skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: On stochastic stability of the integral manifold under an action of permanently acting random perturbations

Abstract

Using Lyapunov function method sufficient conditions of stochastic stability of the given integral manifold under an action of permanently acting random perturbations are obtained.

Authors:
 [1];  [2]
  1. Institute of Mathematics and Mathematical Modeling, Almaty (Kazakhstan)
  2. Al-Farabi Kazakh National University, Almaty (Kazakhstan)
Publication Date:
OSTI Identifier:
22608263
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1759; Journal Issue: 1; Conference: ICAAM 2016: International conference on analysis and applied mathematics, Almaty (Kazakhstan), 7-10 Sep 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DISTURBANCES; FUNCTIONS; INTEGRALS; LYAPUNOV METHOD; MATHEMATICAL SPACE; PERTURBATION THEORY; RANDOMNESS; STABILITY; STOCHASTIC PROCESSES

Citation Formats

Tleubergenov, Marat, and Vassilina, Gulmira. On stochastic stability of the integral manifold under an action of permanently acting random perturbations. United States: N. p., 2016. Web. doi:10.1063/1.4959742.
Tleubergenov, Marat, & Vassilina, Gulmira. On stochastic stability of the integral manifold under an action of permanently acting random perturbations. United States. doi:10.1063/1.4959742.
Tleubergenov, Marat, and Vassilina, Gulmira. 2016. "On stochastic stability of the integral manifold under an action of permanently acting random perturbations". United States. doi:10.1063/1.4959742.
@article{osti_22608263,
title = {On stochastic stability of the integral manifold under an action of permanently acting random perturbations},
author = {Tleubergenov, Marat and Vassilina, Gulmira},
abstractNote = {Using Lyapunov function method sufficient conditions of stochastic stability of the given integral manifold under an action of permanently acting random perturbations are obtained.},
doi = {10.1063/1.4959742},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1759,
place = {United States},
year = 2016,
month = 8
}
  • Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a protovoid or supercluster at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario, and itmore » is effective for generating initial conditions for N-body simulations with rare objects in the computational volume. 21 references.« less
  • We extend our previous work, in which we applied high-dimensional model representation (HDMR) and analysis of variance (ANOVA) concepts to the characterization of a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field. That example was treated as a onedimensional problem, because those were the only data available. In this study, we develop a more rigorous two-dimensional model for characterizing random, anisotropic grain noise in titanium alloys. Such a model is necessary if we are to accurately capture the 'clumping' of crystallites into long chains that appear during themore » processing of the metal into a finished product. The mathematical model starts with an application of the Karhunen-Loève (K-L) expansion for the random Euler angles, θ and φ, that characterize the orientation of each crystallite in the sample. The random orientation of each crystallite then defines the stochastic nature of the electrical conductivity tensor of the metal. We study two possible covariances, Gaussian and double-exponential, which are the kernel of the K-L integral equation, and find that the double-exponential appears to satisfy measurements more closely of the two. Results based on data from a Ti-7Al sample will be given, and further applications of HDMR and ANOVA will be discussed.« less
  • Following the suggestion that substorm breakup might be caused by an interchange or ballooning instability, several magnetohydrodynamic (MHD) and gyrokinetic stability analysis have been performed for plasma sheet magnetic field geometries. However, the stochastic ion dynamics in the highly stressed, thin high-[beta] near earth plasma sheet violate the locality requirements of MHD and the invariance of the magnetic moment, [mu], required by gyrokinetic theories. In this paper, a proper quadratic form energy principle (for low frequency modes [omega][lt][omega][sub [ital b]], [omega][sub [ital b]] being the bounce frequency) which includes the dynamics of stochastic ions is developed, and it is demonstratedmore » that the stochastic plasma is less stable than the corresponding adiabatic plasma.« less
  • A "transverse" motion of strongly relativistic electrons in a long linear accelerator, induced by errors in compensation for the earth's magnetic field and in the accelerating sections of the installation, is investigated. Owing to the great length of the accelerator the small perturbations are capable of strongly deflecting the particle from the accelerator axis. (R.V.J.)
  • 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.