Related papers: Numerical Simulation of Three-Dimensional Dendrite…
Dendrites with developed sidebranches are numerically studied with a coupled map lattice model. The competitive dynamics among sidebranches determines the shape of the envelope. The envelope has a parabolic shape near the tip of the…
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…
We present a numerical study of sidebranching of a solidifying dendrite by means of a phase--field model. Special attention is paid to the regions far from the tip of the dendrite, where linear theories are no longer valid. Two regions have…
Dendritic crystal growth in a pure undercooled melt is simulated quantitatively in three dimensions using a phase-field approach. The full non-axisymmetric morphology of the steady-state dendrite tip and $\sigma^*$ are determined as a…
We investigate dendritic sidebranching during crystal growth in an undercooled melt by simulation of a phase-field model which incorporates thermal noise of microscopic origin. As a non-trivial quantitative test of this model, we first show…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
Coupled aggregation and sedimentation processes were studied by means of three dimensional computer simulations. For this purpose, a large prism with no periodic boundary conditions for the sedimentation direction was considered.…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
The magnetic properties of single-domain nanoparticles with different geometric shapes, crystalline anisotropies and lattice structures are investigated. A recently proposed scaling approach is shown to be universal and in agreement with…
The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…
The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and…
We consider the number of configurations of a surface in two dimensions that has a prescribed length and encloses a prescribed perimeter with respect to a baseline. An approximate analytical treatment in a semi--continuum compares…
Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The…
We develop tools to study the topology and geometry of self-affine fractals in dimension three and higher. We use the self-affine structure and obtain rather detailed information about the connectedness of interior and boundary sets, and on…
We experimentally generate three-dimensional speckles with customized intensity statistics. By modulating the phase front of a laser beam, far-field speckle patterns maintain the designed intensity probability density function while…
The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Nice power-law scaling…
The Delone (Selling) scalars, which are used in unit cell reduction and in lattice type determination, are studied in $\mathbb{C}^3$, the space of three complex variables. The three complex coordinate planes are composed of the six Delone…