Structure of a linear array of hollow vortices of finite cross-section

Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A[1/2]/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable

A CLT for Plancherel representations of the infinite-dimensional unitary group

We study asymptotics of traces of (noncommutative) monomials formed by images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge to (commutative) moments of a Gaussian process that can be viewed as a collection of simply yet nontrivially correlated two-dimensional Gaussian Free Fields. The limiting process has previously arisen via the global scaling limit of spectra for submatrices of Wigner Hermitian random matrices. This note is an announcement, proofs will appear elsewhere.Comment: 12 page

Addition of a sequence from α2-antiplasmin transforms human serum albumin into a blood clot component that speeds clot lysis

<p>Abstract</p> <p>Background</p> <p>The plasma protein α₂-antiplasmin (α₂AP) is cross-linked to fibrin in blood clots by the transglutaminase factor XIIIa, and in that location retards clot lysis. Competition for this effect could be clinically useful in patients with thrombosis. We hypothesized that fusion of N-terminal portions of α₂-antiplasmin to human serum albumin (HSA) and production of the chimeric proteins in <it>Pichia pastoris </it>yeast would produce a stable and effective competitor protein.</p> <p>Results</p> <p>Fusion protein α₂AP(13-42)-HSA was efficiently secreted from transformed yeast and purified preparations contained within a mixed population the full-length intact form, while fusions with longer α₂AP moieties were inefficiently secreted and/or degraded. The α₂AP(13-42)-HSA protein, but not recombinant HSA, was cross-linked to both chemical lysine donors and fibrin or fibrinogen by factor XIIIa, although with less rapid kinetics than native α₂AP. Excess α₂AP(13-42)-HSA competed with α₂AP for cross-linking to chemical lysine donors more effectively than a synthetic α₂AP(13-42) peptide, and reduced the α₂AP-dependent resistance to fibrinolysis of plasma clots equally effectively as the peptide. Native α₂AP was found in <it>in vivo </it>clots in rabbits to a greater extent than α₂AP(13-42), however.</p> <p>Conclusion</p> <p>In this first report of transfer of transglutamination substrate status from one plasma protein to another, fusion protein α₂AP(13-42)-HSA was shown to satisfy initial requirements for a long-lasting, well-tolerated competitive inhibitor of α₂-antiplasmin predicted to act in a clot-localized manner.</p

Imaginary geometry III: reversibility of SLEκ for κ ∈ (4, 8)

Suppose that D ⊆ C is a Jordan domain and x; y ∈ ∂D are distinct. Fix K 2 (4; 8), and let η be an SLE k process from x to y in D. We prove that the law of the time-reversal of η is, up to reparametrization, an SLE K process from y to x in D. More generally, we prove that SLE k (ρ1; ρ2) processes are reversible if and only if both ρ i are at least K=2-4, which is the critical threshold at or below which such curves are boundary filling. Our result supplies the missing ingredient needed to show that for all k ∈ (4; 8), the so-called conformal loop ensembles CLE K are canonically defined, with almost surely continuous loops. It also provides an interesting way to couple two Gaussian free fields (with different boundary conditions) so that their difference is piecewise constant and the boundaries between the constant regions are SLE K curves

Duality and KPZ in Liouville Quantum Gravity

We present a (mathematically rigorous) probabilistic and geometrical proof of the KPZ relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gravity. It uses the properly regularized quantum area measure d\mu_\gamma=\epsilon^{\gamma^2/2} e^{\gamma h_\epsilon(z)}dz, where dz is Lebesgue measure on D, \gamma is a real parameter, 0\leq \gamma <2, and h_\epsilon(z) denotes the mean value on the circle of radius \epsilon centered at z of an instance h of the Gaussian free field on D. The proof extends to the boundary geometry. The singular case \gamma >2 is shown to be related to the quantum measure d\mu_{\gamma'}, \gamma' < 2, by the fundamental duality \gamma\gamma'=4.Comment: 4 pages, 1 figur

Using a Gridded Global Dataset to Characterize Regional Hydroclimate in Central Chile

Central Chile is facing dramatic projections of climate change, with a consensus for declining precipitation, negatively affecting hydropower generation and irrigated agriculture. Rising from sea level to 6000 m within a distance of 200 km, precipitation characterization is difficult because of a lack of long-term observations, especially at higher elevations. For understanding current mean and extreme conditions and recent hydroclimatological change, as well as to provide a baseline for downscaling climate model projections, a temporally and spatially complete dataset of daily meteorology is essential. The authors use a gridded global daily meteorological dataset at 0.25° resolution for the period 1948–2008, adjusted by monthly precipitation observations interpolated to the same grid using a cokriging method with elevation as a covariate. For validation, daily statistics of the adjusted gridded precipitation are compared to station observations. For further validation, a hydrology model is driven with the gridded 0.25° meteorology and streamflow statistics are compared with observed flow. The high elevation precipitation is validated by comparing the simulated snow extent to Moderate Resolution Imaging Spectroradiometer (MODIS) images. Results show that the daily meteorology with the adjusted precipitation can accurately capture the statistical properties of extreme events as well as the sequence of wet and dry events, with hydrological model results displaying reasonable agreement with observed streamflow and snow extent. This demonstrates the successful use of a global gridded data product in a relatively data-sparse region to capture hydroclimatological characteristics and extremes

