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1. The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow

   https://doi.org/10.1007/s11242-024-02070-3  

   Arbabi, Sepehr ; Sahimi, Muhammad ( March 2024 , Transport in Porous Media)

   Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient$${\varvec{\nabla }}P$$$\nabla P$and the fluid velocityv. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitude$$\omega _z$$${\omega }_z$of the vorticity is nearly zero. As Re increases, however, so also does$$\omega _z$$${\omega }_z$, and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocityv, given by,$$-{\varvec{\nabla }}P=(\mu /K_e)\textbf{v}+\beta _n\rho |\textbf{v}|^2\textbf{v}$$$-\nabla P=(\mu /K_e)v+{\beta }_n\rho {\left|v\right|}^{2}v$, provides accurate representation of the numerical data, where$$\mu$$$\mu$and$$\rho$$$\rho$are the fluid’s viscosity and density,$$K_e$$$K_e$is the effective Darcy permeability in the linear regime, and$$\beta _n$$${\beta }_n$is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation.

    

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2. Green function estimates on complements of low-dimensional uniformly rectifiable sets

   https://doi.org/10.1007/s00208-022-02379-8  

   David, Guy ; Feneuil, Joseph ; Mayboroda, Svitlana ( March 2022 , Mathematische Annalen)

   It has been recently established in David and Mayboroda (Approximation of green functions and domains with uniformly rectifiable boundaries of all dimensions.arXiv:2010.09793) that on uniformly rectifiable sets the Green function is almost affine in the weak sense, and moreover, in some scenarios such Green function estimates are equivalent to the uniform rectifiability of a set. The present paper tackles a strong analogue of these results, starting with the “flagship degenerate operators on sets with lower dimensional boundaries. We consider the elliptic operators$$L_{\beta ,\gamma } =- {\text {div}}D^{d+1+\gamma -n} \nabla $$$L_{\beta ,\gamma }=-\text{div}{D}^{d+1+\gamma -n}\nabla$associated to a domain$$\Omega \subset {\mathbb {R}}^n$$$\Omega \subset R^n$with a uniformly rectifiable boundary$$\Gamma $$$\Gamma$of dimension$$d < n-1$$$d<n-1$, the now usual distance to the boundary$$D = D_\beta $$$D=D_{\beta }$given by$$D_\beta (X)^{-\beta } = \int _{\Gamma } |X-y|^{-d-\beta } d\sigma (y)$$$D_{\beta }{\left(X\right)}^{-\beta }={\int }_{\Gamma }{|X-y|}^{-d-\beta }d\sigma \left(y\right)$for$$X \in \Omega $$$X\in \Omega$, where$$\beta >0$$$\beta >0$and$$\gamma \in (-1,1)$$$\gamma \in (-1,1)$. In this paper we show that the Green functionGfor$$L_{\beta ,\gamma }$$$L_{\beta ,\gamma }$, with pole at infinity, is well approximated by multiples of$$D^{1-\gamma }$$$D^{1-\gamma }$, in the sense that the function$$\big | D\nabla \big (\ln \big ( \frac{G}{D^{1-\gamma }} \big )\big )\big |^2$$$|D\nabla (ln(\frac{G}{D^{1-\gamma }})){|}^2$satisfies a Carleson measure estimate on$$\Omega $$$\Omega$. We underline that the strong and the weak results are different in nature and, of course, at the level of the proofs: the latter extensively used compactness arguments, while the present paper relies on some intricate integration by parts and the properties of the “magical distance function from David et al. (Duke Math J, to appear).

    

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3. Deformations and moduli of irregular canonical covers with $$K^2=4p_g-8$$

   https://doi.org/10.1007/s13163-023-00462-5  

   Bangere, Purnaprajna ; Gallego, Francisco Javier ; Mukherjee, Jayan ; Raychaudhury, Debaditya ( March 2023 , Revista Matemática Complutense)

   In this article, we study the moduli of irregular surfaces of general type with at worst canonical singularities satisfying$$K^2 = 4p_g-8$$$K^2=4p_g-8$, for any even integer$$p_g\ge 4$$$p_g\ge 4$. These surfaces also have unbounded irregularityq. We carry out our study by investigating the deformations of the canonical morphism$$\varphi :X\rightarrow {\mathbb {P}}^N$$$\phi :X\to P^N$, where$$\varphi $$$\phi$is a quadruple Galois cover of a smooth surface of minimal degree. These canonical covers are classified in Gallego and Purnaprajna (Trans Am Math Soc 360(10):5489-5507, 2008) into four distinct families, one of which is the easy case of a product of curves. The main objective of this article is to study the deformations of the other three, non trivial, unbounded families. We show that any deformation of$$\varphi $$$\phi$factors through a double cover of a ruled surface and, hence, is never birational. More interestingly, we prove that, with two exceptions, a general deformation of$$\varphi $$$\phi$is two-to-one onto its image, whose normalization is a ruled surface of appropriate irregularity. We also show that, with the exception of one family, the deformations ofXare unobstructed even though$$H^2(T_X)$$$H^2\left(T_X\right)$does not vanish. Consequently,Xbelongs to a unique irreducible component of the Gieseker moduli space. These irreducible components are uniruled. As a result of all this, we show the existence of infinitely many moduli spaces, satisfying the strict Beauville inequality$$p_g > 2q-4$$$p_g>2q-4$, with an irreducible component that has a proper quadruple sublocus where the degree of the canonical morphism jumps up. These components are above the Castelnuovo line, but nonetheless parametrize surfaces with non birational canonical morphisms. The existence of jumping subloci is a contrast with the moduli of surfaces with$$K^2 = 2p_g- 4$$$K^2=2p_g-4$, studied by Horikawa. Irreducible moduli components with a jumping sublocus also present a similarity and a difference to the moduli of curves of genus$$g\ge 3$$$g\ge 3$, for, like in the case of curves, the degree of the canonical morphism goes down outside a closed sublocus but, unlike in the case of curves, it is never birational. Finally, our study shows that there are infinitely many moduli spaces with an irreducible component whose general elements have non birational canonical morphism and another irreducible component whose general elements have birational canonical map.

