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

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

Bipolar orientations on planar maps and SLE <inf>12</inf>

We give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the "peano curve" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a $\sqrt{4/3}$-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter $\kappa=12$ (i.e., SLE$_{12}$). This result is universal in the sense that it holds for bipolar-oriented triangulations, quadrangulations, $k$-angulations, and maps in which face sizes are mixed

Advances in tunable powerful lasers: The advanced free-electron laser

In the past several decades, remarkable progress in laser science and technology has made it possible to obtain laser light from the ultra-violet to the far infra-red from a variety of laser types, and at power levels from milliwatts to kilowatts (and, some day, megawatts). However, the availability of tunable lasers at ``high`` power (above a few tens of watts) is more limited. Figure 1, an assessment of the availability of tunable lasers, shows the covered range to be about 400 to 2000 nanometers. A variety of dye lasers cover the visible and near infra red, each one of which is tunable over approximately a 10% range. In the same region, the TI:saphire laser is adjustable over a 20 to 25% range. And finally, optical parametric oscillators can cover the range from about 400 nanometers out to about 2000 nm (even farther at reduced energy output). The typical output energy per pulse may vary from a few to one hundred millijoules, and since repetition rates of 10 to 100 Hertz are generally attainable, average output powers of tens of watts are possible. In recent years, a new approach to powerful tunable lasers -- the Free-Electron Laser (FEL) -- has emerged. In this paper we will discuss advances in FEL technology which not only enable tunability at high average power over a very broad range of wavelengths, but also make this device more usable. At present, that range is about one micron to the far infra red; with extensions of existing technology, it should be extendable to the vacuum ultra violet region

Another derivation of the geometrical KPZ relations

We give a physicist's derivation of the geometrical (in the spirit of Duplantier-Sheffield) KPZ relations, via heat kernel methods. It gives a covariant way to define neighborhoods of fractals in 2d quantum gravity, and shows that these relations are in the realm of conformal field theory

Disk Heating, Galactoseismology, and the Formation of Stellar Halos

Deep photometric surveys of the Milky Way have revealed diffuse structures encircling our Galaxy far beyond the "classical" limits of the stellar disk. This paper reviews results from our own and other observational programs, which together suggest that, despite their extreme positions, the stars in these structures were formed in our Galactic disk. Mounting evidence from recent observations and simulations implies kinematic connections between several of these distinct structures. This suggests the existence of collective disk oscillations that can plausibly be traced all the way to asymmetries seen in the stellar velocity distribution around the Sun. There are multiple interesting implications of these findings: they promise new perspectives on the process of disk heating, they provide direct evidence for a stellar halo formation mechanism in addition to the accretion and disruption of satellite galaxies, and, they motivate searches of current and near-future surveys to trace these oscillations across the Galaxy. Such maps could be used as dynamical diagnostics in the emerging field of "Galactoseismology", which promises to model the history of interactions between the Milky Way and its entourage of satellites, as well examine the density of our dark matter halo. As sensitivity to very low surface brightness features around external galaxies increases, many more examples of such disk oscillations will likely be identified. Statistical samples of such features not only encode detailed information about interaction rates and mergers, but also about long sought-after dark matter halo densities and shapes. Models for the Milky Way's own Galactoseismic history will therefore serve as a critical foundation for studying the weak dynamical interactions of galaxies across the universe.Comment: 20 pages, 5 figures, accepted in for publication in a special edition of the journal "Galaxies", reporting the proceedings of the conference "On the Origin (and Evolution) of Baryonic Galaxy Halos", Puerto Ayora, Ecuador, March 13-17 2017, Eds. Duncan A. Forbes and Ericson D. Lope

Conformal loop ensembles and the stress-energy tensor

We give a construction of the stress-energy tensor of conformal field theory (CFT) as a local "object" in conformal loop ensembles CLE_\kappa, for all values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the central charges 0 < c <= 1, and including all CFT minimal models). We provide a quick introduction to CLE, a mathematical theory for random loops in simply connected domains with properties of conformal invariance, developed by Sheffield and Werner (2006). We consider its extension to more general regions of definition, and make various hypotheses that are needed for our construction and expected to hold for CLE in the dilute regime. Using this, we identify the stress-energy tensor in the context of CLE. This is done by deriving its associated conformal Ward identities for single insertions in CLE probability functions, along with the appropriate boundary conditions on simply connected domains; its properties under conformal maps, involving the Schwarzian derivative; and its one-point average in terms of the "relative partition function." Part of the construction is in the same spirit as, but widely generalizes, that found in the context of SLE_{8/3} by the author, Riva and Cardy (2006), which only dealt with the case of zero central charge in simply connected hyperbolic regions. We do not use the explicit construction of the CLE probability measure, but only its defining and expected general properties.Comment: 49 pages, 3 figures. This is a concatenated, reduced and simplified version of arXiv:0903.0372 and (especially) arXiv:0908.151

Shock-induced reaction in several liquids

Single-shock experiments have been completed in several liquids using multiple, embedded, electromagnetic Lagrangian particle velocity and impulse gauges to measure shock waveforms. The liquids include acrylonitrile, bromoform, diiodomethane, phenylacetylene, bromocyclopropane, and carbon disulfide. Some of these are known to exhibit shock-induced reaction and others are considered to be candidates for reaction studies. The ''universal'' liquid Hugoniot, which depends only on initial condition sound speed, was used to calculate the unreacted Hugoniot. Sound velocities were measured for those liquids with no data available. The effects of shock-induced reaction are clearly identified in the particle velocity waveforms for some materials, but there are remaining questions about whether reactions occur in others. The most impressive results are that the full reactive, two-wave structure was measured in phenylacetylene. On the reacting materials with two-wave structures, the particle velocity waveforms had a decrease behind the top of the first wave. This is thought to be evidence of an early reaction which occurs at the top of the first (nonreactive) wave. 12 refs., 2 figs., 1 tab

Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of 1/f1/f Noises generated by Gaussian Free Fields

We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian Free Field (2dGFF) along various planar curves. Our method extends the recent analysis of Fyodorov Bouchaud from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a {\it duality relation} satisfied by the suitable generating function of free energy cumulants in the high-temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the $[0,1]$ interval. We provide numerical checks of the circular and the interval case and discuss universality and various extensions. Relevance to the distribution of length of a segment in Liouville quantum gravity is noted.Comment: 25 pages, 12 figures Published version. Misprint corrected, references and note adde

Species of ground beetle (Coleoptera: Carabidae) in organic apple orchards of British Columbia

In a two year study, 14 genera of Carabidae (Agonum Bonelli, Amara Bonelli, Anisodactylus Dejean, Bembidion Latreille, Carabus Linné, Harpalus Latreille, Lebia Latreille, Loricera Latreille, Poecilus Bonelli, Pterostichus Bonelli, Scaphinotus Dejean, Stenolophus Stephens, Syntomus Hope and Trechus Clairville) represented by 44 species were identified from six commercial organic apple orchards in the southern Similkameen valley in British Columbia, Canada; 13 of these species were not native to the area. The 4,299 specimens were caught in 'ramp' pitfall traps, with the genera Pterostichus and Harpalus comprising 56% and 43%, respectively. Numbers of Carabidae ranged from 11-21 species per orchard, with their presence detected throughout the collection period