Author: John F. Lindner

  • Chemical Wires

    John F. Lindner

    Working with Mahala Wanner and Gus Thomas, Niklas Manz and I recently published an article Chemical wires: reaction-diffusion waves as analogues of electron drift in the journal Transport Phenomena. Mahala began the work during our summer 2022 REU, and Gus continued it for his 2025 Senior IS. We used chemical reaction-diffusion waves in narrow channels…

  • e is Transcendental

    John F. Lindner

    Introduction The Euler-Napier-Bernoulli constant is not just irrational, it is transcendental, as first proved by Charles Hermite in 1873. Inspired by the work of Mathologer (Burkard Polster with Marty Ross), here I offer an elementary proof of ‘s transcendence. As warmup, I first present a well-known proof of its irrationality while hinting at the proof…

  • My First Patent

    John F. Lindner

    In last month’s blog post, I described my second patent, which raises the question, What was my first patent? In 1998, my colleagues and I were issued United States Patent No. US 5 789 961  “Nose- and coupling-tuned signal processor with arrays of nonlinear elements”. The work began during my 1994-1995 sabbatical with the Applied…

  • My Second Patent

    John F. Lindner

    Today, about six years after beginning the relevant research, my colleagues and I were issued United States Patent No. US 12 450 468 B2, “Physics augmented neural networks configured for operating in environments that mix order and chaos”. The work began during my 2019-2020 sabbatical at the Nonlinear Artificial Intelligence Lab at North Carolina State…

  • Extreme SI Prefixes

    John F. Lindner

    In the spring of 2020, on my NC State sabbatical, during the initial lock-down for the worst pandemic of my lifetime, I stayed busy in part by writing a text called g = 2: A Gentle Introduction to Relativistic Quantum Mechanics. In the text, I tried using SI prefixes to simply express small quantities but was…

  • Wooster Physicists

    John F. Lindner

    I recently discovered that the College’s yearbooks, The Index, are now online, and I spent several days extracting some physics history, supplemented by the Alumni Catalogue 1870-1925 and several Annual Catalogues, also online, as well as the Physics Department’s web site, which for many years I helped build and maintain. I cross checked the online…

  • Growing Neural Networks

    John F. Lindner

    Artificial neural networks are increasingly important in society, technology, and science, and they are increasingly large and energy hungry. Indeed, the escalating energy footprint of large-scale computing is a growing economic and societal burden. Must we always use brute force, or can we get by with less? I just co-authored an article in Proceedings of…

  • Logic with Nonlinear Maps

    John F. Lindner

    In 1999, Bryan Prusha ’98 and I wrote an article for Physics Letters A illustrating why logic requires nonlinearity. Recently, with Bill Ditto, I revisited this theme by demonstrating how to encode all 16 binary boolean (true-false) functions in single iterations of a unimodal map, just published in Physica D. These encodings may facilitate the…

  • Barred Warped Wobbly Spiral

    John F. Lindner

    Advances in astronomy can rewrite even introductory textbooks. Although no spacecraft have yet exited our Milky Way galaxy to image it from the outside, the Gaia astrometry space telescope recently completed a dozen years of accurately measuring the positions, distances, and motions of billions of Milky Way stars from a Lissajou orbit about the Earth–Sun…

  • Weak Prime Number Theorem

    John F. Lindner

    As a child, I was inspired by Arthur C. Clarke‘s 1956 science fiction novel The City and the Stars to search for patterns in prime numbers. Chapter 6 begins: Jeserac sat motionless within a whirlpool of numbers. The first thousand primes, expressed in the binary scale that had been used for all arithmetical operations since…

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