Quivers, curves, and the tropical vertex

Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. Commutators in the group are related to Euler characteristics of the moduli spaces of quiver representations and the Gromov-Witten theory of toric surfaces. After a short survey of the subject (based on lectures of Pandharipande at the 2009 Geometry summer school in Lisbon), we prove new results about the rays and symmetries of scattering diagrams of commutators (including previous conjectures by Gross-Siebert and Kontsevich). Where possible, we present both the quiver and Gromov-Witten perspectives.Comment: 43 page

More on Phase Structure of Nonlocal 2D Generalized Yang-Mills Theories (nlgYM2_2's)

We study the phase structure of nonlocal two dimensional generalized Yang - Mills theories (nlgYM$_2$) and it is shown that all order of $\phi^{2k}$ model of these theories has phase transition only on compact manifold with $g = 0$(on sphere), and the order of phase transition is 3. Also it is shown that the $\phi^2 + \frac{2\alpha}{3}\phi^3$ model of nlgYM$_2$ has third order phase transition on any compact manifold with $1 < g < 1+ \frac{\hat{A}}{|\eta_c|}$, and has no phase transition on sphere.Comment: 11 pages, no figure

Thermal fluctuations in the lattice Boltzmann method for non-ideal fluids

We introduce thermal fluctuations in the lattice Boltzmann method for non-ideal fluids. A fluctuation-dissipation theorem is derived within the Langevin framework and applied to a specific lattice Boltzmann model that approximates the linearized fluctuating Navier-Stokes equations for fluids based on square-gradient free energy functionals. The obtained thermal noise is shown to ensure equilibration of all degrees of freedom in a simulation to high accuracy. Furthermore, we demonstrate that satisfactory results for most practical applications of fluctuating hydrodynamics can already be achieved using thermal noise derived in the long wavelength-limit.Comment: 15 pages, 5 figure

Statistical aspects of carbon fiber risk assessment modeling

The probabilistic and statistical aspects of the carbon fiber risk assessment modeling of fire accidents involving commercial aircraft are examined. Three major sources of uncertainty in the modeling effort are identified. These are: (1) imprecise knowledge in establishing the model; (2) parameter estimation; and (3)Monte Carlo sampling error. All three sources of uncertainty are treated and statistical procedures are utilized and/or developed to control them wherever possible

spl(2,1) dynamical supersymmetry and suppression of ferromagnetism in flat band double-exchange models

The low energy spectrum of the ferromagnetic Kondo lattice model on a N-site complete graph extended with on-site repulsion is obtained from the underlying spl(2,1) algebra properties in the strong coupling limit. The ferromagnetic ground state is realized for 1 and N+1 electrons only. We identify the large density of states to be responsible for the suppression of the ferromagnetic state and argue that a similar situation is encountered in the Kagome, pyrochlore, and other lattices with flat bands in their one-particle density of states.Comment: 7 pages, 1 figur

Two-pion exchange potential and the πN\pi N amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped tar fil

Peripheral visual response time to colored stimuli imaged on the horizontal meridian

Two male observers were administered a binocular visual response time task to small (45 min arc), flashed, photopic stimuli at four dominant wavelengths (632 nm red; 583 nm yellow; 526 nm green; 464 nm blue) imaged across the horizontal retinal meridian. The stimuli were imaged at 10 deg arc intervals from 80 deg left to 90 deg right of fixation. Testing followed either prior light adaptation or prior dark adaptation. Results indicated that mean response time (RT) varies with stimulus color. RT is faster to yellow than to blue and green and slowest to red. In general, mean RT was found to increase from fovea to periphery for all four colors, with the curve for red stimuli exhibiting the most rapid positive acceleration with increasing angular eccentricity from the fovea. The shape of the RT distribution across the retina was also found to depend upon the state of light or dark adaptation. The findings are related to previous RT research and are discussed in terms of optimizing the color and position of colored displays on instrument panels

Emergent bipartiteness in a society of knights and knaves

We propose a simple model of a social network based on so-called knights-and-knaves puzzles. The model describes the formation of networks between two classes of agents where links are formed by agents introducing their neighbours to others of their own class. We show that if the proportion of knights and knaves is within a certain range, the network self-organizes to a perfectly bipartite state. However, if the excess of one of the two classes is greater than a threshold value, bipartiteness is not observed. We offer a detailed theoretical analysis for the behaviour of the model, investigate its behaviou r in the thermodynamic limit, and argue that it provides a simple example of a topology-driven model whose behaviour is strongly reminiscent of a first-order phase transitions far from equilibrium.Comment: 12 pages, 5 figure

Optical stark effect in the 2-photon spectrum of NO

A large optical Stark effect has been observed in the two-photon spectrum X(2)Pi yields A(2)Sigma(+)_ in NO. It is explained as a near-resonant process in which the upper state of the two-photon transition is perturbed by interactions with higher-lying electronic states coupled by the laser field. A theoretical analysis is presented along with coupling parameters determined from ab initio wave functions. The synthetic spectrum reproduces the major experimental features