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The epitaxial growth process of a high symmetry surface occurs because adatoms meet and nucleate new islands, that eventually coalesce and complete atomic layers. During multilayer growth, nucleation usually takes place on top of terraces…

Statistical Mechanics · Physics 2007-05-23 Paolo Politi , Claudio Castellano

In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling functions of the surface fluctuations coincide with limit…

Mathematical Physics · Physics 2011-11-10 Patrik L. Ferrari , Michael Praehofer

We study irreversible dimer nucleation on top of terraces during epitaxial growth in one and two dimensions, for all values of the step-edge barrier. The problem is solved exactly by transforming it into a first passage problem for a random…

Statistical Mechanics · Physics 2007-05-23 Paolo Politi , Claudio Castellano

In the framework of the second-quantization representation of the master equation governing the irreversible epitaxial growth, exact equations describing the evolution of the island densities has been obtained. Their decoupling within a…

Statistical Mechanics · Physics 2015-06-15 V. I. Tokar , H. Dreyssé

The typical island distance $\ell$ in submonlayer epitaxial growth depends on the growth conditions via an exponent $\gamma$. This exponent is known to depend on the substrate dimensionality, the dimension of the islands, and the size $i^*$…

Statistical Mechanics · Physics 2016-08-31 Harald Kallabis , Paul L. Krapivsky , Dietrich E. Wolf

Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming…

Statistical Mechanics · Physics 2011-09-23 T. J. Oliveira , F. D. A. Aarao Reis

We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local…

Statistical Mechanics · Physics 2007-05-23 F. Hivert , S. Nechaev , G. Oshanin , O. Vasilyev

Understanding surface dynamics during epitaxial film growth is key to growing high quality materials with controllable properties. X-ray photon correlation spectroscopy (XPCS) using coherent x-rays opens new opportunities for in situ…

We investigate the influence of intermixing on heteroepitaxial growth dynamics, using a two-dimensional point island model, expected to be a good approximation in the early stages of epitaxy. In this model, which we explore both…

Statistical Mechanics · Physics 2015-06-22 K. I. Mazzitello , L. M. Delgado , J. L. Iguain

We describe a theoretical study of the role of adsorbate interactions in island nucleation and growth, using Ag/Pt(111) heteroepitaxy as an example. From density-functional theory, we obtain the substrate-mediated Ag adatom pair interaction…

Materials Science · Physics 2009-10-31 Kristen A. Fichthorn , Matthias Scheffler

We introduce a class of cellular automata growth models on the two-dimensional integer lattice with finite cross neighborhoods. These dynamics are determined by a Young diagram $\mathcal Z$ and the radius $\rho$ of the neighborhood, which…

Probability · Mathematics 2023-07-17 Daniel Blanquicett , Janko Gravner , David Sivakoff , Luke Wilson

A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at…

Pattern Formation and Solitons · Physics 2009-11-10 K. Tucci , M. G. Cosenza

The distribution of capture zones formed during the nucleation and growth of point islands on a one-dimensional substrate during monomer deposition is considered for general critical island size $i$. A fragmentation theory approach yields…

Adaptation and Self-Organizing Systems · Physics 2015-05-28 M. Grinfeld , W. Lamb , P. A. Mulheran , K. P. O'Neill

Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…

Probability · Mathematics 2023-04-05 Vincent Bansaye , Michele Salvi

In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are…

Chaotic Dynamics · Physics 2015-05-13 Xavier Calbet , Ricardo Lopez-Ruiz

We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier $\Delta E_S$ for descending atoms. The theory is based on the concept of the residence time of an adatom on the…

Materials Science · Physics 2007-05-23 Joachim Krug , Paolo Politi , Thomas Michely

We investigate island formation during heteroepitaxial growth using an atomistic model that incorporates deposition, activated diffusion and stress relaxation. For high misfit the system naturally evolves into a state characterized by a…

Statistical Mechanics · Physics 2009-10-30 Albert-László Barabási

We generated a computational approach to analyze the biomechanics of epithelial cell aggregates, either island or stripes or entire monolayers, that combines both vertex and contact-inhibition-of-locomotion models to include both cell-cell…

We study random sequential adsorption of particles from pool onto a one dimensional substrate following ballistic deposition rules, with separate nucleation and growth processes occurring simultaneously. Nucleation describes the formation…

Statistical Mechanics · Physics 2019-12-10 A. Khanam , J. A. D. Wattis , M. K. Hassan

Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett. {\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate analytically the asymptotic scaled capture-number distribution (CND) for…

Materials Science · Physics 2009-11-10 J. G. Amar , M. N. Popescu