Microstructural and Mechanical-Property Manipulation through Rapid Dendrite Growth and Undercooling in an Fe-based Multinary Alloy

Rapid dendrite growth in single- or dual-phase multicomponent alloys can be manipulated to improve the mechanical properties of such metallic materials. Rapid growth of (αFe) dendrites was realized in an undercooled Fe-5Ni-5Mo-5Ge-5Co (wt.%) multinary alloy using the glass fluxing method. The relationship between rapid dendrite growth and the micro-/nano-mechanical properties of the alloy was investigated by analyzing the grain refinement and microstructural evolution resulting from the rapid dendrite growth. It was found that (αFe) dendrites grow sluggishly within a low but wide undercooling range. Once the undercooling exceeds 250 K, the dendritic growth velocity increases steeply until reaching a plateau of 31.8 ms[superscript −1]. The increase in the alloy Vickers microhardness with increasing dendritic growth velocity results from the hardening effects of increased grain/phase boundaries due to the grain refinement, the more homogeneous distribution of the second phase along the boundaries, and the more uniform distribution of solutes with increased contents inside the grain, as verified also by nanohardness maps. Once the dendritic growth velocity exceeds ~8 ms[superscript −1], the rate of Vickers microhardness increase slows down significantly with a further increase in dendritic growth velocity, owing to the microstructural transition of the (αFe) phase from a trunk-dendrite to an equiaxed-grain microstructure.Singapore-MIT Allianc

Efficient 3D Face Recognition with Gabor Patched Spectral Regression

In this paper, we utilize a novel framework for 3D face recognition, called 3D Gabor Patched Spectral Regression (3D GPSR), which can overcome some of the continuing challenges encountered with 2D or 3D facial images. In this active field, some obstacles, like expression variations, pose correction and data noise deteriorate the performance significantly. Our proposed system addresses these problems by first extracting the main facial area to remove irrelevant information corresponding to shoulders and necks. Pose correction is used to minimize the influence of large pose variations and then the normalized depth and gray images can be obtained. Due to better time-frequency characteristics and a distinctive biological background, the Gabor feature is extracted on depth images, known as 3D Gabor faces. Data noise is mainly caused by distorted meshes, varieties of subordinates and misalignment. To solve these problems, we introduce a Patched Spectral Regression strategy, which can make good use of the robustness and efficiency of accurate patched discriminant low-dimension features and minimize the effect of noise term. Computational analysis shows that spectral regression is much faster than the traditional approaches. Our experiments are based on the CASIA and FRGC 3D face databases which contain a huge number of challenging data. Experimental results show that our framework consistently outperforms the other existing methods with the distinctive characteristics of efficiency, robustness and generality

ı\imathHall algebra of Jordan quiver and ı\imathHall-Littlewood functions

We show that the $\imath$Hall algebra of the Jordan quiver is a polynomial ring in infinitely many generators and obtain transition relations among several generating sets. We establish a ring isomorphism from this $\imath$Hall algebra to the ring of symmetric functions in two parameters $t, \theta$, which maps the $\imath$Hall basis to a class of (modified) inhomogeneous Hall-Littlewood ($\imath$HL) functions. The (modified) $\imath$HL functions admit a formulation via raising and lowering operators. We formulate and prove Pieri rules for (modified) $\imath$HL functions. The modified $\imath$HL functions specialize at $\theta=0$ to the modified HL functions; they specialize at $\theta=1$ to the deformed universal characters of type C, which further specialize at $(t=0, \theta =1)$ to the universal characters of type C.Comment: v2,41 pages,references adde

Quantum Borcherds-Bozec algebras via semi-derived Ringel-Hall algebras II: braid group actions

Based on the realization of quantum Borcherds-Bozec algebra $\widetilde{\mathbf{U}}$ and quantum generalized Kac-Moody algebra ${}^B\widetilde{\mathbf{U}}$ via semi-derived Ringel-Hall algebra of a quiver with loops, we deduce the braid group actions of $\widetilde{\mathbf{U}}$ introduced by Fan and Tong recently and establish braid group actions for ${}^B\widetilde{\mathbf{U}}$ by applying the BGP reflection functors to semi-derived Ringel-Hall algebras.Comment: 18 pages, minor changes, accepted by Bulletin of the London Mathematical Society. arXiv admin note: substantial text overlap with arXiv:2107.0316