On the stability of the μ(I)\mu(I)-rheology for granular flow

This article deals with the Hadamard instability of the so-called $\mu(I)$ model of dense rapidly-sheared granular flow, as reported recently by Barker et al. (2015,this journal, ${\bf 779}$, 794-818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wave-vector stretching by the base flow. We provide a closed form solution for the linear stability problem and show that wave-vector stretching leads to asymptotic stabilization of the non-convective instability found by Barker et al. We also explore the stabilizing effects of higher velocity gradients achieved by an enhanced-continuum model based on a dissipative analog of the van der Waals-Cahn-Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyper-stress, as the analog of a special Korteweg stress, with surface viscosity representing the counterpart of elastic surface tension. Based on the enhanced continuum model, we also present a model of steady shear bands and their non-linear stability against parallel shearing. Finally, we propose a theoretical connection between the non-convective instability of Barker et al. and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the numerical simulation of continuum field equations involving the $\mu(I)$ rheology and variants thereof.Comment: 30 pages, 13 figure

Estimates of M-Harmonic Conjugate Operator

We define the M-harmonic conjugate operator K and prove that for 1<p<∞, there is a constant Cp such that ∫S|Kf|pωdσ≤Cp∫S|f|pωdσ for all f∈Lp(ω) if and only if the nonnegative weight ω satisfies the Ap-condition. Also, we prove that if there is a constant Cp such that ∫S|Kf|pvdσ≤Cp∫S|f|pwdσ for all f∈Lp(w), then the pair of weights (v,w) satisfies the Ap-condition

Estimates of weighted Hardy–Littlewood averages on the p-adic vector space

AbstractIn the p-adic vector space Qpn, we characterize those non-negative functions ψ defined on Zp*={w∈Qp:0<|w|p⩽1} for which the weighted Hardy–Littlewood average Uψ:f→∫Zp*f(t⋅)ψ(t)dt is bounded on Lr(Qpn) (1⩽r⩽∞), and on BMO(Qpn). Also, in each case, we find the corresponding operator norm ‖Uψ‖

Forecast of CO2 Emissions From the U.S. Transportation Sector: Estimation From a Double Exponential Smoothing Model

This study examines whether the decreasing trend in U.S. CO2 emissions from the transportation sector since the end of the 2000s will be shown across all states in the nation for 2012‒2021. A double exponential smoothing model is used to forecast CO2 emissions for the transportation sector in the 50 states and the U.S., and its findings are supported by the validity test of pseudo out-of-sample forecasts. We conclude that the decreasing trend in transportation CO2 emissions in the U.S. will continue in most states in the future

A study on the failure prediction of composite laminates in bending

Failure prediction for composite materials under given loading conditions is important for efficient design in structural applications. Over the past several decades, there are numerous failure criteria proposed to more accurately predict the failure composite laminates. A lot of research was conducted to evaluate and validate the failure prediction capability for failure criteria. The most failure criteria are studied for in-plane loading conditions. Mechanical behavior of composite laminates varies depending on the loading conditions. Even if failure criterion is accurate under the in-plane loads, it cannot be accurate for out-of-plane loads such as bending. In many industrial structures, composite laminates is under out-of-plane load as well as in-plane loads. For the structural stability of the composite structures, it is important to accurately predict failure of composite laminates under bending. In this study, the failure prediction of composite laminates under bending is investigated. The non-linear finite element analysis using Arc-length method is performed. 2D strain-based interactive failure theory [1] that is more accurately final failure of composite laminate under multi-axial loading is applied to predict the final failure of composite laminates under bending. In order to compare the accuracy of the failure predictions, a 3-point bending test are performed for un-symmetric cross-ply [0/90]8 and quasi-isotropic [0/±45/90]2s composite laminates. Also, it is compared with the other failure criteria such as maximum strain, maximum stress and Tsai-Wu theories. Finally, the predicted results using 2D strain-based interactive failure theory more agree well with the experiment than other failure theories. Acknowledgements This work was supported under the framework of Aerospace Technology Development Program (No. 10074270, Development of Manufacturing Core Technology for 3-Dimnesional Woven Integrated Composite Wing Structure of 5,000 Pound VLJ Aircraft) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) This work was supported by the New & Renewable Energy Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 20143030021130) References [1] S. Y. Lee and J. H. Roh, “Two-dimensional strain-based interactive failure theory for multidirectional composite laminates,” Composite Part B: Engineering, vol. 69, pp.69-75, 2015

Measurement of PM2.5 Mass Concentration Using an Electrostatic Particle Concentrator-Based Quartz Crystal Microbalance

Particulate matter (PM) is one of the most critical air pollutants, and various instruments have been developed to measure PM mass concentration. Of these, quartz crystal microbalance (QCM) based instruments have received much attention. However, these instruments are subject to significant drawbacks: particle bounce due to poor adhesion, need for frequent cleanings of the crystal electrode, and non-uniform distribution of collected particles. In this study, we present an electrostatic particle concentrator (EPC)-based QCM (qEPC) instrument capable of measuring the mass concentration of PM 2.5 (PM smaller than 2.5 ??m), while avoiding the drawbacks. Experimental measurements showed high collection efficiencies (~99% at 1.2 liters/min), highly uniform particle distributions for long sampling periods (up to 120 min at 50 ??g/m 3 ), and high mass concentration sensitivity [0.068(Hz/min)/(??g/m 3 )]. The enhanced uniformity of particle deposition profiles and mass concentration sensitivity were made possible by the unique flow and electrical design of the qEPC instrument