Investigation of CAST-10-2/DOA 2 airfoil in NAE high Reynolds number two-dimensional test facility

A common airfoil model with the CAST 10-2/DOA-2 profile and 228 mm (9 inches) chord length was tested. The tests performed in NAE covered the Mach numbers from 0.3 to 0.8 and Reynolds numbers from 10 to 30 million. The model was tested with transition free and with transition fixed at 5 percent chord for both the upper and the lower surfaces. The data obtained were analyzed for the effects of Reynolds number, transition fixing and Mach number. The role of the boundary layer on the displacement effect, the interaction with the shock wave and the trailing edge separation are examined. The results are summarized as follows: (1) the airfoil performance depends strongly on Reynolds number and transition fixing; (2) with transition fixed, the aerodynamic quantities such as lift, pitching moment and drag show a monotonic variation with Reynolds number; (3) with transition free, the aerodynamic quantities vary less regularly with Reynolds number and a slight parametric dependency is shown. The weak dependency is due to the compensatory effect of the forward shift of the transition position and the thinning of the turbulent boundary layer as Reynolds number increases; (4) the shock Mach number and the shock position are weakly dependent on Reynolds number; and (5) the long extent of the laminar boundary layer at transonic speeds reduces the drag appreciably at low Reynolds numbers. The drag bucket around the design Mach number can be observed below Reynolds number 15 million

Ramification points of Seiberg-Witten curves

When the Seiberg-Witten curve of a four-dimensional N = 2 supersymmetric gauge theory wraps a Riemann surface as a multi-sheeted cover, a topological constraint requires that in general the curve should develop ramification points. We show that, while some of the branch points of the covering map can be identified with the punctures that appear in the work of Gaiotto, the ramification points give us additional branch points whose locations on the Riemann surface can have dependence not only on gauge coupling parameters but on Coulomb branch parameters and mass parameters of the theory. We describe how these branch points can help us to understand interesting physics in various limits of the parameters, including Argyres-Seiberg duality and Argyres-Douglas fixed points

ADE Spectral Networks

We introduce a new perspective and a generalization of spectral networks for 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ associated to Lie algebras $\mathfrak{g} = \textrm{A}_n$, $\textrm{D}_n$, $\textrm{E}_{6}$, and $\textrm{E}_{7}$. Spectral networks directly compute the BPS spectra of 2d theories on surface defects coupled to the 4d theories. A Lie algebraic interpretation of these spectra emerges naturally from our construction, leading to a new description of 2d-4d wall-crossing phenomena. Our construction also provides an efficient framework for the study of BPS spectra of the 4d theories. In addition, we consider novel types of surface defects associated with minuscule representations of $\mathfrak{g}$.Comment: 68 pages plus appendices; visit http://het-math2.physics.rutgers.edu/loom/ to use 'loom,' a program that generates spectral networks; v2: version published in JHEP plus minor correction

Supersolid and charge density-wave states from anisotropic interaction in an optical lattice

We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well controlled numerical method based on the tensor network algorithm, we calculate phase diagram of the resultant effective Hamiltonian in a two-dimensional square lattice - an anisotropic Hubbard model of hard-core bosons with attractive interaction in one direction and repulsive interaction in the other direction. Besides the conventional superfluid and the Mott insulator states, we find the striped and the checkerboard charge density wave states and the supersolid phase that interconnect the superfluid and the striped solid states. The transition to the supersolid phase has a mechanism different from the case of the soft-core Bose Hubbard model.Comment: 5 pages, 5 figures

Evidence of spin liquid with hard-core bosons in a square lattice

We show that laser assisted hopping of hard core bosons in a square optical lattice can be described by an antiferromagnetic $J_{1}$-$J_{2}$ XY model with tunable ratio of $J_{2}/J_{1}$. We numerically investigate the phase diagram of the $J_{1}$-$J_{2}$ XY model using both the tensor network algorithm for infinite systems and the exact diagonalization for small clusters and find strong evidence that in the intermediate region around $$, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Neel state on the $J_{2}\ll J_{1}$ side and the stripe antiferromagnetic phase on the $$ side. This finding opens up the possibility of studying the exotic spin liquid phase in a realistic experimental system using ultracold atoms in an optical lattice.Comment: 5 pages, 5 figure