ABSTRACT
We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one-dimensional random dynamical system with additive noise. The result is achieved with the help of rigorous computer assisted estimates. We first approximate the stationary distribution of the random dynamical system and then compute certified error intervals for the Lyapunov exponent. We find that the sign of the Lyapunov exponent changes at least three times when increasing the noise amplitude. We also show numerical evidence that the standard non-rigorous numerical approximation by finite-time Lyapunov exponent is valid with our model for a sufficiently large number of iterations. Our method is expected to work for a broad class of nonlinear stochastic phenomena.
ABSTRACT
Contactless thermal imaging generally relies on mid-infrared cameras and fluorescence imaging with temperature-sensitive phosphors. Fluorescent thermometry in the near-infrared (NIR) region is an emerging technique for analysing deep biological tissues but still requires observation depth calibration. We present an NIR fluorescence time-gated imaging (TGI) thermometry technology based on fluorescence lifetime, an intrinsic fluorophore time constant unrelated to observation depth. Fluorophore used is NaYF4 co-doped with Nd3+ and Yb3+ that emits fluorescence at 1000 nm. An agarose gel-based phantom with the fluorophore embedded at a 5-mm depth was covered by sheets of meat to vary the observation depth. The temperature was determined independently from depth by sequences of NIR fluorescence decay images, and the rate of change in the fluorescence lifetime per temperature was almost constant (-0.0092 ~ -0.010 °C-1) at depths ranging from 0 to 1.4 mm of meat, providing non-contact and absolute measurements of temperature in deep biological tissues.
