Avalanches dynamics in reaction fronts in disordered flows

Infection fronts in randomly varying transmission-rate media

We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that the critical average transmission rate for the steady-state propagation of the infection is overestimated by the naive mean-field homogenization. Furthermore, we observe that the velocity, profile, and harmfulness of the fronts, given a specific average transmission, are sensitive to the details of randomness. In particular, we find that the harmfulness of the front is larger the more uniform the transmission rate is, suggesting potential optimization in vaccination strategies under constraints like fixed average-transmission rates or limited vaccine resources. The large-scale geometry of the advancing fronts presents nevertheless robust universal features and, for a statistically isotropic and short-range correlated disorder, we get a roughness exponent α≈0.42±0.10 and a dynamical exponent z≈1.6±0.10, which are roughly compatible with the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. We find that the KPZ term and the disorder-induced effective noise are present and have a kinematic origin.

Thermal and compositional driven convection in thin reaction fronts

Chemical reaction fronts separate regions of reacted and unreacted substances as they propagate in liquids. These fronts may induce density gradients due to different chemical compositions and temperatures across the front. In this paper, we investigate buoyancy-induced convection driven by both types of gradients. We consider a thin front approximation where the normal front velocity depends only on the front curvature. This model applies for small curvature fronts independent of the specific type of chemical reaction. For density changes due only to heat variations near the front, we find that convection can take place for either upward or downward propagating fronts if density gradients are above a threshold. Convection can set in even if the fluid with lower density is above the higher density fluid. Our model consists of Navier-Stokes equations coupled to the front propagation equation. We carry out a linear stability analysis to determine the parameters for the onset of convection. We study the nonlinear front propagation for liquids confined in narrow two-dimensional domains. Convection leads to fronts of steady shape, propagating with constant velocities.

Crackling Dynamics in the Mechanical Response of Knitted Fabrics

Crackling noise, which occurs in a wide range of situations, is characterized by discrete events of various sizes, often correlated in the form of avalanches. We report experimental evidence that the mechanical response of a knitted fabric displays such broadly distributed events both in the force signal and in the deformation field, with statistics analogous to that of earthquakes or soft amorphous materials. A knit consists of a regular network of frictional contacts, linked by the elasticity of the yarn. When deformed, the fabric displays spatially extended avalanchelike yielding events resulting from collective interyarn contact slips. We measure the size distribution of these avalanches, at the stitch level from the analysis of nonelastic displacement fields and externally from force fluctuations. The two measurements yield consistent power law distributions reminiscent of those found in other avalanching systems. Our study shows that a knitted fabric is not only a thread-based metamaterial with highly sought after mechanical properties, but also an original, model system, with topologically protected structural order, where an intermittent, scale-invariant response emerges from minimal ingredients, and thus a significant landmark in the study of out-of-equilibrium universality.

Front tracking velocimetry in advection-reaction-diffusion systems

In advection-reaction-diffusion systems, the spreading of a reactive scalar can be significantly influenced by the flow field in which it grows. In systems with sharp boundaries between reacted and unreacted regions, motion of the reaction fronts that lie at those boundaries can quantify spreading. Here, we present an algorithm for measuring the velocity of reaction fronts in the presence of flow, expanding previous work on tracking reaction fronts without flow. The algorithm provides localized measurements of front speed and can distinguish its two components: one from chemical dynamics and another from the underlying flow. We validate that the algorithm returns the expected front velocity components in two simulations and then show that in complex experimental flows, the measured front velocity maps fronts from one time step to the next self-consistently. Finally, we observe a variation of the chemical speed with flow speed in a variety of experiments with different time scales and length scales.