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1. Cosmetic operations and Khovanov multicurves

   https://doi.org/10.1007/s00208-023-02697-5  

   Kotelskiy, Artem; Lidman, Tye; Moore, Allison_H; Watson, Liam; Zibrowius, Claudius (September 2023, Mathematische Annalen)

   Abstract We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants$${\widetilde{{{\,\textrm{Kh}\,}}}}$$ $\widetilde{\text{Kh}}$and$${\widetilde{{{\,\textrm{BN}\,}}}}$$ $\widetilde{\text{BN}}$. We apply the same techniques to reprove a result of Wang about the Cosmetic Crossing Conjecture and split links. Along the way, we show that$${\widetilde{{{\,\textrm{Kh}\,}}}}$$ $\widetilde{\text{Kh}}$and$${\widetilde{{{\,\textrm{BN}\,}}}}$$ $\widetilde{\text{BN}}$detect if a Conway tangle is split. 

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2. Observation of momentum-dependent charge density wave gap in a layered antiferromagnet GdTe3

   https://doi.org/10.1038/s41598-023-44851-8  

   Regmi, Sabin; Bin Elius, Iftakhar; Sakhya, Anup Pradhan; Jeff, Dylan; Sprague, Milo; Mondal, Mazharul Islam; Jarrett, Damani; Valadez, Nathan; Agosto, Alexis; Romanova, Tetiana; et al (December 2023, Scientific Reports)

   Abstract Charge density wave (CDW) ordering has been an important topic of study for a long time owing to its connection with other exotic phases such as superconductivity and magnetism. The$$R{\textrm{Te}}_{3}$$ $R{\text{Te}}_3$(R= rare-earth elements) family of materials provides a fertile ground to study the dynamics of CDW in van der Waals layered materials, and the presence of magnetism in these materials allows to explore the interplay among CDW and long range magnetic ordering. Here, we have carried out a high-resolution angle-resolved photoemission spectroscopy (ARPES) study of a CDW material$${\textrm{Gd}}{\textrm{Te}}_{3}$$ $\text{Gd}{\text{Te}}_3$, which is antiferromagnetic below$$\sim \mathrm {12~K}$$ $\sim 12K$, along with thermodynamic, electrical transport, magnetic, and Raman measurements. Our ARPES data show a two-fold symmetric Fermi surface with both gapped and ungapped regions indicative of the partial nesting. The gap is momentum dependent, maximum along$${\overline{\Gamma }}-\mathrm{\overline{Z}}$$ $\overline{\Gamma }-\overline{Z}$and gradually decreases going towards$${\overline{\Gamma }}-\mathrm{\overline{X}}$$ $\overline{\Gamma }-\overline{X}$. Our study provides a platform to study the dynamics of CDW and its interaction with other physical orders in two- and three-dimensions. 

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3. Uniform stabilization in Besov spaces with arbitrary decay rates of the magnetohydrodynamic system by finite-dimensional interior localized static feedback controllers

   https://doi.org/10.1007/s40687-024-00490-7  

   Lasiecka, Irena; Priyasad, Buddhika; Triggiani, Roberto (December 2024, Research in the Mathematical Sciences)

   Abstract We consider thed-dimensional MagnetoHydroDynamics (MHD) system defined on a sufficiently smooth bounded domain,$$d = 2,3$$ $d=2,3$with homogeneous boundary conditions, and subject to external sources assumed to cause instability. The initial conditions for both fluid and magnetic equations are taken of low regularity. We then seek to uniformly stabilize such MHD system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of explicitly constructed, static, feedback controls, which are localized on an arbitrarily small interior subdomain. In additional, they will be minimal in number. The resulting space of well-posedness and stabilization is a suitable product space$$\displaystyle \widetilde{\textbf{B}}^{2- ^{2}\!/_{p}}_{q,p}(\Omega )\times \widetilde{\textbf{B}}^{2- ^{2}\!/_{p}}_{q,p}(\Omega ), \, 1< p < \frac{2q}{2q-1}, \, q > d,$$ ${\tilde{B}}_{q,p}^{2{-}^2{/}_p}\left(\Omega \right)\times {\tilde{B}}_{q,p}^{2{-}^2{/}_p}\left(\Omega \right),1<p<\frac{2q}{2q-1},q>d,$of tight Besov spaces for the fluid velocity component and the magnetic field component (each “close” to$$\textbf{L}^3(\Omega )$$ $L^3\left(\Omega \right)$for$$d = 3$$ $d=3$). Showing maximal$$L^p$$ $L^p$-regularity up to$$T = \infty $$ $T=\infty$for the feedback stabilized linear system is critical for the analysis of well-posedness and stabilization of the feedback nonlinear problem. 

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4. A search for top-squark pair production, in final states containing a top quark, a charm quark and missing transverse momentum, using the 139 fb−1 of pp collision data collected by the ATLAS detector

   https://doi.org/10.1007/JHEP07(2024)250  

   Aad, G; Abbott, B; Abeling, K; Abicht, N J; Abidi, S H; Aboulhorma, A; Abramowicz, H; Abreu, H; Abulaiti, Y; Acharya, B S; et al (July 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> This paper presents a search for top-squark pair production in final states with a top quark, a charm quark and missing transverse momentum. The data were collected with the ATLAS detector during LHC Run 2 and correspond to an integrated luminosity of 139 fb⁻¹of proton-proton collisions at a centre-of-mass energy of$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV. The analysis is motivated by an extended Minimal Supersymmetric Standard Model featuring a non-minimal flavour violation in the second- and third-generation squark sector. The top squark in this model has two possible decay modes, either$$ {\tilde{t}}_1\to c{\overset{\sim }{\chi}}_1^0 $$ ${\tilde{t}}_1\to c{\tilde{\chi }}_1^0$or$$ {\tilde{t}}_1\to t{\overset{\sim }{\chi}}_1^0 $$ ${\tilde{t}}_1\to t{\tilde{\chi }}_1^0$, where the$$ {\overset{\sim }{\chi}}_1^0 $$ ${\tilde{\chi }}_1^0$is undetected. The analysis is optimised assuming that both of the decay modes are equally probable, leading to the most likely final state of$$ tc+{E}_T^{\textrm{miss}} $$ $\mathrm{tc}+E_T^{\text{miss}}$. Good agreement is found between the Standard Model expectation and the data in the search regions. Exclusion limits at 95% CL are obtained in the$$ m\left({\tilde{t}}_1\right) $$ $m\left({\tilde{t}}_1\right)$vs.$$ m\left({\overset{\sim }{\chi}}_1^0\right) $$ $m\left({\tilde{\chi }}_1^0\right)$plane and, in addition, limits on the branching ratio of the$$ {\tilde{t}}_1\to t{\overset{\sim }{\chi}}_1^0 $$ ${\tilde{t}}_1\to t{\tilde{\chi }}_1^0$decay as a function ofm($$ {\tilde{t}}_1 $$ ${\tilde{t}}_1$) are also produced. Top-squark masses of up to 800 GeV are excluded for scenarios with light neutralinos, and top-squark masses up to 600 GeV are excluded in scenarios where the neutralino and the top squark are almost mass degenerate. 

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5. Length and Velocity Scales in Protoplanetary Disk Turbulence

   https://doi.org/10.3847/1538-4357/ad2c89  

   Sengupta, Debanjan; Cuzzi, Jeffrey N; Umurhan, Orkan M; Lyra, Wladimir (April 2024, The Astrophysical Journal)

   Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, Ω_L, is the local Keplerian frequency Ω_K. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by $\sqrt{\alpha }H$and $\sqrt{\alpha }c$, in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where Ω_L≥ Ω_Kand show that, under these conditions, the characteristic length and velocity scales are respectively $\sqrt{\alpha /R\prime }H$and $\sqrt{\alpha R\prime }c$, where $R\prime \equiv {\mathrm{\Omega }}_L/{\mathrm{\Omega }}_K$is twice the Rossby number. It follows that $\alpha =\tilde{\alpha }/R\prime$, where $\sqrt{\tilde{\alpha }}c$is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For $R\prime >1$, the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation. 

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