Wood is a highly heterogeneous material characterized by a number of properties that vary significantly among samples. Even in woods of the same density, substantial differences in properties show up depending on the distribution pattern of their cell walls. With the aim of deep understanding of the wood variation, we examine this pattern from the physical perspectives using samples of the same density but with significantly different shrinkages. The power spectrum, which represents the regularity of the occurrence of cell walls or lumen, was obtained through Fourier transform processing of micrographs of the transverse sections of wood samples. The set of eigenvalues calculated from the variance–covariance matrix comprising the spectra is identified with a Hamiltonian representing the energy eigenstate of the wood. The cell wall distribution can then be analyzed from within thermodynamics and statistical mechanics. The eigenvalues from the images of latewood were widely distributed compared with those from earlywood. The first eigenvalue is equivalent to the Helmholtz free energy, and thus the high-shrinkage samples showed large Helmholtz free energy because of the high presence of latewood. The Shannon entropy calculated from the probability associated with each energy eigenstate was larger in images of earlywood than latewood. That is, low-shrinkage samples have a more homogeneous structure than high-shrinkage samples. These results were strongly consistent with observations from micrographs and previous knowledge of the physical properties of woods. The physical approaches proposed in this study is independent of the origin of the data and therefore has a wide application.

中文翻译：

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基于特征值分析的木材细胞壁分布的能量学

木材是一种高度异质的材料，其特点是许多样品之间的特性差异很大。即使在密度相同的木材中，其性能也会出现显着差异，具体取决于其细胞壁的分布方式。为了深入了解木材的变化，我们从物理角度使用相同密度但收缩率明显不同的样品检查了这种模式。功率谱代表细胞壁或管腔的发生规律，是通过对木材样品横截面显微照片进行傅里叶变换处理而获得的。根据包含光谱的方差-协方差矩阵计算出的一组特征值，用代表木材能量本征态的哈密顿量进行识别。然后可以从热力学和统计力学内分析细胞壁的分布。与早木相比，晚木图像的特征值分布广泛。第一个特征值等于亥姆霍兹自由能，因此，高收缩率样品显示出较大的亥姆霍兹自由能，这是因为高胶木的存在。根据与每种能量本征态相关的概率计算得出的香农熵在早材图像中要比晚材图像大。也就是说，低收缩率样品比高收缩率样品具有更均匀的结构。这些结果与显微照片的观察和对木材物理性质的先前了解非常一致。