In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying
The concomitant mechanical deformation and solidification of melts are relevant to a broad range of phenomena. Examples include the preparation of cotton candy, the atomization of metals, the manufacture of glass fibers, and the formation of elongated structures in volcanic eruptions known as Pele’s hair. Usually, solidlike deformations during solidification are neglected as the melt is much more malleable in its initial liquidlike form. Here we demonstrate how elastic deformations in the midst of solidification, i.e., while the melt responds as a very soft solid (
 NSFPAR ID:
 10214686
 Publisher / Repository:
 Proceedings of the National Academy of Sciences
 Date Published:
 Journal Name:
 Proceedings of the National Academy of Sciences
 Volume:
 118
 Issue:
 10
 ISSN:
 00278424
 Page Range / eLocation ID:
 Article No. e2020701118
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract , for any even integer$$K^2 = 4p_g8$$ ${K}^{2}=4{p}_{g}8$ . These surfaces also have unbounded irregularity$$p_g\ge 4$$ ${p}_{g}\ge 4$q . We carry out our study by investigating the deformations of the canonical morphism , where$$\varphi :X\rightarrow {\mathbb {P}}^N$$ $\phi :X\to {P}^{N}$ is a quadruple Galois cover of a smooth surface of minimal degree. These canonical covers are classified in Gallego and Purnaprajna (Trans Am Math Soc 360(10):54895507, 2008) into four distinct families, one of which is the easy case of a product of curves. The main objective of this article is to study the deformations of the other three, non trivial, unbounded families. We show that any deformation of$$\varphi $$ $\phi $ factors through a double cover of a ruled surface and, hence, is never birational. More interestingly, we prove that, with two exceptions, a general deformation of$$\varphi $$ $\phi $ is twotoone onto its image, whose normalization is a ruled surface of appropriate irregularity. We also show that, with the exception of one family, the deformations of$$\varphi $$ $\phi $X are unobstructed even though does not vanish. Consequently,$$H^2(T_X)$$ ${H}^{2}\left({T}_{X}\right)$X belongs to a unique irreducible component of the Gieseker moduli space. These irreducible components are uniruled. As a result of all this, we show the existence of infinitely many moduli spaces, satisfying the strict Beauville inequality , with an irreducible component that has a proper quadruple sublocus where the degree of the canonical morphism jumps up. These components are above the Castelnuovo line, but nonetheless parametrize surfaces with non birational canonical morphisms. The existence of jumping subloci is a contrast with the moduli of surfaces with$$p_g > 2q4$$ ${p}_{g}>2q4$ , studied by Horikawa. Irreducible moduli components with a jumping sublocus also present a similarity and a difference to the moduli of curves of genus$$K^2 = 2p_g 4$$ ${K}^{2}=2{p}_{g}4$ , for, like in the case of curves, the degree of the canonical morphism goes down outside a closed sublocus but, unlike in the case of curves, it is never birational. Finally, our study shows that there are infinitely many moduli spaces with an irreducible component whose general elements have non birational canonical morphism and another irreducible component whose general elements have birational canonical map.$$g\ge 3$$ $g\ge 3$ 
Abstract This paper examined the effect of Si addition on the cracking resistance of Inconel 939 alloy after laser additive manufacturing (AM) process. With the help of CALculation of PHAse Diagrams (CALPHAD) software ThermoCalc, the amounts of specific elements (C, B, and Zr) in liquid phase during solidification, cracking susceptibility coefficients (CSC) and cracking criterion based on
values ($$\left {{\text{d}}T/{\text{d}}f_{{\text{s}}}^{1/2} } \right$$ $\left(\text{d}T/\text{d}{f}_{\text{s}}^{1/2}\right)$T : solidification temperature,f _{s}: mass fraction of solid during solidification) were evaluated as the indicators for composition optimization. It was found that CSC together with values provided a better prediction for cracking resistance.$$\left {{\text{d}}T/{\text{d}}f_{{\text{s}}}^{1/2} } \right$$ $\left(\text{d}T/\text{d}{f}_{\text{s}}^{1/2}\right)$Graphical abstract 
Abstract Using mass–radius composition models, small planets (
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Abstract Microscale inorganic particles (d > 1 µm) have reduced surface area and higher density, making them negatively buoyant in most dipcoating mixtures. Their controlled delivery in hardtoreach places through entrainment is possible but challenging due to the density mismatch between them and the liquid matrix called liquid carrier system (LCS). In this work, the particle transfer mechanism from the complex density mismatching mixture was investigated. The LCS solution was prepared and optimized using a polymer binder and an evaporating solvent. The inorganic particles were dispersed in the LCS by stirring at the just suspending speed to maintain the pseudo suspension characteristics for the heterogeneous mixture. The effect of solid loading and the binder volume fraction on solid transfer has been reported at room temperature. Two coating regimes are observed (i) heterogeneous coating where particle clusters are formed at a low capillary number and (ii) effective viscous regime, where full coverage can be observed on the substrate. ‘Zero’ particle entrainment was not observed even at a low capillary number of the mixture, which can be attributed to the presence of the binder and hydrodynamic flow of the particles due to the stirring of the mixture. The critical film thickness for particle entrainment is
for 6.5% binder and$${h}^{*}=0.16a$$ ${h}^{\ast}=0.16a$ for 10.5% binder, which are smaller than previously reported in literature. Furthermore, the transferred particle matrices closely follow the analytical expression (modified LLD) of density matching suspension which demonstrate that the density mismatch effect can be neutralized with the stirring energy. The findings of this research will help to understand this highvolume solid transfer technique and develop novel manufacturing processes.$${h}^{*}=0.26a$$ ${h}^{\ast}=0.26a$ 
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