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1. 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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2. Measurement of off-shell Higgs boson production in the $H^{\ast }\to ZZ\to 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV pp collisions with the ATLAS detector

   https://doi.org/10.1088/1361-6633/adcd9a  

   The_ATLAS_Collaboration (May 2025, Reports on Progress in Physics)

   Abstract A measurement of off-shell Higgs boson production in the $H^{\ast }\to ZZ\to 4\ell$decay channel is presented. The measurement uses 140 fb⁻¹of proton–proton collisions at $\sqrt{s}=13$TeV collected by the ATLAS detector at the Large Hadron Collider and supersedes the previous result in this decay channel using the same dataset. The data analysis is performed using a neural simulation-based inference method, which builds per-event likelihood ratios using neural networks. The observed (expected) off-shell Higgs boson production signal strength in the $ZZ\to 4\ell$decay channel at 68% CL is ${0.87}_{-0.54}^{+0.75}$( ${1.00}_{-0.95}^{+1.04}$). The evidence for off-shell Higgs boson production using the $ZZ\to 4\ell$decay channel has an observed (expected) significance of 2.5σ(1.3σ). The expected result represents a significant improvement relative to that of the previous analysis of the same dataset, which obtained an expected significance of 0.5σ. When combined with the most recent ATLAS measurement in the $ZZ\to 2\ell 2\nu$decay channel, the evidence for off-shell Higgs boson production has an observed (expected) significance of 3.7σ(2.4σ). The off-shell measurements are combined with the measurement of on-shell Higgs boson production to obtain constraints on the Higgs boson total width. The observed (expected) value of the Higgs boson width at 68% CL is ${4.3}_{-1.9}^{+2.7}$( ${4.1}_{-3.4}^{+3.5}$) MeV. 

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3. On a Traveling Salesman Problem for Points in the Unit Cube

   https://doi.org/10.1007/s00453-024-01257-w  

   Balogh, József; Clemen, Felix Christian; Dumitrescu, Adrian (September 2024, Algorithmica)

   Abstract LetXbe ann-element point set in thek-dimensional unit cube$$[0,1]^k$$ ${[0,1]}^k$where$$k \ge 2$$ $k\ge 2$. According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour)$$x_1, x_2, \ldots , x_n$$ $x_1,x_2,\dots ,x_n$through thenpoints, such that$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} \le c_k$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}\le c_k$, where$$|x-y|$$ $|x-y|$is the Euclidean distance betweenxandy, and$$c_k$$ $c_k$is an absolute constant that depends only onk, where$$x_{n+1} \equiv x_1$$ $x_{n+1}\equiv x_1$. From the other direction, for every$$k \ge 2$$ $k\ge 2$and$$n \ge 2$$ $n\ge 2$, there existnpoints in$$[0,1]^k$$ ${[0,1]}^k$, such that their shortest tour satisfies$$\left( \sum _{i=1}^n |x_i - x_{i+1}|^k \right) ^{1/k} = 2^{1/k} \cdot \sqrt{k}$$ ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^k\right)}^{1/k}=2^{1/k}·\sqrt{k}$. For the plane, the best constant is$$c_2=2$$ $c_2=2$and this is the only exact value known. Bollobás and Meir showed that one can take$$c_k = 9 \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=9{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$for every$$k \ge 3$$ $k\ge 3$and conjectured that the best constant is$$c_k = 2^{1/k} \cdot \sqrt{k}$$ $c_k=2^{1/k}·\sqrt{k}$, for every$$k \ge 2$$ $k\ge 2$. Here we significantly improve the upper bound and show that one can take$$c_k = 3 \sqrt{5} \left( \frac{2}{3} \right) ^{1/k} \cdot \sqrt{k}$$ $c_k=3\sqrt{5}{\left(\frac{2}{3}\right)}^{1/k}·\sqrt{k}$or$$c_k = 2.91 \sqrt{k} \ (1+o_k(1))$$ $c_k=2.91\sqrt{k}(1+o_k\left(1\right))$. Our bounds are constructive. We also show that$$c_3 \ge 2^{7/6}$$ $c_3\ge 2^{7/6}$, which disproves the conjecture for$$k=3$$ $k=3$. Connections to matching problems, power assignment problems, related problems, including algorithms, are discussed in this context. A slightly revised version of the Bollobás–Meir conjecture is proposed. 

