Collisions at infinity in hyperbolic manifolds

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto

Enhancement of thrust reverser cascade performance using aerodynamic and structural integration

This paper focuses on the design of a cascade within a cold stream thrust reverser during the early, conceptual stage of the product development process. A reliable procedure is developed for the exchange of geometric and load data between a two dimensional aerodynamic model and a three dimensional structural model. Aerodynamic and structural simulations are carried out using realistic operating conditions, for three different design configurations with a view to minimising weight for equivalent or improved aerodynamic and structural performance. For normal operational conditions the simulations show that total reverse thrust is unaffected when the performance of the deformed vanes is compared to the un-deformed case. This shows that for the conditions tested, the minimal deformation of the cascade vanes has no significant affect on aerodynamic efficiency and that there is scope for reducing the weight of the cascade. The pressure distribution through a two dimensional thrust reverser section is determined for two additional cascade vane configurations and it is shown that with a small decrease in total reverse thrust, it is possible to reduce weight and eliminate supersonic flow regimes through the nacelle section. By increasing vane sections in high pressure areas and decreasing sections in low pressure areas the structural performance of the cascade vanes in the weight reduced designs, is improved with significantly reduced levels of vane displacement and stress

Microscopic Model for High-spin vs. Low-spin ground state in [Ni2M(CN)8][Ni_2{M(CN)_8]} (M=MoV,WV,NbIVM=Mo^V, W^V, Nb^{IV}) magnetic clusters

Conventional superexchange rules predict ferromagnetic exchange interaction between Ni(II) and M (M=Mo(V), W(V), Nb(IV)). Recent experiments show that in some systems this superexchange is antiferromagnetic. To understand this feature, in this paper we develop a microscopic model for Ni(II)-M systems and solve it exactly using a valence bond approach. We identify the direct exchange coupling, the splitting of the magnetic orbitals and the inter-orbital electron repulsions, on the M site as the parameters which control the ground state spin of various clusters of the Ni(II)-M system. We present quantum phase diagrams which delineate the high-spin and low-spin ground states in the parameter space. We fit the spin gap to a spin Hamiltonian and extract the effective exchange constant within the experimentally observed range, for reasonable parameter values. We also find a region in the parameter space where an intermediate spin state is the ground state. These results indicate that the spin spectrum of the microscopic model cannot be reproduced by a simple Heisenberg exchange Hamiltonian.Comment: 8 pages including 7 figure

Investigating whether adverse prenatal and perinatal events are associated with non-clinical psychotic symptoms at age 12 years in the ALSPAC birth cohort

Background. Non-clinical psychosis-like symptoms (PLIKS) occur in about 15% of the population. It is not clear whether adverse events during early development alter the risk of developing PLIKS. We aimed to examine whether maternal infection, diabetes or pre-eclampsia during pregnancy, gestational age, perinatal cardiopulmonary resuscitation or 5-min Apgar score were associated with development of psychotic symptoms during early adolescence. Method. A longitudinal study of 6356 12-year-old adolescents who completed a semi-structured interview for psychotic symptoms in the Avon Longitudinal Study of Parents and Children (ALSPAC) birth cohort. Prenatal and perinatal data were obtained from obstetric records and maternal questionnaires completed during pregnancy. Results. The presence of definite psychotic symptoms was associated with maternal infection during pregnancy [adjusted odds ratio (OR) 1.44, 95% confidence interval (CI) 1.11–1.86, p=0.006], maternal diabetes (adjusted OR 3.43, 95% CI 1.14–10.36, p=0.029), need for resuscitation (adjusted OR 1.50, 95% CI 0.97–2.31, p=0.065) and 5-min Apgar score (adjusted OR per unit decrease 1.30, 95% CI 1.12–1.50, p<0.001). None of these associations were mediated by childhood IQ score. Most associations persisted, but were less strong, when including suspected symptoms as part of the outcome. There was no association between PLIKS and gestational age or pre-eclampsia. Conclusions. Adverse events during early development may lead to an increased risk of developing PLIKS. Although the status of PLIKS in relation to clinical disorders such as schizophrenia is not clear, the similarity between these results and findings reported for schizophrenia indicates that future studies of PLIKS may help us to understand how psychotic experiences and clinical disorders develop throughout the life-course

The gravitational lensing signatures of BOSS voids in the cosmic microwave background

We report a $5.3\sigma$ detection of the gravitational lensing effect of cosmic voids from the Baryon Oscillation Spectroscopic (BOSS) Data Release 12 seen in the $Planck$ 2018 cosmic microwave background (CMB) lensing convergence map. To make this detection, we introduce new optimal techniques for void stacking and filtering of the CMB maps, such as binning voids by a combination of their observed galaxy density and size to separate those with distinctive lensing signatures. We calibrate theoretical expectations for the void-lensing signal using mock catalogs generated in a suite of 108 full-sky lensing simulations from Takahashi et al. (2017). Relative to these templates, we measure the lensing amplitude parameter in the data to be $A_L=1.10 \pm 0.21$ using a matched-filter stacking technique, and confirm it using an alternative Wiener filtering method. We demonstrate that the result is robust against thermal Sunyaev-Zel'dovich contamination and other sources of systematics. We use the lensing measurements to test the relationship between the matter and galaxy distributions within voids, and show that the assumption of linear bias with a value consistent with galaxy clustering results is discrepant with observation at $\sim 3\sigma$; we explain why such a result is consistent with simulations and previous results, and is expected as a consequence of void selection effects. We forecast the potential for void-CMB lensing measurements in future data from the Advanced ACT, Simons Observatory and CMB-S4 experiments, showing that, for the same number of voids, the achievable precision improves by a factor of more than two compared to $Planck$.Comment: 20 pages, 8 figures, 3 tables; addressed minor comments from the reviewer; accepted for publication in Ap

On the dispersion of latex particles in a nematic solution. I. Experimental evidence and a simple model

Latex polyballs are suspended in an isotropic micellar solution which exhibits a nematic phase at low temperatures. At the transition, we observe that the particles are either retained or expelled from the structured phase depending on their size. A mean field theory with two coupled order parameters is proposed to account for this behavior at the transition. The experimental and theoretical phase diagrams are in qualitative agreement

Superrigid subgroups and syndetic hulls in solvable Lie groups

This is an expository paper. It is not difficult to see that every group homomorphism from the additive group Z of integers to the additive group R of real numbers extends to a homomorphism from R to R. We discuss other examples of discrete subgroups D of connected Lie groups G, such that the homomorphisms defined on D can ("virtually") be extended to homomorphisms defined on all of G. For the case where G is solvable, we give a simple proof that D has this property if it is Zariski dense. The key ingredient is a result on the existence of syndetic hulls.Comment: 17 pages. This is the final version that will appear in the volume "Rigidity in Dynamics and Geometry," edited by M. Burger and A. Iozzi (Springer, 2002