In-material, lateral, manganin foil gauge measurements were obtained in dense polycrystalline silicon carbide (SiC) shocked to peak longitudinal stresses ranging from 10–24 GPa. The lateral gauge data were analyzed to determine the lateral stresses in the shocked SiC and the results were checked for self-consistency through dynamic two-dimensional computations. Over the stress range examined, the shocked SiC has an extremely high strength: the maximum shear stress supported by the material in the shocked state increases from 4.5 GPa at the Hugoniot elastic limit (HEL) of the material (11.5 GPa) to 7.0 GPa at stresses approximately twice the HEL. The latter value is 3.7% of the shear modulus of the material. The elastic–inelastic transition in the shocked SiC is nearly indistinctive. At stresses beyond twice the HEL, the data suggest a gradual softening with increasing shock compression. The post-HEL material strength evolution resembles neither catastrophic failure due to massive cracking nor classical plasticity response. Stress confinement, inherent in plane shock wave compression, contributes significantly to the observed material response. The results obtained are interpreted qualitatively in terms of an inhomogeneous deformation mechanism involving both in-grain microplasticity and highly confined microfissures.
This is the first part of a series of papers on the spectrum of the SYK model, which is a simple model of the black hole in physics literature. In this paper, we will give a rigorous proof of the almost sure convergence of the global density of the eigenvalues. We also discuss the largest eigenvalue of the SYK model.
Longitudinal stress profiles have been measured in polycrystalline silicon carbide (SiC) shocked to peak stresses from 7.3 to 23 GPa. Dispersive wave fronts, consistent with the expected inelastic response, were observed beyond the previously reported Hugoniot elastic limit (HEL) of 11.7 GPa. Detailed numerical analyses were carried out to interpret the observed inelastic response using both a strain-hardening, plasticity model and a pressure-dependent strength, stress relaxation model. Both models show good agreement with the data; the latter provides a better fit to the transient features in the measurements suggesting rate dependence in the material response. The computed Hugoniot curve matches all of the peak state data for two different types of SiC that display more than 20 % variation in HEL. This suggests that the measured HEL for SiC is not a proper indicator of the material strength in the shocked state. The results also show that the longitudinal data and analyses are insufficient to resolve issues related to material strength and mechanisms governing inelastic deformation in shocked SiC. The need for a more complete characterization of the shock response of a high-strength brittle material is discussed.
The available energy can be effectively upgraded by adopting smart energy conversion measures. The biodegradability of biomass can be improved by employing pretreatment techniques; however, such methods result in reduced energy efficiency. In this study, microwave (MW) irradiation is used for green algae (Enteromorpha) pretreatment in combination with iron oxide nanoparticles (NPs) which act as a heterogeneous catalyst during anaerobic digestion process for biogas enhancement. Batch-wise anaerobic digestion was carried out. The results showed that MW pretreatment and its combination with Fe3O4 NPs produced highest yields of biogas and hydrogen as compared to the individual ones and control. The biogas amount and hydrogen % v/v achieved by MW pretreatment + Fe3O4 NPs group were 328 mL and 51.5%, respectively. The energy analysis indicated that synergistic application of MW pretreatment with Fe3O4 NPs produced added energy while consuming less input energy than MW pretreatment alone. The kinetic parameters of the reaction were scientifically evaluated by using modified Gompertz and Logistic function model for each experimental case. MW pretreatment + Fe3O4 NPs group improved biogas production potential and maximum biogas production rate.
Abstract. We solve Abreu's equation with periodic right hand side, in any dimension. This can be interpreted as prescribing the scalar curvature of a torus invariant metric on an Abelian variety.
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