The Influence of Network Topology on Sound Propagation in Granular Materials

Granular materials, whose features range from the particle scale to the force-chain scale to the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with either of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially-embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures for their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of meso-scale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by meso-scale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.Comment: 19 pages, 9 figures, and 3 table

Anomalous wave reflection from the interface of two strongly nonlinear granular media

Granular materials exhibit a strongly nonlinear behaviour affecting the propagation of information in the medium. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. Here we report the first experimental observation of the dramatic change of reflectivity from the interface of two granular media triggered by a noncontact magnetically induced initial precompression. It may be appropriate to name this phenomenon the "acoustic diode" effect. Based on numerical simulations, we explain this effect by the high gradient of particle velocity near the interface.Comment: 14 pages, 3 figure

Power-Laws in Nonlinear Granular Chain under Gravity

The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows power-laws in depth. The power-law for grain displacement signal is given by $h^{-1/4(1-1/p)}$ where $h$ and $p$ denote depth and the exponent of contact force, and the power-law for the grain velocity is $h^{-1/4({1/3}+1/p)}$. Other depth-dependent power-laws for oscillation frequency, wavelength, and period are given by combining above two and the phase velocity power-law $h^{1/2(1-1/p)}$. We verify above power-laws by comparing with the data obtained by numerical simulations.Comment: 12 pages, 3 figures; Changed conten

Tunability of solitary wave properties in one dimensional strongly nonlinear phononic crystals

One dimentional strongly nonlinear phononic crystals were assembled from chains of PTFE (polytetrafluoroethylene) and stainless steel spheres with gauges installed inside the beads. Trains of strongly nonlinear solitary waves were excited by an impact. A significant modification of the signal shape and an increase of solitary wave speed up to two times (at the same amplitude of dynamic contact force)were achieved through a noncontact magnetically induced precompression of the chains. Data for PTFE based chains are presented for the first time and data for stainless steel based chains were extended into a smaller range of amplitudes by more than one order of magnitude than previously reported. Experimental results were found to be in reasonable agreement with the long wave approximation and with numerical calculations based on Hertz interaction law for discrete chains.Comment: 36 pages, 7 figure

Glucosinolate turnover in Brassicales species to an oxazolidin-2-one, formed via the 2-thione and without formation of thioamide

Agerbirk N, Matthes A, Erthmann P, et al. Glucosinolate turnover in Brassicales species to an oxazolidin-2-one, formed via the 2-thione and without formation of thioamide. Phytochemistry. 2018;153:79-83.Glucosinolates are found in plants of the order Brassicales and hydrolyzed to different breakdown products, particularly after tissue damage. In Barbarea vulgaris R.Br. (Brassicaceae), the dominant glucosinolate in the investigated “G-type” is glucobarbarin, (S)-2-hydroxy-2-phenylethylglucosinolate. Formation of the nitrile from glucobarbarin was observed in vitro, while a previously suggested thioamide (synonym thionamide) was not confirmed. Resedine (5-phenyl-1,3-oxazolidin-2-one) was detected after glucobarbarin hydrolysis in crushed B. vulgaris leaves and siliques, but not in intact parts. The abundance increased for several hours after completion of hydrolysis. The corresponding 1,3-oxazolidine-2-thione (OAT), with the common name barbarin, was also formed, and appeared to be the precursor of resedine. Addition of each of two non-endogenous OATs, (S)-5-ethyl-5-methylOAT and (R)-5-vinylOAT (R-goitrin), to a leaf homogenate resulted in formation of the corresponding 1,3-oxazolidin-2-ones (OAOs), confirming the metabolic connection of OAT to OAO. Formation of OAOs was inhibited by prior brief heating of the homogenate, suggesting enzyme involvement. We suggest the conversion of OATs to OAOs to be catalyzed by an enzyme (“oxazolidinethionase”) responsible for turnover of OAT formed in intact plants. Resedine had been reported as an alkaloid from another species - Reseda luteola L. (Resedaceae) - naturally containing the glucosinolate glucobarbarin. However, resedine was not detected in intact R. luteola plants, but formed after tissue damage. The formation of resedine in two families suggests a broad distribution of putative OATases in the Brassicales; potentially involved in glucosinolate turnover that needs myrosinase activity as the committed step. In agreement with the proposed function of OATase, several candidate genes for myrosinases in glucosinolate turnover in intact plants were discovered in the B. vulgaris genome. We also suggest that biotechnological conversion of OATs to OAOs might improve the nutritional value of Brassicales protein. HPLC-MS/MS methods for detection of these glucobarbarin products are described