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1. Steady Rayleigh–Bénard convection between no-slip boundaries

   https://doi.org/10.1017/jfm.2021.1042  

   Wen, Baole; Goluskin, David; Doering, Charles R. (February 2022, Journal of Fluid Mechanics)

   The central open question about Rayleigh–Bénard convection – buoyancy-driven flow in a fluid layer heated from below and cooled from above – is how vertical heat flux depends on the imposed temperature gradient in the strongly nonlinear regime where the flows are typically turbulent. The quantitative challenge is to determine how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ in the $$Ra\to \infty$$ limit for fluids of fixed finite Prandtl number $Pr$ in fixed spatial domains. Laboratory experiments, numerical simulations and analysis of Rayleigh's mathematical model have yet to rule out either of the proposed ‘classical’ $$Nu \sim Ra^{1/3}$$ or ‘ultimate’ $$Nu \sim Ra^{1/2}$$ asymptotic scaling theories. Among the many solutions of the equations of motion at high $Ra$ are steady convection rolls that are dynamically unstable but share features of the turbulent attractor. We have computed these steady solutions for $Ra$ up to $$10^{14}$$ with $Pr=1$ and various horizontal periods. By choosing the horizontal period of these rolls at each $Ra$ to maximize $Nu$ , we find that steady convection rolls achieve classical asymptotic scaling. Moreover, they transport more heat than turbulent convection in experiments or simulations at comparable parameters. If heat transport in turbulent convection continues to be dominated by heat transport in steady rolls as $$Ra\to \infty$$ , it cannot achieve the ultimate scaling. 

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2. Measurements of branching fractions and asymmetry parameters of $$ {\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0} $$, $$ {\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0} $$, and $$ {\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -} $$ decays at Belle

   https://doi.org/10.1007/JHEP06(2021)160  

   Jia, S.; Tang, S. S.; Shen, C. P.; Adachi, I.; Aihara, H.; Al Said, S.; Asner, D. M.; Aulchenko, V.; Aushev, T.; Ayad, R.; et al (June 2021, Journal of High Energy Physics)

   A bstract Using a data sample of 980 fb − 1 collected with the Belle detector at the KEKB asymmetric-energy e + e − collider, we study the processes of $$ {\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0} $$ Ξ c 0 → Λ K ¯ ∗ 0 , $$ {\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0} $$ Ξ c 0 → Σ 0 K ¯ ∗ 0 , and $$ {\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -} $$ Ξ c 0 → Σ + K ∗ − for the first time. The relative branching ratios to the normalization mode of $$ {\Xi}_c^0\to {\Xi}^{-}{\pi}^{+} $$ Ξ c 0 → Ξ − π + are measured to be $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.18\pm 0.02\left(\mathrm{stat}.\right)\pm 0.01\left(\mathrm{syst}.\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.69\pm 0.03\left(\mathrm{stat}.\right)\pm 0.03\left(\mathrm{syst}.\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.34\pm 0.06\left(\mathrm{stat}.\right)\pm 0.02\left(\mathrm{syst}.\right),\end{array}} $$ B Ξ c 0 → Λ K ¯ ∗ 0 / B Ξ c 0 → Ξ − π + = 0.18 ± 0.02 stat . ± 0.01 syst . , B Ξ c 0 → Σ 0 K ¯ ∗ 0 / B Ξ c 0 → Ξ − π + = 0.69 ± 0.03 stat . ± 0.03 syst . , B Ξ c 0 → Σ + K ∗ − / B Ξ c 0 → Ξ − π + = 0.34 ± 0.06 stat . ± 0.02 syst . , where the uncertainties are statistical and systematic, respectively. We obtain $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0}\right)=\left(3.3\pm 0.3\left(\mathrm{stat}.\right)\pm 0.2\left(\mathrm{syst}.\right)\pm 1.0\left(\mathrm{ref}.\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^0{\overline{K}}^{\ast 0}\right)=\left(12.4\pm 0.5\left(\mathrm{stat}.\right)\pm 0.5\left(\mathrm{syst}.\right)\pm 3.6\left(\mathrm{ref}.\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast 0}\right)=\left(6.1\pm 1.0\left(\mathrm{stat}.\right)\pm 0.4\left(\mathrm{syst}.\right)\pm 1.8\left(\mathrm{ref}.\right)\right)\times {10}^{-3},\end{array}} $$ B Ξ c 0 → Λ K ¯ ∗ 0 = 3.3 ± 0.3 stat . ± 0.2 syst . ± 1.0 ref . × 10 − 3 , B Ξ c 0 → Σ 0 K ¯ ∗ 0 = 12.4 ± 0.5 stat . ± 0.5 syst . ± 3.6 ref . × 10 − 3 , B Ξ c 0 → Σ + K ∗ 0 = 6.1 ± 1.0 stat . ± 0.4 syst . ± 1.8 ref . × 10 − 3 , where the uncertainties are statistical, systematic, and from $$ \mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right) $$ B Ξ c 0 → Ξ − π + , respectively. The asymmetry parameters $$ \alpha \left({\Xi}_c^0\to \Lambda {\overline{K}}^{\ast 0}\right) $$ α Ξ c 0 → Λ K ¯ ∗ 0 and $$ \alpha \left({\Xi}_c^0\to {\Sigma}^{+}{K}^{\ast -}\right) $$ α Ξ c 0 → Σ + K ∗ − are 0 . 15 ± 0 . 22(stat . ) ± 0 . 04(syst . ) and − 0 . 52 ± 0 . 30(stat . ) ± 0 . 02(syst . ), respectively, where the uncertainties are statistical followed by systematic. 

