Numerical simulation of steady inspiratory flow through a multiply branched model of the human central airways

info:eu-repo/semantics/published

How to beat the Rayleigh limit?

The problem of achieving super-resolution, i.e. resolution beyond the classical Rayleigh distance of half a wavelength, is a real challenge in several imaging problems. The development of computer-assisted instruments and the possibility of inverting the recorded data has clearly modified the traditional concept of resolving power of an instrument. We show that, in the framework of inverse problem theory, the achievable resolution limit arises no longer from a universal rule but instead from a practical limitation due to noise amplification in the data inversion process. We analyze under what circumstances super-resolution can be achieved and we show how to assess the actual resolution limits in a given experiment, as a function of the noise level and of the available a priori knowledge about the object function. We emphasize the importance of the a priori knowledge of its effective support and we show that significant super-resolution can be achieved for "subwavelength sources", i.e. objects which are smaller than the probing wavelength.

Localization in systems of non-identical oscillators

A singular perturbation method is applied to a non-conservative system of two weakly coupled strongly nonlinear non-identical oscillators. For certain parameters, localized solutions exist for which the amplitude of one oscillator is an order of magnitude smaller than the other. It is shown that these solutions are described by coupled equations for the phase difference and scaled amplitudes. Three types of localized solutions are obtained as solutions to these equations which correspond to phase locking, phase drift, and phase entrainment. Quantitative results for the phases and amplitudes of the oscillators and the stability of these phenomena are expressed in terms of the parameters of the model.