Cardiac arrhythmias are a common cause of sudden death worldwide. However, despite decades of thorough investigation the underlying biophysical mechanisms of cardiac arrhythmias are still... Show moreCardiac arrhythmias are a common cause of sudden death worldwide. However, despite decades of thorough investigation the underlying biophysical mechanisms of cardiac arrhythmias are still insufficiently understood due to incomplete theories and the lack of precise spatiotemporal control in experiments. In the last decade, the problem of insufficient spatiotemporal control has started to be tackled by means of a new technique, called optogenetics. This technique employs expression of light-activated proteins, which are activated or deactivated in time and space by switching on/off light (in the near-ultraviolet to near-infrared wavelength range) in specific patterns thus realizing fully biological spatiotemporal control. However, with a few notable exceptions, cardiac optogenetic studies have only confirmed previously known mechanisms and yielded no or little novel mechanistic insights. In this thesis, to fill this gap, we combined nonlinear dynamics theory, numerical simulations and optogenetic experiments with unique spatiotemporal control to theoretically predict and demonstrate novel arrhythmogenic phenomena in cardiac tissue. Thanks to the robustness of the optogenetics methods and generality of the applied theories and computations, this thesis uncovered novel mechanisms for the biophysics of cardiac tissue that are applicable to the functioning of excitable systems in general. Show less
In this thesis I considered the dynamics of self-propelling particles (SPP). Flocking of living organisms like birds, fishes, ants, bacteria etc. is an area where the theory of the collective... Show moreIn this thesis I considered the dynamics of self-propelling particles (SPP). Flocking of living organisms like birds, fishes, ants, bacteria etc. is an area where the theory of the collective behaviour of SPP can be applied. One can often see how these animals develop coherent motion, amazing the observer by the diversity of its forms and shapes. In this thesis a hydrodynamic model with so-called kinematic constraints, which are imposed on the orientations of the velocities of the particles, is proposed. The tendency of the particles to adjust their velocities to the ones of the neighbours leads to the emergence of a coherent motion. In our model two types of stationary flows are obtained: linear and vortical hydrodynamic flows. A remarkable property of the vortical flow is that it has finite flocking behaviour, where the density and the velocity fields are coupled. From the physical point of view these flows are of interest because of their realization in nature. The stability properties of the stationary flows are determined. Further a hydrodynamic model is derived from the discrete description using the averaging procedure. The connection between the discrete and continuous approaches is analysed. Show less
