Kirsten Martens

Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter

This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media occurs via local plastic events, corresponding to small size rearrangements, that yield a long range stress redistribution over the system. Within a minimalistic mesoscopic model that incorporates these local dynamics, we study the spatial organisation of the local plastic events. The most important parameter in this study is the typical restructuring time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot et al., Eur. Phys. J. E, 2010, 33, 183] we observed the spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. The bands consist of a large number of plastic events within a solid region that remains elastic. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens et al., Phys. Rev. Lett., 2011, 106, 156001]. We analyse in detail the dependence of the shear bands on system size, shear rate and restructuring time. Further, we rationalise the scenario within a mean field version of the spatial model that produces a non monotonous flow curve for large restructuring times. This explains the instability of the homogeneous flow below a critical shear rate, that corresponds to the minimum of the curve. Our study therefore strongly supports the idea that the characteristic time scales involved in the local dynamics are at the physical origin of permanent shear bands.

Connecting diffusion and dynamical heterogeneities in actively deformed amorphous systems.

In this Letter, we explore the relations between tracer diffusion and flow heterogeneities in amorphous materials. On the basis of scaling arguments and an extensive numerical study of an athermal elastoplastic model, we show that there is a direct link between the self-diffusion coefficient and the size of cooperative regions at low strain rates. Both depend strongly on rate and system size. The mean square displacement of passive tracers thus gives information about the microscopic rheology, such as the geometry of cooperative regions and their scaling with strain rate and system size.

Driving Rate Dependence of Avalanche Statistics and Shapes at the Yielding Transition

We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elastoplastic model, we analyze system size and shear-rate dependence of the stress-drop duration and size distributions together with their average temporal shape. We find critical exponents different from mean-field predictions, and a clear asymmetry for individual avalanches. We probe scaling relations for the rate dependency of the dynamics and we report a crossover towards mean-field results for strong driving.

Relaxation in Yield Stress Systems through Elastically Interacting Activated Events

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. The ballistic regime at short time scales is associated with a compressed exponential decay in the dynamical structure factor, followed by a subdiffusive crossover prior to the onset of diffusion. We relate this crossover to spatiotemporal correlations and thus go beyond established mean field predictions.

Designed patterns: Flexible control of precipitation through electric currents

Understanding and controlling precipitation patterns formed in reaction-diffusion processes is of fundamental importance with high potential for technical applications. Here we present a theory showing that precipitation resulting from reactions among charged agents can be controlled by an appropriately designed, time-dependent electric current. Examples of current dynamics yielding periodic bands of prescribed wavelength, as well as more complicated structures are given. The pattern control is demonstrated experimentally using the reaction-diffusion process 2AgNO3 + K2Cr2O7-->under Ag2Cr2O7 + 2KNO3.

Probability distributions for the run-and-tumble bacterial dynamics: An analogy to the Lorentz model

AbstractIn this paper, we exploit an analogy of the run-and-tumble process for bacterial motility with the Lorentz model of electron conduction in order to obtain analytical results for the intermediate scattering function. This allows to obtain an analytical result for the van Hove function in real space for two-dimensional systems. We furthermore consider the 2D circling motion of bacteria close to solid boundaries with tumbling, and show that the analogy to electron conduction in a magnetic field allows to predict the effective diffusion coefficient of the bacteria. The latter is shown to be reduced by the circling motion of the bacteria.

Rheology of athermal amorphous solids: Revisiting simplified scenarios and the concept of mechanical noise temperature

We study the rheology of amorphous solids in the limit of negligible thermal fluctuations. General arguments indicate that the shear-rate dependence of the stress results from an interplay between the time scales of the macroscopic drive and the (cascades of) local particle rearrangements. Such rearrangements are known to induce a redistribution of the elastic stress in the system. Although mechanical noise, i.e., the local stress fluctuations arising from this redistribution, is widely believed to activate new particle rearrangements, we provide evidence that it casts severe doubt on the analogy with thermal fluctuations: mechanical and thermal fluctuations lead to asymptotically different statistics for barrier crossing. These ideas are illustrated and supported by a simple elasto-plastic model whose ingredients are directly connected with the physical processes relevant for the flow.

Guiding fields for phase separation : Controlling liesegang patterns

Liesegang patterns emerge from precipitation processes and may be used to build bulk structures at submicrometer length scales. Thus they have significant potential for technological applications provided adequate methods of control can be devised. Here we describe a simple, physically realizable pattern control based on the notion of driven precipitation, meaning that the phase separation is governed by a guiding field such as, for example, a temperature or pH field. The phase separation is modeled through a nonautonomous Cahn-Hilliard equation whose spinodal is determined by the evolving guiding field. Control over the dynamics of the spinodal gives control over the velocity of the instability front that separates the stable and unstable regions of the system. Since the wavelength of the pattern is largely determined by this velocity, the distance between successive precipitation bands becomes controllable. We demonstrate the above ideas by numerical studies of a one-dimensional system with a diffusive guiding field. We find that the results can be accurately described by employing a linear stability analysis (pulled-front theory) for determining the velocity-local-wavelength relationship. From the perspective of the Liesegang theory, our results indicate that the so-called revert patterns may be naturally generated by diffusive guiding fields.

On the relevance of disorder in athermal amorphous materials under shear

We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called Hébraud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems.Graphical abstract

Domain wall roughness in stripe phase BiFeO3 thin films.

Using the model system of ferroelectric domain walls, we explore the effects of long-range dipolar interactions and periodic ordering on the behavior of pinned elastic interfaces. In piezoresponse force microscopy studies of the characteristic roughening of intrinsic 71° stripe domains in BiFeO3 thin films, we find unexpectedly high values of the roughness exponent ζ=0.74±0.10, significantly different from those obtained for artificially written domain walls in this and other ferroelectric materials. The large value of the exponent suggests that a random field-dominated pinning, combined with stronger disorder and strain effects due to the step-bunching morphology of the samples, could be the dominant source of pinning in the system.