Small-signal solutions of a two-dimensional doubly degenerate taxis system modeling bacterial motion in nutrient-poor environments

A two-dimensional simplified model of an HF chemical laser is introduced. Using an implicit finite difference scheme, the solution of two adjacent parallel streams with diffusion mixing and chemical reaction is generated. A contour of the mixing and reaction boundary is obtained without presupposition. The distribution of the HF(u) concentrations, gas temperature and the optical small signal gain (αu, J) on the flowing plane (X, Y) are presented. Compared with the solution solved directly from a set of Navier–Stokes equations, the results of these two methods agree with each other qualitatively. The influences of the different velocity, temperature (T0) and composition of the two streams on the small signal gain after the nozzle exit are investigated. It is interesting that for larger J with a fixed u, the peaks of αu, J—T0 profiles move towards higher T0. The computing method is simple and only a short computing time is needed.

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A generalized two-dimensional frequency domain least square algorithm for ARMA system modeling

Proceedings of 40th Midwest Symposium on Circuits and Systems. Dedicated to the Memory of Professor Mac Van Valkenburg ◽

10.1109/mwscas.1997.662236 ◽

2005 ◽

Author(s):

Qingwen Zhang ◽

J.R. Roman ◽

D.W. Davis ◽

W.B. Mikhael

Keyword(s):

Frequency Domain ◽

System Modeling ◽

Least Square ◽

Two Dimensional

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ADAPTIVE, FREQUENCY DOMAIN, 2-D MODELING USING SPATIOTEMPORAL SIGNALS

Journal of Circuits System and Computers ◽

10.1142/s0218126696000236 ◽

1996 ◽

Vol 06 (04) ◽

pp. 351-358

Author(s):

WASFY B. MIKHAEL ◽

HAOPING YU

Keyword(s):

Frequency Domain ◽

Moving Average ◽

System Modeling ◽

Arma Model ◽

Model Parameters ◽

Two Dimensional ◽

Convergence Factor ◽

Arma Process ◽

Auto Regressive ◽

Unknown System

In this paper, an adaptive, frequency domain, steepest descent algorithm for two-dimensional (2-D) system modeling is presented. Based on the equation error model, the algorithm, which characterizes the 2-D spatially linear and invariant unknown system by a 2-D auto-regressive, moving-average (ARMA) process, is derived and implemented in the 3-D spatiotemporal domain. At each iteration, corresponding to a given pair of input and output 2-D signals, the algorithm is formulated to minimize the error-function’s energy in the frequency domain by adjusting the 2-D ARMA model parameters. A signal dependent, optimal convergence factor, referred to as the homogeneous convergence factor, is developed. It is the same for all the coefficients but is updated once per iteration. The resulting algorithm is called the Two-Dimensional, Frequency Domain, with Homogeneous µ*, Adaptive Algorithm (2D-FD-HAA). In addition, the algorithm is implemented using the 2-D Fast Fourier Transform (FFT) to enhance the computational efficiency. Computer simulations demonstrate the algorithm’s excellent adaptation accuracy and convergence speed. For illustration, the proposed algorithm is successfully applied to modeling a time varying 2-D system.

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