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Multiplicity fluctuations of intermediate-mass fragments are studied with the percolation model. It is shown that super-Poissonian fluctuations occur near the percolation transition and that this behavior is associated with the…
A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks…
Continuum mechanics describes compressive failure as a standard bifurcation in the response of a material to an increasing load: damage, which initially grows uniformly in the material, localizes within a thin band at failure. Yet,…
The nature of the amorphous state has been notably difficult to ascertain at the microscopic level. In addition to the fundamental importance of understanding the amorphous state, potential changes to amorphous structures as a result of…
Damage spreading for 2D Ising cluster dynamics is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions…
We consider a correlated site percolation problem on a cubic lattice of size $L^3$, with $16\le L\le 512$. The sites of an initially full lattice are removed by a random walk of ${\cal N}=uL^3$ steps. When the parameter $u$ crosses a…
A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during…
We show that the size distributions of fragments created by high energy nuclear collisions are remarkably well reproduced within the framework of a parameter free percolation model. We discuss two possible scenarios to explain this…
A fissioning organism may purge unrepairable damage by bequeathing it preferentially to one of its daughters. Using the mathematical formalism of superprocesses, we propose a flexible class of analytically tractable models that allow quite…
Phase transformations ruled by non-simultaneous nucleation and growth do not lead to random distribution of nuclei. Since nucleation is only allowed in the untransformed portion of space, positions of nuclei are correlated. In this article…
Elements of eigenvectors obtained by exact diagonalization can be considered as two dimensional lattice sites, in which dynamics of a given initial state is seen as a percolating procedure on the lattice sites. Then one can use the…
We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble,…
This is the first of a series of three articles that treats fracture localization as a critical phenomenon. This first article establishes a statistical mechanics based on ensemble averages when fluctuations through time play no role in…
We study the early time dynamics of the 2d ferromagnetic Ising model instantaneously quenched from the disordered to the ordered, low temperature, phase. We evolve the system with kinetic Monte Carlo rules that do not conserve the order…
The problem of flame propagation is studied as an example of unstable fronts that wrinkle on many scales. The analytic tool of pole expansion in the complex plane is employed to address the interaction of the unstable growth process with…
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional…
The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and…
We investigate the fragmentation process of solid materials with crystalline and amorphous phases using the discrete element method. Damage initiates inside spherical samples above the contact zone in a region where the circumferential…