Caroline Perkins

With a heavy heart, we announce that Caroline Brannon Perkins passed away from heart failure on Dec. 31, 2020.

Born 1936 in the Deep South, she is survived by two children (in Pennsylvania and New Mexico) and two sisters (in California and Kentucky). A socially distanced service will be held Sunday, Jan 17 at 2:30PM (for information on joining via computer, please email In lieu of flowers:

Truss myths and analysis

This structure would be a stable truss even though it’s not made entirely of triangles.

I’ve shared my undergrad lecture slides on “myths in truss analysis” so often that I’m making my life easier by now sharing them more broadly: Please let me know if you see errors!


PUBLICATION: Hypervariate Constitutive Modeling Illustrated via Aleatory Uncertainty in a Foundation Model

The free share link (available until May 24, 2018) is…

Abstract: Even if a ceramic’s homogenized properties (such as anisotropically evolving stiffness) truly can be predicted from complete knowledge of sub-continuum morphology (e.g., locations, sizes, shapes, orientations, and roughness of trillions of crystals, dislocations, impurities, pores, inclusions, and/or cracks), the necessary calculations are untenably hypervariate. Non-productive (almost derailing) debates over shortcomings of various first-principles ceramics theories are avoided in this work by discussing numerical coarsening in the context of a pedagogically appealing buckling foundation model that requires only sophomore-level understanding of springs, buckling hinges, dashpots, etc. Bypassing pre-requisites in constitutive modeling, this work aims to help students to understand the difference between damage and plasticity while also gaining experience in Monte-Carlo numerical optimization via scale-bridging that reduces memory and processor burden by orders of magnitude while accurately preserving aleatory (finite-finite-sampling) perturbations that are crucial to accurately predict bifurcations, such as ceramic fragmentation.

This publication helps to set knowledge needed to migrate cracks from initially uniform orientations (represented as dots on the left sphere) to highly textured orientations of vertical cracking (or any other texture based on the loading history).


This publication uses this simple system to explain many complicated concepts:

This paper would serve as a good project for a smart undergrad or first-year grad student to reproduce the results. It would serve as a familiarization exercise to learn basics of scale bridging, the difference between damage and plasticity, the influence of loading rate, the influence of microscale perturbations in macroscale behavior (e.g. reducing peak strength and scale effects), and binning down an excessively large number of internal variables to obtain a tractable decimated set.  All of that without needing to know anything about constitutive modeling – just a basic knowledge of springs and rigid links would be needed.

Again: see it for free (until May 24) at


Python source code is available on request.

Cite the paper as:

Brannon, R., Jensen, K., and Nayak, D., Journal of the European Ceramic Society (2018),

Transform between a cube’s surface and a square

I plan to add this transformation to my upcoming book on computational geometry. This mapping was originally conceived to provide a one-to-one correspondence between RGB color and locations on a dance floor for a positioning correction in a project on robotic square dancers, but then we realized that simply laying down QR codes with coordinate and orientation data would be far more accurate.

So what might be a good application for this transformation? It essentially maps the surface of the RGB cube (i.e., all fully saturated colors) to a square. One possibility would be to extend color plots that are conventionally used to depict one one variable to instead show two variables. In mechanics, for example, engineers typically show two different color plots for pressure and temperature, each with its own a linear legend bar ranging from a logical coordinate eta from 0 to 1, which is mapped to a selected linear color scheme (such as “hue” to range over the rainbow). In the single-variable color plots, the value of eta is set in proportion to the variable being plotted. To avoid needing two separate color plots for pressure and temperature a square color legend could be used with coordinates (eta1, eta2) associated with the two variables. While a “poor man’s” color plot mapping could be RGB[0,eta1,eta2], the one shown here would be far more spectacular because it would represent the full range of fully saturated colors (without “muddy” colors in the interior of the RGB cube) and, furthermore, values outside the range of interest would show as black.

End-of-millennium in Japan: Women, food, and other observations from a first-time visiting scientist

Ed: This post shares an entertaining and insightful essay about customs, food, and women in Japan over 20 years ago. It was written by my friend and colleague, Mark Boslough, after he returned from an engineering business trip in Japan in 1994. I am curious how much has changed over the subsequent 20 years, so please comment if you know which of his observations or impressions no longer apply (or if they never applied in the first place too)!  With Mark’s permission, this version has a few bits [in brackets] that have been altered to remove information that could identify particular individuals or organizations. It also has corrections of some minor typo/style issues. It is written in a style that mimics what Mark’s employer (a major US scientific research laboratory) required after any foreign travel.


  1. Status of Women in Japan
  2. Diary of Food Activities
  3. Unusual Japanese customs (by US standards)

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