Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

Residual Stress Relaxation Induced by Mass Transport Through Interface of the Pd/SrTiO3

Metal interconnections having a small cross-section and short length can be subjected to very large mass transport due to the passing of high current densities. As a result, nonlinear diffusion and electromigration effects which may result in device failure and electrical instabilities may be manifested. Various thicknesses of Pd were deposited over SrTiO3 substrate. Residual stress of the deposited film was evaluated by measuring the variation of d-spacing versus sin2ψ through conventional X-ray diffraction method. It has been found that the lattice misfit within film and substrate might be relaxed because of mass transport. Besides, the relation between residual intrinsic stress and oxygen diffusion through deposited film has been expressed. Consequently, appearance of oxide intermediate layer may adjust interfacial characteristics and suppress electrical conductivity by increasing electron scattering through metallic films

Development of reinforced polyester/graphene nanocomposite showing tailored electrical conductivity

Production process was chosen in order to be readily scalable at the industrial level. The resin/graphene mixture was prepared through high shear mixing at six different weight concentrations between 0% and 10%. Samples were subsequently produced by compression molding. The electrical properties were measured both in-the-plane and across-the-plane using, respectively, a four-point probe and a two-electrode system. The two-electrode system was a dielectric spectrometer, and accordingly, the across-the-plane measurements were conducted in the frequency-domain. Mechanical measurements were conducted using conventional three-point bending and impact setups. The percolation threshold was found to be in the range of 3\u20135 wt.% concentration, for which the conductivity showed a 7 orders of magnitude increase. These results were quite similar to the samples containing around 50 wt.% of glass fibers. Surprisingly, the in-the-plane conductivity was found to be lower than the bulk conductivity, contrary to what was found with the same filler for thermoplastic composites prepared by melt compounding. No significant increase in mechanical properties as a function of filler loading was observed, except maybe a slight increase in the material toughness

Insight into the Directional Thermal Transport of Hexagonal Boron Nitride Composites

cited By 0Ideal dielectric materials for microelectronic devices should have high directionally tailored thermoconductivity with low dielectric constant and loss. Hexagonal boron nitride (hBN) with excellent thermal and dielectric properties shows a promise for the fabrication of thermoconductive dielectric polymer composites. Herein, a simple method for the fabrication of lightweight polymer/hBN composites with high directionally tailored thermoconductivity and excellent dielectric properties is presented. The solid polymer/hBN composites are manufactured by melt-compounding and injection molding. The porous composites are successfully manufactured in an injection molding process through supercritical fluid (SCF) foaming. X-ray tomography provides direct visualization of the internal microstructure and hBN orientation, leading to an in-depth understanding of the directionally dependent thermoconductivity of the polymer/hBN composite. Shear-induced orientation of hBN platelets in the solid HDPE/hBN composites leads to a significant anisotropic thermal conductivity. The solid HDPE/23.2 vol % hBN composites show an in-plane thermoconductivity as high as 10.1 W m-1 K-1, whereas the through-plane thermoconductivity is limited to 0.28 W m-1 K-1. However, the generation of a porous structure via SCF foaming imparts in situ exfoliation, random orientation, and interconnectivity of hBN platelets within the polymer matrix. This results in highly isotropic thermoconductivity with higher bulk thermal conductivity in the lightweight porous composites as compared to their solid counterparts. Furthermore, the electrically insulating composites developed in this study exhibit low dielectric constant and ultralow dielectric loss. Thus, this study presents a simple fabrication method to develop lightweight dielectric materials with tailored thermal conductivity for modern electronics. © 2019 American Chemical Society