A kernel approach to deconvolution of the complex modulus in linear viscoelasticity
A kernel approach to deconvolution of the complex modulus in linear viscoelasticity
复制标题
线性粘弹性复模量反卷积的核方法
DOI：
10.1088/1361-6420/ab2944
复制
发表时间：
2020
期刊：
影响因子：
2.1
通讯作者：
Davies A
中科院分区：
文献类型：
--
作者：
Davies A
粘弹性材料的弛豫谱是在分子水平上描述其弛豫机制的关键。它在获取分子量分布和模拟复杂流体动力学方面也起着重要作用。松弛谱不能直接测量，但可以在宏观水平上从粘弹性响应的实验测量中局部确定。特别是，弛豫谱是弛豫时间的连续分布，至少在局部可以从材料的复模量的测量中恢复。尽管连续光谱的数学表达式在一个多世纪前就已经为人所知，但在过去的几十年里，这些数学表达式是无法实现的。20世纪80年代首次引入了近似离散谱的正则化方法，但直到2012年才提出了在数学框架中恢复连续谱的方法。本文在再现核希尔伯特空间的框架内分析了谱恢复，并确定了复模和谱的自然家园。证明了用复模的导数级数表示逆算子的收敛性。这使得复模的实部和虚部的固有空间的详细表征，并导致一个进一步的定理，该定理确定了光谱的试空间层次。然后详细说明了数据和光谱的同胚试验空间，并通过实例研究证明了它们的有效性。
The relaxation spectrum of a viscoelastic material holds the key to describing its relaxation mechanisms at a molecular level. It also plays a fundamental role in accessing the molecular weight distribution, and in modelling the dynamics of complex fluids. The relaxation spectrum cannot be measured directly, but it may be locally determined from experimental measurements of viscoelastic response at a macroscopic level. In particular, the relaxation spectrum is a continuous distribution of relaxation times which may be recovered, at least locally, from measurements of the complex modulus of the material. Although mathematical expressions for the continuous spectrum have been known for well over a century, these were inaccessible to numerical implementation for decades. Regularization methods for approximating discrete line spectra were first introduced in the 1980s, but it was not until 2012 that methods for recovering continuous spectra in a mathematical framework were proposed. In this paper, we analyze spectrum recovery within the framework of reproducing kernel Hilbert spaces and identify such spaces as natural homes for the complex modulus and spectrum. Theorems are proved establishing the convergence of inverse operators expressed as series of derivatives of the complex modulus. This enables a detailed characterization of the native spaces of the real and imaginary parts of the complex modulus, and leads to a further theorem which identifies a hierarchy of trial spaces for the spectrum. Homeomorphic trial spaces for data and spectra are then specified in detail, and their efficacy demonstrated by means of a case study.
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论褪色的记忆
影响因子：
1.1
作者：
D. Graffi;R. Gilbert
通讯作者：
R. Gilbert
模空间上的射影结构、平丛和凯勒度量
DOI：
--
发表时间：
1988
期刊：
影响因子：
--
作者：
N. V. Ivanov
通讯作者：
N. V. Ivanov
DOI：
--
发表时间：
2017
期刊：
影响因子：
--
作者：
R. J. Loy;F. Hoog;R. Anderssen
通讯作者：
R. Anderssen
具有紧凑支撑的弛豫谱不存在结果
DOI：
--
发表时间：
2016
期刊：
影响因子：
--
作者：
R. Douglas;H. Gruffudd
通讯作者：
H. Gruffudd