This are some of the things that are keeping me busy at the moment…

1. **Avalanches in yield stress systems**

In collaboration with Chen Liu, Francesco Puosi, Kirsten Martens and Jean-Louis Barrat, we have studied the stress time series caused by plastic avalanches in athermally sheared amorphous solids, using both atomistic simulations and a coarse-grained elasto-plastic model. In particular, we have analyzed the strain-rate dependence of the avalanche statistics and temporal shapes.

Together with Kamran Karimi and Jean-Louis Barrat we have extended our study to the case of inertial systems, when the assumption of a very fast energy dissipation does not hold.

Now the challenge is to compare our predictions with experiments, and obtain a more quantitatively picture of avalanches related to yielding phenomena.

2. **Creep and spatio-temporal patterns in disorder elastic interfaces**

In collaboration with Laura Foini, Thierry Giamarchi, Alejandro Kolton and Alberto Rosso we have developed a novel numerical technique that captures the ultra-slow creep regime of elastic interfaces moving in disordered media over huge time scales. We point out the existence of activated events that involve collective reorganizations similar to avalanches, but, at variance with them, display correlated spatio-temporal patterns that resemble the complex sequence of aftershocks observed after a large earthquake.

Besides the academic interest in the problem, the understanding of this phenomenon could be of major importance for spintronics devices. That’s why we are extending our work to provide explicit predictions for magnetic domain wall in thin films.

3. **Contrasting depinning and yielding
**The last few years have seen an increasing interest of the statistical physics community in the study of the yielding phenomenon of a driven amorphous material. Foams, colloidal glasses, granular materials or bulk metallic glasses respond elastically when a small external strain is applied, but they yield and flow due to internal plastic rearrangements if the drive is large enough. The dynamical crossover between these two regimes can be understood as a dynamical phase transition and, in fact, it was shown to be accompanied by critical-like phenomena like growing correlation lengths and avalanches.

On the other hand, we assist to more than 30 years now in the development and understanding of the out-of-equilibrium driven phenomenon known as the depinning of elastic manifolds in random media. Systems such as magnetic and ferroelectric domain walls, contact lines in wetting, fracture fronts, and arrays of vortices in type-II superconductors, present a common phenomenology when we consider them as elastic objects embedded in a disordered medium and driven by an external force. If the external force is weak, the elastic object eventually gets pinned in the disordered landscape and its steady velocity is zero. If the force is strong enough, instead, the manifold will overcome even the largest pinning centers, reaching a steady state of mean finite velocity. This dynamical phase transition is well-documented in a literature that nowadays goes well beyond the depinning itself, describing also the equilibrium problem of the elastic line, thermally activated dynamical regimes, different effective elasticities and disorder types, the fast flow regime at large driving and, in all these cases, the relation between geometry and transport properties.

Given the enormous qualitative similarity between the yielding transition and the depinning transition (no-flow to flow when overcoming a critical threshold of external drive) people were tempted to categorize them in the same family of dynamical phenomena. Nevertheless, the differences among these two out-of-equilibrium transitions are not minor and forcing the analogy beyond its boundaries can constitute a misstep.

In the PSM group in Grenoble and in collaboration with our colleagues in Paris and Bariloche we are to digging into the similarities and differences between these two phenomena, trying to address questions such as:

*Are yielding and depinning essentially the same dynamical phase transition? Shall we extrapolate the knowledge on depinning to the yielding scenario by mapping one to one physical quantities? To which extent should we expect universality in the yielding transition? Is there an equivalence between stress-driven and strain-driven protocols? How should we address them in simplified models? Which are the relevant transport properties of driven amorphous solids? Are they linked to geometrical properties as in elastic manifolds?*

4. **Relaxation in amorphous systems**

*In collaboration with: Kirsten Martens and Jean-Louis Barrat*

We study consequences of long-range elasticity in thermally assisted dynamics of yield stress materials. Within a two-dimensional mesoscopic model we calculate the mean-square displacement and the dynamical structure factor for tracer particle trajectories. We associate a ballistic regime at short time scales with a compressed exponential decay in the dynamical structure factor, and contrast our results with experimental findings.

5. **2D and 3D parallel kinetic Monte Carlo simulation of Coulomb glasses**

*In collaboration with: Matteo Palassini and Alejandro Kolton*

We developed a parallel rejection algorithm to tackle the problem of low acceptance in Monte Carlo methods, and apply it to the simulation of the hopping conduction in Coulomb glasses using Graphics Processing Units, for which we also parallelize the update of local energies. Both in 2D and 3D we study the temperature dependence of the conductivity at low fields, and characterize the “Coulomb gap” of the density of states. The final goal of the project is to upgrade the model to study transport on nano-arrays of metals and semiconductors embedded in insulating media.

6. **Plastic effects at the depinning transition**

*In collaboration with: Sebastián Bustingorry and Alejandro Kolton*

Using a 2D Phi4 model we simulate a single interface in a 2D disorder potential, subject either to constant force or constant velocity protocols. In contrast with effectively elastic models like the QEW, this approach allows for the occurrence of overhangs and bubbles close to the interface, what is observed in experiments.

7. **Topological patterns in ferromagnetic and ferroelectric thin films**

*In collaboration with: Sebastián Bustingorry and Alejandro Kolton*

Using a 2D Phi4 model with long-range interactions and a pseudo-spectral method, we simulate the dynamics and statics of stripes, bubbles and dislocations according to the strength of the different interactions and external applied fields. These studies are developed in collaboration with experiments.