Gaussian 09 Rev D 01 Em64t Torre





 
 
 
 
 
 
 

Gaussian 09 Rev D 01 Em64t Torre

Smart noise injection (SNI) is used for modeling and analysis of the behavior of nonlinear systems. Studies on SNI can lead to a better understanding of the behavior of the system, identification of the model parameters and design of better control strategies to tame the nonlinearities. In this paper, the effectiveness of a smart combination of three different noise sources (white Gaussian noise, exponentially distributed noise and fractional Gaussian noise) in analyzing the nonlinear behavior of a closed-loop system is studied. The basic idea behind the smart combination of noise sources is to capture the essence of nonlinearity in the system with the least distortion for the analysis and identification tasks. Five-order rational nonlinear functions are fitted to the behaviors of the system and the nonlinear behaviors are captured using the three different noise sources. The results indicate that the fractional Gaussian noise is the most effective noise source in analyzing and quantifying the nonlinear behavior of the system.

In this paper we introduce a new quantum mechanical model based on the gaussian wave function. We use the gaussian wave function ansatz for the exact ground state of the harmonic oscillator. We then show that the gaussian ansatz applies to the theory of many-body systems as well. Our model is based on the use of a new dynamical variables instead of the conventional coordinates. Then in the context of the Landau-Lifshitz equation we proceed to show that the second order time derivatives of the new dynamical variables can be expressed as linear functions of the velocity variables and then integrate the new dynamical variables to the new dynamic variables. Then one can obtain the quadratic form of the new Lagrange function with the constraint.

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Jun 09, 2011
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