"Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains"

A paper of mine was just published in final form. Here are some details.

Title: Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains

Authors: Guo Deng, Christopher J. Lustri, and Mason A. Porter

Abstract: We study ``nanoptera," which are nonlocalized solitary waves with exponentially small but nondecaying oscillations, in two singularly perturbed Hertzian chains with precompression. These two systems are woodpile chains (which we model as systems of Hertzian particles and springs) and diatomic Hertzian chains with alternating masses. We demonstrate that nanoptera arise from the Stokes phenomenon and appear as special curves (called Stokes curves) are crossed in the complex plane. We use techniques from exponential asymptotics to obtain approximations of the oscillation amplitudes. Our analysis demonstrates that traveling-wave solutions in a singularly perturbed woodpile chain have a single Stokes curve, which generates oscillations behind the wave front. Comparing these asymptotic predictions with numerical simulations reveals that our asymptotic approximation accurately describes the nondecaying oscillatory behavior in a woodpile chain. We perform a similar analysis of a diatomic Hertzian chain, and we show that each nanopteron solution has two distinct exponentially small oscillatory contributions. We demonstrate that there exists a set of mass ratios for which these two contributions cancel to produce localized solitary waves. This result builds on prior experimental and numerical observations that there exist mass ratios that support localized solitary waves in diatomic Hertzian chains without precompression. Comparing our asymptotic and numerical results for a diatomic Hertzian chain with precompression reveals that our exponential asymptotic approach accurately predicts the oscillation amplitude for a wide range of system parameters, but it fails to identify several values of the mass ratio that correspond to localized solitary-wave solutions.

2021 Baseball Comeback Players of the Year

Baseball's comeback players of the year for 2021 have been announced. The American League winner is Trey Mancini of the Baltimore Orioles, and the National League winner is now-retired Buster Posey of the San Francisco Giants.

2021 Baseball Most Valuable Player Awards

Baseball announced its 2021 Most Valueable Player Awards today as the culmination of this year's awards. Once again, the results are unsurprising. Shohei Ohtani of the Los Angeles Angels was a unanimous winner in the American League (duh), and Bryce Harper of the Philadelphia Phillies won in the National League.

2021 Cy Young Awards

Major League Baseball has announced its 2021 Cy Young Awards for pitching excellence. Robbie Ray of the Toronto Blue Jays won the award in the American League, and Corbin Burnes of the Milwaukee Brewers won in the National League.

The National League race was very close; Burnes narrowly beat out Zack Wheeler of the Philadelphia Phillies and the Los Angeles Dodgers' Max Scherzer wasn't horribly far away either. Walker Buehler of the Dodgers finished 4th in the balloting.

2021 Baseball Managers of the Year

Major League Baseball has announced its 2021 Managers of the Year. The Americal League Manager of the Year is Kevin Cash of the Tampa Bay Rays, and the National League Manager of the year is Gabe Kapler of the San Fransisco Giants.

As with the Rookies of the Year, neither winner is surprising.

2021 Baseball Rookies of the Year

The 2021 Rookies of the Year were announced today. Jonathan India of the Cincinnati Reds won in the National League, and Randy Arozarena of the Tampa Bay Rays won in the American League.

Neither choice is surprising.

Some More Trips

I have had a few more short academic trips in the last couple of weeks. I spent a day at Harvey Mudd to talk to the students in Heather Zinn Brooks's class on mathematics and democracy. Then I took a trip to Michigan state to give an applied-mathematics colloquium, and now I am in San Diego State to give a mathematics colloquium.

Major League Relievers of the Year

The Mariano Rivera Award and Trevor Hoffmann Award have been awarded to the top relievers in the American League and National League, respectively. Liam Hendricks of the Chicago White Sox won the former, and Josh Hader of the Milwakuee Brewers won the latter.

"Pull Out All the Stops: Textual Analysis via Punctuation Sequences"

One of my papers, which has been available publicly for more than a year, is finally out in final form, with its coordinates (its page numbers and so on). Here are the details.

Title: Pull Out All the Stops: Textual Analysis via Punctuation Sequences

Authors: Alexandra N. M. Darmon, Marya Bazzi, Sam D. Howison, and Mason A. Porter

Abstract: Whether enjoying the lucid prose of a favourite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em dashes, compound adjectives, and Oxford commas), readers will notice stylistic signatures not only in word choice and grammar but also in punctuation itself. Indeed, visual sequences of punctuation from different authors produce marvellously different (and visually striking) sequences. Punctuation is a largely overlooked stylistic feature in stylometry, the quantitative analysis of written text. In this paper, we examine punctuation sequences in a corpus of literary documents and ask the following questions: Are the properties of such sequences a distinctive feature of different authors? Is it possible to distinguish literary genres based on their punctuation sequences? Do the punctuation styles of authors evolve over time? Are we on to something interesting in trying to do stylometry without words, or are we full of sound and fury (signifying nothing)?

In our investigation, we examine a large corpus of documents from Project Gutenberg (a digital library with many possible editorial influences). We extract punctuation sequences from each document in our corpus and record the number of words that separate punctuation marks. Using such information about punctuation-usage patterns, we attempt both author and genre recognition, and we also examine the evolution of punctuation usage over time. Our efforts at author recognition are particularly successful. Among the features that we consider, the one that seems to carry the most explanatory power is an empirical approximation of the joint probability of the successive occurrence of two punctuation marks. In our conclusions, we suggest several directions for future work, including the application of similar analyses for investigating translations and other types of categorical time series.