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4. Abelian varieties of prescribed order over finite fields

   https://doi.org/10.1007/s00208-024-03084-4  

   van_Bommel, Raymond; Costa, Edgar; Li, Wanlin; Poonen, Bjorn; Smith, Alexander (March 2025, Mathematische Annalen)

   Abstract Given a prime powerqand$$n \gg 1$$ $n\gg 1$, we prove that every integer in a large subinterval of the Hasse–Weil interval$$[(\sqrt{q}-1)^{2n},(\sqrt{q}+1)^{2n}]$$ $[{(\sqrt{q}-1)}^{2n},{(\sqrt{q}+1)}^{2n}]$is$$\#A({\mathbb {F}}_q)$$ $\#A\left(F_q\right)$for some ordinary geometrically simple principally polarized abelian varietyAof dimensionnover$${\mathbb {F}}_q$$ $F_q$. As a consequence, we generalize a result of Howe and Kedlaya for$${\mathbb {F}}_2$$ $F_2$to show that for each prime powerq, every sufficiently large positive integer is realizable, i.e.,$$\#A({\mathbb {F}}_q)$$ $\#A\left(F_q\right)$for some abelian varietyAover$${\mathbb {F}}_q$$ $F_q$. Our result also improves upon the best known constructions of sequences of simple abelian varieties with point counts towards the extremes of the Hasse–Weil interval. A separate argument determines, for fixedn, the largest subinterval of the Hasse–Weil interval consisting of realizable integers, asymptotically as$$q \rightarrow \infty $$ $q\to \infty$; this gives an asymptotically optimal improvement of a 1998 theorem of DiPippo and Howe. Our methods are effective: We prove that if$$q \le 5$$ $q\le 5$, then every positive integer is realizable, and for arbitraryq, every positive integer$$\ge q^{3 \sqrt{q} \log q}$$ $\ge q^{3\sqrt{q}logq}$is realizable. 

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5. Kinetic Simulations of the Kruskal–Schwarzschild Instability in Accelerating Striped Outflows: Dynamics and Energy Dissipation

   https://doi.org/10.3847/1538-4357/adc446  

   Groger, William; Hakobyan, Hayk; Sironi, Lorenzo (April 2025, The Astrophysical Journal)

   Abstract Astrophysical relativistic outflows are launched as Poynting-flux dominated, yet the mechanism governing efficient magnetic dissipation, which powers the observed emission, is still poorly understood. We study magnetic energy dissipation in relativistic “striped” jets, which host current sheets separating magnetically dominated regions with opposite field polarity. The effective gravity forcegin the rest frame of accelerating jets drives the Kruskal–Schwarzschild instability (KSI), a magnetic analog of the Rayleigh–Taylor instability. By means of 2D and 3D particle-in-cell simulations, we study the linear and nonlinear evolution of the KSI. The linear stage is well described by linear stability analysis. The nonlinear stages of the KSI generate thin (skin-depth-thick) current layers, with length comparable to the dominant KSI wavelength. There, the relativistic drift-kink mode and the tearing mode drive efficient magnetic dissipation. The dissipation rate can be cast as an increase in the effective width Δ_effof the dissipative region, which follows $d{\Delta }_{\mathrm{eff}}/dt\simeq 0.05\sqrt{{\Delta }_{\mathrm{eff}}g}$. Our results have important implications for the location of the dissipation region in gamma-ray burst and active galactic nuclei jets. 

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