Nonlinear Low-to-High-Frequency Energy Cascades in Diatomic Granular Crystals

We study wave propagation in strongly nonlinear one-dimensional diatomic granular crystals under an impact load. Depending on the mass ratio of the “light” to “heavy” beads, this system exhibits rich wave dynamics from highly localized traveling waves to highly dispersive waves featuring strong attenuation. We demonstrate experimentally the nonlinear resonant and antiresonant interactions of particles, and we verify that the nonlinear resonance results in strong wave attenuation, leading to highly efficient nonlinear energy cascading without relying on material damping. In this process, mechanical energy is transferred from low to high frequencies, while propagating waves emerge in both ordered and chaotic waveforms via a distinctive spatial cascading. This energy transfer mechanism from lower to higher frequencies and wave numbers is of particular significance toward the design of novel nonlinear acoustic metamaterials with inherently passive energy redistribution properties

Nonlinearity and Topology

The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons, hopfions, monopoles to name just a few. Interaction among and collision of these nontrivial defects itself is a topic of great interest. Curvature and underlying geometry also affect the shape, interaction and behavior of these defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as well as topological materials such as Dirac and Weyl semimetals, are also elucidated

Influence of fly ash blending on hydration and physical behavior of Belite-Alite-Ye'elimite cements

A cement powder, composed of belite, alite and ye’elimite, was blended with 0, 15 and 30 wt% of fly ash and the resulting lended cements were further characterized. During hydration, the presence of fly ash caused the partial inhibition of both AFt degradation and belite reactivity, even after 180 days. The compressive strength of the corresponding mortars increased by increasing the fly ash content (68, 73 and 82 MPa for mortars with 0, 15 and 30 wt% of fly ash, respectively, at 180 curing days), mainly due to the diminishing porosity and pore size values. Although pozzolanic reaction has not been directly proved there are indirect evidences.This work is part of the Ph.D. of D. Londono-Zuluaga funded by Beca Colciencias 646—Doctorado en el exterior and Enlaza Mundos 2013 program grant. Cement and Building materials group (CEMATCO) from National University of Colombia is acknowledged for providing the calorimetric measurements. Funding from Spanish MINECO BIA2017-82391-R and I3 (IEDI-2016-0079) grants, co-funded by FEDER, are acknowledged

Linear and nonlinear dynamics of isospectral granular chains

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertzcontact law interaction between the granular particles. The system dynamics can thus be tuned easily frombeing linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, weintroduce both discrete and continuous spectral transformation schemes to generate a family of granular chainsthat are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, wealso introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically thatthe corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In thelinear regime, we highlight the commonalities and differences in the elastic wave transmission characteristicsof such isospectral systems, and emphasize that the presented mathematical framework allows one to suitablytailor the wave transmission through a general class of granular chains. Moreover, we show how the dynamicresponse of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain andhow nonlinearity breaks the notion of linear isospectrality