Pablo Gutiérrez

Transition from pulses to fronts in the cubic-quintic complex Ginzburg-Landau equation

The cubic–quintic complex Ginzburg–Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov–Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts. This fact is consistent with numerical simulations.

LOCALIZED STRUCTURES IN NONEQUILIBRIUM SYSTEMS

We study numerically a prototype equation which arises generically as an envelope equation for a weakly inverted bifurcation associated to traveling waves: The complex quintic Ginzburg–Landau equation. We show six different stable localized structures including stationary pulses, moving pulses, stationary holes and moving holes, starting from localized initial conditions with periodic and Neumann boundary conditions.

Statistics of injected power on a bouncing ball subjected to a randomly vibrating piston.

We present an experimental study on the statistical properties of the injected power needed to maintain an inelastic ball bouncing constantly on a randomly accelerating piston in the presence of gravity. We compute the injected power at each collision of the ball with the moving piston by measuring the velocity of the piston and the force exerted on the piston by the ball. The probability density function of the injected power has its most probable value close to zero and displays two asymmetric exponential tails, depending on the restitution coefficient, the piston acceleration, and its frequency content. This distribution can be deduced from a simple model assuming quasi-Gaussian statistics for the force and velocity of the piston.

Phase transition in an out-of-equilibrium monolayer of dipolar vibrated grains

We report an experimental study on the transition between a disordered liquidlike state and an ordered solidlike one, in a collection of magnetically interacting macroscopic grains. A monolayer of magnetized particles is vibrated vertically at a moderate density. At high excitation a disordered, liquidlike state is observed. When the driving dimensionless acceleration Γ is quasistatically reduced, clusters of ordered grains grow below a critical value, Γ(c). These clusters have a well-defined hexagonal and compact structure. If the driving is subsequently increased, these clusters remain stable up to a higher critical value, Γ(l). Thus, the solid-liquid transition exhibits a hysteresis cycle. However, the lower onset Γ(c) is not well defined as it depends strongly on the acceleration ramp speed and also on the magnetic interaction strength. Metastability is observed when the driving is rapidly quenched from high acceleration, Γ>Γ(l), to a low final excitation, Γ(q). After this quench, solid clusters nucleate after a time lag, τ(o), either immediately (τ(o)=0) or after some time lag (τ(o)>0) that can vary from seconds up to several hundreds of seconds. The immediate growth occurs below a particular acceleration value, Γ(s) (~/<Γ(c)). In all cases, for t≥τ(o) a solid clusters temporal growth can be phenomenologically described by a stretched exponential law. The evolution of the parameters of this law as a function of Γ(q) is presented and the values of fitted parameters are discussed.

Effects of fiscal policy on private consumption: evidence from structural-balance fiscal rule deviations

We use a new narrative measure of fiscal shocks to study how private consumption reacts to government spending increases. Our fiscal shocks arise from three announcements of expansionary fiscal rule deviations in a small and open economy where fiscal policy follows a structural-balance fiscal rule. All those deviations were announced to be mainly on the spending side. We find a negative response of private consumption in the face of those announcements. Our findings are consistent with the existence of consumers expecting some irreversibility in government spending increases and, as a consequence, a rise in future taxes to make the newly announced fiscal spending path consistent with the intertemporal government budget constraint.

Existence Range of Pulses in the Quintic Complex Ginzburg‐Landau Equation

Given a system in the vicinity of an oscillatory subcritical bifurcation (Hopf) that presents localized structures, we model its dynamics with the Quintic Complex Ginzburg‐Landau Equation. For pulse‐type structures, we study the bifurcation to fronts via a quasi‐analytical approach.

Streaming patterns in Faraday waves

Waves patterns in the Faraday instability have been studied for decades. Besides the rich dynamics that can be observed on the waves at the interface, Faraday waves hide beneath them an elusive range of flow patterns --or streaming patterns-- which have not been studied in detail until now. The streaming patterns are responsible for a net circulation in the flow which are reminiscent of convection cells. In this article, we analyse these streaming flows by conducting experiments in a Faraday-wave setup. To visualize the flows, tracers are used to generate both trajectory maps and to probe the streaming velocity field via Particle Image Velocimetry (PIV). We identify three types of patterns and experimentally show that identical Faraday waves can mask streaming patterns that are qualitatively very different. Next we propose a three-dimensional model that explains streaming flows in quasi-inviscid fluids. We show that the streaming inside the fluid arises from a complex coupling between the bulk and the boundary layers. This coupling can be taken into account by applying modified boundary conditions in a three-dimensional Navier-Stokes formulation for the streaming in the bulk. Numerical simulations based on this theoretical framework show good qualitative and quantitative agreement with experimental results. They also highlight the relevance of three-dimensional effects in the streaming patterns. Our simulations reveal that the variety of experimental patterns is deeply linked to the boundary condition at the top interface, which may be strongly affected by the presence of contaminants along the surface.

Measurements of Surface Deformation in Highly-Reflecting Liquid-Metals

We present an experimental study of surface deformation in a liquid metal . The investigation has two main parts. First we present an optical setup allowing to obtain the surface profile along a line, for a highly-reflecting liquid-metal. We track the diffusion of a laser sheet on the surface from two opposite angles, avoiding saturations due to specular reflection. In the second part, the technique is used to study some aspects of the wave-vortex interaction problem. Special attention is given to the surface deformation produced by a flow composed by moving vortices. Asymmetric height statistics are observed and discussed. Some indications of wave emission are presented. Finally, the attenuation of propagating waves by the same flow is briefly discussed.