Quantum Loewner evolution

What is the scaling limit of diffusion-limited aggregation (DLA) in the plane? This is an old and famously difficult question. One can generalize the question in two ways: first, one may consider the dielectric breakdown model η-DBM, a generalization of DLA in which particle locations are sampled from the η th power of harmonic measure, instead of harmonic measure itself. Second, instead of restricting attention to deterministic lattices, one may consider η-DBM on random graphs known or believed to conve rge in law to a Liouville quantum gravity (LQG) surface with parameter γ e [0,2]. In this generality, we propose a scaling limit candidate called quantum Loewner evolution, QLE(γ 2 ,η). QLE is defined in terms of the radial Loewner equation like radial stochastic Loewner evolution, except that it is driven by a measure-valued diffusion v t derived from LQG rather than a multiple of a standard Brownian motion. We formalize the dynamics of v t using a stochastic partial differential equation. For each γ e [0, 2], there are two or three special values of η for which we establish the existence of a solution to these dynamics and explicitly describe the stationary law of v t . We also explain discrete versions of our construction that relate DLA to loop-erased random walks and the Eden model to percolation. A certain "reshuffling" trick (in which concentric annular regions are rotated randomly, like slot-machine reels) facilitates explicit calculation. We propose QLE(2, 1) as a scaling limit for DLA on a random spanning-tree-decorated planar map and QLE(8/3, 0) as a scaling limit for the Eden model on a random triangulation. We propose using QLE(8/3, 0) to endow pure LQG with a distance function, by interpreting the region explored by a branching variant of QLE(8/3, 0), up to a fixed time, as a metric ball in a random metric space

A re-interpretation of the Triangulum-Andromeda stellar clouds: a population of halo stars kicked out of the Galactic disk

The Triangulum-Andromeda stellar clouds (TriAnd1 and TriAnd2) are a pair of concentric ring- or shell-like over-densities at large $R$ ($\approx$ 30 kpc) and $Z$ ($\approx$ -10 kpc) in the Galactic halo that are thought to have been formed from the accretion and disruption of a satellite galaxy. This paper critically re-examines this formation scenario by comparing the number ratio of RR Lyrae to M giant stars associated with the TriAnd clouds with other structures in the Galaxy. The current data suggest a stellar population for these over-densities ($f_{\rm RR:MG} < 0.38$ at 95% confidence) quite unlike any of the known satellites of the Milky Way ($f_{\rm RR:MG} \approx 0.5$ for the very largest and $f_{\rm RR:MG} >>1$ for the smaller satellites) and more like the population of stars born in the much deeper potential well inhabited by the Galactic disk ($f_{\rm RR:MG} < 0.01$). N-body simulations of a Milky-Way-like galaxy perturbed by the impact of a dwarf galaxy demonstrate that, in the right circumstances, concentric rings propagating outwards from that Galactic disk can plausibly produce similar over-densities. These results provide dramatic support for the recent proposal by Xu et al. (2015) that, rather than stars accreted from other galaxies, the TriAnd clouds could represent stars kicked-out from our own disk. If so, these would be the first populations of disk stars to be found in the Galactic halo and a clear signature of the importance of this second formation mechanism for stellar halos more generally. Moreover, their existence at the very extremities of the disk places strong constraints on the nature of the interaction that formed them.Comment: 27 pages, 8 figures; published in MNRA

Popular music, psychogeography, place identity and tourism: The case of Sheffield

Tourism and cultural agencies in some English provincial cities are promoting their popular music ‘heritage’ and, in some cases, contemporary musicians through the packaging of trails, sites, ‘iconic’ venues and festivals. This article focuses on Sheffield, a ‘post-industrial’ northern English city which is drawing on its associations with musicians past and present in seeking to attract tourists. This article is based on interviews with, among others, recording artists, promoters, producers and venue managers, along with reflective observational and documentary data. Theoretical remarks are made on the representations of popular musicians through cultural tourism strategies, programmes and products and also on the ways in which musicians convey a ‘psychogeographical’ sense of place in the ‘soundscape’ of the city