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1. Global well-posedness for 2D generalized parabolic Anderson model via paracontrolled calculus

   https://doi.org/10.1007/s40072-025-00358-z  

   Shen, Hao; Zhu, Rongchan; Zhu, Xiangchan (May 2025, Stochastics and Partial Differential Equations: Analysis and Computations)

   Abstract This article revisits the problem of global well-posedness for the generalized parabolic Anderson model on$$\mathbb {R}^+\times \mathbb {T}^2$$ $R^{+}\times T^2$within the framework of paracontrolled calculus (Gubinelli et al. in Forum Math, 2015). The model is given by the equation:$$\begin{aligned} (\partial _t-\Delta ) u=F(u)\eta \end{aligned}$$ $\begin{array}{c}({\partial }_t-\Delta )u=F\left(u\right)\eta \end{array}$where$$\eta \in C^{-1-\kappa }$$ $\eta \in C^{-1-\kappa }$with$$1/6>\kappa >0$$ $1/6>\kappa >0$, and$$F\in C_b^2(\mathbb {R})$$ $F\in C_b^2\left(R\right)$. Assume that$$\eta \in C^{-1-\kappa }$$ $\eta \in C^{-1-\kappa }$and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work by Chandra et al. (A priori bounds for 2-d generalised Parabolic Anderson Model,,2024), to represent the leading error term as a transport type term, and our techniques encompass the paracontrolled calculus, the maximum principle, and the localization approach (i.e. high-low frequency argument). 

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2. Pressure drop measurements over anisotropic porous substrates in channel flow

   https://doi.org/10.1007/s00348-024-03873-2  

   Vijay, Shilpa; Luhar, Mitul (September 2024, Experiments in Fluids)

   AbstractPrevious theoretical and simulation results indicate that anisotropic porous materials have the potential to reduce turbulent skin friction in wall-bounded flows. This study experimentally investigates the influence of anisotropy on the drag response of porous substrates. A family of anisotropic periodic lattices was manufactured using 3D printing. Rod spacing in different directions was varied systematically to achieve different ratios of streamwise, wall-normal, and spanwise bulk permeabilities ($$\kappa _{xx}$$ ${\kappa }_{\mathrm{xx}}$,$$\kappa _{yy}$$ ${\kappa }_{\mathrm{yy}}$, and$$\kappa _{zz}$$ ${\kappa }_{\mathrm{zz}}$). The 3D printed materials were flush-mounted in a benchtop water channel. Pressure drop measurements were taken in the fully developed region of the flow to systematically characterize drag for materials with anisotropy ratios$$\frac{\kappa _{xx}}{\kappa _{yy}} \in [0.035,28.6]$$ $\frac{{\kappa }_{\mathrm{xx}}}{{\kappa }_{\mathrm{yy}}}\in [0.035,28.6]$. Results show that all materials lead to an increase in drag compared to the reference smooth wall case over the range of bulk Reynolds numbers tested ($$\hbox {Re}_b \in [500,4000]$$ ${\text{Re}}_b\in [500,4000]$). However, the relative increase in drag is lower for streamwise-preferential materials. We estimate that the wall-normal permeability for all tested cases exceeded the threshold identified in previous literature ($$\sqrt{\kappa _{yy}}^+> 0.4$$ ${\sqrt{{\kappa }_{\mathrm{yy}}}}^{+}>0.4$) for the emergence of energetic spanwise rollers similar to Kelvin–Helmholtz vortices, which can increase drag. The results also indicate that porous walls exhibit a departure from laminar behavior at different values for bulk Reynolds numbers depending on the geometry. Graphical abstract 

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3. Violent Nonlinear Collapse in the Interior of Charged Hairy Black Holes

   https://doi.org/10.1007/s00205-024-02038-z  

   Van_de_Moortel, Maxime (October 2024, Archive for Rational Mechanics and Analysis)

