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1. Steady Radiating Gravity waves: An Exponential Asymptotics Approach

   https://doi.org/10.1007/s42286-023-00081-z  

   Kataoka, Takeshi ; Akylas, T. R. ( January 2024 , Water Waves)

   The radiation of steady surface gravity waves by a uniform stream$$U_{0}$$$U_0$over locally confined (width$$L$$$L$) smooth topography is analyzed based on potential flow theory. The linear solution to this classical problem is readily found by Fourier transforms, and the nonlinear response has been studied extensively by numerical methods. Here, an asymptotic analysis is made for subcritical flow$$D/\lambda > 1$$$D/\lambda >1$in the low-Froude-number ($$F^{2} \equiv \lambda /L \ll 1$$$F^2\equiv \lambda /L\ll 1$) limit, where$$\lambda = U_{0}^{2} /g$$$\lambda =U_0^2/g$is the lengthscale of radiating gravity waves and$$D$$$D$is the uniform water depth. In this regime, the downstream wave amplitude, although formally exponentially small with respect to$$F$$$F$, is determined by a fully nonlinear mechanism even for small topography amplitude. It is argued that this mechanism controls the wave response for a broad range of flow conditions, in contrast to linear theory which has very limited validity.

    

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2. Evaporation-controlled dripping-onto-substrate (DoS) extensional rheology of viscoelastic polymer solutions

   https://doi.org/10.1038/s41598-022-08448-x  

   Robertson, Benjamin P. ; Calabrese, Michelle A. ( March 2022 , Scientific Reports)

   Extensional flow properties of polymer solutions in volatile solvents govern many industrially-relevant coating processes, but existing instrumentation lacks the environment necessary to control evaporation. To mitigate evaporation during dripping-onto-substrate (DoS) extensional rheology measurements, we developed a chamber to enclose the sample in an environment saturated with solvent vapor. We validated the evaporation-controlled DoS device by measuring a model high molecular weight polyethylene oxide (PEO) in various organic solvents both inside and outside of the chamber. Evaporation substantially increased the extensional relaxation time$$\lambda _{E}$$${\lambda }_E$for PEO in volatile solvents like dichloromethane and chloroform. PEO/chloroform solutions displayed an over 20-fold increase in$$\lambda _{E}$$${\lambda }_E$due to the formation of an evaporation-induced surface film; evaporation studies confirmed surface features and skin formation reminiscent of buckling instabilities commonly observed in drying polymer solutions. Finally, the relaxation times of semi-dilute PEO/chloroform solutions were measured with environmental control, where$$\lambda _{E}$$${\lambda }_E$scaled with concentration by the exponent$$m=0.62$$$m=0.62$. These measurements validate the evaporation-controlled DoS environment, and confirm that chloroform is a good solvent for PEO, with a Flory exponent of$$\nu =0.54$$$\nu =0.54$. Our results are the first to control evaporation during DoS extensional rheology, and provide guidelines establishing when environmental control is necessary to obtain accurate rheological parameters.

    

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3. Sparse representation of vectors in lattices and semigroups

   https://doi.org/10.1007/s10107-021-01657-8  

   Aliev, Iskander ; Averkov, Gennadiy ; De Loera, Jesús A. ; Oertel, Timm ( May 2021 , Mathematical Programming)

   We study the sparsity of the solutions to systems of linear Diophantine equations with and without non-negativity constraints. The sparsity of a solution vector is the number of its nonzero entries, which is referred to as the$$\ell _0$$${\ell }_0$-norm of the vector. Our main results are new improved bounds on the minimal$$\ell _0$$${\ell }_0$-norm of solutions to systems$$A\varvec{x}=\varvec{b}$$$Ax=b$, where$$A\in \mathbb {Z}^{m\times n}$$$A\in Z^{m\times n}$,$${\varvec{b}}\in \mathbb {Z}^m$$$b\in Z^m$and$$\varvec{x}$$$x$is either a general integer vector (lattice case) or a non-negative integer vector (semigroup case). In certain cases, we give polynomial time algorithms for computing solutions with$$\ell _0$$${\ell }_0$-norm satisfying the obtained bounds. We show that our bounds are tight. Our bounds can be seen as functions naturally generalizing the rank of a matrix over$$\mathbb {R}$$$R$, to other subdomains such as$$\mathbb {Z}$$$Z$. We show that these new rank-like functions are all NP-hard to compute in general, but polynomial-time computable for fixed number of variables.

    

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4. Plasmonically enhanced mid-IR light source based on tunable spectrally and directionally selective thermal emission from nanopatterned graphene

   https://doi.org/10.1038/s41598-020-73582-3  

   Shabbir, Muhammad Waqas ; Leuenberger, Michael N. ( October 2020 , Scientific Reports)

   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{\text{V}}^{-1}{\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 deriving 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.

    

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5. Borexino’s search for low-energy neutrinos associated with gravitational wave events from GWTC-3 database: Borexino Collaboration

   https://doi.org/10.1140/epjc/s10052-023-11688-4  

   Basilico, D. ; Bellini, G. ; Benziger, J. ; Biondi, R. ; Caccianiga, B. ; Calaprice, F. ; Caminata, A. ; Chepurnov, A. ; D’Angelo, D. ; Derbin, A. ; et al ( June 2023 , The European Physical Journal C)

   The search for neutrino events in correlation with gravitational wave (GW) events for three observing runs (O1, O2 and O3) from 09/2015 to 03/2020 has been performed using the Borexino data-set of the same period. We have searched for signals of neutrino-electron scattering and inverse beta-decay (IBD) within a time window of$$\pm \, 1000$$$\pm 1000$ s centered at the detection moment of a particular GW event. The search was done with three visible energy thresholds of 0.25, 0.8 and 3.0 MeV. Two types of incoming neutrino spectra were considered: the mono-energetic line and the supernova-like spectrum. GW candidates originated by merging binaries of black holes (BHBH), neutron stars (NSNS) and neutron star and black hole (NSBH) were analyzed separately. Additionally, the subset of most intensive BHBH mergers at closer distances and with larger radiative mass than the rest was considered. In total, follow-ups of 74 out of 93 gravitational waves reported in the GWTC-3 catalog were analyzed and no statistically significant excess over the background was observed. As a result, the strongest upper limits on GW-associated neutrino and antineutrino fluences for all flavors ($$\nu _e, \nu _\mu , \nu _\tau $$${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$) at the level$$10^9{-}10^{15}~\textrm{cm}^{-2}\,\textrm{GW}^{-1}$$${10}^9-{10}^{15}{\text{cm}}^{-2}{\text{GW}}^{-1}$have been obtained in the 0.5–5 MeV neutrino energy range.

    

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