High resolution two-dimensional minimum free energy AR spectral estimation

For explaining the Manduca wing gradient (Nardi & Kafatos, 1976) a model which postulates a proximo-distal gradient in cellular adhesiveness is considered. The model is based on Steinberg's (1963) differential adhesiveness hypothesis. Rosette formation in certain trans-posed and/or reoriented grafts can be adequately explained by this model. Several predictions, formulated by using the concept of surface free energy as a thermodynamic measure of adhesiveness, have been tested and proven correct. (1) Transposed grafts tend to assume circular forms, which are configurations of minimum free energy. (2) Because of the pressure difference expected across the interface of two cell populations with different surface free energies, cell densities increase in both distally and proximally transposed grafts. As a corollary to this rule, final size of a graft is a function of its distance from the original position.(3) Histological sections of host-graft boundaries suggest minimal cell contact at the interface. In proximal grafts placed in distal regions, cell density is far lower near the host-graft inter face, as compared to the high interior density; the peripheries of distal grafts do not show this effect. (4) Juxtaposition of three different wing regions in all possible arrangements yields the expected two-dimensional configurations. (5) Differences in adhesiveness can be demonstrated by allowing two different wing grafts to interact in an essentially neutral environment (i.e. at a leg or antenna site). As the distance between two given graft regions increases, the extent of their final contact decreases. When applied to other insect systems, the model not only offers an alternative interpretation for results currently explained by diffusible substance models, but also accounts for certain features that were unexplained by other models.

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Wavelet-Based FDTD and High Resolution Spectral Estimation for Calculation of Band Structures in Two-Dimensional Phononic Crystals

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.575.108 ◽

2014 ◽

Vol 575 ◽

pp. 108-114

Author(s):

Zhi Zhong Yan

Keyword(s):

High Resolution ◽

Spectral Estimation ◽

Phononic Crystal ◽

Fdtd Method ◽

Phononic Crystals ◽

Two Dimensional ◽

Band Structures ◽

Time Stepping ◽

Long Time ◽

Difference Time

This paper discusses the wavelet-based Finite Difference Time Domain (FDTD) method and high resolution spectral estimation with a specific problem of sound wave propagation through phononic crystals. If the band structures of a phononic crystal are calculated by the traditional FDTD method combined with the fast Fourier transform (FFT), good estimation of the eigenfrequencies can only be ensured by the postprocessing of sufficiently long time series generated by a large number of FDTD iterations. In this paper, a postprocessing method based on the high-resolution spectral estimation via the Yule-Walker method is proposed to overcome the difficulty. Numerical simulation results for two-dimensional phononic crystal show that, the wavelet-based FDTD method improves the efficiency of the time stepping algorithm, and high resolution spectral estimation shows the advantages over the classic FFT-based postprocessing.

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