Nicolás Mujica

Experimental observation and characterization of the magnetorotational instability

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.

Sudden Chain Energy Transfer Events in Vibrated granular Media

In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again, either randomly or with some regularity in time depending on the experimental or numerical parameters. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles.

Ultrasound as a probe of dislocation density in aluminum

Abstract Dislocations are at the heart of the plastic behavior of crystalline materials yet it is notoriously difficult to perform quantitative, non-intrusive measurements of their single or collective properties. Dislocation density is a critical variable that determines dislocation mobility, strength and ductility. On the one hand, individual dislocations can be probed in detail with transmission electron microscopy. On the other hand, their collective properties must be simulated numerically. Here we show that ultrasound technology can be used to measure dislocation density. This development rests on theory—a generalization of the Granato–Lucke theory for the interaction of elastic waves with dislocations—and resonant ultrasound spectroscopy (RUS) measurements. The chosen material is aluminum, to which different dislocation contents were induced through annealing and cold-rolling processes. The dislocation densities obtained with RUS compare favorably with those inferred from X-ray diffraction, using the modified Williamson–Hall method.

Soliton pair interaction law in parametrically driven Newtonian fluid

An experimental and theoretical study of the motion and interaction of the localized excitations in a vertically driven small rectangular water container is reported. Close to the Faraday instability, the parametrically driven damped nonlinear Schrödinger equation models this system. This model allows one to characterize the pair interaction law between localized excitations. Experimentally we have a good agreement with the pair interaction law.

Fluctuations and criticality of a granular solid-liquid-like phase transition.

We present an experimental study of density and order fluctuations in the vicinity of the solid-liquid-like transition that occurs in a vibrated quasi-two-dimensional granular system. The two-dimensional projected static and dynamic correlation functions are studied. We show that density fluctuations, characterized through the structure factor, increase in size and intensity as the transition is approached, but they do not change significantly at the transition itself. The dense, metastable clusters, which present square symmetry, also increase their local order in the vicinity of the transition. This is characterized through the bond-orientational order parameter Q4, which in Fourier space shows an Ornstein-Zernike-like behavior. Depending on the filling density and vertical height, the transition can be of first- or second-order type. In the latter case, the associated correlation length ξ4, the relaxation time τ4, the zero k limit of Q4 fluctuations (static susceptibility), the pair correlation function of Q4, and the amplitude of the order parameter obey critical power laws, with saturations due to finite size effects. Their respective critical exponents are ν(perpendicular))=1, ν(parallel)=2, γ=1, η=0.67, and β=1/2, whereas the dynamical critical exponent z=ν(parallel)/ν(perpendicular)=2. These results are consistent with model C of dynamical critical phenomena, valid for a nonconserved critical order parameter (bond-orientation order) coupled to a conserved field (density).

MEASURING DISLOCATION DENSITY IN ALUMINUM WITH RESONANT ULTRASOUND SPECTROSCOPY

Dislocations in a material will, when present in enough numbers, change the speed of propagation of elastic waves. Consequently, two material samples, differing only in dislocation density, will have different elastic constants, a quantity that can be measured using Resonant Ultrasound Spectroscopy. Measurements of this effect on aluminum samples are reported. They compare well with the predictions of the theory.

Hysteretic gravity-wave bifurcation in a highly turbulent swirling flow

We report on experimental observations of a gravity-wave instability forced by a highly turbulent free-surface Taylor-Couette flow. Bistability and hysteresis are observed at the bifurcation from a turbulent base state, with an axisymmetric mean flow, to a turbulent gravity-wave state, with an azimuthal m = 1 pattern related to the mean flow and free surface. We show that the critical Reynolds number at which the wave state appears is not sharply defined as it depends on turbulent fluctuations.

Universality and criticality of a second-order granular solid-liquid-like phase transition.

We experimentally study the critical properties of the nonequilibrium solid-liquid-like transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the bond-orientational order parameter Q(4), which measures the degree of local crystallization. Two setups are compared, which present the transition at different critical accelerations as a result of modifying the energy dissipation parameters. In both setups five independent critical exponents are measured, associated to different properties of Q(4): the correlation length, relaxation time, vanishing wavenumber limit (static susceptibility), the hydrodynamic regime of the pair correlation function, and the amplitude of the order parameter. The respective critical exponents agree in both setups and are given by ν(⊥)=1,ν(∥)=2,γ=1,η≈0.6-0.67, and β=1/2, whereas the dynamical critical exponent is z=ν(∥)/ν(⊥)=2. The agreement on five exponents is an exigent test for the universality of the transition. Thus, while dissipation is strictly necessary to form the crystal, the path the system undergoes toward the phase separation is part of a well-defined universality class. In fact, the local order shows critical properties while density does not. Being the later conserved, the appropriate model that couples both is model C in the Hohenberg and Halperin classification. The measured exponents are in accord with the nonequilibrium extension to model C if we assume that α, the exponent associated in equilibrium to the specific heat divergence but with no counterpart in this nonequilibrium experiment, vanishes.

Dynamics of a first-order transition to an absorbing state.

A granular system confined in a quasi-two-dimensional box that is vertically vibrated can transit to an absorbing state in which all particles bounce vertically in phase with the box, with no horizontal motion. In principle, this state can be reached for any density lower than the one corresponding to one complete monolayer, which is then the critical density. Below this critical value, the transition to the absorbing state is of first order, with long metastable periods, followed by rapid transitions driven by homogeneous nucleation. Molecular dynamics simulations and experiments show that there is a dramatic increase on the metastable times far below the critical density; in practice, it is impossible to observe spontaneous transitions close to the critical density. This peculiar feature is a consequence of the nonequilibrium nature of this first-order transition to the absorbing state. A Ginzburg-Landau model, with multiplicative noise, describes qualitatively the observed phenomena and explains the macroscopic size of the critical nuclei. The nuclei become of small size only close to a second critical point where the active phase becomes unstable via a saddle node bifurcation. It is only close to this second critical point that experiments and simulations can evidence spontaneous transitions to the absorbing state while the metastable times grow dramatically moving away from it.

Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise

We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor–Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gravity-wave state develops, with an m = 1 azimuthal wave number. The bifurcation is discontinuous and presents hysteresis. In contrast to previously reported work (Mujica N and Lathrop D 2006 J. Fluid Mech. 51 49–62), here we compare our experimental results with a universal model based on a quintic subcritical amplitude equation with additive noise. In general, the model describes correctly the mean free-surface oscillation amplitude and its fluctuations, although differences exist in the bistability region width and the free-surface fluctuations in the gravity wave state. These differences are due to the finite time measurements and non-linear effects, respectively. Indeed, we show that longer measurement times allow the system to transit in either direction (from or to the base state), which results in the shrinking of the bistability region. For very long measurement times, and in a very narrow range of rotation rates, the system presents a series of random reversals between both states. Finally, by removing the mean wave and flow oscillations in the measured free-surface and bulk pressure signals, we demonstrate that their dynamic fluctuations depend on the system state.