相关论文: Fractal to Nonfractal Phase Transition in the Diel…
We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip-splitting of branches forms a fixed…
We study the growth of fractal clusters in the Dielectric Breakdown Model (DBM) by means of iterated conformal mappings. In particular we investigate the fractal dimension and the maximal growth site (measured by the Hoelder exponent…
It is argued that the dielectric-breakdown model has an upper critical $\eta_c$ equal to 4, for which the clusters become one-dimensional. A renormalization group treatment of the model is presented near the critical $\eta$.
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…
Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique…
The nonequilibrium phase transition in the triplet-creation model is investigated using critical spreading and the conservative diffusive contact process. The results support the claim that at high enough diffusion the phase transition…
A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
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…
Fractonic matter can undergo unconventional phase transitions driven by the condensation of particles that move along subdimensional manifolds. We propose that this type of quantum critical point can be realized in a bilayer of crossed…
Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial…
Recently, a hybrid percolation transitions (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. In spite of considerable effort to develop the…
The cellular automaton model is used to simulate diffusion and aggregation with dissociation of point particles in 2D. A continuous phase transition is found that separates creation of compact aggregates and fractal ones. The transition is…
Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass…
Fracture processes in multi-phase solids are inherently complex due to multiple competing mechanisms. Here, we investigate the elastic and fracture behaviour of two-phase solids, comprising a fragile phase and a tough phase using a…