Density control and local regularity

AbstractWe establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4, respectively, obtaining criteria for the smooth local extensibility of these flows. As a corollary, we obtain new characterisations of singularity formation and use this to obtain a local estimate on the Hausdorff measure of the singular sets of these flows at the first singular time. Finally, we show that smooth blow-ups at rapidly forming singularities of these flows are necessarily nontrivial and admit a positive lower bound on their heat ball energies. These results crucially depend on some local monotonicity formulæ for these flows recently established by Ecker (Calc Var Partial Differ Equ 23(1):67–81, 2005) and the Afuni (Calc Var 555(1):1–14, 2016; Adv Calc Var 12(2):135–156, 2019).

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Defect Density Control Using an Intrinsic Layer to Enhance Conversion Efficiency in an Optimized SnS Solar Cell

Journal of Electronic Materials ◽

10.1007/s11664-021-08881-0 ◽

2021 ◽

Author(s):

M. T. Islam ◽

Atul Kumar ◽

A. K. Thakur

Keyword(s):

Solar Cell ◽

Conversion Efficiency ◽

Defect Density ◽

Density Control

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Local Regularity of Weak Solutions to Quasilinear Elliptic Systems with One-Sided Condition on Quadratic Nonlinearity in the Gradient

Journal of Mathematical Sciences ◽

10.1007/s10958-021-05380-9 ◽

2021 ◽

Author(s):

A. A. Arkhipova

Keyword(s):

Weak Solutions ◽

Elliptic Systems ◽

Quadratic Nonlinearity ◽

Local Regularity ◽

Quasilinear Elliptic Systems ◽

Regularity Of Weak Solutions ◽

Quasilinear Elliptic

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Cellular Network Planning via Local Regularity Optimization

2021 IEEE 93rd Vehicular Technology Conference (VTC2021-Spring) ◽

10.1109/vtc2021-spring51267.2021.9448925 ◽

2021 ◽

Author(s):

Mohsen Abedi ◽

Risto Wichman

Keyword(s):

Cellular Network ◽

Network Planning ◽

Local Regularity ◽

Cellular Network Planning

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Optimization of Laser Powder Bed Fusion Processing Using a Combination of Melt Pool Modeling and Design of Experiment Approaches: Density Control

Journal of Manufacturing and Materials Processing ◽

10.3390/jmmp3010021 ◽

2019 ◽

Vol 3 (1) ◽

pp. 21 ◽

Cited By ~ 9

Author(s):

Morgan Letenneur ◽

Alena Kreitcberg ◽

Vladimir Brailovski

Keyword(s):

Scanning Speed ◽

Powder Bed Fusion ◽

Laser Powder Bed Fusion ◽

Powder Bed ◽

Density Prediction ◽

Melt Pool ◽

Density Control ◽

Pool Model ◽

Conventional Material ◽

Prediction Approach

A simplified analytical model of the laser powder bed fusion (LPBF) process was used to develop a novel density prediction approach that can be adapted for any given powder feedstock and LPBF system. First, calibration coupons were built using IN625, Ti64 and Fe powders and a specific LPBF system. These coupons were manufactured using the predetermined ranges of laser power, scanning speed, hatching space, and layer thickness, and their densities were measured using conventional material characterization techniques. Next, a simplified melt pool model was used to calculate the melt pool dimensions for the selected sets of printing parameters. Both sets of data were then combined to predict the density of printed parts. This approach was additionally validated using the literature data on AlSi10Mg and 316L alloys, thus demonstrating that it can reliably be used to optimize the laser powder bed metal fusion process.

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