Criticality in droplet fragmentation

Critical behavior of power transmission network complex dynamics in the OPA model

Many complex infrastructure systems, such as electric power transmission grids, display characteristics of a critical or near critical behavior with a risk of large cascading failures. Understanding this risk and its relation to the system state as it evolves could allow for a more realistic risk assessment and even for mitigation measures. We use the OPA model of cascading blackouts and grid evolution to describe and quantify regimes of criticality of the power grid.

Role of cohesive energy in droplet fragmentation

Using molecular-dynamics simulation, we investigate the fragmentation behavior of droplets after collision with a wall. We demonstrate that the ratio of the impact to the cohesive energy E(coh) of the droplet is the key quantity characterizing the droplet fragmentation process. To show this both van der Waals-bonded Ar and N(2) droplets and polar H(2)O droplets are studied. If the impact energy per molecule E<(0.35-0.4)E(coh), the droplet is reflected without fragmenting. Beyond that impact energy fragmentation of the droplet abruptly starts. At E=E(coh), the fragmentation process already results in a fine dispersal of the droplet into daughter droplets; the maximum fragment contains only less than 4% of the initial droplet mass and around one-third of the droplet has been shattered into isolated molecules. The disintegration process continuously increases with collision energy. These findings are relevant for the process of droplet fragmentation as used in the method of impact desolvation of electrosprayed microdroplets mass spectrometry.

Experimental analysis of lateral impact on planar brittle material

The fragmentation of alumina and glass plates due to lateral impact is studied. A few hundred plates have been fragmented at different impact velocities and the produced fragments are analyzed. The method employed in this work allows one to investigate some geometrical properties of the fragments, besides the traditional size distribution usually studied in former experiments. We found that, although both materials exhibit qualitative similar fragment size distribution function, their geometrical properties appear to be quite different. A schematic model for two-dimensional fragmentation is also presented and its predictions are compared to our experimental results. The comparison suggests that the analysis of the fragments' geometrical properties constitutes a more stringent test of the theoretical models' assumptions than the size distribution.

Phase transition in liquid drop fragmentation

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl . Upon varying the gas pressure, a critical value is found where the size distribution becomes a pure power law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in nuclear multifragmentation studies. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2 . The sizes of the largest and average fragments, on the other hand, do not go to zero abruptly but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian.

Fracture and second-order phase transitions

Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio shows a behavior analogous to the magnetization in known magnetic systems with second-order phase transitions. We obtain a universal critical exponent beta approximately = 0.5 independent of the probability distribution used to assign the strengths of individual fibers.

Quantum tunneling fragmentation model

A nonthermal quantum mechanical statistical fragmentation model based on tunneling of particles through potential barriers is studied in compact two- and three-dimensional systems. It is shown that this fragmentation dynamics gives origin to several static and dynamic scaling relations. The critical exponents are found and compared with those obtained in classical statistical models of fragmentation of general interest, in particular with thermal fragmentation involving classical processes over potential barriers. Besides its general theoretical interest, the fragmentation dynamics discussed here is complementary to classical fragmentation dynamics of interest in chemical kinetics and can be useful in the study of a number of other dynamic processes such as nuclear fragmentation.

Bethe lattice representation for sandpiles

Avalanches in sandpiles are represented by a process of percolation in a Bethe lattice with a feedback mechanism. The results indicate that the frequency spectrum and probability distribution of avalanches provide a better resemblance to the experimental results than other models using cellular automata simulations. Apparent discrepancies between experiments performed by different authors are reconciled. Critical behavior is expressed here by the critical properties of percolation phenomena.