Krylov-Veretennikov formula for functionals from the stopped Wiener process

We consider a class of measures absolutely continuous with respect to the distribution of the stopped Wiener process $w(\cdot\wedge\tau)$. Multiple stochastic integrals, that lead to the analogue of the It\^o-Wiener expansions for such measures, are described. An analogue of the Krylov-Veretennikov formula for functionals $f=\varphi(w(\tau))$ is obtained

Edge and Cusp Mesoscopic Eigenvalue Statistics for Wigner-type Matrices

We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics of Wigner-type matrices at the edge and cusp singularities, and the local minima of the limiting spectral density. Subsequently, we identify a continuous one-parameter family of functionals that govern the limiting bias and variance. We show that the variance is equivalent to a suitable weighted $\dot{H}^{1/2}$-norm of the test function. Our analysis entirely covers both transitionary regimes: between the square-root singularity at a regular edge and the cubic-root singularity at a cusp, and between a sharp cusp and a non-zero local minimum in the bulk of the limiting spectral density

The Effects of Morphology and Surface Oxidation of Stainless Steel Powder in Laser Based-Powder Bed Fusion

Laser based-powder bed fusion (LB-PBF) is one of the many techniques within additive manufacturing (AM) that allows for near net shape manufacturing of metallic components. By using powder feedstock, it is possible to spread thin layers of powder and further selectively fuse powder in a repetitive manner until the component is completed. The majority of the powder grades for AM are produced using vacuum induction melting and inert gas atomization (VIGA). The process produces spherical powder with high purity, but at a premium cost. In order to improve the utilization of LB-PBF further, more cost-efficient powder grades must be introduced to the market. This work therefore addresses three grades of 316L stainless steel powder with regard to the surface oxide characteristics and processability in AM, a vacuum induction melted and inert gas atomized (VIGA) grade, an air-melted and nitrogen gas atomized (GA) grade and a water-atomized (WA) grade. The chemical surface characterization revealed that the two gas-atomized powders had comparable oxidation states, with minor differences in particulate coverage between the two grades. Since the GA powder contained more Si, it was found in higher concentrations in the oxide particulates. The WA grade, however, had a larger surface coverage of particulates (rich in Cr and Si), yet had a thinner oxide layer surrounding the particulates compared to the gas atomized grades. However, the particulate features on the WA grade did not seem to affect the printability, as densities of > 99.95% were reached without discernible defects in the microstructure. While the printability was comparable with the GA grade at a layer thickness of 20 \ub5m, the limitation of the WA powder were noticed at a higher layer thicknesses (40 \ub5m), where up to about 1 vol.% of porosity was obtained. Furthermore, LB-PBF processing of WA powder was found to result in a rather homogenous precipitation of nanometric oxide inclusions within the microstructure. Consequently, this work investigated whether the oxide inclusions could contribute to an oxide dispersion strengthening effect. The average size of these oxides was found to be 56 nm, with an average number density of 2.8 7 1015 m-3. The oxides were observed to be amorphous with a characteristic core-shell structure. Concerning the mechanical strength, the WA samples had slightly reduced yield strength (~500 MPa) in comparison to the GA samples (~600 MPa). Hence, no oxide dispersion strengthening effect was observed, as the average size and number density of oxides was not optimized