相关论文: Generalized Dielectric Breakdown Model

We consider a general model of branch competition that automatically leads to a critical branching configuration. This model is inspired by the $4-\eta$ expansion of the dielectric breakdown model (DBM), but the mechanism of arriving at the…

Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic…

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…

We study dielectric breakdown in a semi-classical bond percolation model for nonlinear composite materials introduced by us and the related breakdown exponent near the percolation threshold in two dimensions. The breakdown exponent after…

We analyze the combined effect of a Laplacian field and quenched disorder for the generation of fractal structures with a study, both numerical and theoretical, of the quenched dielectric breakdown model (QDBM). The growth dynamics is shown…

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…

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…

Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…

In our previous studies, we developed discrete-space Birth, Death and Innovation Models (BDIM) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and…

Motivated by recent experiments on the finite temperature Mott transition in VO2 films, we propose a classical coarse-grained dielectric breakdown model where each degree of freedom represents a nanograin which transitions from insulator to…

The renowned general epidemic process describes the stochastic evolution of a population of individuals which are either susceptible, infected or dead. A second order phase transition belonging to the universality class of dynamic isotropic…

The prediction of a dielectric breakdown in a high-voltage device is based on criteria that evaluate the electric field along field lines. Therefore it is necessary to efficiently compute the electric field at arbitrary points in space. A…

Everyday thousands of meteoroids enter the Earth's atmosphere. The vast majority burn up harmlessly during the descent, but the larger objects survive, occasionally experiencing intense fragmentation events, and reach the ground. These…

In the magnetic Eden model (MEM), particles have a spin and grow in contact with a thermal bath. Although Ising-like interactions affect the growth dynamics, deposited spins are frozen and not allowed to flip. This review article focuses on…

The diffusion limited aggregation model (DLA) and the more general dielectric breakdown model (DBM) are solved exactly in a two dimensional cylindrical geometry with periodic boundary conditions of width 2. Our approach follows the exact…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter…

We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these…

A new type of disorder-driven electronic percolation transition is found for two-dimensional electron gas (2DEG), based on a quantum cellular automaton model. This transition is shown to be accompanied with a metal-insulator transition, as…

We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed…