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In this work electron backscattered diffraction (EBSD)-assisted slip trace analysis and transmission electron microscopy have been utilized to investigate the interaction of basal dislocations with precipitates in the Mg alloys Mg-1%wt.Mn-0.7%wt.Nd (MN11) and Mg-9%wt.Al-1%wt.Zn (AZ91), with the ultimate aim of determining the origin of their poor precipitation hardening. Precipitates in these alloys have a plate-shaped morphology, with plates being, respectively, perpendicular (MgxNdy) and parallel (Mg17Al12) to the basal plane of the magnesium matrix. Mechanical tests were carried out in solid solution and peak-aged samples, in tension and compression, both at RT and at moderate temperature (250C). EBSD-assisted slip trace analysis revealed a clear dominance of basal slip under a wide range of testing conditions in the peak-aged MN11 and AZ91 alloys. At room temperature, the origin of the low precipitation hardening observed lies at the easiness with which precipitates are sheared by basal dislocations, due to the lattice matching at the interface with the Mg matrix. At high temperature, dislocation-precipitate interactions are highly dependent on the deformation mode. In tension, enhanced basal slip localization gives rise to high stress concentrations at the intersection between coarse slip traces and particle interfaces, leading to precipitate fracture; in compression, a more homogenous distribution of basal slip leads to the dominance of particle shearing. Our study demonstrates experimentally that basal dislocations are able to shear, and even fracture, the MgxNdy and Mg17Al12 plates when, for appropriate testing conditions, the local stress due to dislocation accumulation at particle interfaces exceeds the precipitate strength.

Supernovae (SNe) that have been multiply-imaged by gravitational lensing are rare and powerful probes for cosmology. Each detection is an opportunity to develop the critical tools and methodologies needed as the sample of lensed SNe increases by orders of magnitude with the upcoming Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope. The latest such discovery is of the quadruply-imaged Type Ia SN 2022qmx (aka, "SN Zwicky") at $z=0.3544$. SN Zwicky was discovered by the Zwicky Transient Facility (ZTF) in spatially unresolved data. Here we present follow-up Hubble Space Telescope observations of SN Zwicky, the first from the multi-cycle "LensWatch" program. We measure photometry for each of the four images of SN Zwicky, which are resolved in three WFC3/UVIS filters (F475W, F625W, F814W) but unresolved with WFC3/IR~F160W, and present an analysis of the lensing system using a variety of independent lens modeling methods. We find consistency between lens model predicted time delays ($\lesssim1$ day), and delays estimated with the single epoch of HST colors ($\lesssim3.5$ days), including the uncertainty from chromatic microlensing ($\sim1$-$1.5$ days). Our lens models converge to an Einstein radius of $\theta_E=(0.168^{+0.009}_{-0.005})\prime\prime$, the smallest yet seen in a lensed SN system. The "standard candle" nature of SN Zwicky provides magnification estimates independent of the lens modeling that are brighter than predicted by $\sim1.7^{+0.8}_{-0.6}$mag and $\sim0.9^{+0.8}_{-0.6}$mag for two of the four images, suggesting significant microlensing and/or additional substructure beyond the flexibility of our image-position mass models.

In this work we establish functional asymmetric versions of the celebrated Blaschke-Santal\'o inequality. As consequences of these inequalities we recover their geometric counterparts with equality cases, as well as, another inequality with strong probabilistic flavour that was firstly obtained by Lutwak, Yang and Zhang. We present a brief study on an $L_p$ functional analogue to the center of mass that is necessary for our arguments and that might be of independent interest., Comment: 13 pages. Comments are welcome!

