Self-patterning Gd nano-fibers in Mg-Gd alloys.

Manipulating the shape and distribution of strengthening units, e.g. particles, fibers, and precipitates, in a bulk metal, has been a widely applied strategy of tailoring their mechanical properties.

Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT.

We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum.