Yang-Mills Flow and Uniformization Theorems

We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structure, and that the convergence of the flow to the fixed points is consistent with the Poincare Uniformization Theorem. We construct a similar system for the three-dimensional case. Here the connection is built from a Riemannian geometry, an SO(3) connection and two other 1-form fields which take their values in the SO(3) algebra. The flat connections include the eight homogeneous geometries relevant to the three-dimensional uniformization theorem conjectured by W. Thurston. The fixed points of the flow include, besides the flat connections (and their local deformations), non-flat solutions of the Yang-Mills equations. These latter "instanton" configurations may be relevant to the fact that generic 3-manifolds do not admit one of the homogeneous geometries, but may be decomposed into "simple 3-manifolds" which do.Comment: 21 pages, Latex, 5 Postscript figures, uses epsf.st

Normalized Ricci flow on Riemann surfaces and determinants of Laplacian

In this note we give a simple proof of the fact that the determinant of Laplace operator in smooth metric over compact Riemann surfaces of arbitrary genus $g$ monotonously grows under the normalized Ricci flow. Together with results of Hamilton that under the action of the normalized Ricci flow the smooth metric tends asymptotically to metric of constant curvature for $g\geq 1$, this leads to a simple proof of Osgood-Phillips-Sarnak theorem stating that that within the class of smooth metrics with fixed conformal class and fixed volume the determinant of Laplace operator is maximal on metric of constant curvatute.Comment: a reference to paper math.DG/9904048 by W.Mueller and K.Wendland where the main theorem of this paper was proved a few years earlier is adde

Stability analysis of the Witten black hole (cigar soliton) under world-sheet RG flow

We analyze the stability of the Euclidean Witten black hole (the cigar soliton in mathematics literature) under first-order RG (Ricci) flow of the world-sheet sigma model. This analysis is from the target space point of view. We find that the Witten black hole has no unstable normalizable perturbative modes in a linearized mode analysis in which we consider circularly symmetric perturbations. Finally, we discuss a result from mathematics that implies the existence of a non-normalizable mode of the Witten black hole under which the geometry flows to the sausage solution studied by Fateev, Onofri and Zamolodchikov.Comment: 17 pages, version to appear in Physical Review D, and now has complete proof of stability for circularly symmetric perturbations, in response to referee comment

Numerical calculation of transonic boattail flow

A viscid-inviscid interaction procedure for the calculation of subsonic and transonic flow over a boattail was developed. This method couples a finite-difference inviscid analysis with an integral boundary-layer technique. Results indicate that the effect of the boundary layer is as important as an accurate inviscid method for this type of flow. Theoretical results from the solution of the full transonic-potential equation, including boundary layer effects, agree well with the experimental pressure distribution for a boattail. Use of the small disturbance transonic potential equation yielded results that did not agree well with the experimental results even when boundary-layer effects were included in the calculations

Linear and nonlinear optical properties of carbon nanotube-coated single-mode optical fiber gratings

