Experimental and numerical observation of dark and bright breathers in the band gap of a diatomic electrical lattice

We observe dark and bright intrinsic localized modes (ILMs), also known as discrete breathers, experimentally and numerically in a diatomic-like electrical lattice. The experimental generation of dark ILMs by driving a dissipative lattice with spatially homogenous amplitude is, to our knowledge, unprecedented. In addition, the experimental manifestation of bright breathers within the band gap is also novel in this system. In experimental measurements the dark modes appear just below the bottom of the top branch in frequency. As the frequency is then lowered further into the band gap, the dark ILMs persist, until the nonlinear localization pattern reverses and bright ILMs appear on top of the finite background. Deep into the band gap, only a single bright structure survives in a lattice of 32 nodes. The vicinity of the bottom band also features bright and dark self-localized excitations. These results pave the way for a more systematic study of dark breathers and their bifurcations in diatomic-like chains.VI Plan Propio of the University of Seville, Spain (VI PPITUS)AEI/FEDER, UE MAT2016- 79866-

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of linear modes. We identify a number of discrete breathers both existing in the bulk and also (predominantly) ones arising at the domain boundaries, localized either along the arm-chair or along the zig-zag edges. The types of edge-localized breathers observed and computed emerge in distinct frequency bands near the Dirac-point frequency of the dispersion surface while driving the lattice subharmonically (in a spatially homogeneous manner). These observations/computations can represent a starting point towards the exploration of the interplay of nonlinearity and topology in an experimentally tractable system such as the honeycomb electrical lattice.AEI/FEDER (UE) MAT2016- 79866-RUniversity of Seville (Spain) VI PPITU

Energy localization and transport in two-dimensional electrical lattices

Intrinsic localized modes (ILMs) have been generated and characterized in two-dimensional nonlinear electrical lattices which were driven by a spatially-uniform voltage signal. These ILMs were found to be either stationary or mobile, depending on the details of the lattice unit-cell, as had already been reported in one-dimensional lattices; however, the mo- tion of these ILMs is qualitatively di erent in that it lacks a consistent direction. Furthermore, the hop- ping speed seems to be somewhat reduced in two di- mensions due to an enhanced Peierls-Nabarro (PN)- barrier. We investigate both square and honeycomb lattices composed of 6 x 6 elements. These direct ob- servations were further supported by numerical simu- lations based on realistic models of circuit components. The numerical study moreover allowed for an analysis of ILM dynamics and pattern formation for larger lat- tice sizes

Generation of localized modes in an electrical lattice using subharmonic driving

We show experimentally and numerically that an intrinsic localized mode (ILM) can be stably produced (and experimentally observed) via subharmonic, spatially homogenous driving in the context of a nonlinear electrical lattice. The precise nonlinear spatial response of the system has been seen to depend on the relative location in frequency between the driver frequency, $\omega_d$, and the bottom of the linear dispersion curve, $\omega_0$. If $\omega_d / 2$ lies just below $\omega_0$, then a single ILM can be generated in a 32-node lattice, whereas when $\omega_d / 2$ lies within the dispersion band, a spatially extended waveform resembling a train of ILMs results. To our knowledge, and despite its apparently broad relevance, such an experimental observation of subharmonically driven ILMs has not been previously reported

There is no Theory of Everything: a physics perspective on emergence

The main purpose of this book is to introduce a broader audience to emergence by illustrating how discoveries in the physical sciences have informed the ways we think about it.  In a nutshell, emergence asserts that non-reductive behavior arises at higher levels of organization and complexity. As physicist Philip Anderson put it, “more is different.”  Along the text's conversational tour through the terrain of quantum physics, phase transitions, nonlinear and statistical physics, networks and complexity, the author highlights the various philosophical nuances that arise in encounters with emergence. The final part of the book zooms out to reflect on some larger lessons that emergence affords us. One of those larger lessons is the realization that the great diversity of theories and models, and the great variety of independent explanatory frameworks, will always be with us in the sciences and beyond. There is no “Theory of Everything” just around the corner waiting to be discovered. One of the main benefits of this book is that it will make a number of exciting scientific concepts that are not normally covered at this level accessible to a broader audience. The overall presentation, including the use of examples, analogies, metaphors, and biographical interludes, is geared for the educated non-specialist