Related papers: Lattice Model for Approximate Self-Affine Soil Pro…
We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further…
Recently it was shown that self-organized criticality is an important ingredient of the dynamics of cumulus clouds (Physical Review E, 103(5), p.052106, 2021). Here we introduce a new algorithm to simulate cumulus clouds in two-dimensional…
The phase-field crystal (PFC) model describes crystal structures at diffusive timescales through a periodic, microscopic density field. It has been proposed to model elasticity in crystal growth and encodes most of the phenomenology related…
In this paper we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows to understand many experiments of thin film deposition. In the first…
Semiconductor surfaces were divided into charge categories, i.e. surface acceptor, donor and neutral ones that are suitable for simulations of their properties within a slab model. The potential profiles, close to the charged surface…
We revisit the problem of the stress distribution in a frictional sandpile under gravity, equipped with a new numerical model of granular assemblies with both normal and tangential (frictional) inter-granular forces. Numerical simulations…
In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…
The most important characteristics of the fragmentation of heterogeneous solids is that the mass (size) distribution of pieces is described by a power law functional form. The exponent of the distribution displays a high degree of…
We have performed a detailed Monte Carlo study of a diffusionless $(1+1)$-dimensional solid-on-solid model of particle deposition and evaporation that not only tunes the roughness of an equilibrium surface but also demonstrates the need for…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the…
We study the scaling properties of self-flattening surfaces under global suppression on surface fluctuations. Evolution of self-flattening surfaces is described by restricted solid-on-solid type monomer deposition-evaporation model with…
Self-aggregation of tropical convection is a universal feature observed in a diverse range of atmospheric environments. Several preceding models conceptualized the self-aggregation of convection as a phase transition driven by collisions…
The relationship between geometric and dynamic properties of fractal-like aggregates is studied in the continuum mass and momentum-transfer regimes. The synthetic aggregates were generated by a cluster-cluster aggregation algorithm. The…
It is well known by analysts that a concept lattice has an exponential size in the data. Thus, as soon as he works with real data, the size of the concept lattice is a fundamental problem. In this chapter, we propose to investigate factor…
In many areas of research it is interesting how lattices can be filled with particles that have no nearest neighbors, or they are in limited quantities. Examples may be found in statistical physics, chemistry, materials science, discrete…
The flattening of a crystal cone below its roughening transition is studied by means of a step flow model. Numerical and analytical analyses show that the height profile, h(r,t), obeys the scaling scenario dh/dr = F(r t^{-1/4}). The scaling…
We consider a size-structured aggregation and growth model of phytoplankton community proposed by Ackleh and Fitzpatrick [2]. The model accounts for basic biological phenomena in phytoplankton community such as growth, gravitational…
The lattice Schwinger model (SM), the discrete version of QED in 1+1 dimensions, is a well-studied test bench for lattice gauge theories. Here we study the fractal properties of the SM. We reveal the self-similarity of the ground state,…
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…