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Nanoindentation was performed on individual grains of a polycrystalline Mg sample with c-axis declination angles ranging from parallel (0°) to perpendicular (90°) to the c-axis. Hardness was highest at ∼0°, decreased up to ∼55°, and then increased at ∼90° to an intermediate level. At ∼0°, high-density 〈c + a〉 dislocations extended deep into the crystal, contributing to high hardness. At ∼55°, 〈c + a〉 dislocations were confined near the indent, and occasional extension twinning reoriented the crystal to ∼45°, promoting 〈a〉 slip in both matrix and twin, leading to low hardness. At ∼90°, extension twinning reoriented the crystal to ∼0°, inducing texture hardening and intermediate hardness. Despite the complex stress state in nanoindentation, which fundamentally differs from the uniaxial stress in bulk tensile and compression tests, the combined contributions of dislocation and twinning still give rise to measurable hardness anisotropy, suggesting nanoindentation as a high-throughput technique for probing orientation-dependent mechanical behavior in Mg. 

We prove that all 3D steady gradient Ricci solitons are O(2)-symmetric. The O(2)-symmetry is the most universal symmetry in Ricci flows with any type of symmetries. Our theorem is also the first instance of symmetry theorem for Ricci flows that are not rotationally symmetric. We also show that the Bryant soliton is the unique 3D steady gradient Ricci soliton with positive curvature that is asymptotic to a ray. 

In situelectrochemical analysis enables access to metal aquo PCET model complexes which are synthetically elaborated and speciation was determined. 

In 1996, H.-D. Cao constructed a U(n)-invariant steady gradient Kähler-Ricci soliton on Cn and asked whether every steady gradient Kähler-Ricci soliton of positive curvature on Cn is necessarily U(n)-invariant (and hence unique up to scaling). Recently, Apostolov-Cifarelli answered this question in the negative for n=2. Here, we construct a family of U(1)×U(n−1)-invariant, but not U(n)-invariant, complete steady gradient Kähler-Ricci solitons with strictly positive curvature operator on real (1,1)-forms (in particular, with strictly positive sectional curvature) on Cn for n≥3, thereby answering Cao's question in the negative for n≥3. This family of steady Ricci solitons interpolates between Cao's U(n)-invariant steady Kähler-Ricci soliton and the product of the cigar soliton and Cao's U(n−1)-invariant steady Kähler-Ricci soliton. This provides the Kähler analog of the Riemannian flying wings construction of Lai. In the process of the proof, we also demonstrate that the almost diameter rigidity of Pn endowed with the Fubini-Study metric does not hold even if the curvature operator is bounded below by 2 on real (1,1)-forms. 

In this work, we performed in situ nanoindentation in TEM to capture the real-time 〈c + a〉 dislocation and twinning activities in pure Mg during loading and unloading. We demonstrated that the screw component of 〈c + a〉 dislocations glides continuously, while the edge components rapidly become sessile during loading. The twin tip propagation is intermittent, whereas the twin boundary migration is more continuous. During unloading, we observed the elastic strain relaxation causes both 〈c + a〉 dislocation retraction and detwinning. Moreover, we note that the plastic zone comprised of 〈c + a〉 dislocations in Mg is well-defined, which contrasts with the diffused plastic zones observed in face-centered cubic metals under the nanoindentation impressions. Additionally, molecular dynamics simulations were performed to study the formation and evolution of deformation-induced crystallographic defects at the early stages of indentation. We observed that, in addition to 〈a〉 dislocations, the I1 stacking fault bounded with a 〈1/2c+p〉 Frank loop can be generated from the plastic zone ahead of the indenter, and potentially serve as a nucleation source for abundant 〈c + a〉 dislocations observed experimentally. These new findings are anticipated to provide new knowledge on the deformation mechanisms of Mg, which are difficult to obtain through conventional ex situ approaches. These observations may serve as a baseline for simulation work that investigate the dynamics of 〈c + a〉 dislocation slip and twinning in Mg and alloys. 

Precession electron diffraction (PED) is a powerful technique for revealing the crystallographic orientation of samples at the nanoscale. However, the quality of orientation indexing is strongly influenced by the quality of diffraction patterns. In this study, we have developed a novel algorithm called Auto-CLAHE (automatic contrast-limited adaptive histogram equalization), which automatically enhances low-intensity diffraction pattern signals using contrast-limited adaptive histogram equalization (CLAHE). The degree of enhancement is dynamically adjusted based on the overall intensity of the diffraction pattern, with greater enhancement applied to patterns with fewer spots (i.e., away from zone axes) and little or no enhancement applied to patterns with many spots (i.e., at a zone axis). By improving the visibility of low-intensity diffraction spots, Auto-CLAHE significantly improves the template matching between experimentally acquired and simulated diffraction patterns, leading to orientation maps with dramatically higher quality and lower noise. We anticipate that Auto-CLAHE provides an efficient and practical solution for preprocessing PED data, enabling higher-quality crystal orientation mapping to be routinely obtained. 

Abstract. This is a survey on the recent developments on steady gradi- ent Ricci solitons. In any dimension n ≥ 3, we constructed a new family of steady gradient Ricci solitons with positive curvature operator. In dimension three, these solitons are flying wings, as conjectured by Hamilton. We also proved that all 3D steady gradient Ricci solitons are O(2)-symmetric.