This paper was published in OPTICS LETTERS and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OL.36.002104. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law[EN] Single-wall carbon nanotube deposition on the cladding of optical fibers has been carried out to fabricate an all-fiber nonlinear device. Two different nanotube deposition techniques were studied. The first consisted of repeatedly immersing the optical fiber into a nanotube supension, increasing the thickness of the coating in each step. The second deposition involved wrapping a thin film of nanotubes around the optical fiber. For both cases, interaction of transmitted light through the fiber core with the external coating was assisted by the cladding mode resonances of a tilted fiber Bragg grating. Ultrafast nonlinear effects of the nanotube-coated fiber were measured by means of a pump-probe pulses experiment. © 2011 Optical Society of America.This work was financially supported by the European Commission under the FP7 EURO-FOS Network of Excellence (ICT-2007-2-224402), the Ministerio de Educación y Ciencia SINADEC project (TEC2008-06333), and the Natural Sciences and Engineering Research Council of Canada (NSERC). The work of G. E. Villanueva was supported by the Ministerio de Educación y Ciencia Formación de Profesorado Universitario programs. The work of P. Pérez-Millán was supported by the Juan de la Cierva program, JCI-2009-05805.Villanueva Ibáñez, GE.; Jakubinek, M.; Simard, B.; Oton Nieto, CJ.; Matres Abril, J.; Shao, L.; Pérez Millán, P.... (2011). Linear and nonlinear optical properties of carbon nanotube-coated single-mode optical fiber gratings. Optics Letters. 36(11):2104-2106. https://doi.org/10.1364/OL.36.002104S210421063611Sakakibara, Y., Rozhin, A. G., Kataura, H., Achiba, Y., & Tokumoto, M. (2005). Carbon Nanotube-Poly(vinylalcohol) Nanocomposite Film Devices: Applications for Femtosecond Fiber Laser Mode Lockers and Optical Amplifier Noise Suppressors. Japanese Journal of Applied Physics, 44(4A), 1621-1625. doi:10.1143/jjap.44.1621Chow, K. K., Yamashita, S., & Song, Y. W. (2009). A widely tunable wavelength converter based on nonlinear polarization rotation in a carbon-nanotube-deposited D-shaped fiber. Optics Express, 17(9), 7664. doi:10.1364/oe.17.007664Set, S. Y., Yaguchi, H., Tanaka, Y., & Jablonski, M. (2004). Ultrafast Fiber Pulsed Lasers Incorporating Carbon Nanotubes. IEEE Journal of Selected Topics in Quantum Electronics, 10(1), 137-146. doi:10.1109/jstqe.2003.822912Chow, K. K., Tsuji, M., & Yamashita, S. (2010). Single-walled carbon-nanotube-deposited tapered fiber for four-wave mixing based wavelength conversion. Applied Physics Letters, 96(6), 061104. doi:10.1063/1.3304789Chow, K. K., & Yamashita, S. (2009). Four-wave mixing in a single-walled carbon-nanotube-deposited D-shaped fiber and its application in tunable wavelength conversion. Optics Express, 17(18), 15608. doi:10.1364/oe.17.015608Choi, S. Y., Rotermund, F., Jung, H., Oh, K., & Yeom, D.-I. (2009). Femtosecond mode-locked fiber laser employing a hollow optical fiber filled with carbon nanotube dispersion as saturable absorber. Optics Express, 17(24), 21788. doi:10.1364/oe.17.021788Chan, C.-F., Chen, C., Jafari, A., Laronche, A., Thomson, D. J., & Albert, J. (2007). Optical fiber refractometer using narrowband cladding-mode resonance shifts. Applied Optics, 46(7), 1142. doi:10.1364/ao.46.001142Kingston, C. T., Jakubek, Z. J., Dénommée, S., & Simard, B. (2004). Efficient laser synthesis of single-walled carbon nanotubes through laser heating of the condensing vaporization plume. Carbon, 42(8-9), 1657-1664. doi:10.1016/j.carbon.2004.02.020Jakubinek, M. B., Johnson, M. B., White, M. A., Guan, J., & Simard, B. (2010). Novel Method to Produce Single-Walled Carbon Nanotube Films and Their Thermal and Electrical Properties. Journal of Nanoscience and Nanotechnology, 10(12), 8151-8157. doi:10.1166/jnn.2010.3014Vallaitis, T., Koos, C., Bonk, R., Freude, W., Laemmlin, M., Meuer, C., … Leuthold, J. (2008). Slow and fast dynamics of gain and phase in a quantum dot semiconductor optical amplifier. Optics Express, 16(1), 170. doi:10.1364/oe.16.00017

Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]

Electron tunneling time measured by photoluminescence excitation correlation spectroscopy

The tunneling time for electrons to escape from the lowest quasibound state in the quantum wells of GaAs/AlAs/GaAs/AlAs/GaAs double-barrier heterostructures with barriers between 16 and 62 Å has been measured at 80 K using photoluminescence excitation correlation spectroscopy. The decay time for samples with barrier thicknesses from 16 Å (≈12 ps) to 34 Å(≈800 ps) depends exponentially on barrier thickness, in good agreement with calculations of electron tunneling time derived from the energy width of the resonance. Electron and heavy hole carrier densities are observed to decay at the same rate, indicating a coupling between the two decay processes

Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference