In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying
The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid’s internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddlesplay arrangements, characterised by the elastic constant
 Award ID(s):
 1654283
 NSFPAR ID:
 10153761
 Publisher / Repository:
 Nature Publishing Group
 Date Published:
 Journal Name:
 Nature Communications
 Volume:
 10
 Issue:
 1
 ISSN:
 20411723
 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 Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultralow Reynolds numbers
. Fluid drag is conceptualized via a critical Reynolds number:$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{}}{\bf{3}}}{\boldsymbol{)}}$$ $\left({10}^{7}\lesssim \mathrm{Re}\lesssim {10}^{3}\right)$ , where$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$ $\mathrm{Re}=\frac{{v}_{0}{x}_{0}}{\nu}$v _{0}corresponds to the maximum wetting speed on a flat, dry surface andx _{0}is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thinfilm region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv _{0}andx _{0}measurements using Water , viscous FC70$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$ $\left({v}_{0}\approx 2\phantom{\rule{0ex}{0ex}}m/s,\phantom{\rule{0ex}{0ex}}25\phantom{\rule{0ex}{0ex}}\mu m\lesssim {x}_{0}\lesssim 28\phantom{\rule{0ex}{0ex}}\mu m\right)$ and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$ $\left({v}_{0}\approx 0.3\phantom{\rule{0ex}{0ex}}m/s,\phantom{\rule{0ex}{0ex}}18.6\phantom{\rule{0ex}{0ex}}\mu m\lesssim {x}_{0}\lesssim 38.6\phantom{\rule{0ex}{0ex}}\mu m\right)$ .$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$ $\left({v}_{0}\approx 1.2\phantom{\rule{0ex}{0ex}}m/s,\phantom{\rule{0ex}{0ex}}11.8\phantom{\rule{0ex}{0ex}}\mu m\lesssim {x}_{0}\lesssim 33.3\phantom{\rule{0ex}{0ex}}\mu m\right)$ 
Abstract Positive
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Abstract We perform pathintegral molecular dynamics (PIMD), ringpolymer MD (RPMD), and classical MD simulations of H
O and D$$_2$$ ${}_{2}$ O using the qTIP4P/F water model over a wide range of temperatures and pressures. The density$$_2$$ ${}_{2}$ , isothermal compressibility$$\rho (T)$$ $\rho \left(T\right)$ , and selfdiffusion coefficients$$\kappa _T(T)$$ ${\kappa}_{T}\left(T\right)$D (T ) of H O and D$$_2$$ ${}_{2}$ O are in excellent agreement with available experimental data; the isobaric heat capacity$$_2$$ ${}_{2}$ obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$C_P(T)$$ ${C}_{P}\left(T\right)$ O and D$$_2$$ ${}_{2}$ O exhibit a liquidliquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$ ${}_{2}$ O and D$$_2$$ ${}_{2}$ O can be fitted remarkably well using the TwoStateEquationofState (TSEOS). Using the TSEOS, we estimate that the LLCP for qTIP4P/F H$$_2$$ ${}_{2}$ O, from PIMD simulations, is located at$$_2$$ ${}_{2}$ MPa,$$P_c = 167 \pm 9$$ ${P}_{c}=167\pm 9$ K, and$$T_c = 159 \pm 6$$ ${T}_{c}=159\pm 6$ g/cm$$\rho _c = 1.02 \pm 0.01$$ ${\rho}_{c}=1.02\pm 0.01$ . Isotope substitution effects are important; the LLCP location in qTIP4P/F D$$^3$$ ${}^{3}$ O is estimated to be$$_2$$ ${}_{2}$ MPa,$$P_c = 176 \pm 4$$ ${P}_{c}=176\pm 4$ K, and$$T_c = 177 \pm 2$$ ${T}_{c}=177\pm 2$ g/cm$$\rho _c = 1.13 \pm 0.01$$ ${\rho}_{c}=1.13\pm 0.01$ . Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of qTIP4P/F water,$$^3$$ ${}^{3}$ MPa,$$P_c = 203 \pm 4$$ ${P}_{c}=203\pm 4$ K, and$$T_c = 175 \pm 2$$ ${T}_{c}=175\pm 2$ g/cm$$\rho _c = 1.03 \pm 0.01$$ ${\rho}_{c}=1.03\pm 0.01$ ). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of$$^3$$ ${}^{3}$ for D$$T_c$$ ${T}_{c}$ O and, particularly, H$$_2$$ ${}_{2}$ O suggest that improved water models are needed for the study of supercooled water.$$_2$$ ${}_{2}$ 
Abstract We present a proof of concept for a spectrally selective thermal midIR source based on nanopatterned graphene (NPG) with a typical mobility of CVDgrown graphene (up to 3000
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