Phonons and d-wave pairing in the two-dimensional Hubbard model

We analyze the influence of phonons on the d-wave pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction U, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the B1g buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale is small. However, in situations where d-wave superconductivity and other tendencies, e.g. antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.Comment: 4 pages, 3 figure

Stabilizing Superconductivity in Nanowires by Coupling to Dissipative Environments

We present a theory for a finite-length superconducting nanowire coupled to an environment. We show that in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to explain the "anti-proximity effect" recently seen by Tian et. al. in Zinc nanowires.Comment: 4 pages, 3 figure

Choice of computational method for swimming and pumping with nonslender helical filaments at low Reynolds number

The flows induced by biological and artificial helical filaments are important to many possible applications including microscale swimming and pumping. Microscale helices can span a wide range of geometries, from thin bacterial flagella to thick helical bacterial cell bodies. While the proper choice of numerical method is critical for obtaining accurate results, there is little guidance about which method is optimal for a specified filament geometry. Here, using two physical scenarios-a swimmer with a head and a pump-we establish guidelines for the choice of numerical method based on helical radius, pitch, and filament thickness. For a range of helical geometries that encompass most natural and artificial helices, we create benchmark results using a surface distribution of regularized Stokeslets and then evaluate the accuracy of resistive force theory, slender body theory, and a centerline distribution of regularized Stokeslets. For the centerline distribution of regularized Stokeslets or slender body theory, we tabulate appropriate blob size and Stokeslet spacing or segment length, respectively, for each geometry studied. Finally, taking the computational cost of each method into account, we present the optimal choice of numerical method for each filament geometry as a guideline for future investigations involving filament-induced flows. (C) 2016 AIP Publishing LLC

Maximum likelihood estimation by monte carlo simulation:Toward data-driven stochastic modeling

We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results

Low-Reynolds number swimming in gels

Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling wave deformations in the "two-fluid" model of a gel, which treats the network and solvent as two coupled elastic and viscous continuum phases. We show that geometric nonlinearities must be incorporated to obtain physically meaningful results. We identify a transition between regimes where the network deforms to follow solvent flows and where the network is stationary. Swimming speeds can be enhanced relative to Newtonian fluids when the network is stationary. Compressibility effects can also enhance swimming velocities. Finally, microscopic details of sheet-network interactions influence the boundary conditions between the sheet and network. The nature of these boundary conditions significantly impacts swimming speeds.Comment: 6 pages, 5 figures, submitted to EP

Extended X-Ray Emission from QSOs

We report Chandra ACIS observations of the fields of 4 QSOs showing strong extended optical emission-line regions. Two of these show no evidence for significant extended X-ray emission. The remaining two fields, those of 3C 249.1 and 4C 37.43, show discrete (but resolved) X-ray sources at distances ranging from ~10 to ~40 kpc from the nucleus. In addition, 4C 37.43 also may show a region of diffuse X-ray emission extending out to ~65 kpc and centered on the QSO. It has been suggested that extended emission-line regions such as these may originate in the cooling of a hot intragroup medium. We do not detect a general extended medium in any of our fields, and the upper limits we can place on its presence indicate cooling times of at least a few 10^9 years. The discrete X-ray emission sources we detect cannot be explained as the X-ray jets frequently seen associated with radio-loud quasars, nor can they be due to electron scattering of nuclear emission. The most plausible explanation is that they result from high-speed shocks from galactic superwinds resulting either from a starburst in the QSO host galaxy or from the activation of the QSO itself. Evidence from densities and velocities found from studies of the extended optical emission around QSOs also supports this interpretation.Comment: Accepted by ApJ. 9 pages including 5 figure