The sejugal furrow in camel spiders and acariform mites

Camel spiders (Arachnida: Solifugae) are one of the arachnid groups characterised by a prosomal dorsal shield composed of three distinct elements: the pro-, meso- and metapeltidium. These are associated respectively with prosomal appendages one to four, five, and six. What is less well known, although noted in the historical literature, is that the coxae of the 4th and 5th prosomal segments (i.e. walking legs 2 and 3) of camel spiders are also separated ventrally by a distinct membranous region, which is absent between the coxae of the other legs. We suggest that this essentially ventral division of the prosoma specifically between coxae 2 and 3 is homologous with the so-called sejugal furrow (the sejugal interval sensu van der Hammen). This division constitutes a fundamental part of the body plan in acariform mites (Arachnida: Acariformes). If homologous, this sejugal furrow could represent a further potential synapomorphy for (Solifugae + Acariformes); a relationship with increasing morphological and molecular support. Alternatively, outgroup comparison with sea spiders (Pycnogonida) and certain early Palaeozoic fossils could imply that the sejugal furrow defines an older tagma, derived from a more basal grade of organisation. In this scenario the (still) divided prosoma of acariform mites and camel spiders would be plesiomorphic. This interpretation challenges the textbook arachnid character of a peltidium (or ‘carapace’) covering an undivided prosoma

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

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

Revealing quantum statistics with a pair of distant atoms

Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct measurement of the exchange symmetry of their wave function even in conditions where the particles always remain spatially well separated and thus the exchange contribution to their interaction energy is negligible. We present two protocols revealing the bosonic or fermionic nature of a pair of particles and discuss possible implementations with a pair of trapped atoms or ions.Comment: 4+13 pages, v2 corresponds to the version published by PR

Propagation and spectral properties of quantum walks in electric fields

We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field $\Phi$, e.g., on whether $\Phi/(2\pi)$ is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.Comment: 7 pages, 4 figure

A simple abstraction of arrays and maps by program translation

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,.. .). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the " Dutch flag " algorithm

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