Propagation can be encumbered in an excitable cable in which intrinsic properties change abruptly. A sudden increase in diameter or a decrease in conductivity or excitability can lead to propagation block or delay in propagation with or without reflection. We study such transient phenomena from a geometric point of view. A simple two-cell caricature, with one cell enlarged to mimic diameter inc...

An excitable medium is a nonlinear dissipative dynamical system able to sustain undamped wave propagation. Examples of excitable media include cardiac tissue and neural media. This thesis investigates a class of novel dynamical phenomena in excitable media, known collectively as oscillatory waves. The examples of oscillatory waves considered here are Tango waves, breathers and pulse generators....

We propose to combine multiple laser beams into a single diffraction-limited beam by beam self-focusing (collapse) in a Kerr medium. Beams with total power above critical are first combined in the near field and then propagated in the optical fiber/waveguide with Kerr nonlinearity. Random fluctuations during propagation eventually trigger a strong self-focusing event and produce a diffraction-l...

The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing along a curvilinear trajectory in inhomogeneous and nonlinear saturable media. CGO method reduces the problem of Gaussian beam propagation in inhomogeneous and nonlinear media to solving ordinary differential equations for the complex curvature of the wave front and for ...

In order to quantify near-infrared spectroscopic (NIRS) data on an inhomogeneous medium, knowledge of the contribution of the various parts of the medium to the total NIRS signal is required. This is particularly true in the monitoring of cerebral oxygenation by NIRS, where the contribution of the overlying tissues must be known. The concept of the time point spread function (TPSF), which is us...

The analysis of the vector wave equation was conducted. The class of self-similar solutions with inhomogeneous polarization corresponding to the resonator modes is deduced. The modes with inhomogeneous polarization can be selected by a diffraction element with polarization selectivity used as one of the resonator mirrors. Diffraction elements with high polarization selectivity about 100% are ne...

To understand inhomogeneous reactions perpendicular to the current collector in an electrode for batteries, a method combining operando synchrotron X-ray diffraction and two-layer electrodes with different porosities is developed. The two layers are built using two different active materials (LiNi0.80Co0.15Al0.05O2 and LiMn2O4), therefore, tracing each diffraction pattern reveals which active m...

Biological tissues exhibit elastic x-ray scatter properties unique to individual tissue types. It has been suggested that these properties could be exploited in the discrimination of tissues in diagnostic radiology, particularly in mammographic imaging. The work in this thesis investigates the elastic scatter from human breast tissues with a view to moving the Diffraction Enhanced Breast Imagin...