Related papers: Fractality in selfsimilar minimal mass structures
A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology. We proposed a new theory that allowed us to model the most challenging cases of atomic self-assembling whose…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
The scope of the paper is a theoretical analysis of the dynamical system, the model of which was reduced to Weierstrasse function. A fractal structure of the trajectory was proved and the entropy of the system information designated.
Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a…
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid…
Many biological materials consist of sparse networks of disordered fibres, embedded in a soft elastic matrix. The interplay between rigid and soft elements in such composite networks leads to mechanical properties that can go far beyond the…
The concept of cracking refers to the tendency of a fluid distribution to "split'', once it abandons the equilibrium. In this manuscript we develop a general formalism to describe the occurrence of cracking within a dissipative fluid…
An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey…
It is shown here that fracture after a brief plastic strain, typically of a few percents, is a necessary consequence of the polycrystalline nature of the materials. The polycrystal undergoing plastic deformation is modeled as a flowing…
The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free", indicating some type of criticality. In spite of attempts to…
The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
In the prototype sandpile model of self-organized criticality time series obtained by decomposing avalanches into waves of toppling show intermittent fluctuations. The q-th moments of wave size differences possess local multiscaling and…
Molecular-dynamics simulations of fracture in metallic glass-like systems are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
Analytical solutions and a vast majority of numerical ones for fracture propagation in saturated porous media yield smooth behavior while experiments, field observations and a few numerical solutions reveal stepwise crack advancement and…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
Critical gravitational collapse and self similarity are used to probe the mass distribution of subsolar objects. We demonstrate that at very low mass the distribution is given by a power law, with an exponent opposite in sign to that…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…