Related papers: Scale decomposition of molecular beam epitaxy
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
In this paper we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Covering elastic substrates with stiff biomimetic scales significantly alters the bending behavior via scales engagement. This engagement is the dominant source of nonlinearity in small deflection regime. As deformation proceeds, an…
Recently, the nucleation rate on top of a terrace during the irreversible growth of a crystal surface by MBE has been determined exactly. In this paper we go beyond the standard model usually employed to study the nucleation process, and we…
Epithelial cells can assemble into cohesive colonies and collectively interact with substrates by generating extracellular forces through focal adhesions. Recently, a molecularly based thermodynamic model, which integrates both the…
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)…
Motivated by recent experimental studies in microbiology, we suggest a modification of the classic ballistic deposition model of surface growth, where the memory of a deposition at a site induces more depositions at that site or its…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions - both in theory and from observations. Despite promising findings on the…
This paper presents a convergence analysis of the evolving surface finite element method (ESFEM) applied to the original Eyles-King-Styles model of tumour growth. The model consists of a Poisson equation in the bulk, a forced mean curvature…
We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…
Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the…
In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance,…
The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much…
Epitaxial graphene is grown on a non-polar n+ 6H-SiC m-plane substrate and studied using atomic scale scanning tunneling microscopy. Multilayer graphene is found throughout the surface and exhibits rotational disorder. Moir\'e patterns of…
Quantifying wettability at the nanoscale remains challenging, as macroscopic contact-angle measurements fail to capture the molecular interactions that define hydrophilic and hydrophobic behavior. We derive an analytical relation linking…
In this paper we study the evolution of the wave function with the system size in a locally periodic structure. In particular we analyse the dependence of the wave function with the number of unit cells, which also reflects information…
The behavior of a surface energy $\mathcal F(E,u)$, where $E$ is a set of finite perimeter and $u\in L^1(\partial^* E, \mathbb R_+)$ is studied. These energies have been recently considered in the context of materials science to derive a…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…