Canonical bases arising from quantum symmetric pairs

We develop a general theory of canonical bases for quantum symmetric pairs (\mathbf{U}, \mathbf{U}^\imath) with parameters of arbitrary finite type. We construct new canonical bases for the simple integrable $\mathbf{U}$-modules and their tensor products regarded as \mathbf{U}^\imath-modules. We also construct a canonical basis for the modified form of the $\imath$quantum group \mathbf{U}^\imath. To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank one), and integrality of the intertwiners.Comment: v1, 76 pages. v2, 62 pages, much shortened appendix, modified introduction and other corrections, to appear in Invent. Mat

Isospin Diffusion in Heavy-Ion Collisions and the Neutron Skin Thickness of Lead

The correlation between the thickness of the neutron skin in Pb-208, and the degree of isospin diffusion in heavy-ion collisions is examined. The same equation of state is used to compute the degree of isospin diffusion in an isospin-depedent transport model and the neutron skin thickness in the Hartree-Fock approximation. We find that skin thicknesses less than 0.15 fm are excluded by the isospin diffusion data.Comment: 5 pages, 4 figures; few minor corrections and updates; version to appear in PR

A Note on Topological M5-branes and String-Fivebrane Duality

We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motion for the 3-form on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer equation, providing support for a string-fivebrane duality in topological string theory.Comment: 11 pp, plain te

District-level Spatial Analysis of Migration Flows in Ghana: Determinants and Implications for Policy

The present study investigates the determinants of inter-district migration flows over the 1995-2000 period in Ghana. A combination of socio-economic, natural and spatial ‘district-level’ attributes are considered as potential variables explaining the direction of migration flows. In addition to the ‘net’ migration model, ‘in’ and ‘out’ migration models are also employed within the context of the gravity model. Results in the three models consistently show that people move out of districts with less employment and choose districts with high employment rate as destinations. While shorter distance to roads encourages out-migration, districts with better water access seem to attract migrants. Generally, people move out of predominantly agrarian districts to relatively more urbanized districts.Gross migration, Net migration, Inter-district migration flows, spatial analysis, Ghana, Africa, Community/Rural/Urban Development, Labor and Human Capital,

Constraining the Skyrme effective interactions and the neutron skin thickness of nuclei using isospin diffusion data from heavy ion collisions

Recent analysis of the isospin diffusion data from heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections has led to the extraction of a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density. This imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nuclei. Among the 21 sets of Skyrme interactions commonly used in nuclear structure studies, the 4 sets SIV, SV, G$_\sigma$, and R$_\sigma$ are found to give $L$ values that are consistent with the extracted one. Further study on the correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy in the Skyrme Hartree-Fock approach leads to predicted thickness of the neutron skin of $0.22\pm 0.04$ fm for $^{208}$Pb, $0.29\pm 0.04$ fm for $^{132}$Sn, and $0.22\pm 0.04$ fm for $^{124}$Sn.Comment: 10 pages, 4 figures, 1 Table, Talk given at 1) International Conference on Nuclear Structure Physics, Shanghai, 12-17 June, 2006; 2) 11th China National Nuclear Structure Physics Conference, Changchun, Jilin, 13-18 July, 200

Efficacy of crustal superfluid neutrons in pulsar glitch models

In order to assess the ability of purely crust-driven glitch models to match the observed glitch activity in the Vela pulsar, we conduct a systematic analysis of the dependence of the fractional moment of inertia of the inner crustal neutrons on the stiffness of the nuclear symmetry energy at saturation density $L$. We take into account both crustal entrainment and the fact that only a fraction $Y_{\rm g}$ of the core neutrons may couple to the crust on the glitch-rise timescale. We use a set of consistently-generated crust and core compositions and equations-of-state which are fit to results of low-density pure neutron matter calculations. When entrainment is included at the level suggested by recent microscopic calculations and the core is fully coupled to the crust, the model is only able to account for the Vela glitch activity for a 1.4$M_{\odot}$ star if the equation of state is particularly stiff $L>100$ MeV. However, an uncertainty of about 10\% in the crust-core transition density and pressure allows for the Vela glitch activity to be marginally accounted for in the range $L\approx30-60$MeV consistent with a range of experimental results. Alternatively, only a small amount of core neutrons need be involved. If less than 50\% of the core neutrons are coupled to the crust during the glitch, we can also account for the Vela glitch activity using crustal neutrons alone for EOSs consistent with the inferred range of $L$. We also explore the possibility of Vela being a high-mass neutron star, and of crustal entrainment being reduced or enhanced relative to its currently predicted values.Comment: 10 pages, 6 figure

Categorification of quantum symmetric pairs I

We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$-category \`a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the BGG category $\mathcal{O}$ of type B/C.Comment: final version, to appear in Quantum Topolog

Triton-3He relative and differential flows and the high density behavior of nuclear symmetry energy

Using a transport model coupled with a phase-space coalescence after-burner we study the triton-3He relative and differential transverse flows in semi-central 132Sn+124Sn reactions at a beam energy of 400 MeV/nucleon. We find that the triton-3He pairs carry interesting information about the density dependence of the nuclear symmetry energy. The t-3He relative flow can be used as a particularly powerful probe of the high-density behavior of the nuclear symmetry energy.Comment: 6 pages, 2 figures, Proceeding of The International Workshop on Nuclear Dynamics in Heavy-Ion Reactions and the Symmetry Energ