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Jon Lee

Publications and source records attributed to Jon Lee.

2 recordsLinked to original sources

Multiple parameter vector bending and high-temperature sensors based on asymmetric multimode fiber Bragg gratings inscribed by an infrared femtosecond laser.

We present a multiple parameter integrated fiber sensor that can detect vector bending and ambient temperature simultaneously with a single asymmetric multimode fiber Bragg grating. Multimode Bragg gratings were fabricated in an all-silica core fiber by an infrared femtosecond laser, which showed multiple transmission dips in the transmission spectrum. Bending and ambient temperature fluctuations affect the shapes of multiple transmission dips in different ways. In bending, different dips have different sensitivities. On the other hand, temperature fluctuations tended to influence the dips uniformly across different dips. By analyzing the changing spectrum of dips, one can distinguish the changes induced by bending or temperature fluctuations. Furthermore, the high thermal stability of Bragg gratings inscribed by an infrared femtosecond laser can make this double parameter fiber sensor work in very harsh, high-temperature environments.

Journal Article↗

Topology of trajectories of the 2D Navier-Stokes equations.

In spectral form the 2D incompressible Navier-Stokes equations in a square periodic region will be represented by 430 complex Fourier amplitudes which correspond to isotropic truncation of the upper wave number 16. For small viscosity, we have found five equilibrium states I-V in the entire range of forcing; I-fixed point, II-circle, III-closed orbit, IV-torus, and V-chaos. The fixed-point equilibrium state is the laminar flow. As the forcing passes through a critical value, the fixed point evolves directly to equilibrium state III under a typical multimode forcing. The chaotic transition takes place on a 2-torus-like manifold (equilibrium state IV) which is the product space of a circle and the closed orbit of equilibrium state III, similar to the quasiperiodic 2-torus of Ruelle and Takens. For sufficiently large forcing, the evolution of equilibrium state V is nothing but a simulation of quasistationary 2D turbulence. From the Lyapunov exponents of turbulent flows, we have evaluated the constants in the theoretical results of Foias and his colleagues, which relate the determining mode and fractal dimension with the enstrophy dissipation wave number of 2D turbulence.

Journal Article↗