Related papers: Logarithmic Clustering in Submonolayer Epitaxial G…
The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers, or by positive…
The domino-shuffling algorithm can be seen as a stochastic process describing the irreversible growth of a $(2+1)$-dimensional discrete interface. Its stationary speed of growth $v_{\mathtt w}(\rho)$ depends on the average interface slope…
The study of the density evolution naturally arises in Mean Field Game theory for the estimation of the density of the large population dynamics. In this paper, we study the density evolution of McKean-Vlasov stochastic differential…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
Kinetic Monte-Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy (MBE) experiments. In parallel, simplified approaches such as limited mobility (LM)…
In a series of three papers, we introduced a novel cluster formation model that describes the formation, growth, and disruption of star clusters in high-resolution cosmological simulations. We tested this model on a Milky Way-sized galaxy…
The stationary distribution of the diffusion limit of the 2-island, 2-allele Wright-Fisher with small but otherwise arbitrary mutation and migration rates is investigated. Following a method developed by Burden and Tang (2016, 2017) for…
The role of instability in the growth of a 2D, temporally evolving, `turbulent' free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot-Savart relation. The initial evolution of…
Analytical approaches describing non-Fickian diffusion in complex systems are presented. The corresponding methods are applied to the study of statistical properties of pyramidal islands formation with interacting adsorbate at epitaxial…
A continuum one dimensional model of homoepitaxial growth under oblique incidence is investigated. We carried out numerical integration of a continuum equation incorporating a shadowing search algorithm. The interplay between the…
The growth of large crystallite continuous monolayer materials like molybdenum disulfide (MoS$_2$) with desired morphology via chemical vapor deposition (CVD) remains a challenge. In CVD, the complex interplay of various factors like growth…
Using cosmological N-body simulations of critical (SCDM) and open ($\Omega = 0.3$, OCDM) cold dark matter models, we investigate evolution of cluster galaxies. From our numerical simulation, we construct merging history trees of the…
We have experimentally investigated field induced aggregation of nonmagnetic particles confined in a magnetic fluid layer when rotating magnetic fields were applied. After application of a magnetic field rotating in the plane of the fluid…
We study the dynamical evolution of globular clusters using our new 2-D Monte Carlo code, and we calculate the lifetimes of clusters in the Galactic environment. We include the effects of a mass spectrum, mass loss in the Galactic tidal…
In all spatial dimensions $d$, we study the static and dynamical properties of a generalized Smoluchowski equation which describes the evolution of a gas obeying a logotropic equation of state, $p=A\ln\rho$. A logotrope can be viewed as a…
The thermodynamics of the Stranski-Krastanov mode of epitaxial growth and the effect of the sign of the lattice misfit are discussed. The Stranski-Krastanov mode of growth represents a sequence of layer-by-layer or Frank-van der Merwe…
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…
The observed height distribution of clusters obtained in strained epitaxy has been often interpreted in terms of electronic effects. We show that some aspects can be explained classically by the interplay of strain and edge energies. We…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
We explore the evolution of the aggregate size distribution in systems where aggregates grow by diffusive accretion of mass. Supersaturation is controlled in such a way that the overall aggregate volume grows linearly in time. Classical…