Related papers: Fractality in selfsimilar minimal mass structures
We investigate the geometry of the critical fluctuations for a general system undergoing a thermal second order phase transition. Adopting a generalized effective action for the local description of the fluctuations of the order parameter…
Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker map, as well as spatially periodic systems of interacting particles, have non-equilibrium stationary states with fractal properties when put in contact with…
Electronic nematicity is widely observed in quantum materials with varying degrees of electronic correlation, manifesting through charge, spin, orbital, or superconducting degrees of freedom. A phenomenological model capable of describing…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
Emergent design failures are ubiquitous in complex systems, and often arise when system elements cluster. Approaches to systematically reduce clustering could improve a design's resilience, but reducing clustering is difficult if it is…
Non-local connections, i. e. long-range space-time correlations intrinsic to the observed subatomic dynamics of quantum systems is also exhibited by macro-scale dynamical systems as selfsimilar fractal space-time fluctuations and is…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
We argue that atmospheric cascades can be regarded as example of the self-organized criticality and studied by using Levy flights and nonextensive approach. It allows us to understand the scale-invariant energy fluctuations inside cascades…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
As toy models for space-time on the Planck scale, we consider examples of fermion systems in discrete space-time which are composed of one or two particles defined on two up to nine space-time points. We study the self-organization of the…
We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation…
Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in…
We investigate the conditions required for general spin systems with frustration and disorder to display self-organized criticality, a property which so far has been established only for the fully-connected infinite-range…
We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin…
Topological defects are fundamental to the collective dynamics of non-equilibrium systems and in active matter, mediating spontaneous flows, dynamic self-organization, and emergent pattern formation. Here, we reveal critical states in…
This paper deals with the theoretical and numerical analysis of dynamic fracture of dissimilar chain consisting of masses lined by springs. Such a structure exhibits quite different dynamic properties in comparison with a symmetrical…