    

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4. Azimuthal correlations of heavy-flavor hadron decay electrons with charged particles in pp and p–Pb collisions at $$\pmb {\sqrt{s_{\mathrm{{NN}}}}}$$ = 5.02 TeV

   https://doi.org/10.1140/epjc/s10052-023-11835-x  

   Acharya, S. ; Adamová, D. ; Adler, A. ; Aglieri Rinella, G. ; Agnello, M. ; Agrawal, N. ; Ahammed, Z. ; Ahmad, S. ; Ahn, S. U. ; Ahuja, I. ; et al ( August 2023 , The European Physical Journal C)

   The azimuthal ($$\Delta \varphi $$$\Delta \phi$) correlation distributions between heavy-flavor decay electrons and associated charged particles are measured in pp and p–Pb collisions at$$\sqrt{s_{\mathrm{{NN}}}} = 5.02$$$\sqrt{s_{\mathrm{NN}}}=5.02$TeV. Results are reported for electrons with transverse momentum$$4$4<p_{\text{T}}<16$$$\textrm{GeV}/c$$$\text{GeV}/c$ and pseudorapidity$$|\eta |<0.6$$$\left|\eta \right|<0.6$. The associated charged particles are selected with transverse momentum$$1$1<p_{\text{T}}<7$$$\textrm{GeV}/c$$$\text{GeV}/c$, and relative pseudorapidity separation with the leading electron$$|\Delta \eta | < 1$$$\left|\Delta \eta \right|<1$. The correlation measurements are performed to study and characterize the fragmentation and hadronization of heavy quarks. The correlation structures are fitted with a constant and two von Mises functions to obtain the baseline and the near- and away-side peaks, respectively. The results from p–Pb collisions are compared with those from pp collisions to study the effects of cold nuclear matter. In the measured trigger electron and associated particle kinematic regions, the two collision systems give consistent results. The$$\Delta \varphi $$$\Delta \phi$distribution and the peak observables in pp and p–Pb collisions are compared with calculations from various Monte Carlo event generators.

    

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5. Measurement of the mass dependence of the transverse momentum of lepton pairs in Drell–Yan production in proton–proton collisions at $$\sqrt{s} = 13\,\text {Te\hspace{-.08em}V} $$

   https://doi.org/10.1140/epjc/s10052-023-11631-7  

   Tumasyan, A. ; Adam, W. ; Andrejkovic, J. W. ; Bergauer, T. ; Chatterjee, S. ; Dragicevic, M. ; Valle, A. Escalante ; Frühwirth, R. ; Jeitler, M. ; Krammer, N. ; et al ( July 2023 , The European Physical Journal C)

   The double differential cross sections of the Drell–Yan lepton pair ($$\ell ^+\ell ^-$$${\ell }^{+}{\ell }^{-}$, dielectron or dimuon) production are measured as functions of the invariant mass$$m_{\ell \ell }$$$m_{\ell \ell }$, transverse momentum$$p_{\textrm{T}} (\ell \ell )$$$p_{\text{T}}\left(\ell \ell \right)$, and$$\varphi ^{*}_{\eta }$$${\phi }_{\eta }^{\ast }$. The$$\varphi ^{*}_{\eta }$$${\phi }_{\eta }^{\ast }$observable, derived from angular measurements of the leptons and highly correlated with$$p_{\textrm{T}} (\ell \ell )$$$p_{\text{T}}\left(\ell \ell \right)$, is used to probe the low-$$p_{\textrm{T}} (\ell \ell )$$$p_{\text{T}}\left(\ell \ell \right)$region in a complementary way. Dilepton masses up to 1$$\,\text {Te\hspace{-.08em}V}$$$\text{Te}\text{V}$are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various$$m_{\ell \ell }$$$m_{\ell \ell }$ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$of proton–proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13$$\,\text {Te\hspace{-.08em}V}$$$\text{Te}\text{V}$. Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.

    

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