The effects of mobility of small islands on island growth in molecular beam epitaxy are studied. It is shown that small island mobility affects both the scaling and morphology of islands during growth. Three microscopic models are considered, in which the critical island sizes are i∗ = 1, 2 and 3 (such that islands of size s ≤ i∗ are mobile while islands of size s ≥ i∗ +1 are immobile). As i∗ i...

We report an algorithm for the partition of a line segment according to a given ratio ν. At each step the length distribution among sets of the partition follows a binomial distribution. We call k-set to the set of elements with the same length at the step n. The total number of elements is 2 and the number of elements in a same k-set is C n. In the limit of an infinite partion this object beco...

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 matrix method and the n-equivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can b...

The fractal structure of spin clusters and their boundaries in the critical two-dimensional Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations on relatively small lattices through standard finite-size scaling. The obtained results are in excellent agreement with theoretical predictions and partly provide...

The effects of mobility of small islands on island growth in molecular beam epitaxy are studied. It is shown that mobility of small islands affects both the scaling and morphology of islands during growth. Three microscopic models are considered, in which the critical island sizes are i∗ = 1, 2 and 3 (such that islands of size s ≤ i∗ are mobile while islands of size s ≥ i∗ +1 are immobile). As ...

Size effects concern the anomalous scaling of relevant mechanical properties materials and structures over a sufficiently wide dimensional range. In last few years, thanks to technological advances, such have been experimentally detected also in very high cycle fatigue (VHCF) tests. Research groups at Politecnico di Torino are active this field, observing size on strength, life limit up VHCF re...

This morning's debate is focused on the question of the large-scale homo-geneity of the Universe. I shall present the aarmative position, that there is overwhelming evidence for large scale homogeneity on scales in excess of approximately 50h ?1 Mpc, with a fractal distribution of matter on smaller scales. My worthy opponent, Dr. Luciano Pietronero, will present the counter-argument, that the f...

Cellular automata (CA) have been increasingly applied to ecohydraulics modelling owing to its advantages in simulating local behaviours and spatial patterns. However, methods for evaluating CA model performance, mostly comparing with RS observations, have yet to be established. A conventional way is to compute the overall error between model outputs and observations. This aggregated approach wi...

We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated tha...

This paper presents a quantitative modeling for delineating alteration zones in the hypogene zone of the Miduk porphyry copper deposit (SE Iran) based on the core drilling data. The main goal of this work was to apply the Ordinary Kriging (OK), Artificial Neural Networks (ANNs), and Concentration-Volume (C-V) fractal modelings on Cu grades to separate different alteration zones. Anisotropy was ...