Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation, clusters of any size merge until a giant component dominates the entire system. Here we establish 'fractional percolation', in which the coalescence of clusters that substantially differ in size is systematically suppressed. We identify and study percolation models that exhibit multiple jumps in the order parameter where the position and magnitude of the jumps are randomly distributed-characteristic of crackling noise. This enables us to express crackling noise as a result of the simple concept of fractional percolation. In particular, the framework allows us to link percolation with phenomena exhibiting non-self-averaging and power law fluctuations such as Barkhausen noise in ferromagnets.

Small amounts of a wetting liquid render sand a stiff and moldable material. The cohesive forces between the sand grains are caused by capillary bridges at the points of contact. Due to the finite strength of these bridges wet sand undergoes a transition from an arrested (i.e., solidified) to a fluidized state under an externally applied shear force. The transition between these two dynamic states is studied in a MD-type simulation of a two-dimensional assembly of bidisperse frictionless disks under the action of a cosine force profile. In addition to soft core repulsion the disks interact through a hysteretic and short ranged attractive force modeling the effect of the capillary bridges. In this model the transition between the fluidized and the arrested state is discontinuous and hysteretic. The parameter dependence of the critical force for solidification is modeled by combining theoretical arguments with a detailed numerical exploration of the transition. We address a range of densities from slightly below close packing until slightly above densities where the system approaches a shear-banded state. Differences and similarities of the transition in wet granulates to the jamming transition are also addressed.

Soft particulate media include a wide range of systems involving athermal dissipative particles both in non-living and biological materials. Characterization of flows of particulate media is of great practical and theoretical importance. A fascinating feature of these systems is the existence of a critical rigidity transition in the dense regime dominated by highly intermittent fluctuations that severely affects the flow properties. Here, we unveil the underlying mechanisms of rare fluctuations in soft particulate flows. We find that rare fluctuations have different origins above and below the critical jamming density and become suppressed near the jamming transition. We then conjecture a time-independent local fluctuation relation, which we verify numerically, and that gives rise to an effective temperature. We discuss similarities and differences between our proposed effective temperature with the conventional kinetic temperature in the system by means of a universal scaling collapse.

The glass transition remains unclarified in condensed matter physics. Investigating the mechanical properties of glass is challenging because any global deformation that might result in shear rejuvenation would require a prohibitively long relaxation time. Moreover, glass is well known to be heterogeneous, and a global perturbation would prevent exploration of local mechanical/transport properties. However, investigation based on a local probe, i.e., microrheology, may overcome these problems. Here, we establish active microrheology of a bulk metallic glass, via a probe particle driven into host medium glass. This technique is amenable to experimental investigations via nanoindentation tests. We provide distinct evidence of a strong relationship between the microscopic dynamics of the probe particle and the macroscopic properties of the host medium glass. These findings establish active microrheology as a promising technique for investigating the local properties of bulk metallic glass.

When dry ganular matter is tilted beyond a critical angle θc, grains start to flow until a state is reached where the slope of the surface is smaller than θc. In dry granulates this relaxation preferentially involves surface fluxes. In contrast wet granulates yield in the bulk. We uncover the origin of this behaviour by focusing on the structure of the balance equations of the forces, rather than applying a continuum model. The predictive power of the approach is demonstrated by a parameter-free prediction of the yielding of 2D packings with thermal motion and mass disorder.

Particulate matter, such as foams, emulsions, and granular materials, attain rigidity in a dense regime: the rigid phase can yield when a threshold force is applied. The rigidity transition in particulate matter exhibits bona fide scaling behavior near the transition point. However, a precise determination of exponents describing the rigidity transition has raised much controversy. Here, we pinpoint the causes of the controversies. We then establish a conceptual framework to quantify the critical nature of the yielding transition. Our results demonstrate that there is a spectrum of possible values for the critical exponents for which, without a robust framework, one cannot distinguish the genuine values of the exponents. Our approach is two-fold: (i) a precise determination of the transition density using rheological measurements and (ii) a matching rule that selects the critical exponents and rules out all other possibilities from the spectrum. This enables us to determine exponents with unprecedented accuracy and resolve the long-standing controversy over exponents of jamming. The generality of the approach paves the way to quantify the critical nature of many other types of rheological phase transitions such as those in oscillatory shearing.

We have performed extensive one dimensional particle-in-cell (PIC) simulations to explore generation of electrostatic waves driven by two-stream instability (TSI) that arises due to the interaction between two symmetric counterstreaming electron beams. The electron beams are considered to be cold, collisionless and magnetic-field-free in the presence of neutralizing background of static ions. Here, electrons are described by the non-extensive q-distributions of the Tsallis statistics. Results shows that the electron holes structures are different for various q values such that: (i) for q > 1 cavitation of electron holes are more visible and the excited waves were more strong (ii) for q < 1 the degree of cavitation decreases and for q = 0.5 the holes are not distinguishable. Furthermore, time development of the velocity root-mean-square (VRMS) of electrons for different q-values demonstrate that the maximum energy conversion is increased upon increasing the non-extensivity parameter q up to the values q > 1. The normalized total energy history for a arbitrary entropic index q = 1.5, approves the energy conserving in our PIC simulation.

We report on universality in boundary domain growth in cluster aggregation in the limit of maximum concentration. Maximal concentration means that the diffusivity of the clusters is effectively zero and, instead, clusters merge successively in a percolation process, which leads to a sudden growth of the boundary domains. For two-dimensional square lattices of linear dimension L, independent of the models studied here, we find that the maximum of the boundary interface width, the susceptibility χ, exhibits the scaling χ ~ Lγ with the universal exponent γ = 1. The rapid growth of the boundary domain at the percolation threshold, which is guaranteed to occur for almost any cluster percolation process, underlies the the universal scaling of χ.