   Abstract We construct a new one-parameter family, indexed by$$\epsilon $$ $ϵ$, of two-ended, spatially-homogeneous black hole interiors solving the Einstein–Maxwell–Klein–Gordon equations with a (possibly zero) cosmological constant$$\Lambda $$ $\Lambda$and bifurcating off a Reissner–Nordström-(dS/AdS) interior ($$\epsilon =0$$ $ϵ=0$). For all small$$\epsilon \ne 0$$ $ϵ\ne 0$, we prove that, although the black hole is charged, its terminal boundary is an everywhere-spacelikeKasner singularity foliated by spheres of zero radiusr. Moreover, smaller perturbations (i.e. smaller$$|\epsilon |$$ $\left|ϵ\right|$) aremore singular than larger ones, in the sense that the Hawking mass and the curvature blow up following a power law of the form$$r^{-O(\epsilon ^{-2})}$$ $r^{-O\left({ϵ}^{-2}\right)}$at the singularity$$\{r=0\}$$ $\{r=0\}$. This unusual property originates from a dynamical phenomenon—violent nonlinear collapse—caused by the almost formation of a Cauchy horizon to the past of the spacelike singularity$$\{r=0\}$$ $\{r=0\}$. This phenomenon was previously described numerically in the physics literature and referred to as “the collapse of the Einstein–Rosen bridge”. While we cover all values of$$\Lambda \in \mathbb {R}$$ $\Lambda \in R$, the case$$\Lambda <0$$ $\Lambda <0$is of particular significance to the AdS/CFT correspondence. Our result can also be viewed in general as a first step towards the understanding of the interior of hairy black holes. 

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4. Fast and fair randomized wait-free locks

   https://doi.org/10.1007/s00446-024-00474-4  

   Ben-David, Naama; Blelloch, Guy E (March 2025, Distributed Computing)

   Abstract We present a randomized approach for wait-free locks with strong bounds on time and fairness in a context in which any process can be arbitrarily delayed. Our approach supports a tryLock operation that is given a set of locks, and code to run when all the locks are acquired. A tryLock operation may fail if there is contention on the locks, in which case the code is not run. Given an upper bound$$\kappa $$ $\kappa$known to the algorithm on the point contention of any lock, and an upper boundLon the number of locks in a tryLock’s set, a tryLock will succeed in acquiring its locks and running the code with probability at least$$1/(\kappa L)$$ $1/\left(\kappa L\right)$. It is thus fair. Furthermore, if the maximum step complexity for the code in any lock isT, the operation will take$$O(\kappa ^2 L^2 T)$$ $O\left({\kappa }^2{L}^{2}T\right)$steps, regardless of whether it succeeds or fails. The operations are independent, thus if the tryLock is repeatedly retried on failure, it will succeed in$$O(\kappa ^3 L^3 T)$$ $O\left({\kappa }^3{L}^{3}T\right)$expected steps. If the algorithm does not know the bounds$$\kappa $$ $\kappa$andL, we present a variant that can guarantee a probability of at least$$1/\kappa L\log (\kappa L T)$$ $1/\kappa Llog\left(\kappa LT\right)$of success. We assume an oblivious adversarial scheduler, which does not make decisions based on the operations, but can predetermine any schedule for the processes, which is unknown to our algorithm. Furthermore, to account for applications that change their future requests based on the results of previous tryLock operations, we strengthen the adversary by allowing decisions of the start times and lock sets of tryLock operations to be made adaptively, given the history of the execution so far. 

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5. Connection probabilities of multiple FK-Ising interfaces

   https://doi.org/10.1007/s00440-024-01269-1  

   Feng, Yu; Peltola, Eveliina; Wu, Hao (June 2024, Probability Theory and Related Fields)

   Abstract We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight$${q \in [1,4)}$$ $q\in [1,4)$. Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values ofqthan the FK-Ising model ($$q=2$$ $q=2$). Given the convergence of interfaces, the conjectural formulas for other values ofqcould be verified similarly with relatively minor technical work. The limit interfaces are variants of$$\text {SLE}_\kappa $$ ${\text{SLE}}_{\kappa }$curves (with$$\kappa = 16/3$$ $\kappa =16/3$for$$q=2$$ $q=2$). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all$$q \in [1,4)$$ $q\in [1,4)$, thus providing further evidence of the expected CFT description of these models. 

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