Random Initial Condition

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 78 Experts worldwide ranked by ideXlab platform

Erwan Faou - One of the best experts on this subject based on the ideXlab platform.

  • Linearized Wave Turbulence Convergence Results for Three-Wave Systems
    Communications in Mathematical Physics, 2020
    Co-Authors: Erwan Faou
    Abstract:

    We consider stochastic and deterministic three-wave semi-linear systems with bounded and almost continuous set of frequencies. Such systems can be obtained by considering nonlinear lattice dynamics or truncated partial differential equations on large periodic domains. We assume that the nonlinearity is small and that the noise is small or void and acting only in the angles of the Fourier modes (Random phase forcing). We consider Random Initial data and assume that these systems possess natural invariant distributions corresponding to some Rayleigh–Jeans stationary solutions of the wave kinetic equation appearing in wave turbulence theory. We consider Random Initial modes drawn with probability laws that are perturbations of theses invariant distributions. In the stochastic case, we prove that in the asymptotic limit (small nonlinearity, continuous set of frequency and small noise), the renormalized fluctuations of the amplitudes of the Fourier modes converge in a weak sense towards the solution of the linearized wave kinetic equation around these Rayleigh–Jeans spectra. Moreover, we show that in absence of noise, the deterministic equation with the same Random Initial Condition satisfies a generic Birkhoff reduction in a probabilistic sense, without kinetic description at least in some regime of parameters.

Weisheng Chen - One of the best experts on this subject based on the ideXlab platform.

Jianxin Xu - One of the best experts on this subject based on the ideXlab platform.

Paulo R Guimaraes - One of the best experts on this subject based on the ideXlab platform.

  • Random Initial Condition in small barabasi albert networks and deviations from the scale free behavior
    Physical Review E, 2005
    Co-Authors: Paulo R Guimaraes, Marcus A M De Aguiar, Jordi Bascompte, Pedro Jordano, Sergio Futardo Dos Reis
    Abstract:

    Barabasi-Albert networks are constructed by adding nodes via preferential attachment to an Initial core of nodes. We study the topology of small scale-free networks as a function of the size and average connectivity of their Initial Random core. We show that these two parameters may strongly affect the tail of the degree distribution, by consistently leading to broad-scale or single-scale networks. In particular, we argue that the size of the Initial network core and its density of connections may be the main responsible for the exponential truncation of the power-law behavior observed in some small scale-free networks.

Zhongsheng Hou - One of the best experts on this subject based on the ideXlab platform.

  • discrete time adaptive ilc for non parametric uncertain nonlinear systems with iteration varying trajectory and Random Initial Condition
    Asian Journal of Control, 2013
    Co-Authors: Ronghu Chi, Zhongsheng Hou, Shangtai Jin, Danwei Wang
    Abstract:

    This paper presents a new discrete-time adaptive iterative learning control approach (AILC) for a class of time-varying nonlinear systems with nonparametric uncertainties and non-repeatable external disturbances by incorporating a novel iterative estimate scheme. A major distinct feature of the presented approach is that uncertainties can be completely compensated for, using only I/O data. Another distinct feature is that the pointwise convergence is achieved over a finite time interval without requiring the matching Condition on Initial states and reference trajectory. Rigorous mathematical analysis is developed, and simulation results illustrate the effectiveness of the proposed approach.

  • a discrete time adaptive ilc for systems with Random Initial Condition and iteration varying trajectory
    IFAC Proceedings Volumes, 2008
    Co-Authors: Ronghu Chi, Shulin Sui, Zhongsheng Hou
    Abstract:

    Abstract A discrete-time adaptive ILC scheme is presented for systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new AILC can incorporate a recursive Least-Squares algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the Initial states are Random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis. An extension of the new AILC is also developed by using nonlinear data weighting to systems without assuming any growth Conditions on the nonlinearity.