An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Optically referenced broadband electronic synthesizer with 15 digits of resolution

Fundamental science, as well as all communications and navigation systems, are heavily reliant on the phase, timing, and synchronization provided by low‐noise and agile frequency sources. Although research into varied photonic and electronic schemes have strived to improve upon the spectral purity of microwave and millimeter‐wave signals, the reliance on conventional electronic synthesis for tuning has resulted in limited progress in broadband sources. Using a digital‐photonic synthesizer architecture that derives its time‐base from a high‐stability optical reference cavity, we generate frequency‐agile and wideband microwave signals with exceptional dynamic range and with a fractional frequency instability of 1 × 10⁻¹⁵ at 1 s. The presented architecture demonstrates digitally controlled, user defined and broadband frequency tuning from RF to 100 GHz with orders‐of‐magnitude improvement in noise performance over room‐temperature electronic wide‐bandwidth synthesis schemes.

     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.