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Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
We investigate numerically the yielding transition of a two dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, that we derive from the full (tensorial) description of…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in…
A crucially important material parameter for all amorphous solids is the yield stress, which is the value of the stress for which the material yields to plastic flow when it is strained quasi-statically at zero temperature. It is difficult…
We formulate a stochastic equation to model the erosion of a surface with fixed inclination. Because the inclination imposes a preferred direction for material transport, the problem is intrinsically anisotropic. At zeroth order, the…
We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three…
A new model is proposed to explain coiling of myelins composed of fluid bilayers. This model allows the constituent bilayer cylinders of a myelin to be non-coaxial and the bilayer lateral tension to vary from bilayer to bilayer. The…
A crystal plasticity theory was developed for use in simulations of dynamic loading at high pressures and strain rates. At pressures of the order of the bulk modulus, compressions o(100%) may be induced. At strain rates o(10^9)/s or higher,…
By means of a finite elements technique we solve numerically the dynamics of an amorphous solid under deformation in the quasistatic driving limit. We study the noise statistics of the stress-strain signal in the steady state plastic flow,…
Molecular dynamics simulations were used to quantify mechanically-induced structural evolution in nanocrystalline Al with an average grain size of 5 nm. A polycrystalline sample was cyclically strained at different temperatures, while a…
The General Thermodynamic Theory of Sintering, formulated by the author in 1998 is given. This theory is applied to the problem of swelling of materials under conditions of radiation. Driving forces, caused by the presence of the evolution…
Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation…
It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimental data. Namely, while Koiter's formula predicts linear…
Recent experiments and simulations of amorphous solids plastically deformed by oscillatory drive have foundsurprising behavior - for small strain amplitudes the dynamics can be reversible, which is contrary to the usual notion of plasticity…
We perform large scale simulations of a two dimensional lattice model for amorphous plasticity with random local yield stresses and long-range quadrupolar elastic interactions. We show that as the external stress increases towards the…
Failure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but…
Herein, we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have…
A model which accounts for cracking avalanches in piles of grains subject to external load is introduced and numerically simulated. The stress is stochastically transferred from higher layers to lower ones. Cracked areas exhibit various…
Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not…