Related papers: Growth rate distribution of NH_4Cl dendrite and it…
We apply multifractal analysis to an experimentally obtained quasi-two-dimensional crystal with fourfold symmetry, in order to characterize the sidebranch structure of a dendritic pattern. In our analysis, the stem of the dendritic pattern…
Within the continuum dislocation theory the asymptotic analysis of the plane strain crack problem for a single crystal having only one active slip system on each half-plane is provided. The results of this asymptotic analysis show that the…
We analyze a two-dimensional spring network model comprising breakable and unbreakable springs. Computer simulations showed this system to exhibit intermittent stress drops in a larger strain regime, and these stress drops resulted in…
The crystal size distribution in polynuclear growth is numerically studied using a coupled map lattice model. The width of the size distribution depends on c/D, where c is the growth rate at interface sites and $D$ is the diffusion…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
Growth in crystals can be { usually } described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics…
We investigate analytically and computationally the dynamics of 2D needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $V$ decreases in time $t$…
We numerically investigate the electric potential distribution over a two-dimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal…
In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics,…
In this paper, we analyze the scaling behavior of \emph{Diffusion Limited Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns in a good…
The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence…
Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination…
In this article a collection of random self-similar fractal dendrites is constructed, and their Hausdorff dimension is calculated. Previous results determining this quantity for random self-similar structures have relied on geometrical…
We have performed numerical simulations of dendritic growth at very low undercoolings in two spatial dimension using a phase-field model. In this regime of growth, the dendrites present sharp corners in the tip region while the trailing…
A first-principles statistical theory is constructed for the evolution of two dimensional interfaces in Laplacian fields. The aim is to predict the pattern that the growth evolves into, whether it becomes fractal and if so the…
To seek for a possible origin of fractal pattern in nature, we perform a molecular dynamics simulation for a fragmentation of an infinite fcc lattice. The fragmentation is induced by the initial condition of the model that the lattice…
The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…
A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global…
In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F~t^n, with n<1/2, thus providing a macroscopic realization of…