• Title/Summary/Keyword: perturbation theory

Search Result 311, Processing Time 0.028 seconds

COSMOLOGICAL LINEAR PERTURBATION THEORY (우주구조 선형건드림 이론)

  • Hwang, Jai-Chan
    • Publications of The Korean Astronomical Society
    • /
    • v.26 no.2
    • /
    • pp.55-70
    • /
    • 2011
  • Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

A Variant of the Brillouin-Wigner Perturbation Theory with Epstein-Nesbet Partitioning

  • Lee, Sangyoub;Choi, Cheol Ho;Kim, Eunji;Choi, Young Kyun
    • Bulletin of the Korean Chemical Society
    • /
    • v.34 no.11
    • /
    • pp.3279-3283
    • /
    • 2013
  • We present an elementary pedagogical derivation of the Brillouin-Wigner and the Rayleigh-Schr$\ddot{o}$dinger perturbation theories with Epstein-Nesbet partitioning. A variant of the Brillouin-Wigner perturbation theory is also introduced, which can be easily extended to the quasi-degenerate case. A main advantage of the new theory is that the computing time required for obtaining the successive higher-order results is minimal after the third-order calculation. We illustrate the accuracy of the new perturbation theory for some simple model systems like the perturbed harmonic oscillator and the particle in a box.

ANISOTROPY OF CMBR AND GAUGE INVARIANT COSMIC PERTURBATION THEORIES - SOME AMBIGUITIES AND PROBLEMS

  • XU CHONGMING;WU XUEJUN
    • Journal of The Korean Astronomical Society
    • /
    • v.29 no.spc1
    • /
    • pp.17-18
    • /
    • 1996
  • COBE's results on the anisotropy of the cosmic microwave background radiation (CMBR) is discussed. Some ambiguities in the linear GI cosmic perturbation theory are clarified. The problem of the last scattering surface and the deficiencies of the linear cosmic perturbation theory are mentioned. The possible ways to overcome the theoretical difficulties are discussed also.

  • PDF

Lagrangian Perturbation Theory for the Cosmological Structure Formation with 2-component Fluid

  • Ahn, Kyungjin
    • The Bulletin of The Korean Astronomical Society
    • /
    • v.42 no.2
    • /
    • pp.55.3-55.3
    • /
    • 2017
  • We present the preliminary result of our Lagrangian perturbation theory for the large-scale structure formation, in the presence of the cold dark matter (CDM) and the baryonic fluid. In the linear order, two mutually independent pseudo-particles can describe the evolution of density fluctuations and the accuracy of the calculation is better than the 4-mode (growing, decaying, streaming, compensated) Eulerian linear perturbation theory. In the $2^{nd}$ order, the separability of pseudo-particles is not as straightforward as in the linear order, and the related difficulty in developing the $2^{nd}$ order theory will also be presented.

  • PDF

Overlay Multicast Update Strategy Based on Perturbation Theory

  • Shen, Ye;Feng, Jing;Ma, Weijun;Jiang, Lei;Yin, Min
    • KSII Transactions on Internet and Information Systems (TIIS)
    • /
    • v.11 no.1
    • /
    • pp.171-192
    • /
    • 2017
  • The change of any element in the network is possible to cause performance degradation of the multicast network. So it is necessary to optimize the topology path through the multicast update strategy, which directly affects the performance and user experience of the overlay multicast. In view of the above, a new multicast tree update strategy based on perturbation theory Musp (Multicast Update Strategy based on Perturbation theory) is proposed, which reduces the data transmission interruption caused by the multicast tree update and improves user experiences. According to the multicast tree's elements performance and the topology structure, the Musp strategy defines the multicast metric matrix and based on the matrix perturbation theory it also defines the multicast fluctuation factor. Besides it also demonstrates the calculability of the multicast fluctuation factor presents the steps of the Musp algorithm and calculates the complexity. The experimental results show that compared with other update strategies, as for the sensitivity of the multicast fluctuation factor's energized multicast tree to the network disturbance, the maximum delay of the Musp update strategy is minimal in the case of the local degradation of network performance.

Structure and Thermodynamic Properties of Simple Coulomb Liquids Using Perturbation Theory (섭동론에 의한 간단한 쿨롱 액체의 구조 및 열역학적 성질)

  • Shin Dong Young;Lee Jae Weon;Ree T.;Ree Francis H.
    • Journal of the Korean Chemical Society
    • /
    • v.35 no.4
    • /
    • pp.308-315
    • /
    • 1991
  • The structure and thermodynamic properties of body centered cubic structure of simple Coulombic liquids are computed from the perturbation theory for one-component plasma. A comparison of perturbation theory (PT) and Monte Carlo (MC) simulation shows excellent agreement. The hardsphere perturbation theory is applicable to a long-range attractive system, such as the one-component plasma. A comparison of the radial distribution function (g(r)) and the structure factor (S(q)) for PT data and MC data shows agreement. Thus the perturbation theory is an applicable method to explain the structure and thermodynamic properties of Coulomb liquids.

  • PDF

Eigenvalue Perturbation of Augmented Matrix for Control Parameter (제어기 정수에 대한 확대행렬의 고유치 perturbation)

  • Shim, K.S.;Song, S.G.;Nam, H.K.;Kim, Y.G.;Moon, C.J.
    • Proceedings of the KIEE Conference
    • /
    • 2001.05a
    • /
    • pp.17-19
    • /
    • 2001
  • In this paper, eigenvalue perturbation theory and its applications for the augmented system matrix are described. This theory is quite useful in the cases where any change in a system parameter results in signifiant changes to most of the elements of the augmented matrix or where the forming of sensitivity matrix so complicate. And AMEP(augmented matrix eigenvalue perturbation) for the excitation system parameters are computed for analysis of small signal stability of KEPCO 215-machine 791-bus system.

  • PDF

Simplified Nonlinear Control for Planar Motor based on Singular Perturbation Theory (특이섭동이론을 기반으로한 평판모터의 비선형 제어)

  • Seo, HyungDuk;Shin, Donghoon;Lee, Youngwoo;Chung, Chung Choo
    • The Transactions of The Korean Institute of Electrical Engineers
    • /
    • v.64 no.2
    • /
    • pp.289-296
    • /
    • 2015
  • In this paper, we propose the nonlinear control based on singular perturbation theory for position tracking and yaw regulation of planar motor. Singular perturbation theory is characterized by the existence of slow and fast transients in the system dynamics. The proposed method consists of auxiliary control to decouple error dynamics. We develop model reduction with control input. Also, we derIve decoupled error dynamics with auxiliary input. The controller is designed in order to guarantee the desired position and yaw regulation without current feedback or estimation. Simulation results validate the effect of proposed method.

Stability Analysis of Mathieu Equation by Floquet Theory and Perturbation Method (Floquet 이론과 섭동법에 의한 Mathieu Equation의 안정성해석)

  • Park, Chan Il
    • Transactions of the Korean Society for Noise and Vibration Engineering
    • /
    • v.23 no.8
    • /
    • pp.734-741
    • /
    • 2013
  • In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES

  • Kang, Yong Han;Jeong, Jin-Mun
    • Bulletin of the Korean Mathematical Society
    • /
    • v.51 no.1
    • /
    • pp.13-27
    • /
    • 2014
  • The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.