Title: A simple analytic model for predicting the wicking velocity in micropillar arrays

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 ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$$\left({10}^{-7}\lesssim \mathrm{Re}\lesssim {10}^{-3}\right)$. Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$$\mathrm{Re}=\frac{{v}_{0}{x}_{0}}{\nu}$, wherev_{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 thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv_{0}andx_{0}measurements using Water$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$$\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)$, viscous FC-70$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$$\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)$and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$$\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)$.

Vyas, Nikhil; Williams, R. Ryan(
, Theory of Computing Systems)

Abstract

We continue the program of proving circuit lower bounds via circuit satisfiability algorithms. So far, this program has yielded several concrete results, proving that functions in$\mathsf {Quasi}\text {-}\mathsf {NP} = \mathsf {NTIME}[n^{(\log n)^{O(1)}}]$$\mathrm{Quasi}-\mathrm{NP}=\mathrm{NTIME}\left[{n}^{{\left(\mathrm{log}n\right)}^{O\left(1\right)}}\right]$and other complexity classes do not have small circuits (in the worst case and/or on average) from various circuit classes$\mathcal { C}$$C$, by showing that$\mathcal { C}$$C$admits non-trivial satisfiability and/or#SAT algorithms which beat exhaustive search by a minor amount. In this paper, we present a new strong lower bound consequence of having a non-trivial#SAT algorithm for a circuit class${\mathcal C}$$C$. Say that a symmetric Boolean functionf(x_{1},…,x_{n}) issparseif it outputs 1 onO(1) values of${\sum }_{i} x_{i}$${\sum}_{i}{x}_{i}$. We show that for every sparsef, and for all “typical”$\mathcal { C}$$C$, faster#SAT algorithms for$\mathcal { C}$$C$circuits imply lower bounds against the circuit class$f \circ \mathcal { C}$$f\circ C$, which may bestrongerthan$\mathcal { C}$$C$itself. In particular:

#SAT algorithms forn^{k}-size$\mathcal { C}$$C$-circuits running in 2^{n}/n^{k}time (for allk) implyNEXPdoes not have$(f \circ \mathcal { C})$$(f\circ C)$-circuits of polynomial size.

Applying#SAT algorithms from the literature, one immediate corollary of our results is thatQuasi-NPdoes not haveEMAJ∘ACC^{0}∘THRcircuits of polynomialmore »size, whereEMAJis the “exact majority” function, improving previous lower bounds againstACC^{0}[Williams JACM’14] andACC^{0}∘THR[Williams STOC’14], [Murray-Williams STOC’18]. This is the first nontrivial lower bound against such a circuit class.

Masterson, Megan; McDonald, Michael; Ansarinejad, Behzad; Bayliss, Matthew; Benson, Bradford A.; Bleem, Lindsey E.; Calzadilla, Michael S.; Edge, Alastair C.; Floyd, Benjamin; Kim, Keunho J.; et al(
, The Astrophysical Journal)

Abstract

We present a multiwavelength analysis of the galaxy cluster SPT-CL J0607-4448 (SPT0607), which is one of the most distant clusters discovered by the South Pole Telescope atz= 1.4010 ± 0.0028. The high-redshift cluster shows clear signs of being relaxed with well-regulated feedback from the active galactic nucleus (AGN) in the brightest cluster galaxy (BCG). Using Chandra X-ray data, we construct thermodynamic profiles and determine the properties of the intracluster medium. The cool-core nature of the cluster is supported by a centrally peaked density profile and low central entropy (${K}_{0}={18}_{-9}^{+11}$keV cm^{2}), which we estimate assuming an isothermal temperature profile due to the limited spectral information given the distance to the cluster. Using the density profile and gas cooling time inferred from the X-ray data, we find a mass-cooling rate${\stackrel{\u0307}{M}}_{\mathrm{cool}}={100}_{-60}^{+90}\phantom{\rule{0.25em}{0ex}}{M}_{\odot}$yr^{−1}. From optical spectroscopy and photometry around the [Oii] emission line, we estimate that the BCG star formation rate is${\mathrm{SFR}}_{[\mathrm{O}\phantom{\rule{0.25em}{0ex}}\mathrm{II}]}={1.7}_{-0.6}^{+1.0}\phantom{\rule{0.25em}{0ex}}{M}_{\odot}$yr^{−1}, roughly two orders of magnitude lower than the predicted mass-cooling rate. In addition, using ATCA radio data at 2.1 GHz, we measure a radio jet power${P}_{\mathrm{cav}}={3.2}_{-1.3}^{+2.1}\times {10}^{44}$erg s^{−1}, which is consistent withmore »the X-ray cooling luminosity (${L}_{\mathrm{cool}}={1.9}_{-0.5}^{+0.2}\times {10}^{44}$erg s^{−1}withinr_{cool}= 43 kpc). These findings suggest that SPT0607 is a relaxed, cool-core cluster with AGN-regulated cooling at an epoch shortly after cluster formation, implying that the balance between cooling and feedback can be reached quickly. We discuss the implications for these findings on the evolution of AGN feedback in galaxy clusters.

