Gradient flows without blow-up for Lefschetz thimbles

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. We study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.Comment: 31 pages, 11 figures, (v2) conclusion part is expande

Random Matrix Models for Dirac Operators at finite Lattice Spacing

We study discretization effects of the Wilson and staggered Dirac operator with $N_{\rm c}>2$ using chiral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a determinantal expression over complex pairs of eigenvalues, and real eigenvalues corresponding to eigenvectors of positive or negative chirality as well as for the eigenvalue densities. The explicit dependence on the lattice spacing can be readily read off from our results which are compared to numerical simulations of Wilson-chRMT. For the staggered Dirac operator we have studied random matrices modeling the transition from non-degenerate eigenvalues at non-zero lattice spacing to degenerate ones in the continuum limit.Comment: 7 pages, 6 figures, Proceedings for the XXIX International Symposium on Lattice Field Theory, July 10 -- 16 2011, Squaw Valley, Lake Tahoe, California, PACS: 12.38.Gc, 05.50.+q, 02.10.Yn, 11.15.H

The Factorization Method for Simulating Systems With a Complex Action

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix theory of finite density QCD where we compare with analytic results. In this model we find non--commutativity of the limits $\mu\to 0$ and $N\to\infty$ which could be of relevance in QCD at finite density.Comment: Talk by K.N.A. at Confinement 2003, Tokyo, July 2003, 5 pages, 4 figures, ws-procs9x6.cl

South Carolina mayflies (Insecta: Ephemeroptera) of Conservation Concern

Abstract: Nine mayfly species (Insecta: Ephemeroptera) that may be of conservation concern in South Carolina are discussed. Three such species associated with sand-bottomed streams are Acanthametropus pecatonica (Burks, 1953), Dolania americana Edmunds & Traver, 1959 and Homeoneuria dolani Edmunds, Berner & Traver, 1958. Three species of potential concern are associated with Hornleaf Riverweed (Podostemum ceratophyllum Michaux, 1803), and they include Barbaetis benfieldi Kennedy, 1985, Heterocloeon berneri (Muller-Liebenau, 1974) and Tsalia berneri (Allen & Edmunds, 1958). Mayflies of slow or stagnant waters that may be of conservation concern in South Carolina include Arthroplea bipunctata (McDunnough, 1924), Macaffertium lenati (McCafferty, 1990) and Siphlonurus decorus Traver, 1932. Biological, ecological and geographic distribution studies of each species are reviewed. The South Carolina record of A. bipunctata is questionable. New data are provided for S. decorus

Ephemeroptera of Canada

Thus far, 335 currently valid species in 82 genera and 21 families of mayflies (Ephemeroptera) have been documented from Canada, remarkably representing a little more than half of the combined species richness of Canada, Mexico and the USA. The current known species richness for Canada represents an increase of 11.3% as compared to that reported in 1979. Species richness is greatest in the families Heptageniidae (83), Baetidae (76) and Ephemerellidae (45). A total of 328 DNA Barcode Index Numbers (BINs) are available for Canadian mayfly species. The greatest net gains anticipated for future species tallies are for Baetidae (25), Heptageniidae (10) and Leptophlebiidae (10). A total of 66 more species overall is anticipated for Canada, with greatest gains potentially coming from lentic habitats across Canada and from far eastern and far western areas in general. However, even metropolitan areas should not be overlooked for the potential of discovery

Measurement and Modeling of the Acoustic Response in a High Pressure Combustor

In this paper, a one dimensional acoustic network model is presented which can be used as a design tool to predict the limit cycle pressure oscillations in a gas turbine combustor. Analytically represented models are combined with measured flame transfer functions and well defined boundary conditions. Additionally acoustic damping due to turbulence, acoustic reflection at contractions, modification of the acoustic speed of sound due to a mean flow and effect of temperature gradient that play a role in the acoustic modeling of combustion systems have been included in this network model. The model is applied on a high-pressure laboratory combustor. Finally, the measured and predicted dynamic behaviour in the combustor is compared. The results indicate the network modelling approach is a promising design tool for gas turbine combustion application

Large NN expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs

In this paper we explain the relation between the free energy of the SYK model for $N$ Majorana fermions with a random $q$-body interaction and the moments of its spectral density. The high temperature expansion of the free energy gives the cumulants of the spectral density. Using that the cumulants are extensive we find the $p$ dependence of the $1/N^2$ correction of the $2p$-th moments obtained in 1801.02696. Conversely, the $1/N^2$ corrections to the moments give the correction (even $q$) to the $\beta^6$ coefficient of the high temperature expansion of the free energy for arbitrary $q$. Our result agrees with the $1/q^3$ correction obtained by Tarnopolsky using a mean field expansion. These considerations also lead to a more powerful method for solving the moment problem and intersection-graph enumeration problems. We take advantage of this and push the moment calculation to $1/N^3$ order and find surprisingly simple enumeration identities for intersection graphs. The $1/N^3$ corrections to the moments, give corrections to the $\beta^8$ coefficient (for even $q$) of the high temperature expansion of the free energy which have not been calculated before. Results for odd $q$, where the SYK `Hamiltonian' is the supercharge of a supersymmetric theory are discussed as well