We present \ci\,(2--1) and multi-transition $^{12}$CO observations of a dusty star-forming galaxy, ACT\,J2029+0120, which we spectroscopically confirm to lie at $z$\,=\,2.64. We detect CO(3--2), CO(5--4), CO(7--6), CO(8--7), and \ci\,(2--1) at high significance, tentatively detect HCO$^{+}$(4--3), and place strong upper limits on the integrated strength of dense gas tracers (HCN(4--3) and CS(7--6)). Multi-transition CO observations and dense gas tracers can provide valuable constraints on the molecular gas content and excitation conditions in high-redshift galaxies. We therefore use this unique data set to construct a CO spectral line energy distribution (SLED) of the source, which is most consistent with that of a ULIRG/Seyfert or QSO host object in the taxonomy of the \textit{Herschel} Comprehensive ULIRG Emission Survey. We employ RADEX models to fit the peak of the CO SLED, inferring a temperature of T$\sim$117 K and $n_{\text{H}_2}\sim10^5$ cm$^{-3}$, most consistent with a ULIRG/QSO object and the presence of high density tracers. We also find that the velocity width of the \ci\ line is potentially larger than seen in all CO transitions for this object, and that the $L'_{\rm C\,I(2-1)}/L'_{\rm CO(3-2)}$ ratio is also larger than seen in other lensed and unlensed submillimeter galaxies and QSO hosts; if confirmed, this anomaly could be an effect of differential lensing of a shocked molecular outflow., Comment: Accepted for publication in ApJ

We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers-Shephard type inequalities as well as some generalizations of the geometric Rogers-Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis-Whitney inequalities. We also obtain a sharp local Loomis-Whitney inequality., Comment: 40 pages

We show that the $\Lp$ Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg inequalities. Our approach allows also to characterize directly the corresponding equality cases., Comment: 16 pages. Corrected version to appear in Journal of Functional Analysis

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form $\gamma=(\langle u_i,v_j\rangle)_{i,j=1}^n$, where the vectors $u_i$ and $v_j$ are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of $\alpha=\frac{m}{n}$, where the previous vectors are sampled according to the Haar measure in the unit sphere of $\mathbb R^m$. In particular, we prove the existence of an $\alpha_0>0$ such that if $\alpha\leq \alpha_0$, $\gamma$ is nonlocal with probability tending to $1$ as $n\rightarrow \infty$, while for $\alpha> 2$, $\gamma$ is local with probability tending to $1$ as $n\rightarrow \infty$., Comment: v2: minor modifications to match the journal version, 16 pages, 0 figures

In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of several symmetrizations of the body, such as, its difference body. We characterize the equality cases in all these inequalities. Our method is based on the extension of the notion of a convolution body of two convex sets to any pair of log-concave functions and the study of some geometrical properties of these new sets., Comment: 25 pages

In this note we study how a concentration phenomenon can be transmitted from one measure $\mu$ to a push-forward measure $\nu$. In the first part, we push forward $\mu$ by $\pi:supp(\mu)\rightarrow \Ren$, where $\pi x=\frac{x}{\norm{x}_L}\norm{x}_K$, and obtain a concentration inequality in terms of the medians of the given norms (with respect to $\mu$) and the Banach-Mazur distance between them. This approach is finer than simply bounding the concentration of the push forward measure in terms of the Banach-Mazur distance between $K$ and $L$. As a corollary we show that any normed probability space with good concentration is far from any high dimensional subspace of the cube. In the second part, two measures $\mu$ and $\nu$ are given, both related to the norm $\norm{\cdot}_L$, obtaining a concentration inequality in which it is involved the Banach-Mazur distance between $K$ and $L$ and the Lipschitz constant of the map that pushes forward $\mu$ into $\nu$. As an application, we obtain a concentration inequality for the cross polytope with respect to the normalized Lebesgue measure and the $\ell_1$ norm., Comment: 12 pages

A quantitative version of Minkowski sum, extending the definition of $\theta$-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties on Convex Geometry involving convolution bodies or polar projection bodies. The extension of this new version to more than two sets is also given., Comment: 22 pages. Accepted for Advances in Mathematics

A contour dynamics model for electrical discharges is obtained and analyzed. The model is deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion. The dispersion relation for a non planar 2-D discharge is calculated. The development and propagation of finger-like patterns are studied and their main features quantified., Comment: 4 pages, 2 fig