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Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
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…
We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals $1/\lambda^n$ in generation $n$, in terms of a rescaling factor $\lambda$. Without interactions between the…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
Bone adapts in response to its mechanical environment. This evolution of bone density is one of the most important mechanisms for developing fracture resistance. A finite element framework for simulating bone adaptation, commonly called…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
Tidal dissipation is known as one of the main drivers of the secular evolution of planetary systems. It directly results from dissipative mechanisms that occur in planets and stars' interiors and strongly depends on the structure and…
In diffusion processes of solid materials, such as in the classical thermal shock problem and the recent lithium ion battery, the maximum diffusion induced stress (DIS) is a very important quantity. However a widely accepted, accurate and…
We report on an extensive characterization of the cracking noise produced by charcoal samples when dampened with ethanol. We argue that the evaporation of ethanol causes transient and irregularly distributed internal stresses that promote…
We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…
Architected materials can exhibit remarkable combinations of stiffness, strength, and toughness, yet their application is currently limited by an incomplete understanding of how cracks initiate and propagate through their discrete…
The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation.…
A numerical realization of an elastic beam lattice is used to obtain scaling exponents relevant to the extent of damage within the controlled, catastrophic and total regimes of mode-I brittle fracture. The relative fraction of damage at the…
Background: Models describing nuclear fragmentation and fragmentation-fission deliver important input for planning nuclear physics experiments and future radioactive ion beam facilities. These models are usually benchmarked against data…
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…
We present a new method for the calculation of fragment size correlations in a discrete finite system in which correlations explicitly due to the finite extent of the system are suppressed. To this end, we introduce a combinatorial model,…
Phase-field approaches to fracture based on energy minimization principles have been rapidly gaining popularity in recent years, and are particularly well-suited for simulating crack initiation and growth in complex fracture networks. In…
Nanoindentation techniques recently developed to measure the mechanical response of crystals under external loading conditions reveal new phenomena upon decreasing sample size below the microscale. At small length scales, material…