Controlling dipole-dipole frequency shifts in a lattice-based optical atomic clock

Motivated by the ideas of using cold alkaline earth atoms trapped in an optical lattice for realization of optical atomic clocks, we investigate theoretically the perturbative effects of atom-atom interactions on a clock transition frequency. These interactions are mediated by the dipole fields associated with the optically excited atoms. We predict resonance-like features in the frequency shifts when constructive interference among atomic dipoles occur. We theoretically demonstrate that by fine-tuning the coherent dipole-dipole couplings in appropriately designed lattice geometries, the undesirable frequency shifts can be greatly suppressed.Comment: 14 pages, 4 figure

Yb3+ doping effects on thermal conductivity and thermal expansion of Yttrium aluminium garnet

Yttrium Aluminium Garnet (YAG) is an attractive candidate as thermal barrier material used for turbine blade in aero engines, due to its relatively low thermal conductivity, low oxygen diffusivity and good phase stability at high temperature. YAG has a complex crystal structure, in which Y3+ ions locate in dodecahedron and Al3+ ions in octahedron and tetrahedron. Replacing the host cations with rare earth elements can cause the structure change which influences the thermal properties of YAG. Because the space inside the octahedron is relatively small, Yb3+ ions which have the smallest ionic radial size in the lanthanide series, have been selected and attempted to be doped on dodecahedral and octahedral sites to investigate the effects on thermal conductivity and thermal expansion. The variation of lattice constant indicates that Yb3+ ions are located on the dodecahedron or octahedron. In addition, when Yb3+ ions replace Al3+ ions on octahedral sites, the thermal conductivity at room temperature is dramatically reduced and the coefficient of thermal expansion is over 10×10−6 K−1 at high temperature, which results from the expansion of octahedron due to the much larger radius of Yb3+ ion compared with the host cation (Al3+ ion). On the contrary, replacing Y3+ ions with Yb3+ ions in dodecahedron, the thermal conductivity also gradually reduces to the similar value but the coefficient of thermal expansion is getting smaller, due to the relatively small ionic radius of Yb3+ causing the contraction of the dodecahedron. Therefore, a dopant with much larger radius would be preferred in both dodecahedron and octahedron to significant reduce thermal conductivity as well as increase coefficient of thermal expansion of YAG, by introducing large radial difference between the dopant and the host cations

Stoichiometry control of magnetron sputtered Bi2_2Sr2_2Ca1−x_{1-x}Yx_xCu2_2Oy_y (0≤\lex≤\le0.5) thin film, composition spread libraries: Substrate bias and gas density factors

A magnetron sputtering method for the production of thin-film libraries with a spatially varying composition, x, in Bi2Sr2Ca1-xYxCu2Oy (0<=x<=0.5) has been developed. Two targets with a composition of Bi2Sr2YCu2O_{8.5 + \delta} and Bi_2Sr_2CaCu_2O_{8 + \delta} are co-sputtered with appropriate masks. The target masks produce a linear variation in opposite, but co-linear radial direction, and the rotation speed of the substrate table is sufficient to intimately mix the atoms. EDS/WDS composition studies of the films show a depletion of Sr and Bi that is due to oxygen anion resputtering. The depletion is most pronounced at the centre of the film (i.e. on-axis with the target) and falls off symmetrically to either side of the 75 mm substrate. At either edge of the film the stoichiometry matches the desired ratios. Using a 12 mTorr process gas of argon and oxygen in a 2:1 ratio, the strontium depletion is corrected. The bismuth depletion is eliminated by employing a rotating carbon brush apparatus which supplies a -20 V DC bias to the sample substrate. The negative substrate bias has been used successfully with an increased chamber pressure to eliminate the resputtering effect across the film. The result is a thin film composition spread library with the desired stoichiometry.Comment: 16 pages, 12 figures, 4 tables, submitted to Physica C - Superconductivity (April 15, 2005), elsart.st

Continuous Truth II: Reflections

Abstract. In the late 1960s, Dana Scott first showed how the Stone-Tarski topological interpretation of Heyting’s calculus could be extended to model intuitionistic analysis; in particular Brouwer’s continuity prin-ciple. In the early ’80s we and others outlined a general treatment of non-constructive objects, using sheaf models—constructions from topos theory—to model not only Brouwer’s non-classical conclusions, but also his creation of “new mathematical entities”. These categorical models are intimately related to, but more general than Scott’s topological model. The primary goal of this paper is to consider the question of iterated extensions. Can we derive new insights by repeating the second act? In Continuous Truth I, presented at Logic Colloquium ’82 in Florence, we showed that general principles of continuity, local choice and local com-pactness hold in the gros topos of sheaves over the category of separable locales equipped with the open cover topology. We touched on the question of iteration. Here we develop a more gen-eral analysis of iterated categorical extensions, that leads to a reflection schema for statements of predicative analysis. We also take the opportunity to revisit some aspects of both Continuous Truth I and Formal Spaces (Fourman &amp; Grayson 1982), and correct two long-standing errors therein