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3. Steady Rayleigh–Bénard convection between stress-free boundaries

   https://doi.org/10.1017/jfm.2020.812  

   Wen, Baole; Goluskin, David; LeDuc, Matthew; Chini, Gregory P.; Doering, Charles R. (December 2020, Journal of Fluid Mechanics)

   null (Ed.)

   Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios $${\rm \pi} /5\leqslant \varGamma \leqslant 4{\rm \pi}$$ , where $$\varGamma$$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $$10^3\leqslant Ra\leqslant 10^{11}$$ , and four orders of magnitude in the Prandtl number, $$10^{-2}\leqslant Pr\leqslant 10^2$$ . At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $$Ra \rightarrow \infty$$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $$Ra^{1/3}$$ uniformly in $Pr$ . The prefactor of this scaling depends on $$\varGamma$$ and is largest at $$\varGamma \approx 1.9$$ . The Reynolds number $Re$ for large- $Ra$ rolls scales as $$Pr^{-1} Ra^{2/3}$$ with a prefactor that is largest at $$\varGamma \approx 4.5$$ . All of these large- $Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox ( Phys. Fluids , vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $$\varGamma$$ is smaller. 

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4. Asymptotics of the eigenmodes and stability of an elastic structure with general feedback matrix

   https://doi.org/10.1093/imamat/hxz019  

   Shubov, Marianna A; Kindrat, Laszlo P (October 2019, IMA Journal of Applied Mathematics)

   Abstract The distribution of natural frequencies of the Euler–Bernoulli beam subject to fully non-dissipative boundary conditions is investigated. The beam is clamped at the left end and equipped with a 4-parameter ($$\alpha ,\beta ,k_1,k_2$$) linear boundary feedback law at the right end. The $$2 \times 2$$ boundary feedback matrix relates the control input (a vector of velocity and its spatial derivative at the right end), to the output (a vector of shear and moment at the right end). The initial boundary value problem describing the dynamics of the beam has been reduced to the first order in time evolution equation in the state Hilbert space equipped with the energy norm. The dynamics generator has a purely discrete spectrum (the vibrational modes) denoted by $$\{\nu _n\}_{n\in \mathbb {Z}^{\prime}}$$. The role of the control parameters is examined and the following results have been proven: (i) when $$\beta \neq 0$$, the set of vibrational modes is asymptotically close to the vertical line on the complex $$\nu$$-plane given by the equation $$\Re \nu = \alpha + (1-k_1k_2)/\beta$$; (ii) when $$\beta = 0$$ and the parameter $$K = (1-k_1 k_2)/(k_1+k_2)$$ is such that $$\left |K\right |\neq 1$$ then the following relations are valid: $$\Re (\nu _n/n) = O\left (1\right )$$ and $$\Im (\nu _n/n^2) = O\left (1\right )$$ as $$\left |n\right |\to \infty$$; (iii) when $$\beta =0$$, $|K| = 1$, and $$\alpha = 0$$, then the following relations are valid: $$\Re (\nu _n/n^2) = O\left (1\right )$$ and $$\Im (\nu _n/n) = O\left (1\right )$$ as $$\left |n\right |\to \infty$$; (iv) when $$\beta =0$$, $|K| = 1$, and $$\alpha>0$$, then the following relations are valid: $$\Re (\nu _n/\ln \left |n\right |) = O\left (1\right )$$ and $$\Im (\nu _n/n^2) = O\left (1\right )$$ as $$\left |n\right |\to \infty$$. 

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5. Measurement of the very rare K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ decay

   https://doi.org/10.1007/JHEP06(2021)093  

   Cortina Gil, E.; Kleimenova, A.; Minucci, E.; Padolski, S.; Petrov, P.; Shaikhiev, A.; Volpe, R.; Numao, T.; Petrov, Y.; Velghe, B.; et al (June 2021, Journal of High Energy Physics)

   A bstract The NA62 experiment reports the branching ratio measurement $$ \mathrm{BR}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right)=\left({10.6}_{-3.4}^{+4.0}\left|{}_{\mathrm{stat}}\right.\pm {0.9}_{\mathrm{syst}}\right)\times {10}^{-11} $$ BR K + → π + ν ν ¯ = 10.6 − 3.4 + 4.0 stat ± 0.9 syst × 10 − 11 at 68% CL, based on the observation of 20 signal candidates with an expected background of 7.0 events from the total data sample collected at the CERN SPS during 2016–2018. This provides evidence for the very rare K + → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ decay, observed with a significance of 3.4 σ . The experiment achieves a single event sensitivity of (0 . 839 ± 0 . 054) × 10 − 11 , corresponding to 10.0 events assuming the Standard Model branching ratio of (8 . 4 ± 1 . 0) × 10 − 11 . This measurement is also used to set limits on BR( K + → π + X ), where X is a scalar or pseudo-scalar particle. Details are given of the analysis of the 2018 data sample, which corresponds to about 80% of the total data sample. 

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