Shabbir, Muhammad Waqas; Leuenberger, Michael N.(
, Scientific Reports)

Abstract

We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000$$\hbox {cm}^2\,\hbox {V}^{-1}\,\hbox {s}^{-1}$$${\text{cm}}^{2}\phantom{\rule{0ex}{0ex}}{\text{V}}^{-1}\phantom{\rule{0ex}{0ex}}{\text{s}}^{-1}$), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of anin-planeelectric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from$$\lambda =3$$$\lambda =3$to 12$$\upmu$$$\mu $m by adjusting the size of and distance between the circular holes in a hexagonal or square lattice structure. Most importantly, the LSPs along with an optical cavity increase the emittance of graphene from about 2.3% for pristine graphene to 80% for NPG, thereby outperforming state-of-the-art pristine graphene light sources operating in the near-infrared by at least a factor of 100. According to our COMSOL calculations, a maximum emission power per area of$$11\times 10^3$$$11\times {10}^{3}$W/$$\hbox {m}^2$$${\text{m}}^{2}$at$$T=2000$$$T=2000$K for a bias voltage of$$V=23$$$V=23$V is achieved by controlling the temperature of the hot electrons through the Joule heating. By generalizing Planck’s theory to any grey body and derivingmore »the completely general nonlocal fluctuation-dissipation theorem with nonlocal response of surface plasmons in the random phase approximation, we show that the coherence length of the graphene plasmons and the thermally emitted photons can be as large as 13$$\upmu$$$\mu $m and 150$$\upmu$$$\mu $m, respectively, providing the opportunity to create phased arrays made of nanoantennas represented by the holes in NPG. The spatial phase variation of the coherence allows for beamsteering of the thermal emission in the range between$$12^\circ$$${12}^{\circ}$and$$80^\circ$$${80}^{\circ}$by tuning the Fermi energy between$$E_F=1.0$$${E}_{F}=1.0$eV and$$E_F=0.25$$${E}_{F}=0.25$eV through the gate voltage. Our analysis of the nonlocal hydrodynamic response leads to the conjecture that the diffusion length and viscosity in graphene are frequency-dependent. Using finite-difference time domain calculations, coupled mode theory, and RPA, we develop the model of a mid-IR light source based on NPG, which will pave the way to graphene-based optical mid-IR communication, mid-IR color displays, mid-IR spectroscopy, and virus detection.

Gburek, Timothy; Siana, Brian; Alavi, Anahita; Emami, Najmeh; Richard, Johan; Freeman, William R.; Stark, Daniel P.; Snapp-Kolas, Christopher(
, The Astrophysical Journal)

