On the linear convergence of additive Schwarz methods for the pp-Laplacian

We consider additive Schwarz methods for boundary value problems involving the $p$-Laplacian. While the existing theoretical estimates for the convergence rate of additive Schwarz methods for the $p$-Laplacian are sublinear, the actual convergence rate observed by numerical experiments is linear. In this paper, we bridge the gap between these theoretical and numerical results by analyzing the linear convergence rate of additive Schwarz methods for the $p$-Laplacian. In order to estimate the linear convergence rate of the methods, we present two essential components. Firstly, we present a new abstract convergence theory of additive Schwarz methods written in terms of a quasi-norm. This quasi-norm exhibits behavior similar to the Bregman distance of the convex energy functional associated to the problem. Secondly, we provide a quasi-norm version of the Poincar'{e}--Friedrichs inequality, which is essential for deriving a quasi-norm stable decomposition for a two-level domain decomposition setting.Comment: 23 pages, 2 figure

High-resolution, reconfigurable printing of liquid metals with three-dimensional structures

We report an unconventional approach for high-resolution, reconfigurable 3D printing using liquid metals for stretchable, 3D integrations. A minimum line width of 1.9 ??m can be reliably formed using direct printing, and printed patterns can be reconfigured into diverse 3D structures with maintaining pristine resolutions. This reconfiguration can be performed multiple times, and it also generates a thin oxide interface that can be effective in preventing the spontaneous penetration of gallium atoms into different metal layers while preserving electrical properties under ambient conditions. Moreover, these free-standing features can be encapsulated with stretchable, conformal passivations. We demonstrate applications in the form of a reconfigurable antenna, which is tunable by changing geometeries, and reversibly movable interconnections used as mechanical switches. The free-standing 3D structure of electrodes is also advantageous for minimizing the number and space between interconnections, which is important for achieving higher integrations, as demonstrated in an array of microLEDs

Nano-mechanical behavior of ultra-stable amorphous metallic thin films

Metallic glass has amorphous structure that behave mechanically like solids but show catastrophic failure due to shear band propagation induced by short range order structure, and they are generally produced by quenching. Recently, it is observed that the slower cooling rate provides the larger time available for atoms to rearrange structure before freezing in glassy state, leading to glass transition temperature and thermal stability. These glasses with enhanced thermal stability synthesized by controlled cooling rate make it useful in various field such as mechanical or oxidation protection material. However, mechanical behavior for metallic glass with extraordinary thermodynamic and kinetic stability has not been studied. In this research, we developed a ultrastable metallic glass thin film by physical vapor deposition process at ambient temperature. Thermal stability is investigated using acceleration testing. Mechanical properties are measured using in-situ tensile testing and discuss thermal stability and fracture behavior dependent on compositio

Reliability Assessment of Low-Power Processor Packages for Supercomputers

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Relationship between the dye/additive interaction and inkjet ink droplet formation

ArticleDYES AND PIGMENTS. 95(3):502-511 (2012)journal articl

Dye aggregation and interaction of dyes with a water-soluble polymer in ink-jet ink for textiles

Detailed understanding of the interaction between dyes and additives and the aggregation behaviour of the dye molecules in aqueous solutions is required to develop ink-jet ink for textiles. In the present study, the aggregation behaviour of three acid dyes (CI Acid Red 88, CI Acid Red 13 and CI Acid Red 27) containing different number of sulphonate groups in aqueous solutions was investigated by means of visible absorption spectroscopy. As a result, the higher the solubility of the dyes in water (the larger the number of sulphonate groups in the dyes), the lower are the aggregation constants of the dyes. For all the dyes, the aggregation constants decreased with increasing temperature, indicating the exothermic process of the dye aggregation. The thermodynamic process for CI Acid Red 88 with one sulphonate group is less enthalpic and more entropic than that for CI Acid Red 13, which contains two sulphonate groups. CI Acid Red 27, which includes three sulphonate groups, hardly forms any aggregates. To elucidate the effects of the polymer additive, the binding constants of the dyes with the water-soluble polymer, poly(vinylpyrrolidone) and the aggregation constants of the dyes in aqueous polymer solutions were also estimated. In addition, the binding constants were influenced by the number of sulphonate groups in the acid dyes: the larger number of sulphonate groups diminished the binding constants. The aggregation constants in the presence of poly(vinylpyrrolidone) were smaller than those in its absence at every temperature for all dyes. This suggests that poly(vinylpyrrolidone) has disaggregation effects. Furthermore, poly(vinylpyrrolidone) makes the aggregation process less enthalpic with a greater entropic change. Thus, the aggregation process of the dyes in the polymer solutions is thermodynamically different from that in water, reflecting the interactions between the dyes and the polymer.ArticleCOLORATION TECHNOLOGY. 128(3):184-191 (2012)journal articl

Incipient plasticity and fully plastic contact behavior of copper coated with a graphene layer

Cu coated with a graphene layer increases the elastic modulus from 163.4 GPa to 176.7 GPa, as analyzed for the initial elastic loading during nanoindentation by the Hertzian contact theory. This is attributed to stiffening, due to the ultra-high elastic modulus of the graphene layer, and the compressive in-plane residual stresses in the Cu surface volume introduced by the lattice mismatch between graphene and Cu. The graphene layer induces incipient plasticity, manifested by pop-in events during nanoindentation loading, at shallower indentation depths. This could be due to the compressive in-plane residual stress in the Cu surface volume; however, this compressive stress does not significantly change the critical resolved shear stress for the incipient plasticity. Even in the fully plastic contact region, at an indentation depth of 100 nm, the graphene layer affects the stress distribution underneath the indenter, resulting in a lower pile-up height. When considering this reduced pile-up height, the graphene layer is found to enhance elastic modulus by 5%, whereas it has no effect on hardness