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1. 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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2. A cluster of results on amplituhedron tiles

   https://doi.org/10.1007/s11005-024-01854-4  

   Even-Zohar, Chaim; Lakrec, Tsviqa; Parisi, Matteo; Sherman-Bennett, Melissa; Tessler, Ran; Williams, Lauren (September 2024, Letters in Mathematical Physics)

   Abstract The amplituhedron is a mathematical object which was introduced to provide a geometric origin of scattering amplitudes in$$\mathcal {N}=4$$ $N=4$super Yang–Mills theory. It generalizescyclic polytopesand thepositive Grassmannianand has a very rich combinatorics with connections to cluster algebras. In this article, we provide a series of results about tiles and tilings of the$$m=4$$ $m=4$amplituhedron. Firstly, we provide a full characterization of facets of BCFW tiles in terms of cluster variables for$$\text{ Gr}_{4,n}$$ ${\text{Gr}}_{4,n}$. Secondly, we exhibit a tiling of the$$m=4$$ $m=4$amplituhedron which involves a tile which does not come from the BCFW recurrence—thespuriontile, which also satisfies all cluster properties. Finally, strengthening the connection with cluster algebras, we show that each standard BCFW tile is the positive part of a cluster variety, which allows us to compute the canonical form of each such tile explicitly in terms of cluster variables for$$\text{ Gr}_{4,n}$$ ${\text{Gr}}_{4,n}$. This paper is a companion to our previous paper “Cluster algebras and tilings for the$$m=4$$ $m=4$amplituhedron.” 

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3. Torsion phenomena for zero-cycles on a product of curves over a number field

   https://doi.org/10.1007/s40993-024-00519-4  

   Gazaki, Evangelia; Love, Jonathan (March 2024, Research in Number Theory)

   Abstract For a smooth projective varietyXover an algebraic number fieldka conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map ofXis a torsion group. In this article we consider a product$$X=C_1\times \cdots \times C_d$$ $X=C_1\times \cdots \times C_d$of smooth projective curves and show that if the conjecture is true for any subproduct of two curves, then it is true forX. For a product$$X=C_1\times C_2$$ $X=C_1\times C_2$of two curves over$$\mathbb {Q} $$ $Q$with positive genus we construct many nontrivial examples that satisfy the weaker property that the image of the natural map$$J_1(\mathbb {Q})\otimes J_2(\mathbb {Q})\xrightarrow {\varepsilon }{{\,\textrm{CH}\,}}_0(C_1\times C_2)$$ $J_1\left(Q\right)\otimes J_2\left(Q\right)\stackrel{\epsilon }{\to }{\text{CH}}_0(C_1\times C_2)$is finite, where$$J_i$$ $J_i$is the Jacobian variety of$$C_i$$ $C_i$. Our constructions include many new examples of non-isogenous pairs of elliptic curves$$E_1, E_2$$ $E_1,E_2$with positive rank, including the first known examples of rank greater than 1. Combining these constructions with our previous result, we obtain infinitely many nontrivial products$$X=C_1\times \cdots \times C_d$$ $X=C_1\times \cdots \times C_d$for which the analogous map$$\varepsilon $$ $\epsilon$has finite image. 

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4. The geometric distribution of Selmer groups of elliptic curves over function fields

   https://doi.org/10.1007/s00208-022-02429-1  

   Feng, Tony; Landesman, Aaron; Rains, Eric M. (September 2022, Mathematische Annalen)

   Abstract Fix a positive integernand a finite field$${\mathbb {F}}_q$$ $F_q$. We study the joint distribution of the rank$${{\,\mathrm{rk}\,}}(E)$$ $\mathrm{rk}\left(E\right)$, then-Selmer group$$\text {Sel}_n(E)$$ ${\text{Sel}}_n\left(E\right)$, and then-torsion in the Tate–Shafarevich group Equation missing<#comment/>asEvaries over elliptic curves of fixed height$$d \ge 2$$ $d\ge 2$over$${\mathbb {F}}_q(t)$$ $F_q\left(t\right)$. We compute this joint distribution in the largeqlimit. We also show that the “largeq, then large height” limit of this distribution agrees with the one predicted by Bhargava–Kane–Lenstra–Poonen–Rains. 

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5. Modular apparatus for nuclear reactions spectroscopy (MARS): characterization and first application to determine $$^{12}$$C($$^6$$Li,$$^4$$He)$$^{14}\hbox {N}^{g.s}$$ nuclear reaction cross sections

   https://doi.org/10.1140/epjp/s13360-025-06305-0  

   Garrido-Gómez, L; Vegas-Díaz, A; Alvarez, M_A G; Fernández-García, J P; Fernández, B; Ferrer, F J; Lopez-Aires, D (May 2025, The European Physical Journal Plus)

   Abstract This work presents MARS (Modular apparatus for nuclear reactions spectroscopy) and its characterization prior to its first application to measure$$^6$$ $_{}^6$Li+$$^{12}$$ $_{}^{12}$C nuclear reactions. Measurements were performed at the 3 MV tandem accelerator of the CNA (National Accelerator Center), in Seville, Spain. The$$^{6}$$ $_{}^6$Li projectiles were accelerated at energies around the$$^6$$ $_{}^6$Li+$$^{12}$$ $_{}^{12}$C Coulomb barrier ($$V^{\text {cm}}_{B}\sim 3.0$$ $V_B^{\text{cm}}\sim 3.0$MeV - center of mass and$$V^{\text {lab}}_{B}\sim 4.5$$ $V_B^{\text{lab}}\sim 4.5$MeV - laboratory frame). Using a$$^{6}\hbox {Li}^{2+}$$ $_{}^6{\text{Li}}^{2+}$beam, we measured at 13 laboratory energies from 4.00 to 7.75 MeV. Thus, we present the excitation function of$$^{12}$$ $_{}^{12}$C($$^6$$ $_{}^6$Li,$$^4$$ $_{}^4$He)$$^{14}\hbox {N}^{g.s.}$$ $_{}^{14}{\text{N}}^{g.s.}$reaction, at 2 backward angles ($$110.0^\circ $$ $110.0^{\circ }$and$$140.0^\circ $$ $140.0^{\circ }$). The projectile dissociation, leading to this reaction, increases with the bombarding energies around the Coulomb barrier. This dissociation is favored at an optimum energy$$E_{b}^{\text {op}}$$ $E_b^{\text{op}}$$$\ge $$ $\ge$$$V_{B}$$ $V_B$+$$|Q_{bu}|$$ $|Q_{\mathrm{bu}}|$, where$$V_{B}$$ $V_B$is the Coulomb barrier of the system, and$$|Q_{bu}|$$ $|Q_{\mathrm{bu}}|$is the module ofQ-value for the$$^6$$ $_{}^6$Li dissociation into$$^4$$ $_{}^4$He+$$^2$$ $_{}^2$H. This result corroborates a systematic analysis of weakly bound projectiles reacting on several targets [1]. 

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