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1. The origin of microtwinning in HAYNES® 244® superalloy

   https://doi.org/10.1038/s43246-025-01030-8  

   Tucker, Victoria; Mann, Thomas R; Roginski, Andrew; Fahrmann, Michael G; Monclús, Miguel A; LLorca, Javier; Titus, Michael S (December 2026, Communications Materials)

   Abstract Superalloys exhibit varying deformation mechanisms at differing temperatures and strain rates. The HAYNES^®244^®superalloy stands out due to its consistent mechanism of planar fault formation. This distinctive behavior is attributed to the presence of the Ni₂(Cr, Mo, W)$${\gamma }^{{\prime\prime} {\prime} }$$ ${\gamma }^{″\prime }$intermetallic phase, wherein stacking faults form by partial dislocations and subsequently thicken into microtwins via the transmission of partials on adjacent planes. Here we find that, in contrast to conventional$${\gamma }^{{\prime} }$$ ${\gamma }^{\prime }$-strengthened superalloys where deformation begins in theγmatrix, twinning in the 244 alloy initiates at theγ–$${\gamma }^{{\prime\prime} {\prime} }$$ ${\gamma }^{″\prime }$interface within the$${\gamma }^{{\prime\prime} {\prime} }$$ ${\gamma }^{″\prime }$precipitates and then extends outward into the matrix. Our study supports previous hypotheses on twin formation using advanced techniques such as high-resolution scanning transmission electron microscopy, in-situ transmission electron microscopy, and high-strain-rate testing. Contrary to conventional literature, where twinning is often considered detrimental, our work highlights twinning as a unique and significant behavior across temperatures up to the precipitate dissolution temperature and strain rates as high as 500 s⁻¹. In-depth analysis of this alloy at the onset of plasticity and characterization of theγ–$${\gamma }^{{\prime\prime} {\prime} }$$ ${\gamma }^{″\prime }$interface highlights a new and additional structural driving force for the stability of the deformation twinning mechanism. 

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2. Carleson’s $$\varepsilon ^{2}$$ conjecture in higher dimensions

   https://doi.org/10.1007/s00222-025-01337-w  

   Fleschler, Ian; Tolsa, Xavier; Villa, Michele (July 2025, Inventiones mathematicae)

   Abstract In this paper we prove a higher dimensional analogue of Carleson’s$$\varepsilon ^{2}$$ ${\epsilon }^2$conjecture. Given two arbitrary disjoint Borel sets$$\Omega ^{+},\Omega ^{-}\subset \mathbb{R}^{n+1}$$ ${\Omega }^{+},{\Omega }^{-}\subset R^{n+1}$, and$$x\in \mathbb{R}^{n+1}$$ $x\in R^{n+1}$,$$r>0$$ $r>0$, we denote$$ \varepsilon _{n}(x,r) := \frac{1}{r^{n}}\, \inf _{H^{+}} \mathcal{H}^{n} \left ( ((\partial B(x,r)\cap H^{+}) \setminus \Omega ^{+}) \cup (( \partial B(x,r)\cap H^{-}) \setminus \Omega ^{-})\right ), $$ ${\epsilon }_n(x,r):=\frac{1}{r^n}\underset{H^{+}}{inf}{H}^n\left(\right(\left(\partial B\right(x,r)\cap H^{+})\setminus {\Omega }^{+})\cup (\left(\partial B\right(x,r)\cap H^{-})\setminus {\Omega }^{-}\left)\right),$where the infimum is taken over all open affine half-spaces$$H^{+}$$ $H^{+}$such that$$x \in \partial H^{+}$$ $x\in \partial H^{+}$and we define$$H^{-}= \mathbb{R}^{n+1} \setminus \overline{H^{+}}$$ $H^{-}=R^{n+1}\setminus \overline{H^{+}}$. Our first main result asserts that the set of points$$x\in \mathbb{R}^{n+1}$$ $x\in R^{n+1}$where$$ \int _{0}^{1} \varepsilon _{n}(x,r)^{2} \, \frac{dr}{r}< \infty $$ ${\int }_0^1{\epsilon }_n{(x,r)}^2\frac{dr}{r}<\infty$is$$n$$ $n$-rectifiable. For our second main result we assume that$$\Omega ^{+}$$ ${\Omega }^{+}$,$$\Omega ^{-}$$ ${\Omega }^{-}$are open and that$$\Omega ^{+}\cup \Omega ^{-}$$ ${\Omega }^{+}\cup {\Omega }^{-}$satisfies the capacity density condition. For each$$x \in \partial \Omega ^{+} \cup \partial \Omega ^{-}$$ $x\in \partial {\Omega }^{+}\cup \partial {\Omega }^{-}$and$$r>0$$ $r>0$, we denote by$$\alpha ^{\pm }(x,r)$$ ${\alpha }^{\pm }(x,r)$the characteristic constant of the (spherical) open sets$$\Omega ^{\pm }\cap \partial B(x,r)$$ ${\Omega }^{\pm }\cap \partial B(x,r)$. We show that, up to a set of$$\mathcal{H}^{n}$$ $H^n$measure zero,$$x$$ $x$is a tangent point for both$$\partial \Omega ^{+}$$ $\partial {\Omega }^{+}$and$$\partial \Omega ^{-}$$ $\partial {\Omega }^{-}$if and only if$$ \int _{0}^{1} \min (1,\alpha ^{+}(x,r) + \alpha ^{-}(x,r) -2) \frac{dr}{r} < \infty . $$ ${\int }_0^{1}min(1,{\alpha }^{+}(x,r)+{\alpha }^{-}(x,r)-2)\frac{dr}{r}<\infty .$The first result is new even in the plane and the second one improves and extends to higher dimensions the$$\varepsilon ^{2}$$ ${\epsilon }^2$conjecture of Carleson. 

