Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains

Topological phases supporting non-abelian anyonic excitations have been proposed as candidates for topological quantum computation. In this paper, we study disordered non-abelian anyonic chains based on the quantum groups $SU(2)_k$, a hierarchy that includes the $\nu=5/2$ FQH state and the proposed $\nu=12/5$ Fibonacci state, among others. We find that for odd $k$ these anyonic chains realize infinite randomness critical {\it phases} in the same universality class as the $S_k$ permutation symmetric multi-critical points of Damle and Huse (Phys. Rev. Lett. 89, 277203 (2002)). Indeed, we show that the pertinent subspace of these anyonic chains actually sits inside the ${\mathbb Z}_k \subset S_k$ symmetric sector of the Damle-Huse model, and this ${\mathbb Z}_k$ symmetry stabilizes the phase.Comment: 13 page

A concept for a fuel efficient flight planning aid for general aviation

A core equation for estimation of fuel burn from path profile data was developed. This equation was used as a necessary ingredient in a dynamic program to define a fuel efficient flight path. The resultant algorithm is oriented toward use by general aviation. The pilot provides a description of the desired ground track, standard aircraft parameters, and weather at selected waypoints. The algorithm then derives the fuel efficient altitudes and velocities at the waypoints

Non-Linear Beam Splitter in Bose-Einstein Condensate Interferometers

A beam splitter is an important component of an atomic/optical Mach-Zehnder interferometer. Here we study a Bose Einstein Condensate beam splitter, realized with a double well potential of tunable height. We analyze how the sensitivity of a Mach Zehnder interferometer is degraded by the non-linear particle-particle interaction during the splitting dynamics. We distinguish three regimes, Rabi, Josephson and Fock, and associate to them a different scaling of the phase sensitivity with the total number of particles.Comment: draft, 19 pages, 10 figure

A stochastic model for early placental development

In the human, placental structure is closely related to placental function and consequent pregnancy outcome. Studies have noted abnormal placental shape in small-for-gestational age infants which extends to increased lifetime risk of cardiovascular disease. The origins and determinants of placental shape are incompletely under-stood and are difficult to study in vivo. In this paper we model the early development of the placenta in the human, based on the hypothesis that this is driven by dynamics dominated by a chemo-attractant effect emanating from proximal spiral arteries in the decidua. We derive and explore a two-dimensional stochastic model for these events, and investigate the effects of loss of spiral arteries in regions near to the cord insertion on the shape of the placenta. This model demonstrates that placental shape is highly variable and disruption of spiral arteries can exert profound effects on placental shape, particularly if this disruption is close to the cord insertion. Thus, placental shape reflects the underlying maternal vascular bed. Abnormal placental shape may reflect an abnormal uterine environment, which predisposes to pregnancy complications

Nonlinearity of vacuum reggeons and exclusive diffractive production of vector mesons at HERA

The processes of exclusive photo- and electroproduction of vector mesons $\rho^0$(770), $\phi$(1020) and $J/\psi$(3096) at collision energies $30 GeV<W<300 GeV$ and transferred momenta squared $0<-t<2 GeV^2$ are considered in the framework of a phenomenological Regge-eikonal scheme with nonlinear Regge trajectories in which their QCD asymptotic behavior is taken into account explicitly. By comparison of available experimental data from ZEUS and H1 Collaborations with the model predictions it is demonstrated that corresponding angular distributions and integrated cross-sections in the above-mentioned kinematical range can be quantitatively described with use of two $C$-even vacuum Regge trajectories. These are the "soft" pomeron dominating the high energy reactions without a hard scale and the "hard" pomeron giving an essential contribution to photo- and electroproduction of heavy vector mesons and deeply virtual electroproduction of light vector mesons.Comment: 25 pages, 12 figure

Tear film thickness variations and the role of the tear meniscus

A mathematical model is developed to investigate the two-dimensional variations in the thickness of tear fluid deposited on the eye surface during a blink. Such variations can become greatly enhanced as the tears evaporate during the interblink period.\ud The four mechanisms considered are: i) the deposition of the tear film from the upper eyelid meniscus, ii) the flow of tear fluid from under the eyelid as it is retracted and from the lacrimal gland, iii) the flow of tear fluid around the eye within the meniscus and iv) the drainage of tear fluid into the canaliculi through the inferior and superior puncta.\ud There are two main insights from the modelling. First is that the amount of fluid within the tear meniscus is much greater than previously employed in models and this significantly changes the predicted distribution of tears. Secondly the uniformity of the tear film for a single blink is: i) primarily dictated by the storage in the meniscus, ii) quite sensitive to the speed of the blink and the ratio of the viscosity to the surface tension iii) less sensitive to the precise puncta behaviour, the flow under the eyelids or the specific distribution of fluid along the meniscus at the start of the blink. The modelling briefly examines the flow into the puncta which interact strongly with the meniscus and acts to control the meniscus volume. In addition it considers flow from the lacrimal glands which appears to occurs continue even during the interblink period when the eyelids are stationary

General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it includes Appendi