相关论文: Fractal formation and ordering in Random Sequentia…
We reveal the fractal nature of patterns arising in random sequential adsorption of particles with continuum power-law size distribution, $P(R)\sim R^{\alpha-1}$, $R \le R_{\rm max}$. We find that the patterns become more and more ordered…
We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…
We investigate the process of random sequential adsorption of polydisperse particles whose size distribution exhibits a power-law dependence in the small size limit, $P(R)\sim R^{\alpha-1}$. We reveal a relation between pattern formation…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…
We discuss the formation of stochastic fractals and multifractals using the kinetic equation of fragmentation approach. We also discuss the potential application of this sequential breaking and attempt to explain how nature creats fractals.
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
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…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic…
We consider the model of random sequential adsorption, with depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large…
We present a model of one-dimensional irreversible adsorption in which particles once adsorbed immediately shrink to a smaller size or expand to a larger size. Exact solutions for the fill factor and the particle number variance as a…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in…
Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the…
We discuss two important techniques, series expansion and Monte Carlo simulation, for random sequential adsorption study. Random sequential adsorption is an idealization for surface deposition where the time scale of particle relaxation is…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…