Reversible signal transmission in an active mechanical metamaterial

Mechanical metamaterials are designed to enable unique functionalities, but are typically limited by an initial energy state and require an independent energy input to function repeatedly. Our study introduces a theoretical active mechanical metamaterial that incorporates a biological reaction mechanism to overcome this key limitation of passive metamaterials. Our material allows for reversible mechanical signal transmission, where energy is reintroduced by the biologically motivated reaction mechanism. By analysing a coarse grained continuous analogue of the discrete model, we find that signals can be propagated through the material by a travelling wave. Analysis of the continuum model provides the region of the parameter space that allows signal transmission, and reveals similarities with the well-known FitzHugh-Nagumo system. We also find explicit formulae that approximate the effect of the timescale of the reaction mechanism on the signal transmission speed, which is essential for controlling the material.Comment: 20 pages, 7 figure

Averages of shifted convolutions of d3(n)d_3(n)

We investigate the first and second moments of shifted convolutions of the generalised divisor function $d_3(n)$.Comment: 22 page

Warsaw from the French Perspective: A Comparative Study of Liability Limits under the Warsaw Convention

The Warsaw Convention, now over 45 years old, was originally designed to aid the growth of a new, undeveloped, and somewhat perplexing commercial enterprise--the international air transportation industry. Unfortunately, the drafters of the Convention took a narrow, and perhaps ill-advised, view of regulation of liability. They limited the carriers\u27 liability for damage to an amount that could easily have been foreseen to be unworkable and they defined the concept of fault in ambiguous terms. While this fledgling attempt to codify an area of private international law was meant to provide a uniformity of terms that would be workable in a variety of legal systems, the result has been an increasing breakdown of the Convention\u27s concepts in the courts of the ratifying states. This note will analyze one of the inadequacies of the Warsaw Convention--the limitation of liability for passenger injury--on a comparative basis. The analysis will first give a brief historical background of the Warsaw Convention. Second, the basic nature of French tort concepts in relation to carrier liability and the specific application of those concepts to airline cases in France will be discussed. Finally, a brief overview of the standards employed in England, Germany, and the Soviet Union will be given

Should Judges Have a Duty of Tech Competence?

In an era in which lawyers are increasingly held to a higher standard of “tech competence” in their representation of clients, shouldn’t we similarly require judges to be conversant in relevant technology? Using real world examples of judicial missteps with or refusal to use technology, and drawn from actual cases and judicial disciplinary proceedings, this Article argues that in today’s Digital Age, judicial technological competence is necessary. At a time when courts themselves have proven vulnerable to cyberattacks, and when courts routinely tackle technology related issues like data privacy and the admissibility of digital evidence, Luddite judges are relics that the future—not to mention the present—can ill afford