Abstract
We ventured in this chapter to a particularly distant field in the application of memory functions. The topic treated was granular materials. The memories were not functions of time but of depth in a granular compact and played the role of time-dependent memories after a t − z transformation. A telegrapher’s equation analysis was constructed on the basis of a simple exponential approximation to the memory. An eigenvalue analysis was developed which allowed us to understand experimental observations on packed powders of uranium dioxide and similar systems which show oscillatory behavior in their density distributions. Those considerations were useful to the manufacture of technological items such as engine blocks. We commented on three different origins of the spatial memories. One was based on considerations of how stress is distributed as a result of variations of size and shape of the particles forming the material. Another was based on effective medium theory. A third appeared from simple but reasonable assumptions regarding constitutive relations.
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Notes
- 1.
A part of Mark Endicott’s dissertation and Anastasia Ieride’s preliminary research dealt with this topic although their work with me is still in an unpublished state.
- 2.
Granular compacts was not the only common interest that Joe and I had. The story of Tarzan was another although we had no interest in Weissmuller or the movies. While Joe was an expert, the character in the novels was of great interest to the entire research group throughout my years as an advisor. Any of my ex-students will testify that we called our weekly research meetings bundolos after the word for ‘kill’ in the language of the apes as set forth by Edgar Rice Burroughs. The nomenclature originated from the fact no quarter was given or expected when we presented our research results to one another in those meetings.
- 3.
Note that, as a consequence of the t − z transformation, z here is playing the role of time t.
- 4.
I am indebted to Marek Kuś for the detailed demonstration. On the basis of his arguments, we have been able to present an analysis of a combination of random telegraphs for the quite different topic of charge mobility. See Kenkre et al. (1998b) where the technique is explained.
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Kenkre, V.M.(. (2021). Spatial Memories and Granular Compaction. In: Memory Functions, Projection Operators, and the Defect Technique. Lecture Notes in Physics, vol 982. Springer, Cham. https://doi.org/10.1007/978-3-030-68667-3_9
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