Energy equipartition in two-dimensional granular systems with spherical intruders

We study the effects of a line of spherical interstitial particles (or intruders) placed between two adjacent uncompressed chains of larger particles in a square packing of spheres, using experiments and numerical simulations. We excite one of the chains of particles adjacent to the intruders with an impact and show how energy is transmitted across the system until equipartition is reached from the excited (or impacted) chain to the absorbing (or adjacent) chain. The coupling of the two chains, although a purely two-dimensional effect, is modeled by a simplified one-and-a-half-dimensional system in which transverse motions of the particles are neglected

Sequential phosphorylation of SLP-76 at tyrosine 173 is required for activation of T and mast cells.

Cooperatively assembled signalling complexes, nucleated by adaptor proteins, integrate information from surface receptors to determine cellular outcomes. In T and mast cells, antigen receptor signalling is nucleated by three adaptors: SLP-76, Gads and LAT. Three well-characterized SLP-76 tyrosine phosphorylation sites recruit key components, including a Tec-family tyrosine kinase, Itk. We identified a fourth, evolutionarily conserved SLP-76 phosphorylation site, Y173, which was phosphorylated upon T-cell receptor stimulation in primary murine and Jurkat T cells. Y173 was required for antigen receptor-induced phosphorylation of phospholipase C-γ1 (PLC-γ1) in both T and mast cells, and for consequent downstream events, including activation of the IL-2 promoter in T cells, and degranulation and IL-6 production in mast cells. In intact cells, Y173 phosphorylation depended on three, ZAP-70-targeted tyrosines at the N-terminus of SLP-76 that recruit and activate Itk, a kinase that selectively phosphorylated Y173 in vitro. These data suggest a sequential mechanism whereby ZAP-70-dependent priming of SLP-76 at three N-terminal sites triggers reciprocal regulatory interactions between Itk and SLP-76, which are ultimately required to couple active Itk to its substrate, PLC-γ1

Performance comparison between a nonlinear energy sink and a linear tuned vibration absorber for broadband control

The performance of a linear tuned vibration absorber (LTVA) and a nonlinear energy sink (NES) for the vibration mitigation of an uncertain linear primary system is investigated. An analytic tuning rule for the LTVA when the primary system contains uncertainty is derived. The behavior of the linear system coupled to the NES is analyzed theoretically. A tuning methodology for the NES in the deterministic as well as for the uncertain case is presented. © The Society for Experimental Mechanics, Inc. 2016

Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model

Present paper is the first one in the series devoted to the dynamics of traveling waves emerging in the uncompressed, tri-atomic granular crystals. This work is primarily concerned with the dynamics of one-dimensional periodic granular trimer (tri-atomic) chains in the state of acoustic vacuum. Each unit cell consists of three spherical particles of different masses subject to periodic boundary conditions. Hertzian interaction law governs the mutual interaction of these particles. Under the assumption of zero pre-compression, this interaction is modeled as purely nonlinear, which means the absence of linear force component. The dynamics of such chains is governed by the two system parameters that scale the mass ratios between the particles of the unit cell. Such a system supports two different classes of periodic solutions namely the traveling and standing waves. The primary objective of the present study is the numerical analysis of the bifurcation structure of these solutions with emphasis on the dynamics of traveling waves. In fact, understanding of the bifurcation structure of the traveling wave solutions emerging in the unit-cell granular trimer is rather important and can shed light on the more complex nonlinear wave phenomena emerging in semi-infinite trimer chains. (c) 2016 Elsevier B.V. All rights reserved

Traveling waves in trimer granular lattice II: Asymptotic prediction of weakly attenuated pulses

In the present study we consider the impulsive response of perfectly aligned, uncompressed, tri-atomic (trimer) granular lattice. In this study, we demonstrate that under particular choice of the system parameters - impulsively loaded, trimer granular lattice can support formation of highly localized, weakly attenuated pulses. These pulses are manifested by the completely non-symmetric wave profiles and can be attributed to the special family of solitary like waves forming in the non-homogenous, periodic trimer granular lattice in the state of acoustic vacuum. Using the recently developed analytical procedure based on the singular, multi-scale perturbation analysis, we derive a simplified reduced order model predicting the special regions in the space of the system parameters corresponding to the formation of the weakly attenuated pulses. Predictions of the asymptotical model are found to be in very good agreement with the results of numerical simulations of the full trimer granular lattice. From a practical point of view, these results can have important implications in complex, structural optimization problems of wave manipulation in the repetitive granular metamaterials. (C) 2016 Elsevier B.V. All rights reserved

Effective particles and classification of periodic orbits of homogeneous granular chains with no precompression

peer reviewedWe develop a systematic methodology for classifying the periodic orbits of homogeneous ordered granular chains with no dissipation, under the assumption that all granules oscillate with the same frequency. The analysis is based on the idea of balancing linear momentum for sets of auxiliary models consisting of “effective particles.” The auxiliary models may be defined for any given finite, ordered granular chain composed of n identical granules (beads) that interact with each other through strongly nonlinear Hertzian interaction law. In turn, the auxiliary models may be effectively used for theoretically predicting the total number of periodic orbits and the corresponding amplitude ratios of the granules. Good correspondence between the theoretical models and results of direct numerical simulations is reported. The results presented herein can be used to understand the complex intrinsic dynamics of ordered granular media, and to systematically study the generation of mode localization in these strongly nonlinear systems. The derived analytical models can be utilized to predict the response of the effective particles, and based on that, to predict primary pulse transmission in periodic layered media with granular interfaces. Moreover, our analysis can be extended to the general class of nonlinear chains of particles with smooth interacting potentials and possible separation between particles during the motion

Consecutive transitions from localized to delocalized transport states in the anharmonic chain of three coupled oscillators

In the present paper, we study the mechanism of formation and bifurcations of highly nonstationary regimes manifested by different energy transport intensities, emerging in an anharmonic trimer model. The basic model under investigation comprises a chain of three coupled anharmonic oscillators subject to localized excitation, where the initial energy is imparted to the first oscillator only. We report the formation of three basic nonstationary transport states traversed by locally excited regimes. These states differ by spatial energy distribution, as well as by the intensity of energy transport along the chain. In the current study, we focus on numerical and analytical investigation of the intricate resonant mechanism governing the inter-state transitions of locally excited regimes. Results of the analytical study are in good agreement with the numerical simulations of the trimer model. Published by AIP Publishing