No abstract

We consider anomalous diffusion of a particle moving in a tilted periodic potential in the presence of Lévy noise and nonlinear friction. Using Monte Carlo simulations, we have found some interesting characteristics of diffusion in such a nonlinear system: when the noise intensity is weak and the external force is close to the critical value at which local minima of the potential just vanish, the nonmonotonic behavior of the effective diffusion index and the superballistic diffusion are observed. This is due to the bimodal nature of the velocity distribution, and thus the test particles exist in either a running state or a long-tailed behind state in the spatial coordinate; the latter is disintegrated into small pieces of the probability peaks. We provide a relation between the group diffusion coefficient and the phase diffusion coefficient. It is shown that the distance between the above two-state centers increasing with time plays the definitive role in the superballistic group diffusion.

No abstract

Moving in the force-free field and tilted periodic potential, the diffusion of the inertial particle driven by the correlated Lévy noise and the dissipative nonlinearity, is investigated in this paper. We find that the non-negative time correlation, especially the underlying long-range correlation in the process, widens the particle's coordinate distribution which behaves as a trimodal shape, highlighting the bimodal nature of the velocity distribution, which finally yields the anomalous diffusive behavior in the force-free field, i.e., Δx 2 (t) ∼ t α eff , α eff > 1. Besides this, due to the time correlation, in the periodic potential the velocity distribution behaves as a trimodal shape and presents a nonmonotonic transform with the correlation time increasing. The anomalous diffusive behavior still exists but the effective diffusion index is larger than the force-free field. We consider these phenomena to originate from the contribution of both the dissipative nonlinearity and the non-negative time correlation.

The essential step in determination of height in confocal microscopy is localization of the axial peak positions. A sinc 2 -fitting algorithm was developed to achieve a reliable and theoretically accurate method for height extraction in surface topography measurements. We demonstrate that the sinc 2 model closely matches the rigorously calculated axial response for some typical cases, such as low-or high-aperture focusing when scanning a planar object. Compared with the existing methods, such as polynomial fitting and Gaussian fitting, sinc 2 fitting can be used to easily determine the initial values of the fitted parameters. In addition, the method is computationally efficient and theoretically rigorous.