Comment by readingnews
7 hours ago
Not sure why you have to read 3/4 of the article to get to a _link_ to a pdf which _only_ has the _abstract_ of the actual paper:
N. Benjamin Murphy and Kenneth M. Golden* (golden@math.utah.edu), University of Utah, Department of Mathematics, 155 S 1400 E, Rm. 233, Salt Lake City, UT 84112-0090. Random Matrices, Spectral Measures, and Composite Media.
Well I'm not sure why I have to dig my way past this comment to find the substantive discussion.
Quanta is not doing hypey PR research press releases, these are substantive articles about the ongoing work of researchers.
heres's a corresponding video: https://www4.math.duke.edu/media/index.html?v=3d280c1b658455...
"We consider composite media with a broad range of scales, whose effective properties are important in materials science, biophysics, and climate modeling. Examples include random resistor networks, polycrystalline media, porous bone, the brine microstructure of sea ice, ocean eddies, melt ponds on the surface of Arctic sea ice, and the polar ice packs themselves. The analytic continuation method provides Stieltjes integral representations for the bulk transport coefficients of such systems, involving spectral measures of self-adjoint random operators which depend only on the composite geometry. On finite bond lattices or discretizations of continuum systems, these random operators are represented by random matrices and the spectral measures are given explicitly in terms of their eigenvalues and eigenvectors. In this lecture we will discuss various implications and applications of these integral representations. We will also discuss computations of the spectral measures of the operators, as well as statistical measures of their eigenvalues. For example, the effective behavior of composite materials often exhibits large changes associated with transitions in the connectedness or percolation properties of a particular phase. We demonstrate that an onset of connectedness gives rise to striking transitional behavior in the short and long range correlations in the eigenvalues of the associated random matrix. This, in turn, gives rise to transitional behavior in the spectral measures, leading to observed critical behavior in the effective transport properties of the media."
From the abstract:
In this lecture we will discuss computations of the spectral measures of this operator which yield effective transport properties, as well as statistical measures of its eigenvalues.
So a lecture and not a paper, sadly.