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1. Strong optomechanical interactions with long-lived fundamental acoustic waves

   https://doi.org/10.1364/OPTICA.476764  

   Xu, Wendao; Iyer, Arjun; Jin, Lei; Set, Sze Y.; Renninger, William H. (January 2023, Optica)

   Traveling-wave optomechanical interactions, known as Brillouin interactions, have now been established as a powerful and versatile resource for photonic sources, sensors, and radio-frequency processors. However, established Brillouin-based interactions with sufficient interaction strengths involve short phonon lifetimes, which critically limit their performance for applications, including radio-frequency filtering and optomechanical storage devices. Here, we investigate a new paradigm of optomechanical interactions with tightly confined fundamental acoustic modes, which enables the unique and desirable combination of high optomechanical coupling, long phonon lifetimes, tunable phonon frequencies, and single-sideband amplification. Using sensitive four-wave mixing spectroscopy controlling for noise and spatial mode coupling, optomechanical interactions with long $><\#comment/>2\text{µ<\#comment/>}\mathrm{s}$phonon lifetimes and strong $><\#comment/>400{\mathrm{W}}^{-<\#comment/>1}{\mathrm{m}}^{-<\#comment/>1}$coupling are observed in a tapered fiber. In addition, we demonstrate novel phonon self-interference effects resulting from the unique combination of an axially varying device geometry with long phonon lifetimes. A generalized theoretical model, in excellent agreement with experiments, is developed with broad applicability to inhomogeneous optomechanical systems. 

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2. Femtosecond timing synchronization at megahertz repetition rates for an x-ray free-electron laser

   https://doi.org/10.1364/optica.396728  

   Sato, Tokushi; Letrun, Romain; Kirkwood, Henry J; Liu, Jia; Vagovič, Patrik; Mills, Grant; Kim, Yoonhee; Takem, Cedric_M S; Planas, Marc; Emons, Moritz; et al (January 2020, Optica)

   A critical challenge of pump-probe experiments with x-ray free-electron lasers (XFELs) is accurate synchronization of x-ray and optical pulses. At the European XFEL we observed megahertz rate timing jitter of $24.0\pm <\#comment/>12.4\mathrm{f}\mathrm{s}$. 

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3. On the Size of the Singular Set of Minimizing Harmonic Maps

   https://doi.org/10.1090/memo/1519  

   Mazowiecka, Katarzyna; Miśkiewicz, Michał; Schikorra, Armin (October 2024, Memoirs of the American Mathematical Society)

   We consider minimizing harmonic maps $u$from $\mathrm{\Omega <\#comment/>}\subset <\#comment/>{\mathbb{R}}^n$into a closed Riemannian manifold $\mathcal{N}$and prove: 1. an extension to $n\ge <\#comment/>4$of Almgren and Lieb’s linear law. That is, if the fundamental group of the target manifold $\mathcal{N}$is finite, we have\[ ${\mathcal{H}}^{n-<\#comment/>3}(\mathrm{sing}<\#comment/>u)\le <\#comment/>C{\int <\#comment/>}_{\mathrm{\partial <\#comment/>}\mathrm{\Omega <\#comment/>}}|{\mathrm{\nabla <\#comment/>}}_{T}u{|}^{n-<\#comment/>1}\mathrm{d}{\mathcal{H}}^{n-<\#comment/>1};$\]2. an extension of Hardt and Lin’s stability theorem. Namely, assuming that the target manifold is $\mathcal{N}={\mathbb{S}}^2$we obtain that the singular set of $u$is stable under small $W^{1,n-<\#comment/>1}$-perturbations of the boundary data. In dimension $n=3$both results are shown to hold with weaker hypotheses, i.e., only assuming that the trace of our map lies in the fractional space $W^{s,p}$with $s\in <\#comment/>(\frac{1}{2},1]$and $p\in <\#comment/>[2,\mathrm{\infty <\#comment/>})$satisfying $sp\ge <\#comment/>2$. We also discuss sharpness. 

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4. Spectrally simplified approach for leveraging legacy geostationary oceanic observations

   https://doi.org/10.1364/AO.465491  

   Houskeeper, Henry F.; Hooker, Stanford B.; Cavanaugh, Kyle C. (January 2022, Applied Optics)

   The use of multispectral geostationary satellites to study aquatic ecosystems improves the temporal frequency of observations and mitigates cloud obstruction, but no operational capability presently exists for the coastal and inland waters of the United States. The Advanced Baseline Imager (ABI) on the current iteration of the Geostationary Operational Environmental Satellites, termed the $R$Series (GOES-R), however, provides sub-hourly imagery and the opportunity to overcome this deficit and to leverage a large repository of existing GOES-R aquatic observations. The fulfillment of this opportunity is assessed herein using a spectrally simplified, two-channel aquatic algorithm consistent with ABI wave bands to estimate the diffuse attenuation coefficient for photosynthetically available radiation, $K_d\left(\mathrm{P}\mathrm{A}\mathrm{R}\right)$. First, anin situABI dataset was synthesized using a globally representative dataset of above- and in-water radiometric data products. Values of $K_d\left(\mathrm{P}\mathrm{A}\mathrm{R}\right)$were estimated by fitting the ratio of the shortest and longest visible wave bands from thein situABI dataset to coincident,in situ $K_d\left(\mathrm{P}\mathrm{A}\mathrm{R}\right)$data products. The algorithm was evaluated based on an iterative cross-validation analysis in which 80% of the dataset was randomly partitioned for fitting and the remaining 20% was used for validation. The iteration producing the median coefficient of determination ( $R^2$) value (0.88) resulted in a root mean square difference of $0.319{\mathrm{m}}^{-<\#comment/>1}$, or 8.5% of the range in the validation dataset. Second, coincident mid-day images of central and southern California from ABI and from the Moderate Resolution Imaging Spectroradiometer (MODIS) were compared using Google Earth Engine (GEE). GEE default ABI reflectance values were adjusted based on a near infrared signal. Matchups between the ABI and MODIS imagery indicated similar spatial variability ( $R^2=0.60$) between ABI adjusted blue-to-red reflectance ratio values and MODIS default diffuse attenuation coefficient for spectral downward irradiance at 490 nm, $K_d\left(490\right)$, values. This work demonstrates that if an operational capability to provide ABI aquatic data products was realized, the spectral configuration of ABI would potentially support a sub-hourly, visible aquatic data product that is applicable to water-mass tracing and physical oceanography research. 

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5. Algebraic cobordism and a Conner–Floyd isomorphism for algebraic K-theory

   https://doi.org/10.1090/jams/1045  

   Annala, Toni; Hoyois, Marc; Iwasa, Ryomei (March 2024, Journal of the American Mathematical Society)

   We formulate and prove a Conner–Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable $\mathrm{\infty <\#comment/>}$-category of non- ${\mathbb{A}}^1$-invariant motivic spectra, which turns out to be equivalent to the $\mathrm{\infty <\#comment/>}$-category of fundamental motivic spectra satisfying elementary blowup excision, previously introduced by the first and third authors. We prove that this $\mathrm{\infty <\#comment/>}$-category satisfies ${\mathbb{P}}^1$-homotopy invariance and weighted ${\mathbb{A}}^1$-homotopy invariance, which we use in place of ${\mathbb{A}}^1$-homotopy invariance to obtain analogues of several key results from ${\mathbb{A}}^1$-homotopy theory. These allow us in particular to define a universal oriented motivic ${\mathbb{E}}_{\mathrm{\infty <\#comment/>}}$-ring spectrum $\mathrm{M}\mathrm{G}\mathrm{L}$. We then prove that the algebraic K-theory of a qcqs derived scheme $X$can be recovered from its $\mathrm{M}\mathrm{G}\mathrm{L}$-cohomology via a Conner–Floyd isomorphism\[ ${\mathrm{M}\mathrm{G}\mathrm{L}}^{\ast <\#comment/>\ast <\#comment/>}\left(X\right){\otimes <\#comment/>}_{\mathrm{L}}\mathbb{Z}\left[{\mathrm{\beta <\#comment/>}}^{\pm <\#comment/>1}\right]\simeq <\#comment/>\mathrm{K}{}^{\ast <\#comment/>\ast <\#comment/>}\left(X\right),$\]where $\mathrm{L}$is the Lazard ring and $\mathrm{K}{}^{p,q}\left(X\right)=\mathrm{K}{}_{2q-<\#comment/>p}\left(X\right)$. Finally, we prove a Snaith theorem for the periodized version of $\mathrm{M}\mathrm{G}\mathrm{L}$. 

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