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3. Spectroscopic investigation of $$^{54}$$Cr via $$\alpha $$-transfer reaction

   https://doi.org/10.1140/epja/s10050-025-01619-0  

   Das, Biswajit; Kundu, A; Palit, R; Dey, P; Malik, Vishal; Garg, U; Negi, D; Laskar, S R; Santra, Rajkumar; Jadhav, S K; et al (June 2025, The European Physical Journal A)

   Abstract Low-lying states in$$^{54}$$ $_{}^{54}$Cr have been investigated via the$$\alpha $$ $\alpha$-transfer reaction$$^{50}$$ $_{}^{50}$Ti($$^{7}$$ $_{}^7$Li,t) at a bombarding energy of 20 MeV. The exclusive$$\alpha $$ $\alpha$-transfer channel is separated from other reaction channels through the appropriate energy gate on the complementary particle, triton. Levels of$$^{54}$$ $_{}^{54}$Cr populated exclusively by the$$\alpha $$ $\alpha$-transfer process could be identified up to$$\approx $$ $\approx$5 MeV excitation energy and angular momentum up to$$(8)^{+}$$ ${\left(8\right)}^{+}$, by identifying the corresponding known$$\gamma $$ $\gamma$-rays. These include multiple low-lying non-yrast 2$$^+$$ $_{}^{+}$and 4$$^+$$ $_{}^{+}$states, which would otherwise be unfavorable via fusion evaporation reactions. The feeding-subtracted$$\gamma $$ $\gamma$-ray yields have been extracted to estimate the population of various excited states through the transfer process. The measured integrated transfer cross sections for all the observed yrast and non-yrast states are compared with Coupled Channels calculations usingfrescoto extract the$$\alpha $$ $\alpha$+$$^{50}$$ $_{}^{50}$Ti core spectroscopic factors. For the yrast states, a higher$$\alpha $$ $\alpha$+core overlap is seen for the$$2^+$$ $2^{+}$and$$4^+$$ $4^{+}$states, while it is seen to be less favorable for the$$6^+$$ $6^{+}$and$$(8)^+$$ ${\left(8\right)}^{+}$states when$$\alpha $$ $\alpha$-transfer is considered to occur predominantly as a direct one-step process to the$$^{50}$$ $_{}^{50}$Ti core ground state. The yrast$$2^+$$ $2^{+}$, and$$4^+$$ $4^{+}$states are predominantly populated by single-step transfer, while for the states with spin$$\ge $$ $\ge$5, the possibility of core excitation followed by$$\alpha $$ $\alpha$-transfer shows a larger$$\alpha $$ $\alpha$-core overlap. For the non-yrast$$0^+$$ $0^{+}$,$$2^+$$ $2^{+}$, and$$4^+$$ $4^{+}$states, single-step transfer shows moderate to small$$\alpha $$ $\alpha$-core overlap. No higher spin non-yrast states are observed. 

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4. Spin density matrix elements in exclusive $$\rho ^0$$ meson muoproduction

   https://doi.org/10.1140/epjc/s10052-023-11359-4  

   Alexeev, G D; Alexeev, M G; Alice, C; Amoroso, A; Andrieux, V; Anosov, V; Augsten, K; Augustyniak, W; Azevedo, C_D R; Badelek, B; et al (October 2023, The European Physical Journal C)

   Abstract We report on a measurement of Spin Density Matrix Elements (SDMEs) in hard exclusive$$\rho ^0$$ ${\rho }^0$meson muoproduction at COMPASS using 160 GeV/cpolarised$$ \mu ^{+}$$ ${\mu }^{+}$and$$ \mu ^{-}$$ ${\mu }^{-}$beams impinging on a liquid hydrogen target. The measurement covers the kinematic range 5.0 GeV/$$c^2$$ $c^2$$$< W<$$ $<W<$17.0 GeV/$$c^2$$ $c^2$, 1.0 (GeV/c)$$^2$$ ${}^2$$$< Q^2<$$ $<Q^2<$10.0 (GeV/c)$$^2$$ ${}^2$and 0.01 (GeV/c)$$^2$$ ${}^2$$$< p_{\textrm{T}}^2<$$ $<p_{\text{T}}^2<$0.5 (GeV/c)$$^2$$ ${}^2$. Here,Wdenotes the mass of the final hadronic system,$$Q^2$$ $Q^2$the virtuality of the exchanged photon, and$$p_{\textrm{T}}$$ $p_{\text{T}}$the transverse momentum of the$$\rho ^0$$ ${\rho }^0$meson with respect to the virtual-photon direction. The measured non-zero SDMEs for the transitions of transversely polarised virtual photons to longitudinally polarised vector mesons ($$\gamma ^*_T \rightarrow V^{ }_L$$ ${\gamma }_T^{\ast }\to V_L^{}$) indicate a violation ofs-channel helicity conservation. Additionally, we observe a dominant contribution of natural-parity-exchange transitions and a very small contribution of unnatural-parity-exchange transitions, which is compatible with zero within experimental uncertainties. The results provide important input for modelling Generalised Parton Distributions (GPDs). In particular, they may allow one to evaluate in a model-dependent way the role of parton helicity-flip GPDs in exclusive$$\rho ^0$$ ${\rho }^0$production. 

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5. Construction of a Dirichlet form on Metric Measure Spaces of Controlled Geometry

   https://doi.org/10.1007/s11118-024-10144-6  

   Butaev, Almaz; Luo, Liangbing; Shanmugalingam, Nageswari (March 2025, Potential Analysis)

   Abstract Given a compact doubling metric measure spaceXthat supports a 2-Poincaré inequality, we construct a Dirichlet form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$that is comparable to the upper gradient energy form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$. Our approach is based on the approximation ofXby a family of graphs that is doubling and supports a 2-Poincaré inequality (see [20]). We construct a bilinear form on$$N^{1,2}(X)$$ $N^{1,2}\left(X\right)$using the Dirichlet form on the graph. We show that the$$\Gamma $$ $\Gamma$-limit$$\mathcal {E}$$ $E$of this family of bilinear forms (by taking a subsequence) exists and that$$\mathcal {E}$$ $E$is a Dirichlet form onX. Properties of$$\mathcal {E}$$ $E$are established. Moreover, we prove that$$\mathcal {E}$$ $E$has the property of matching boundary values on a domain$$\Omega \subseteq X$$ $\Omega \subseteq X$. This construction makes it possible to approximate harmonic functions (with respect to the Dirichlet form$$\mathcal {E}$$ $E$) on a domain inXwith a prescribed Lipschitz boundary data via a numerical scheme dictated by the approximating Dirichlet forms, which are discrete objects. 

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