A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow
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A high frequency multi-phase clock generator circuit with a 6b phase rotator is presented for multi-phase wireline receivers. Multi-phase injection is used to efficiently generate and rotate 8 clock phases. Unlike prior rotator-based work, this work does not use time modulation, reducing the resulting deterministic jitter. A model is presented to study the nonlinearity introduced by the technique. The proposed 17 GHz circuit was implemented in the Intel 16 process and consumes 33 mW. The measured RMS jitter is $$\mathbf{9 8} \mathrm{fs}$$, and the measured DNLpp and INLpp are 1.26 and 4.05 LSB respectively.more » « less
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The local temperature solution near the triple-phase line of a solidifying front, its melt, and a surrounding inert phase was obtained analytically including all three phases and solidification kinetics. This analytical solution was validated using a three-phase numerical model of the horizontal ribbon growth of silicon and compared to a two-phase analysis that models the effect of the third phase (e.g. the gas) as an applied heat flux. Although the three-phase solutions have additional modes to represent the gas behavior, for many conditions the two-phase and three-phase models predicted consistent behaviors. However, introduction of a non-zero growth angle causes the gas phase heat fluxes to have strong gradients near the triple-phase line. Even with zero growth angle, there are conditions in which the two-phase and three-phase solutions are very different; one predicting infinite heat fluxes while the other predicts finite fluxes. This depended on the ratios of thermal conductivities, and the angle at which the solid-melt interface intersected the free surface. In particular, when the thermal conductivity of the inert phase was comparable to the melt or solid phases there were significant differences.more » « less
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