Influence of the additional second neighbor hopping on the spin response in the t-J model

The influence of the additional second neighbor hopping t' on the spin response of the t-J model in the underdoped and optimally doped regimes is studied within the fermion-spin theory. Although the additional second neighbor hopping t' is systematically accompanied with the reduction of the dynamical spin structure factor and susceptibility, the qualitative behavior of the dynamical spin structure factor and susceptibility of the t-t'-J model is the same as in the case of t-J model. The integrated dynamical spin structure factor spectrum is almost t' independent, and the integrated dynamical spin susceptibility still shows the particularly universal behavior as $I(\omega,T)\propto {\rm arctan}[a_{1}\omega/T+a_{3}(\omega/T)^{3}]$.Comment: 12 pages, Latex, Four figures are included, final published version [accepted for publication in Phys. Rev. B (July 1 issue)

Converting a CAD Model into a Manufacturing Model for the Components Made of a Multiphase Perfect Material

To manufacture the component made of a multiphase perfect material (including homogeneous and multi heterogeneous materials), it CAD model should be processed and converted into layered manufacturing model for further transformation of numerical control (NC) coding. This paper develops its detailed approaches and corresponding software. The process planning is made first and includes: (1) determining the build orientation of the component; and (2) slicing the component into layers adaptively according to different material regions since different materials have different optimal layer thickness for manufacturing. After the process planning, the layered manufacturing models with necessary information, including fabrication sequence and material information of each layer, are fully generated.Mechanical Engineerin

Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion

A spectrally sparse signal of order $r$ is a mixture of $r$ damped or undamped complex sinusoids. This paper investigates the problem of reconstructing spectrally sparse signals from a random subset of $n$ regular time domain samples, which can be reformulated as a low rank Hankel matrix completion problem. We introduce an iterative hard thresholding (IHT) algorithm and a fast iterative hard thresholding (FIHT) algorithm for efficient reconstruction of spectrally sparse signals via low rank Hankel matrix completion. Theoretical recovery guarantees have been established for FIHT, showing that $O(r^2\log^2(n))$ number of samples are sufficient for exact recovery with high probability. Empirical performance comparisons establish significant computational advantages for IHT and FIHT. In particular, numerical simulations on $3$D arrays demonstrate the capability of FIHT on handling large and high-dimensional real data