direction and time of perturbation on the trunk neuromuscular responses. Twelve able-bodied individuals participated in the study. Participants were seated on a kneeling chair and support surface translations were applied in the forward and backward directions with and without direction and time of perturbation cues. The trunk started moving on average approximately 40ms after the perturbation. During unanticipated perturbations, average latencies of the trunk muscle contractions were in the range between 103.4 and 117.4ms. When participants anticipated the perturbations, trunk muscle latencies were reduced by 16.8±10.0ms and the time it took the trunk to reach maximum velocity was also reduced, suggesting a biomechanical advantage caused by faster muscle responses. These results suggested that trunk muscles have medium latency responses and use reflexive mechanisms. Moreover, anticipation of perturbation decreased trunk muscles latencies, suggesting that the central nervous system modulated readiness of the trunk based on anticipatory information.
Modifying toxicokinetics with antidotes.
Baud, F J; Borron, S W; Bismuth, C
1995-12-01
Five approaches may be described through which antidotes can modify toxicokinetics: (1) Decreased bioavailability of the toxins; (2) Cellular redistribution of the toxin in the organism; (3) Promotion of elimination in an unchanged form; (4) Slowing of metabolic activation pathways; (5) Acceleration of metabolic deactivation pathways. However, the ability to modify toxicokinetics with a new treatment, while demonstrating an understanding of the mechanism of action, must never be construed to be, in and of itself, the goal of therapy. The ultimate evaluation of an antidote modifying toxicokinetics is strictly clinical.
Tracking perturbations in Boolean networks with spectral methods
NASA Astrophysics Data System (ADS)
Kesseli, Juha; Rämö, Pauli; Yli-Harja, Olli
2005-08-01
In this paper we present a method for predicting the spread of perturbations in Boolean networks. The method is applicable to networks that have no regular topology. The prediction of perturbations can be performed easily by using a presented result which enables the efficient computation of the required iterative formulas. This result is based on abstract Fourier transform of the functions in the network. In this paper the method is applied to show the spread of perturbations in networks containing a distribution of functions found from biological data. The advances in the study of the spread of perturbations can directly be applied to enable ways of quantifying chaos in Boolean networks. Derrida plots over an arbitrary number of time steps can be computed and thus distributions of functions compared with each other with respect to the amount of order they create in random networks.
Cosmological perturbations from a spectator field during inflation
NASA Astrophysics Data System (ADS)
Wang, Lingfei; Mazumdar, Anupam
2013-05-01
In this paper we will discuss analytically the perturbations created from a slowly rolling subdominant spectator field which decays much before the end of inflation. The quantum fluctuations of such a spectator field can seed perturbations on very large scales and explain the temperature anisotropy in the cosmic microwave background radiation with moderate non-Gaussianity, provided the relevant modes leave the Hubble patch while the spectator is slowly rolling. Furthermore, the perturbations are purely adiabatic since the inflaton decay dominates and creates all the Standard Model degrees of freedom. We will provide two examples for the spectator field potential, one with a step function profile, and the other with an inflection point. In both the cases we will compute higher order curvature perturbations, i.e. local bispectrum and trispectrum, which can be constrained by the forthcoming Planck data.
Cosmological perturbations of axion with a dynamical decay constant
Kobayashi, Takeshi; Takahashi, Fuminobu
2016-08-25
A QCD axion with a time-dependent decay constant has been known to be able to accommodate high-scale inflation without producing topological defects or too large isocurvature perturbations on CMB scales. We point out that a dynamical decay constant also has the effect of enhancing the small-scale axion isocurvature perturbations. The enhanced axion perturbations can even exceed the periodicity of the axion potential, and thus lead to the formation of axionic domain walls. Unlike the well-studied axionic walls, the walls produced from the enhanced perturbations are not bounded by cosmic strings, and thus would overclose the universe independently of the number of degenerate vacua along the axion potential.
Gyroscope test of gravitation: An analysis of the important perturbations
NASA Technical Reports Server (NTRS)
Oconnell, R. F.
1971-01-01
Two perturbations, the earth's quadrupole moment and the earth's revolution around the sun, are discussed. Schiff's proposed gyroscope test of gravitation is analyzed, along with the capability of deciphering each separate contribution to the angular velocity of spin precession.
Detection of nerve agent via perturbation of supramolecular gel formation.
Hiscock, Jennifer R; Piana, Francesca; Sambrook, Mark R; Wells, Neil J; Clark, Alistair J; Vincent, Jack C; Busschaert, Nathalie; Brown, Richard C D; Gale, Philip A
2013-10-14
The formation of tren-based tris-urea supramolecular gels in organic solvents is perturbed by the presence of the nerve agent soman providing a new method of sensing the presence of organophosphorus warfare agents.
Renormalization-scheme-invariant perturbation theory: Miracle or mirage
Chyla, J.
1985-05-15
A recently proposed solution to the renormalization-scheme ambiguity in perturbation theory is critically analyzed and shown to possess another kind of ambiguity closely related to the one it is supposed to cure.
Approach to exact solutions of cosmological perturbations: Tachyon field inflation
NASA Astrophysics Data System (ADS)
Herrera, Ramón; Pérez, Roberto G.
2016-03-01
An inflationary universe scenario in the context of a tachyon field is studied. This study is carried out using an ansatz for the effective potential of cosmological perturbations U (η ). We describe in great detail the analytical solutions of the scalar and tensor perturbations for two different Ansätze for the effective potential of cosmological perturbations: Easther's model and an effective potential similar to power-law inflation. Also, we find from the background equations that the effective tachyonic potentials V (φ ) in both models satisfy the properties of a tachyonic potential. We consider the recent data from the Planck to constrain the parameters in our effective potential generating the cosmological perturbations.
Does perturbative quantum chromodynamics imply a Regge singularity above unity
Bishari, M.
1982-07-15
It is investigated whether perturbative quantum chromodynamics can have some implications on Regge behavior of deep-inelastic structure functions. The possible indirect but important role of unitarity, in constraining the theory, is pointed out.
Some methods for calculation of perturbations in nuclear reactors
Abramov, B. D.
2015-12-15
Some methods for calculation of local perturbations of neutron fields and reactivity effects accompanying them are considered. Existence, uniqueness, properties and methods for finding solutions to the considered problems are discussed.
Perturbative thermodynamics at nonzero isospin density for cold QCD
NASA Astrophysics Data System (ADS)
Graf, Thorben; Schaffner-Bielich, Juergen; Fraga, Eduardo S.
2016-04-01
We use next-to-leading order in perturbation theory to investigate the effects of a finite isospin density on the thermodynamics of cold strongly interacting matter. Our results include nonzero quark masses and are compared to lattice data.
Global terrestrial biogeochemistry: Perturbations, interactions, and time scales
Braswell, B.H. Jr.
1996-12-01
Global biogeochemical processes are being perturbed by human activity, principally that which is associated with industrial activity and expansion of urban and agricultural complexes. Perturbations have manifested themselves at least since the beginning of the 19th Century, and include emissions of CO{sub 2} and other pollutants from fossil fuel combustion, agricultural emissions of reactive nitrogen, and direct disruption of ecosystem function through land conversion. These perturbations yield local impacts, but there are also global consequences that are the sum of local-scale influences. Several approaches to understanding the global-scale implications of chemical perturbations to the Earth system are discussed. The lifetime of anthropogenic CO{sub 2} in the atmosphere is an important concept for understanding the current and future commitment to an altered atmospheric heat budget. The importance of the terrestrial biogeochemistry relative to the lifetime of excess CO{sub 2} is demonstrated using dynamic, aggregated models of the global carbon cycle.
Capillary-mediated interface perturbations: Deterministic pattern formation
NASA Astrophysics Data System (ADS)
Glicksman, Martin E.
2016-09-01
Leibniz-Reynolds analysis identifies a 4th-order capillary-mediated energy field that is responsible for shape changes observed during melting, and for interface speed perturbations during crystal growth. Field-theoretic principles also show that capillary-mediated energy distributions cancel over large length scales, but modulate the interface shape on smaller mesoscopic scales. Speed perturbations reverse direction at specific locations where they initiate inflection and branching on unstable interfaces, thereby enhancing pattern complexity. Simulations of pattern formation by several independent groups of investigators using a variety of numerical techniques confirm that shape changes during both melting and growth initiate at locations predicted from interface field theory. Finally, limit cycles occur as an interface and its capillary energy field co-evolve, leading to synchronized branching. Synchronous perturbations produce classical dendritic structures, whereas asynchronous perturbations observed in isotropic and weakly anisotropic systems lead to chaotic-looking patterns that remain nevertheless deterministic.
Scalar perturbations on Lemaitre-Tolman-Bondi spacetimes
Zibin, J. P.
2008-08-15
In recent years there has been growing interest in verifying the horizon-scale homogeneity of the Universe that follows from applying the Copernican principle to the observed isotropy. This program has been stimulated by the discovery that a very large void, centered near us, can explain supernova luminosity distance measurements without dark energy. It is crucial to confront such models with as wide a variety of data as possible. With this application in mind, we develop the relativistic theory of linear scalar perturbations on spherically symmetric dust (Lemaitre-Tolman-Bondi) spacetimes, using the covariant 1+1+2 formalism. We show that the evolution of perturbations is determined by a small set of new linear transfer functions. If decaying modes are ignored (to be consistent with the standard inflationary paradigm), the standard techniques of perturbation theory on homogeneous backgrounds, such as harmonic expansion, can be applied, and results closely paralleling those of familiar cosmological perturbation theory can be obtained.
Revised Perturbation Statistics for the Global Scale Atmospheric Model
NASA Technical Reports Server (NTRS)
Justus, C. G.; Woodrum, A.
1975-01-01
Magnitudes and scales of atmospheric perturbations about the monthly mean for the thermodynamic variables and wind components are presented by month at various latitudes. These perturbation statistics are a revision of the random perturbation data required for the global scale atmospheric model program and are from meteorological rocket network statistical summaries in the 22 to 65 km height range and NASA grenade and pitot tube data summaries in the region up to 90 km. The observed perturbations in the thermodynamic variables were adjusted to make them consistent with constraints required by the perfect gas law and the hydrostatic equation. Vertical scales were evaluated by Buell's depth of pressure system equation and from vertical structure function analysis. Tables of magnitudes and vertical scales are presented for each month at latitude 10, 30, 50, 70, and 90 degrees.
Cosmic-string-induced hot dark matter perturbations
NASA Technical Reports Server (NTRS)
Van Dalen, Anthony
1990-01-01
This paper investigates the evolution of initially relativistic matter, radiation, and baryons around cosmic string seed perturbations. A detailed analysis of the linear evolution of spherical perturbations in a universe is carried out, and this formalism is used to study the evolution of perturbations around a sphere of uniform density and fixed radius, approximating a loop of cosmic string. It was found that, on scales less than a few megaparsec, the results agree with the nonrelativistic calculation of previous authors. On greater scales, there is a deviation approaching a factor of 2-3 in the perturbation mass. It is shown that a scenario with cosmic strings, hot dark matter, and a Hubble constant greater than 75 km/sec per Mpc can generally produce structure on the observed mass scales and at the appropriate time: 1 + z = about 4 for galaxies and 1 + z = about 1.5 for Abell clusters.
Noise Reduction in High-Throughput Gene Perturbation Screens
Technology Transfer Automated Retrieval System (TEKTRAN)
Motivation: Accurate interpretation of perturbation screens is essential for a successful functional investigation. However, the screened phenotypes are often distorted by noise, and their analysis requires specialized statistical analysis tools. The number and scope of statistical methods available...
Measurement of rotor system dynamic stiffness by perturbation testing
NASA Technical Reports Server (NTRS)
Bently, D. E.; Muszynska, A.
1985-01-01
Specific aspects of the application of Modal Analysis to rotating machines are discussed. For lowest mode analysis, the circular force perturbation testing gives the best results. Examples of application are presented.
Perturbations of unitary representations of finite dimensional Lie groups
Wickramasekara, S.
2009-12-15
In quantum physical theories, interactions in a system of particles are commonly understood as perturbations to certain observables, including the Hamiltonian, of the corresponding interaction-free system. The manner in which observables undergo perturbations is subject to constraints imposed by the overall symmetries that the interacting system is expected to obey. Primary among these are the spacetime symmetries encoded by the unitary representations of the Galilei group and Poincare group for the non-relativistic and relativistic systems, respectively. In this light, interactions can be more generally viewed as perturbations to unitary representations of connected Lie groups, including the non-compact groups of spacetime symmetry transformations. In this paper, we present a simple systematic procedure for introducing perturbations to (infinite dimensional) unitary representations of finite dimensional connected Lie groups. We discuss applications to relativistic and non-relativistic particle systems.
Generating ekpyrotic curvature perturbations before the big bang
Lehners, Jean-Luc; Turok, Neil; McFadden, Paul; Steinhardt, Paul J.
2007-11-15
We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, which can be entirely described using 4D effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modeled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtained and that the spectral tilt n{sub s} tends to range from slightly blue to red, with 0.97
Trapped energetic ion dynamics affected by localized electric field perturbations
NASA Astrophysics Data System (ADS)
Nishimura, Seiya
2016-01-01
Trapped energetic ion orbits in helical systems are numerically simulated using the Lorentz model. Simulation results of precession drift frequencies of trapped energetic ions are benchmarked by those of analytic solutions. The effects of the electric field perturbation localized at the rational surface on trapped energetic ions are examined, where the perturbation has an arbitrary rotation frequency and an amplitude fixed in time. It is found that the trapped energetic ions resonantly interact with the perturbation, when the rotation frequency of the perturbation is comparable to the precession drift frequencies of trapped energetic ions. The simulation results are suggestive to a mechanism of the energetic-ion-induced interchange mode, which might be associated with the fishbone mode observed in helical systems.
Long-term Dynamical Behavior of Highly Perturbed Natural and Artificial Celestial Bodies
NASA Astrophysics Data System (ADS)
Rosengren, Aaron J.
rigorously for all Keplerian orbits with nonzero angular momentum; they are free of the mathematical singularities associated with circular or equatorial orbits. These approximate equations are written in a concise analytical vector form, which allow our results and demonstrations to attain such extraordinary simplicity and clarity. As a first attempt to understand the disturbed motion, we consider separately the first-order effects of each principal perturbation in altering the orbital elements. We establish that each of these problems is integrable (under certain well-justified assumptions), and that they admit either an exact analytical solution or a complete qualitative description. We then explore the complex interplay between gravitational and non-gravitational perturbations, and examine stable "frozen" orbit configurations and resonances which can occur when these forces act in concert. These results are applied to the study of the dynamics and stability of GEO orbits and to the identification of robust, long-term disposal orbits for geostationary satellites. We further apply these results towards an understanding of the initial albedo dichotomy of Iapetus, Saturn's enigmatic two-faced satellite. As dust is a ubiquitous component of the Solar System, we discuss the application of our averaged model to a number of other planetary systems. We highlight, in particular, the explanatory power of our approach and how it can modify or guide detailed numerical studies. Indeed, analytical and numerical techniques cannot be separated, and a complete, logically ordered picture is obtained only by the application of both methods jointly.
Effects of core perturbations on the structure of the sun
Sweigart, A.V.
1983-10-15
A number of numerical experiments have been carried out in order to investigate the sensivity of the solar luminosity and radius to perturbations within the radiative core. In these experiments the core was perturbed by suddenly mixing various parts of the composition profile during evolutionary sequences for the present Sun. The hydrostatic readjustment caused by these ''mixing events'' induced an immediate change in the surface luminosity and radius on both the hydrodynamic time scale (approx.15 minutes) and the thermal time scale of the superadiabatic layers (approx.1 day). The subsequent evolution of the luminosity and radius perturbations was followed for 5 x 10/sup 5/ yr after each mixing event. The time-dependent behavior of these perturbations was found to depend on where the mixing event occurred. In all cases, however, the ratio W(t) = ..delta.. log R/..delta.. log L had an initial value of 0.71 and showed only a mild time dependence during the first several thousand years. Two other relationships between the luminosity and radius perturbations are also discussed. One of these, V(t) = (d log R/dd)/(d log L/dt), has a fairly constant value of 0.3 +- 0.1. Both perturbations in the mixing-length ratio ..cap alpha.. and perturbations in the magnetic pressure within the solar convective envelope yield the same value for V/(t). During the normal unperturbed evolution of the present Sun, V(t) = 0.4. Our results show that core perturbations such as the present mixing events cannot explain the decrease in the solar radius indicated by the solar eclipse data between 1925 and 1980.
Quasi-closed orbit in a harmonically perturbed magnetic field
Stupakov, G.V. )
1992-11-01
The paper generalizes a notion of the closed orbit for the case when the accelertor lattice is perturbed by a time-dependent harmonic dipole field. The problem is motivated by effects of current ripple in a proton accelerator. Our result allows to estimate the amplitude of the beam excursions as a function of the amplitude and the frequency of the perturbation. It predicts that the deviation of the beam increases as the frequency of the ripple approaches the sideband betatron frequency.
Perturbations from cosmic strings in cold dark matter
NASA Technical Reports Server (NTRS)
Albrecht, Andreas; Stebbins, Albert
1992-01-01
A systematic linear analysis of the perturbations induced by cosmic strings in cold dark matter is presented. The power spectrum is calculated and it is found that the strings produce a great deal of power on small scales. It is shown that the perturbations on interesting scales are the result of many uncorrelated string motions, which indicates a much more Gaussian distribution than was previously supposed.
Linear perturbations of a Schwarzschild blackhole by thin disc - convergence
NASA Astrophysics Data System (ADS)
Čížek, P.; Semerák, O.
2012-07-01
In order to find the perturbation of a Schwarzschild space-time due to a rotating thin disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional ring. This involves solution of stationary axisymmetric Einstein's equations in terms of spherical-harmonic expansions whose convergence however turned out questionable in numerical examples. Here we show, analytically, that the series are almost everywhere convergent, but in some regions the convergence is not absolute.
Right-handed neutrinos as the source of density perturbations
Boubekeur, Lotfi; Creminelli, Paolo
2006-05-15
We study the possibility that cosmological density perturbations are generated by the inhomogeneous decay of right-handed neutrinos. This will occur if a scalar field whose fluctuations are created during inflation is coupled to the neutrino sector. Robust predictions of the model are a detectable level of non-Gaussianity and, if standard leptogenesis is the source of the baryon asymmetry, a baryon isocurvature perturbations at the level of the present experimental constraints.
Matter-wave localization in a weakly perturbed optical lattice
Cheng, Yongshan; Adhikari, S. K.
2011-11-15
By numerical solution and variational approximation of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly interacting Bose-Einstein condensate in a weakly perturbed optical lattice in one and three dimensions. The perturbation achieved through a weak delocalizing expulsive or a linear potential as well as a weak localizing harmonic potential removes the periodicity of the optical lattice and leads to localization. We also studied some dynamics of the localized state confirming its stability.
Perturbation Predictability Can Influence the Long-Latency Stretch Response
Forgaard, Christopher J.; Franks, Ian M.; Maslovat, Dana; Chua, Romeo
2016-01-01
Perturbations applied to the upper limbs elicit short (M1: 25–50 ms) and long-latency (M2: 50–100 ms) responses in the stretched muscle. M1 is produced by a spinal reflex loop, and M2 receives contribution from multiple spinal and supra-spinal pathways. While M1 is relatively immutable to voluntary intention, the remarkable feature of M2 is that its size can change based on intention or goal of the participant (e.g., increasing when resisting the perturbation and decreasing when asked to let-go or relax following the perturbation). While many studies have examined modulation of M2 between passive and various active conditions, through the use of constant foreperiods (interval between warning signal and a perturbation), it has also been shown that the magnitude of the M2 response in a passive condition can change based on factors such as habituation and anticipation of perturbation delivery. To prevent anticipation of a perturbation, most studies have used variable foreperiods; however, the range of possible foreperiod duration differs between experiments. The present study examined the influence of different variable foreperiods on modulation of the M2 response. Fifteen participants performed active and passive responses to a perturbation that stretched wrist flexors. Each block of trials had either a short (2.5–3.5 seconds; high predictability) or long (2.5–10.5 seconds; low predictability) variable foreperiod. As expected, no differences were found between any conditions for M1, while M2 was larger in the active rather than passive conditions. Interestingly, within the two passive conditions, the long variable foreperiods resulted in greater activity at the end of the M2 response than the trials with short foreperiods. These results suggest that perturbation predictability, even when using a variable foreperiod, can influence circuitry contributing to the long-latency stretch response. PMID:27727293
Perturbations from strings don't look like strings!
NASA Technical Reports Server (NTRS)
Albrecht, Andreas; Stebbins, Albert
1991-01-01
A systematic analysis is challenging popular ideas about perturbation from cosmic strings. One way in which the picture has changed is reviewed. It is concluded that, while the scaling properties of cosmic strings figure significantly in the analysis, care must be taken when thinking in terms of single time snapshots. The process of seeding density perturbations is not fundamentally localized in time, and this fact can wash out many of the details which appear in a single snapshot.
Perturbations from cosmic strings in cold dark matter
NASA Technical Reports Server (NTRS)
Albrecht, Andreas; Stebbins, Albert
1991-01-01
A systematic linear analysis of the perturbations induced by cosmic strings in cold dark matter is presented. The power spectrum is calculated and it is found that the strings produce a great deal of power on small scales. It is shown that the perturbations on interesting scales are the result of many uncorrelated string motions, which indicates a much more Gaussian distribution than was previously supposed.
Gauge-invariant perturbations in hybrid quantum cosmology
NASA Astrophysics Data System (ADS)
Castelló Gomar, Laura; Martín-Benito, Mercedes; Mena Marugán, Guillermo A.
2015-06-01
We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.
Effective gravitational couplings for cosmological perturbations in generalized Proca theories
NASA Astrophysics Data System (ADS)
De Felice, Antonio; Heisenberg, Lavinia; Kase, Ryotaro; Mukohyama, Shinji; Tsujikawa, Shinji; Zhang, Ying-li
2016-08-01
We consider the finite interactions of the generalized Proca theory including the sixth-order Lagrangian and derive the full linear perturbation equations of motion on the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a matter perfect fluid. By construction, the propagating degrees of freedom (besides the matter perfect fluid) are two transverse vector perturbations, one longitudinal scalar, and two tensor polarizations. The Lagrangians associated with intrinsic vector modes neither affect the background equations of motion nor the second-order action of tensor perturbations, but they do give rise to nontrivial modifications to the no-ghost condition of vector perturbations and to the propagation speeds of vector and scalar perturbations. We derive the effective gravitational coupling Geff with matter density perturbations under a quasistatic approximation on scales deep inside the sound horizon. We find that the existence of intrinsic vector modes allows a possibility for reducing Geff. In fact, within the parameter space, Geff can be even smaller than the Newton gravitational constant G at the late cosmological epoch, with a peculiar phantom dark energy equation of state (without ghosts). The modifications to the slip parameter η and the evolution of the growth rate f σ8 are discussed as well. Thus, dark energy models in the framework of generalized Proca theories can be observationally distinguished from the Λ CDM model according to both cosmic growth and expansion history. Furthermore, we study the evolution of vector perturbations and show that outside the vector sound horizon the perturbations are nearly frozen and start to decay with oscillations after the horizon entry.
A general theory of linear cosmological perturbations: bimetric theories
NASA Astrophysics Data System (ADS)
Lagos, Macarena; Ferreira, Pedro G.
2017-01-01
We implement the method developed in [1] to construct the most general parametrised action for linear cosmological perturbations of bimetric theories of gravity. Specifically, we consider perturbations around a homogeneous and isotropic background, and identify the complete form of the action invariant under diffeomorphism transformations, as well as the number of free parameters characterising this cosmological class of theories. We discuss, in detail, the case without derivative interactions, and compare our results with those found in massive bigravity.
Newtonian limit of fully nonlinear cosmological perturbations in Einstein's gravity
Hwang, Jai-chan; Noh, Hyerim E-mail: hr@kasi.re.kr
2013-04-01
We prove that in the infinite speed-of-light limit (i.e., non-relativistic and subhorizon limits), the relativistic fully nonlinear cosmological perturbation equations in two gauge conditions, the zero-shear gauge and the uniform-expansion gauge, exactly reproduce the Newtonian hydrodynamic perturbation equations in the cosmological background; as a consequence, in the same two gauge conditions, the Newtonian hydrodynamic equations are exactly recovered in the Minkowsky background.
Process for computing geometric perturbations for probabilistic analysis
Fitch, Simeon H. K. [Charlottesville, VA; Riha, David S [San Antonio, TX; Thacker, Ben H [San Antonio, TX
2012-04-10
A method for computing geometric perturbations for probabilistic analysis. The probabilistic analysis is based on finite element modeling, in which uncertainties in the modeled system are represented by changes in the nominal geometry of the model, referred to as "perturbations". These changes are accomplished using displacement vectors, which are computed for each node of a region of interest and are based on mean-value coordinate calculations.
Correlations in double parton distributions: perturbative and non-perturbative effects
NASA Astrophysics Data System (ADS)
Rinaldi, Matteo; Scopetta, Sergio; Traini, Marco; Vento, Vicente
2016-10-01
The correct description of Double Parton Scattering (DPS), which represents a background in several channels for the search of new Physics at the LHC, requires the knowledge of double parton distribution functions (dPDFs). These quantities represent also a novel tool for the study of the three-dimensional nucleon structure, complementary to the possibilities offered by electromagnetic probes. In this paper we analyze dPDFs using Poincaré covariant predictions obtained by using a Light-Front constituent quark model proposed in a recent paper, and QCD evolution. We study to what extent factorized expressions for dPDFs, which neglect, at least in part, two-parton correlations, can be used. We show that they fail in reproducing the calculated dPDFs, in particular in the valence region. Actually measurable processes at existing facilities occur at low longitudinal momenta of the interacting partons; to have contact with these processes we have analyzed correlations between pairs of partons of different kind, finding that, in some cases, they are strongly suppressed at low longitudinal momenta, while for other distributions they can be sizeable. For example, the effect of gluon-gluon correlations can be as large as 20 %. We have shown that these behaviors can be understood in terms of a delicate interference of non-perturbative correlations, generated by the dynamics of the model, and perturbative ones, generated by the model independent evolution procedure. Our analysis shows that at LHC kinematics two-parton correlations can be relevant in DPS, and therefore we address the possibility to study them experimentally.
CMB hemispherical asymmetry from non-linear isocurvature perturbations
Assadullahi, Hooshyar; Wands, David; Firouzjahi, Hassan; Namjoo, Mohammad Hossein E-mail: firouz@mail.ipm.ir E-mail: david.wands@port.ac.uk
2015-04-01
We investigate whether non-adiabatic perturbations from inflation could produce an asymmetric distribution of temperature anisotropies on large angular scales in the cosmic microwave background (CMB). We use a generalised non-linear δ N formalism to calculate the non-Gaussianity of the primordial density and isocurvature perturbations due to the presence of non-adiabatic, but approximately scale-invariant field fluctuations during multi-field inflation. This local-type non-Gaussianity leads to a correlation between very long wavelength inhomogeneities, larger than our observable horizon, and smaller scale fluctuations in the radiation and matter density. Matter isocurvature perturbations contribute primarily to low CMB multipoles and hence can lead to a hemispherical asymmetry on large angular scales, with negligible asymmetry on smaller scales. In curvaton models, where the matter isocurvature perturbation is partly correlated with the primordial density perturbation, we are unable to obtain a significant asymmetry on large angular scales while respecting current observational constraints on the observed quadrupole. However in the axion model, where the matter isocurvature and primordial density perturbations are uncorrelated, we find it may be possible to obtain a significant asymmetry due to isocurvature modes on large angular scales. Such an isocurvature origin for the hemispherical asymmetry would naturally give rise to a distinctive asymmetry in the CMB polarisation on large scales.
Modularity and the spread of perturbations in complex dynamical systems
NASA Astrophysics Data System (ADS)
Kolchinsky, Artemy; Gates, Alexander J.; Rocha, Luis M.
2015-12-01
We propose a method to decompose dynamical systems based on the idea that modules constrain the spread of perturbations. We find partitions of system variables that maximize "perturbation modularity," defined as the autocovariance of coarse-grained perturbed trajectories. The measure effectively separates the fast intramodular from the slow intermodular dynamics of perturbation spreading (in this respect, it is a generalization of the "Markov stability" method of network community detection). Our approach captures variation of modular organization across different system states, time scales, and in response to different kinds of perturbations: aspects of modularity which are all relevant to real-world dynamical systems. It offers a principled alternative to detecting communities in networks of statistical dependencies between system variables (e.g., "relevance networks" or "functional networks"). Using coupled logistic maps, we demonstrate that the method uncovers hierarchical modular organization planted in a system's coupling matrix. Additionally, in homogeneously coupled map lattices, it identifies the presence of self-organized modularity that depends on the initial state, dynamical parameters, and type of perturbations. Our approach offers a powerful tool for exploring the modular organization of complex dynamical systems.
Finite field-dependent symmetries in perturbative quantum gravity
Upadhyay, Sudhaker
2014-01-15
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also.
Unusual Low-frequency Magnetic Perturbations in TFTR
H. Takahashi; E.D. Fredrickson; M.S. Chance
2001-02-12
Low-frequency magnetic perturbations (less than or equal to 30 kHz) observed in the Tokamak Fusion Test Reactor (TFTR) tokamak do not always conform to expectations from Magneto-Hydro-Dynamic (MHD) modes. The discrepancy between observations and expectations arises from the existence of three classes of magnetic perturbations in TFTR: (1) 'Edge Originated Magnetic Perturbations' (EOMP's), (2) 'Kink-like Modes' (KLM's), and (3) Tearing Modes (TM's). The EOMP class has unusual magnetic phenomenon including up/down asymmetry in poloidal intensity variation that MHD modes alone cannot generate. The contributions of MHD modes in plasma edge regions are too small to explain the magnitude of observed EOMP perturbations. At least two-thirds, possibly nearly all, of magnetic perturbations in a typical EOMP originate from sources other than MHD modes. An EOMP has a unity toroidal harmonic number and a poloidal harmonic number close to a discharge's edge q-value. It produces little temperature fluctuations, except possibly in edge regions. The KLM class produces temperature fluctuations, mostly confined within the q=1 surface with an ideal-mode-like structure, but generates little external magnetic perturbations. The TM class conforms generally to expectations from MHD modes. We propose that current flowing in the Scrape-off-layer (SOL) plasma is a possible origin of EOMP's.
Nonperturbative Quantum Physics from Low-Order Perturbation Theory.
Mera, Héctor; Pedersen, Thomas G; Nikolić, Branislav K
2015-10-02
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish examples of quantum systems where the perturbation results in a certain ionization probability by tunneling processes. Accordingly, the perturbed ground-state energy is shifted and broadened, thus acquiring an imaginary part which is considered to be a paradigm of nonperturbative behavior. Here we demonstrate how the low order coefficients of a divergent perturbation series can be used to obtain excellent approximations to both real and imaginary parts of the perturbed ground state eigenenergy. The key is to use analytic continuation functions with a built-in singularity structure within the complex plane of the coupling constant, which is tailored by means of Bender-Wu dispersion relations. In the examples discussed the analytic continuation functions are Gauss hypergeometric functions, which take as input fourth order perturbation theory and return excellent approximations to the complex perturbed eigenvalue. These functions are Borel consistent and dramatically outperform widely used Padé and Borel-Padé approaches, even for rather large values of the coupling constant.
High-order perturbations of a spherical collapsing star
Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.
2010-11-15
A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.
Effects of core perturbations on the structure of the sun
NASA Technical Reports Server (NTRS)
Sweigart, A. V.
1983-01-01
The effects of perturbing the inner part of the solar core where the hydrogen abundance has been partially depleted by nuclear burning are investigated. Small regions are mixed within the core and the evolution of the resulting luminosity and radius perturbations is followed. The sensitivity of the solar luminosity and radius to mixing events of different sizes and at different locations in the core is determined and several relationships between the luminosity and radius perturbations are examined to see if the value of one of these perturbations can be inferred from a measurement of the other. It is found that any core perturbation which alters the hydrostatic structures will immediately affect the solar luminosity and radius. The behavior of these perturbations depends on the location of the mixing event within the core. Mixing events cannot produce the decrease in the solar radius without leading to a homogeneous evolution of the solar core and/or to a prohibitively large change in the solar luminosity.
Application of the perturbation method in mechanics of deformable solids
NASA Astrophysics Data System (ADS)
Minaeva, N. V.
2008-02-01
Although the solutions of the classical problems of continuum mechanics have been studied sufficiently well, the smallest deviations, for example, of the body boundary or of the material characteristics from the traditional values prevent one from obtaining exact solutions of these problems. In this case, one has to use approximate methods, the most common of which is the perturbation method. The problems studied in [1-6] belong to classical problems in which the perturbation method is used to study the behavior of deformable bodies. A wide survey of studies analyzing the perturbations of the body boundary shape caused by variations in its stress-strain state is given in [5, 6]. In numerous studies, it was noted that the problem on the convergence of approximate solutions and hence the studies of the continuous dependence of the solution of the original problem on the characteristics of perturbations ("imperfections") play an important role. In the present paper, we analyze the forms of mathematical models of deformable bodies by studying whether the solution of the original problem continuously depends on the characteristics of the perturbed shape of the body boundary on which the boundary conditions are posed in terms of stresses and on the characteristics of the material properties. We use the results of this analysis to conclude that, when using the perturbation method, one should state the boundary conditions in terms of stresses on the boundary of the real body in stressed state.
Intersegmental coupling and recovery from perturbations in freely running cockroaches
Couzin-Fuchs, Einat; Kiemel, Tim; Gal, Omer; Ayali, Amir; Holmes, Philip
2015-01-01
Cockroaches are remarkably stable runners, exhibiting rapid recovery from external perturbations. To uncover the mechanisms behind this important behavioral trait, we recorded leg kinematics of freely running animals in both undisturbed and perturbed trials. Functional coupling underlying inter-leg coordination was monitored before and during localized perturbations, which were applied to single legs via magnetic impulses. The resulting transient effects on all legs and the recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architecture and strength by fitting experimental data to a six-leg-unit phase oscillator model. Using maximum-likelihood techniques, we found that a network with nearest-neighbor inter-leg coupling best fitted the data and that, although coupling strengths vary among preparations, the overall inputs entering each leg are approximately balanced and consistent. Simulations of models with different coupling strengths encountering perturbations suggest that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations. PMID:25609786
High-order perturbations of a spherical collapsing star
NASA Astrophysics Data System (ADS)
Brizuela, David; Martín-García, José M.; Sperhake, Ulrich; Kokkotas, Kostas D.
2010-11-01
A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martín-García, and G. A. Mena Marugán, Phys. Rev. DPRVDAQ1550-7998 74, 044039 (2006);10.1103/PhysRevD.74.044039 D. Brizuela, J. M. Martín-García, and G. A. Mena Marugán, Phys. Rev. DPRVDAQ1550-7998 76, 024004 (2007)10.1103/PhysRevD.76.024004]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid’s pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.
Perturbations of the Richardson number field by gravity waves
NASA Technical Reports Server (NTRS)
Wurtele, M. G.; Sharman, R. D.
1985-01-01
An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).
Cystic fibrosis modifier genes.
Davies, Jane; Alton, Eric; Griesenbach, Uta
2005-01-01
Since the recognition that CFTR genotype was not a good predictor of pulmonary disease severity in CF, several candidate modifier genes have been identified. It is unlikely that a single modifier gene will be found, but more probable that several haplotypes in combination may contribute, which in itself presents a major methodological challenge. The aims of such studies are to increase our understanding of disease pathogenesis, to aid prognosis and ultimately to lead to the development of novel treatments. PMID:16025767
Anisotropic singularities in modified gravity models
NASA Astrophysics Data System (ADS)
Figueiró, Michele Ferraz; Saa, Alberto
2009-09-01
We show that the common singularities present in generic modified gravity models governed by actions of the type S=∫d4x-gf(R,ϕ,X), with X=-(1)/(2)gab∂aϕ∂bϕ, are essentially the same anisotropic instabilities associated to the hypersurface F(ϕ)=0 in the case of a nonminimal coupling of the type F(ϕ)R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface (∂f)/(∂R)=0 is attained. Some examples are explicitly discussed.
Hf propagation through actively modified ionospheres
Argo, P.E.; Fitzgerald, T.J.; Wolcott, J.H.; Simons, D.J. ); Warshaw, S.; Carlson, R. )
1990-01-01
We have developed a computer modeling capability to predict the effect of localized electron density perturbations created by chemical releases or high-power radio frequency heating upon oblique, one-hop hf propagation paths. We have included 3-d deterministic descriptions of the depleted or enhanced ionization, including formation, evolution, and drift. We have developed a homing ray trace code to calculate the path of energy propagation through the modified ionosphere in order to predict multipath effects. We also consider the effect of random index of refraction variations using a formalism to calculate the mutual coherence functions for spatial and frequency separations based upon a path integral solution of the parabolic wave equation for a single refracted path through an ionosphere which contains random electron density fluctuations. 5 refs., 8 figs.
Weller, R.E.
1988-10-01
Much of what used to be called immunotherapy is now included in the term biological response modifiers. Biological response modifiers (BRMs) are those agents or approaches that modify the relationship between the tumor and host by modifying the host's biological response to tumor cells with resultant therapeutic effects. Most of the early work with BRMs centered around observations of spontaneous tumor regression and the association of tumor regression with concurrent bacterial infections. The BRM can modify the host response by increasing the host's antitumor responses through augmentation and/or restoration of effector mechanisms or mediators of the host's defense or decrease the deleterious component by the host's reaction, increasing the host's defenses by the administration of natural biologics (or the synthetic derivatives thereof) as effectors or mediators of an antitumor response, augmenting the host's response to modified tumor cells or vaccines, which might stimulate a greater response by the host or increase tumor-cell sensitivity to an existing response, decreasing the transformation and/or increase differentiation (maturation) of tumor cells, or increasing the ability of the host to tolerate damage by cytotoxic modalities of cancer treatment.
Weller, R.E.
1991-10-01
Much of what used to be called immunotherapy is now included in the term biological response modifiers. Biological response modifiers (BRMs) are defined as those agents or approaches that modify the relationship between the tumor and host by modifying the host's biological response to tumor cells with resultant therapeutic effects.'' Most of the early work with BRMs centered around observations of spontaneous tumor regression and the association of tumor regression with concurrent bacterial infections. The BRM can modify the host response in the following ways: Increase the host's antitumor responses through augmentation and/or restoration of effector mechanisms or mediators of the host's defense or decrease the deleterious component by the host's reaction; Increase the host's defenses by the administration of natural biologics (or the synthetic derivatives thereof) as effectors or mediators of an antitumor response; Augment the host's response to modified tumor cells or vaccines, which might stimulate a greater response by the host or increase tumor-cell sensitivity to an existing response; Decrease the transformation and/or increase differentiation (maturation) of tumor cells; or Increase the ability of the host to tolerate damage by cytotoxic modalities of cancer treatment.
NASA Astrophysics Data System (ADS)
Takahashi, Kazufumi; Suyama, Teruaki
2017-01-01
We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black hole solutions in these theories suffer from ghost or gradient instability, while there are some classes of solutions that are stable under linear odd-parity perturbations in the context of mode analysis.
Interacting Modified Cosmic Chaplygin Gas with Variable Cosmological Constant and Viscosity
NASA Astrophysics Data System (ADS)
Saadat, Hassan
2014-12-01
In this paper we study interaction between modified cosmic Chaplygin gas and pressureless matter in presence of both bulk and shear viscosities as a model of our Universe. Also we consider variable cosmological constant and investigate some cosmological parameters such as sound speed and time-dependent density. We investigate stability of model by using first order linear perturbation.
Cosmological perturbation theory in 1+1 dimensions
McQuinn, Matthew; White, Martin E-mail: mwhite@berkeley.edu
2016-01-01
Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an O( 1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ('the Zeldovich approximation') is exact up to shell crossing, and we prove that n{sup th}-order Eulerian perturbation theory converges to the Zeldovich approximation as narrow ∞. In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.
Swamy, Prashant S.; Hu, Hao; Pattathil, Sivakumar; Maloney, Victoria J.; Xiao, Hui; Xue, Liang-Jiao; Chung, Jeng-Der; Johnson, Virgil E.; Zhu, Yingying; Peter, Gary F.; Hahn, Michael G.; Mansfield, Shawn D.; Harding, Scott A.; Tsai, Chung-Jui
2015-01-01
Cortical microtubules are integral to plant morphogenesis, cell wall synthesis, and stomatal behaviour, presumably by governing cellulose microfibril orientation. Genetic manipulation of tubulins often leads to abnormal plant development, making it difficult to probe additional roles of cortical microtubules in cell wall biogenesis. Here, it is shown that expressing post-translational C-terminal modification mimics of α-tubulin altered cell wall characteristics and guard cell dynamics in transgenic Populus tremula x alba that otherwise appear normal. 35S promoter-driven transgene expression was high in leaves but unusually low in xylem, suggesting high levels of tubulin transgene expression were not tolerated in wood-forming tissues during regeneration of transformants. Cellulose, hemicellulose, and lignin contents were unaffected in transgenic wood, but expression of cell wall-modifying enzymes, and extractability of lignin-bound pectin and xylan polysaccharides were increased in developing xylem. The results suggest that pectin and xylan polysaccharides deposited early during cell wall biogenesis are more sensitive to subtle tubulin perturbation than cellulose and matrix polysaccharides deposited later. Tubulin perturbation also affected guard cell behaviour, delaying drought-induced stomatal closure as well as light-induced stomatal opening in leaves. Pectins have been shown to confer cell wall flexibility critical for reversible stomatal movement, and results presented here are consistent with microtubule involvement in this process. Taken together, the data show the value of growth-compatible tubulin perturbations for discerning microtubule functions, and add to the growing body of evidence for microtubule involvement in non-cellulosic polysaccharide assembly during cell wall biogenesis. PMID:26246616
Swamy, Prashant S.; Hu, Hao; Pattathil, Sivakumar; ...
2015-08-05
Cortical microtubules are integral to plant morphogenesis, cell wall synthesis, and stomatal behaviour, presumably by governing cellulose microfibril orientation. Genetic manipulation of tubulins often leads to abnormal plant development, making it difficult to probe additional roles of cortical microtubules in cell wall biogenesis. Here, it is shown that expressing post-translational C-terminal modification mimics of α-tubulin altered cell wall characteristics and guard cell dynamics in transgenic Populus tremula x alba that otherwise appear normal. 35S promoter-driven transgene expression was high in leaves but unusually low in xylem, suggesting high levels of tubulin transgene expression were not tolerated in wood-forming tissues duringmore » regeneration of transformants. Cellulose, hemicellulose, and lignin contents were unaffected in transgenic wood, but expression of cell wall-modifying enzymes, and extractability of lignin-bound pectin and xylan polysaccharides were increased in developing xylem. The results suggest that pectin and xylan polysaccharides deposited early during cell wall biogenesis are more sensitive to subtle tubulin perturbation than cellulose and matrix polysaccharides deposited later. Tubulin perturbation also affected guard cell behaviour, delaying drought-induced stomatal closure as well as light-induced stomatal opening in leaves. Pectins have been shown to confer cell wall flexibility critical for reversible stomatal movement, and results presented here are consistent with microtubule involvement in this process. In conclusion, taken together, the data show the value of growth-compatible tubulin perturbations for discerning microtubule functions, and add to the growing body of evidence for microtubule involvement in non-cellulosic polysaccharide assembly during cell wall biogenesis.« less
Aminoglycoside Modifying Enzymes
Ramirez, Maria S.; Tolmasky, Marcelo E.