Abstract

We present a Keck/MOSFIRE rest-optical composite spectrum of 16 typical gravitationally lensed star-forming dwarf galaxies at 1.7 ≲z≲ 2.6 (z_{mean}= 2.30), all chosen independent of emission-line strength. These galaxies have a median stellar mass of$\mathrm{log}{({M}_{*}/{M}_{\odot})}_{\mathrm{med}}={8.29}_{-0.43}^{+0.51}$and a median star formation rate of${\mathrm{S}\mathrm{F}\mathrm{R}}_{\mathrm{H}\alpha}^{\mathrm{m}\mathrm{e}\mathrm{d}}={2.25}_{-1.26}^{+2.15}\phantom{\rule{0.25em}{0ex}}{M}_{\odot}\phantom{\rule{0.25em}{0ex}}{\mathrm{y}\mathrm{r}}^{-1}$. We measure the faint electron-temperature-sensitive [Oiii]λ4363 emission line at 2.5σ(4.1σ) significance when considering a bootstrapped (statistical-only) uncertainty spectrum. This yields a direct-method oxygen abundance of$12+\mathrm{log}{(\mathrm{O}/\mathrm{H})}_{\mathrm{direct}}={7.88}_{-0.22}^{+0.25}$(${0.15}_{-0.06}^{+0.12}\phantom{\rule{0.33em}{0ex}}{Z}_{\odot}$). We investigate the applicability at highzof locally calibrated oxygen-based strong-line metallicity relations, finding that the local reference calibrations of Bian et al. best reproduce (≲0.12 dex) our composite metallicity at fixed strong-line ratio. At fixedM_{*}, our composite is well represented by thez∼ 2.3 direct-method stellar mass—gas-phase metallicity relation (MZR) of Sanders et al. When comparing to predicted MZRs from the IllustrisTNG and FIRE simulations, having recalculated our stellar masses with more realistic nonparametric star formation histories$(\mathrm{log}{({M}_{*}/{M}_{\odot})}_{\mathrm{med}}={8.92}_{-0.22}^{+0.31})$, we find excellent agreement with the FIRE MZR. Our composite is consistent with no metallicity evolution, atmore »fixedM_{*}and SFR, of the locally defined fundamental metallicity relation. We measure the doublet ratio [Oii]λ3729/[Oii]λ3726 = 1.56 ± 0.32 (1.51 ± 0.12) and a corresponding electron density of${n}_{e}={1}_{-0}^{+215}\phantom{\rule{0.33em}{0ex}}{\mathrm{cm}}^{-3}$(${n}_{e}={1}_{-0}^{+74}\phantom{\rule{0.33em}{0ex}}{\mathrm{cm}}^{-3}$) when considering the bootstrapped (statistical-only) error spectrum. This result suggests that lower-mass galaxies have lower densities than higher-mass galaxies atz∼ 2.

Bazavov, A.; DeTar, C. E.; Du, D.; El-Khadra, A. X.; Gámiz, E.; Gelzer, Z.; Gottlieb, S.; Heller, U. M.; Kronfeld, A. S.; Laiho, J.; et al(
, The European Physical Journal C)

Abstract

We present the first unquenched lattice-QCD calculation of the form factors for the decay$$B\rightarrow D^*\ell \nu $$$B\to {D}^{\ast}\ell \nu $at nonzero recoil. Our analysis includes 15 MILC ensembles with$$N_f=2+1$$${N}_{f}=2+1$flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from$$a\approx 0.15$$$a\approx 0.15$fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valencebandcquarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element$$|V_{cb}|$$$|{V}_{\mathrm{cb}}|$. We obtain$$\left| V_{cb}\right| = (38.40 \pm 0.68_{\text {th}} \pm 0.34_{\text {exp}} \pm 0.18_{\text {EM}})\times 10^{-3}$$$\left({V}_{\mathrm{cb}}\right)=(38.40\pm 0.{68}_{\text{th}}\pm 0.{34}_{\text{exp}}\pm 0.{18}_{\text{EM}})\times {10}^{-3}$. The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall$$\chi ^2\text {/dof} = 126/84$$${\chi}^{2}\text{/dof}=126/84$, which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is inmore »agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict$$R(D^*) = 0.265 \pm 0.013$$$R\left({D}^{\ast}\right)=0.265\pm 0.013$, which confirms the current tension between theory and experiment.

Krishnan, Siva Rama, Bal, John, and Putnam, Shawn A. A simple analytic model for predicting the wicking velocity in micropillar arrays. Scientific Reports 9.1 Web. doi:10.1038/s41598-019-56361-7.

Krishnan, Siva Rama, Bal, John, & Putnam, Shawn A. A simple analytic model for predicting the wicking velocity in micropillar arrays. Scientific Reports, 9 (1). https://doi.org/10.1038/s41598-019-56361-7

@article{osti_10154039,
place = {Country unknown/Code not available},
title = {A simple analytic model for predicting the wicking velocity in micropillar arrays},
url = {https://par.nsf.gov/biblio/10154039},
DOI = {10.1038/s41598-019-56361-7},
abstractNote = {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 ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$(10−7≲Re≲10−3). Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$Re=v0x0ν, wherev0corresponds to the maximum wetting speed on a flat, dry surface andx0is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv0andx0measurements using Water$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v0≈2m/s,25µm≲x0≲28µm), viscous FC-70$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v0≈0.3m/s,18.6µm≲x0≲38.6µm)and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v0≈1.2m/s,11.8µm≲x0≲33.3µm).},
journal = {Scientific Reports},
volume = {9},
number = {1},
publisher = {Nature Publishing Group},
author = {Krishnan, Siva Rama and Bal, John and Putnam, Shawn A.},
}