Resumen de Stochastic dynamics of substrate-confined systems: Fisher fronts and thin liquid films
Svetozar Nesic
In this thesis we have studied the effect of fluctuations in two important paradigms of soft condensed matter physics, namely, Fisher fronts and thin fluid films. Our study of stochastic FKPP traveling waves broadens current knowledge on the influence of thermal noise onto the dynamics of these waves in two space dimensions. The FKPP equation describes the evolution of a stable state into an unstable one by creating a surface (a line in one dimension) that delimits the occupancy of the stable state. This 2d surface contains equipotential lines (points, in 1d) perpendicular to the velocity direction. Due to the pulled nature of the FKPP front, the noise decreases the velocity in such way that, on average, the decrease depends logarithmically on the total number of particles. Hence, even for a macroscopic number of particles, the effect of fluctuations can be observed. In two space dimensions, the stochastic front surface roughens in time with the scale-invariance properties. Indeed, we have shown through extensive simulations of the algorithm based on a special stochastic PDE solver, that the 2d sFKPP traveling wave solutions define a surface that roughens with the same scaling exponents as the KPZ equation in 1d. To further support this claim, we have calculated the distribution function of the fluctuations in surface position, and obtained very good agreement with the distribution of the KPZ surface, which is the Tracy-Widom-GOE distribution. The fact that dimensionality of the universality class is smaller than the one of the sFKPP equation lies in the weak-noise mechanism, which only affects the microscopic region of the front. In the macroscopic region, the weak noise does not produce any additional effect. Namely, above certain length-scale, the effect that fluctuations produce in the microscopic region, simply propagates back to the macroscopic one. We show that the morphology of the microscopic surface defines that of the macroscopic surface after a time related to the total number of particles, providing the same universality class for all equipotential lines…..