2010-01-01
Aminoglycosides have been an essential component of the armamentarium in the treatment of life-threatening infections. Unfortunately, their efficacy has been reduced by the surge and dissemination of resistance. In some cases the levels of resistance reached the point that rendered them virtually useless. Among many known mechanisms of resistance to aminoglycosides, enzymatic modification is the most prevalent in the clinical setting. Aminoglycoside modifying enzymes catalyze the modification at different −OH or −NH2 groups of the 2-deoxystreptamine nucleus or the sugar moieties and can be nucleotidyltranferases, phosphotransferases, or acetyltransferases. The number of aminoglycoside modifying enzymes identified to date as well as the genetic environments where the coding genes are located is impressive and there is virtually no bacteria that is unable to support enzymatic resistance to aminoglycosides. Aside from the development of new aminoglycosides refractory to as many as possible modifying enzymes there are currently two main strategies being pursued to overcome the action of aminoglycoside modifying enzymes. Their successful development would extend the useful life of existing antibiotics that have proven effective in the treatment of infections. These strategies consist of the development of inhibitors of the enzymatic action or of the expression of the modifying enzymes. PMID:20833577
A perturbative correction for electron-inertia in magnetized sheath structures
NASA Astrophysics Data System (ADS)
Gohain, Munmi; Karmakar, Pralay K.
2016-10-01
We propose a hydrodynamic model to study the equilibrium properties of planar plasma sheaths in two-component quasi-neutral magnetized plasmas. It includes weak but finite electron-inertia incorporated via a regular perturbation of the electronic fluid dynamics only relative to a new smallness parameter, δ, assessing the weak inertial-to-electromagnetic strengths. The zeroth-order perturbation around δ leads to the usual Boltzmann distribution law, which describes inertialess thermalized electrons. The forthwith next higher-order yields the modified Boltzmann law describing the putative lowest-order electron-inertial correction, which is applied meticulously to derive the local Bohm criterion for sheath formation. It is found to be influenced jointly by electron-inertial corrective effects, magnetic field and field orientation relative to the bulk plasma flow. We establish that the mutualistic action of electron-inertia amid gyro-kinetic effects slightly enhances the ion-flow Mach threshold value (typically, M i0 ⩾ 1.140), against the normal value of unity, confrontationally towards the sheath entrance. A numerical illustrative scheme is methodically constructed to see the parametric dependence of the new sheath properties on diverse problem arguments. The merits and demerits are highlighted in the light of the existing results conjointly with clear indication to future ameliorations.
Non-Perturbative QCD Coupling and Beta Function from Light Front Holography
Brodsky, Stanley J.; de Teramond, Guy F.; Deur, Alexandre; /Jefferson Lab
2010-05-26
The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q{sup 2}). It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on {alpha}{sub s}{sup AdS} (Q{sup 2}).
Bovine serum albumin with glycated carboxyl groups shows membrane-perturbing activities.
Yang, Shin-Yi; Chen, Ying-Jung; Kao, Pei-Hsiu; Chang, Long-Sen
2014-12-15
The aim of the present study aimed to investigate whether glycated bovine serum albumin (BSA) showed novel activities on the lipid-water interface. Mannosylated BSA (Man-BSA) was prepared by modification of the carboxyl groups with p-aminophenyl α-d-mannopyranoside. In contrast to BSA, Man-BSA notably induced membrane permeability of egg yolk phosphatidylcholine (EYPC)/egg yolk sphingomyelin (EYSM)/cholesterol (Chol) and EYPC/EYSM vesicles. Noticeably, Man-BSA induced the fusion of EYPC/EYSM/Chol vesicles, but not of EYPC/EYSM vesicles. Although BSA and Man-BSA showed similar binding affinity for lipid vesicles, the lipid-bound conformation of Man-BSA was distinct from that of BSA. Moreover, Man-BSA adopted distinct structure upon binding with the EYPC/EYSM/Chol and EYPC/EYSM vesicles. Man-BSA could induce the fusion of EYPC/EYSM/Chol vesicles with K562 and MCF-7 cells, while Man-BSA greatly induced the leakage of Chol-depleted K562 and MCF-7 cells. The modified BSA prepared by conjugating carboxyl groups with p-aminophenyl α-d-glucopyranoside also showed membrane-perturbing activities. Collectively, our data indicate that conjugation of carboxyl groups with monosaccharide generates functional BSA with membrane-perturbing activities on the lipid-water interface.
Magnetic-perturbation-induced plasma transport in H-mode pedestals
NASA Astrophysics Data System (ADS)
Callen, J. D.; Cole, A. J.; Hegna, C. C.
2012-03-01
Plasma toroidal rotation can prevent reconnection of externally applied resonant magnetic perturbation (RMP) fields on rational surfaces and hence magnetic island formation and stochasticity in the edge of tokamak H-mode plasmas. However, magnetic flutter induced by RMPs off the rational surfaces causes a radial electron heat diffusivity χe^RMP˜(δBr/B0)^2χ| F(x) in which χ|˜vTe^2/νe is an effective parallel electron heat diffusivity and F is a spatially varying factor [1]. The flutter also diffuses electrons radially and causes a factor of about 3 smaller increases in density diffusion. Since the electron density transport is non-ambipolar, this flutter process also modifies the radial electric field and plasma toroidal rotation. This work extends the previously developed periodic cylinder screw pinch model [1] of RMP-flutter-induced plasma transport to a full toroidal model which is axisymmetric to lowest order plus gyroradius-small magnetic field perturbations. The possible role of the RMP-flutter-induced plasma transport in reducing pressure gradients in H-mode pedestals and thereby suppressing ELMs will be discussed.[4pt] [1] J.D. Callen et al., UW-CPTC 11-13, http://www.cptc.wisc.edu (submitted to Nucl. Fusion.)
NASA Technical Reports Server (NTRS)
Telewski, F. W.; Jaffe, M. J.
1986-01-01
Field- and greenhouse-grown Abies fraseri (Pursh) Poir. (Fraser fir) were analyzed for wind- or mechanically-induced flexure changes. These changes included inhibition of stem and needle elongation, reinforcement of branch bases around the stem, and increased radial growth in the direction of the mechanical perturbation (MP). Mature trees exposed to high wind conditions were severely flag-formed. These modified tree crowns had a lower drag than crowns of non-flag formed trees in wind-tunnel tests. In both field-grown and greenhouse-grown A. fraseri, MP induced a decrease in flexibility and increased elasticity of the stems. The increased radial growth of the stems overrode the increase in elasticity, resulting in the overall decrease in flexibility. The increase in radial growth caused by wind or mechanical flexure was due to greater cell divisions of the vascular cambium, resulting in increased numbers of tracheids. The decrease in stem elongation in these trees was due, at least in part, to a decrease in tracheid length. The potential biological and mechanical significance of these induced growth changes in trees are addressed. The data support the thigmomorphogenetic theory, which states that plants respond to wind and other mechanical perturbations in a way that is favorable to the plant for continued survival in windy environments.