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Martensites subjected to quasistatic deformation are known to exhibit power law distributed acoustic emission in a broad range of scales, however, the origin of the observed scaling behavior and the mechanism of self-organization towards…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…
The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here to simulate the stress-strain curves for crystals subjected to anti-plane shear-controlled load reversal. We show that the presence of the…
We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…
Motivated by the finding that there is some biological universality in the relationship between school geometry and school biomass of various pelagic fishes in various conditions, I here establish a scaling law for school dimensions: the…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
We study the probability, $P_S(t)$, of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as $D(s) \sim s^\gamma$. $P_S(t)$ exhibits a stretched exponential…
We show that the thermodynamic dislocation theory (TDT) predicts a scaling relation between stresses, strain rates, and temperatures for steady-state deformations of crystalline solids, and that this relation is accurately obeyed by a wide…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\Delta$. We investigate the relative size of the giant component $S$…
The transition from elastic to plastic deformation in crystalline metals shares history dependence and scale-invariant avalanche signature with other non-equilibrium systems under external loading: dilute colloidal suspensions,…
A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales…
A theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1<D<2) and the parameters defining the fatigue crack propagation rate. The…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explicated. We investigate the dynamic behaviors of resource/traffic flow on scale-free…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
According to recent experimental and numerical investigations if the characteristic size of a specimen is in the submicron size regime several new interesting phenomena emerge during the deformation of the samples. Since in such a systems…
The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very…