Tibetan sheep are better able to cope with low energy intake than Small-tailed Han sheep due to lower maintenance energy requirements and higher nutrient digestibilities

Tibetan sheep are indigenous to the Qinghai-Tibetan Plateau (QTP) and are well-adapted to and even thrive under the harsh alpine conditions. Small-tailed Han sheep were introduced to the plateau because of their high prolificacy and are maintained mainly in feedlots. Because of their different backgrounds, we hypothesised that Tibetan and Small-tailed Han sheep would differ in their utilization of energy intake and predicted that Tibetan sheep would cope better with low energy intake than Small-tailed Han sheep. To test this prediction, we determined nutrient digestibilities, energy requirements for maintenance and blood metabolite and hormone concentrations involved in energy metabolism in these breeds. Sheep of each breed (n = 24 of each, all wethers and 1.5 years of age) were distributed randomly into one of four groups and offered ad libitum diets of different digestible energy (DE) densities: 8.21, 9.33, 10.45 and 11.57 MJ DE/kg Dry matter (DM). Following 42 d of measuring feed intake, a 1-week digestion and metabolism experiment was done. DM intakes did not differ between breeds nor among treatments but, by design, DE intake increased linearly in both breeds as dietary energy level increased (P < 0.001). The average daily gain (ADG) was significantly greater in the Tibetan than Small-tailed Han sheep (P = 0.003) and increased linearly in both breeds (P < 0.001). In addition, from the regression analysis of ADG on DE intake, daily DE maintenance requirements were lower for Tibetan than for Small-tailed Han sheep (0.41 vs 0.50 MJ/BW0.75, P < 0.05). The DE and metabolizable energy (ME) digestibilities were higher in the Tibetan than Small-tailed Han sheep (P < 0.001) and increased linearly as the energy level increased in the diet (P < 0.001). At the lowest energy treatment, Tibetan sheep when compared with Small-tailed Han sheep, had: 1) higher serum glucose and glucagon, but lower insulin concentrations (P < 0.05), which indicated a higher capacity for gluconeogenesis and ability to regulate glucose metabolism; and 2) higher non-esterified fatty acids (NEFA) and lower very low density lipoprotein (VLDL) and triglyceride (TG) concentrations (P < 0.05), which indicated a higher capacity for NEFA oxidation but lower ability for triglyceride (TG) synthesis. We concluded that our prediction was supported as these differences between breeds conferred an advantage for Tibetan over Small-tailed Han sheep to cope better with low energy diets

Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions

In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory of gravity are discussed in both rotating Cartesian coordinates and rotating spherical coordinates. The unperturbed rotating body (the ground state) is described as uniformly rotating, stationary and axisymmetric configuration in an asymptotically flat space-time manifold. Deviations from the equilibrium configuration are described by means of a displacement field. In terms of the formalism of relativistic celestial mechanics developed by Damour, Soffel and Xu, and the framework established by Carter and Quintana the post Newtonian equations of the displacement field and the symmetric trace-free shear tensor are obtained. Corresponding post-Newtonian junction conditions at interfaces also the outer surface boundary conditions are presented. The PN junction condition is an extension of Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page

Collective modes of asymmetric nuclear matter in Quantum HadroDynamics

We discuss a fully relativistic Landau Fermi liquid theory based on the Quantum Hadro-Dynamics ($QHD$) effective field picture of Nuclear Matter ({\it NM}). From the linearized kinetic equations we get the dispersion relations of the propagating collective modes. We focus our attention on the dynamical effects of the interplay between scalar and vector channel contributions. A beautiful ``mirror'' structure in the form of the dynamical response in the isoscalar/isovector degree of freedom is revealed, with a complete parallelism in the role respectively played by the compressibility and the symmetry energy. All that strongly supports the introduction of an explicit coupling to the scalar-isovector channel of the nucleon-nucleon interaction. In particular we study the influence of this coupling (to a $\delta$-meson-like effective field) on the collective response of asymmetric nuclear matter ($ANM$). Interesting contributions are found on the propagation of isovector-like modes at normal density and on an expected smooth transition to isoscalar-like oscillations at high baryon density. Important ``chemical'' effects on the neutron-proton structure of the mode are shown. For dilute $ANM$ we have the isospin distillation mechanism of the unstable isoscalar-like oscillations, while at high baryon density we predict an almost pure neutron wave structure of the propagating sounds.Comment: 18 pages (LATEX), 8 Postscript figures, uses "epsfig

Random Networks with given Rich-club Coefficient

In complex networks it is common to model a network or generate a surrogate network based on the conservation of the network's degree distribution. We provide an alternative network model based on the conservation of connection density within a set of nodes. This density is measure by the rich-club coefficient. We present a method to generate surrogates networks with a given rich-club coefficient. We show that by choosing a suitable local linking term, the generated random networks can reproduce the degree distribution and the mixing pattern of real networks. The method is easy to implement and produces good models of real networks.Comment: revised version, new figure

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201