Singular kernels, multiscale decomposition of microstructure, and dislocation models

We consider a model for dislocations in crystals introduced by Koslowski, Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $\Gamma$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound

Entanglement in thermal equilibrium states

We revisist the issue of entanglement of thermal equilibrium states in composite quantum systems. The possible scenarios are exemplified in bipartite qubit/qubit and qubit/qutrit systems.Comment: 4 figure

Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter

We report on a high precision measurement of gravitational acceleration using ultracold strontium atoms trapped in a vertical optical lattice. Using amplitude modulation of the lattice intensity, an uncertainty $\Delta g /g \approx 10^{-7}$ was reached by measuring at the 5$^{th}$ harmonic of the Bloch oscillation frequency. After a careful analysis of systematic effects, the value obtained with this microscopic quantum system is consistent with the one we measured with a classical absolute gravimeter at the same location. This result is of relevance for the recent interpretation of related experiments as tests of gravitational redshift and opens the way to new tests of gravity at micrometer scale.Comment: 4 pages, 4 figure

Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. <br/> According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. <br/> In particular, damage is obtained as limit of periodically distributed microfractures

Coherent transport of atomic wave packets in amplitude-modulated vertical optical lattices

We report on the realization of dynamical control of transport for ultra-cold Sr88 atoms loaded in an accelerated and amplitude-modulated 1D optical lattice. We tailor the energy dispersion of traveling wave packets and reversibly switch between Wannier-Stark localization and driven transport based on coherent tunneling. Within a Loschmidt-echo scheme where the atomic group velocities are reversed at once, we demonstrate a novel mirror for matter waves working independently of the momentum state and discuss possible applications to force measurements at micrometric scales

Embodied intersectionality and the intersectional management of hotel labour: the everyday experiences of social differentiation in customer‐oriented work

This paper contributes to debates on critical diversity and intersectionality by focusing on hotel labour in a global tourist destination, the city of Venice. Through a qualitative study it explores how social differences are experienced by workers and valued by hotel management. We find that while management tends to allocate workers to different jobs according to the perceived ‘desirability’ of their embodied attributes by customers, the gendered and racialised divisions among workers do not simply conform with traditional patterns of ‘back’ and ‘front‐ of‐ house’ occupational positions. Rather they reflect variable compositions along the gender, migration and racial stereotypes reproduced by employers’ attempt to fulfil perceived changing expectations of customers. We develop the notion of ‘intersectional management’ to capture these fluid forms of valorisation of social difference, which appear influenced by workers’ practices of embodied intersectionality through the selective performance of entrenched stereotypes, and their everyday encounters with an internationalising clientele

A uniqueness result for the continuity equation in two dimensions

We consider certain properties of maps of class C 2 from Rd to Rd 121 that are strictly related to Sard\u2019s theorem, and show that some of them can be extended to Lipschitz maps, while others still require some additional regularity. We also give counterexamples showing that, in term of regularity, our results are optimal

On the Lp-differentiability of certain classes of functions

We prove the Lp-differentiability at almost every point for convolution products on \u211dd of the form K*\u3bc, where \u3bc is bounded measure and K is a homogeneous kernel of degree 1-d. From this result we derive the Lp-differentiability for vector fields on R d whose curl and divergence are measures, and also for vector fields with bounded deformation