The most common numeral system is decimal, based on our ten fingers, but countless other systems exist and have been used throughout history. They use a different "base" or "radix". Traces of these alternative systems are still present today: when we buy a dozen eggs, use base 24 and 60 for timekeeping, or hear a French speaker say ``four-twenty four'' to mean eighty-four, a vestige of a vigesimal (base-20) system. We use our fingers to count in the same way that we may use our feet to measure lengths. We rely on these anthropocentric standards to communicate, but we expect natural phenomena to be independent of the language we speak, the metrics we choose, and even the kind of numbers we use. Both numbers and units should be informed by nature, not human conventions. To illustrate this radical idea, I will explore examples from the capillary dynamics of droplets and bubbles, and from explosions—two classical subjects of scaling. Starting with a single power law, I will show that its eventual breakdown is actually a necessity if the associated phenomenon is to be independent of our human imprint. No power law can extend indefinitely.

In complex or disordered media, standing waves can undergo a strange phenomenon that has intrigued physicists and mathematicians for over 60 years, known as “wave localization.” It consists in a concentration of the wave energy in a very restricted sub-region of the complete domain. This localization has major consequences not only on the vibration but also the propagation properties of the system, in particular electronic transport in disordered alloys. It has been demonstrated experimentally in mechanics, acoustics, electromagnetics and quantum physics. In this talk, we will present a theory that highlights the existence of an underlying and universal structure, the localization landscape, obtained by solving a problem associated with the wave equation [1]. In quantum systems, this landscape makes it possible to define an “effective potential” that predicts the localization subregions, the energies of localized modes, the density of states and the long-range decay of wave functions, regardless of the dimension, both in continuous and discrete settings. Finally, we will provide an overview of the applications of this theory to mechanics, semiconductor physics, as well as for molecular and cold atom systems. [1] M. Filoche & S. Mayboroda, PNAS (2012) LF9:14761-14766.

The citation for the 2014 Nobel Prize in Physics was for “the invention of efficient blue light-emitting diodes which has enabled bright and energy-saving white light sources”, thus suggesting that visible LEDs for lighting lead to global energy savings. As is well known among economists (but perhaps less among physicists, engineers and policy makers), the various rebound effects can severely affect the overall energy-consumption gains (if any) when a more energy-efficient technology comes to market. It is an open question to assess whether the III-N LED technology actually leads to energy savings. I will discuss the notion of rebound effect (notably direct and indirect rebound effects) in general, for semiconductor technologies and for the case of the III-N LED technology, notably in light of the surprisingly scarce literature on the topic. I will then discuss what I think this implies when discussing the impacts of our research practices and mostly the potential (social, economic and environmental) impacts of the technologies developed in academic laboratories.