Rigorous coherent-structure theory for falling liquid films: Viscous dispersion effects on bound-state formation and self-organization

We examine the interaction of two-dimensional solitary pulses on falling liquid films. We make use of the second-order model derived by Ruyer-Quil and Manneville [Eur. Phys. J. B 6, 277 (1998); Eur. Phys. J. B 15, 357 (2000); Phys. Fluids 14, 170 (2002)] by combining the long-wave approximation with a weighted residuals technique. The model includes (second-order) viscous dispersion effects which originate from the streamwise momentum equation and tangential stress balance. These effects play a dispersive role that primarily influences the shape of the capillary ripples in front of the solitary pulses. We show that different physical parameters, such as surface tension and viscosity, play a crucial role in the interaction between solitary pulses giving rise eventually to the formation of bound states consisting of two or more pulses separated by well-defined distances and travelling at the same velocity. By developing a rigorous coherent-structure theory, we are able to theoretically predict the pulse-separation distances for which bound states are formed. Viscous dispersion affects the distances at which bound states are observed. We show that the theory is in very good agreement with computations of the second-order model. We also demonstrate that the presence of bound states allows the film free surface to reach a self-organized state that can be statistically described in terms of a gas of solitary waves separated by a typical mean distance and characterized by a typical density

Interfaces in disordered media. Scaling growth, avalanche dynamics, and microfluidic fronts

The long desired possibility to classify the scaling growth of a rough surface in terms of universality classes has become a considerably ambitious task, not to say impossible in some cases. This is particularly true, for instance, in the problem of a fluid filling a disordered medium –where the expression disordered medium applies both to a macroscopic porous medium and a microfluidic device. The point is that all the physical forces that play a role at the advancing front, such as the random capillarity of the medium, the surface tension of the interface or the viscous pressure, induce the roughness of the front to show a rich variety of scaling regimes, with the unavoidable presence of crossover effects. In addition, the so-called anomalous scaling, which reflects that the global scales of a rough surface behave in a different fashion as the corresponding local scales, makes difficult to find different physical situations that are described by exactly the same set of scaling exponents, which would make them belong to the same universality class. On the other hand, the characteristic intermittent avalanche-like behavior displayed by the front gives rise to an even more complicated dynamics, described in terms of spatio-temporal complex dynamics, as it is observed in many other disordered systems. This thesis deals with the scaling properties and avalanche dynamics of interfaces moving in disordered media. Our main motivation in this work has been to understand the underlying physics that governs these complex phenomena, and to relate our findings to the large amount of experimental work carried out in fluid systems, ranging from the macroscopic Hele-Shaw cell to a microchannel

Avalanche dynamics in fluid imbibition near the depinning transition

We study avalanche dynamics and local activity of forced-flow imbibition fronts in disordered media. We focus on the front dynamics as the mean velocity $\bar{v}$ of the interface is decreased and the pinning state is approached. Scaling arguments allow us to obtain the statistics of avalanche sizes and durations, which become power-law distributed due to the existence of a critical point at $\bar{v}= 0$. Results are compared with phase-field numerical simulations

Time dependent couplings and crossover length scales in non-equilibrium surface roughening

We show that time dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in non-equilibrium kinetic roughening models . Three typical situations are studied. In the case of a crossover between two different rough regimes, the time-dependent coupling may result in anomalous scaling for scales above the crossover length. In a different setting, for a crossover from a rough to either a flat or damping regime, the time dependent crossover length may conspire to produce a rough surface, despite the most relevant term tends to flatten the surface. In addition, our analysis sheds light into an existing debate in the problem of spontaneous imbibition, where time dependent couplings naturally arise in theoretical models and experiments.Comment: Accepted for publication in Physical Review E (Rapid Comm.

Lubrication dynamics of a settling plate

If a flat, horizontal, plate settles onto a flat surface, it is known that the gap $h$ decreases with time $t$ as a power-law: $h\sim t^{-1/2}$. We consider what happens if the plate is not initially horizontal, and/or the centre of mass is not symmetrically positioned: does one edge contact the surface in finite time, or does the plate approach the horizontal without making contact? The dynamics of this system is analysed and shown to be remarkably complex.Comment: 22 pages, 9 figure

Aggregation-fragmentation-diffusion model for trail dynamics

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)~w-γ for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. The exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare

Design of a remote instrumentation system and a dedicated circuit for the configuration and quality analysis of rf power amplifiers

The author was working at the Tryo Communications in the i+d department, after some analysis of the fabrication procedures a lag of automation in a specific configuration process for powers amplifiers was detected. After the specifications and requirements compilation, a deeper analysis was done in order to design a system that would involve measure instruments, a server, an own PCB and power amplifiers. That system should be able to do all the configuration process by its own. This initiative is a hardware and software solution that truly has 0 cost in comparison with the benefits provided with the integration of that technologies to the enterprise production chain. Most of the repetitive processes are becoming automated by machines to improve efficiency and serial manufacturing. This is a concept that could be applied in many terms but this project is focused on the automation using electronics applied to RF and it also contains a software integration.El autor trabajaba en Tryo Communications en el departamento de i + d, tras un análisis de los procedimientos de fabricación se detectó una falta de automatización en un proceso de configuración específico para amplificadores de potencia. Después de la compilación de especificaciones y requerimientos, se realizó un análisis más profundo para diseñar un sistema que involucraría instrumentos de medida, un servidor, una propia PCB y amplificadores de potencia. Ese sistema debe ser capaz de hacer todo el proceso de configuración por su cuenta. Esta iniciativa es una solución de hardware y software que realmente tiene 0 costo en comparación con los beneficios proporcionados con la integración de esas tecnologías a la cadena de producción de la empresa. La mayoría de los procesos repetitivos están siendo automatizados por las máquinas para mejorar la eficiencia y la fabricación en serie. Este es un concepto que se podría aplicar en muchos términos, pero este proyecto se centra en la automatización utilizando la electrónica aplicada a RF y también contiene una integración de software

Persistent stability of a chaotic system

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has generic instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems