Related papers: Well-posedness for a molecular beam epitaxy model

We have synthesized Fe$_{1+y}$Te thin films by means of molecular beam epitaxy (MBE) under Te-limited growth conditions. We found that epitaxial layer-by-layer growth is possible for a wide range of excess Fe values, wider than expected…

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the non linear molecular beam epitaxy (MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory is…

We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, on flat (fixed-size) and expanding substrates (ES). In both $d=1+1$ and $2+1$, we find that growth regime height…

We prove global well-posedness for some molecular beam epitaxy models. This requires proving some bounds on the gradient of solutions. We also obtain some global bounds on the roughness of solutions.

Molecular-beam epitaxy (MBE) provides a simple but powerful way to synthesize large-area high-quality thin films and heterostructures of a wide variety of materials including accomplished group III-V and II-VI semiconductors as well as…

In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open…

Epitaxial growth of WTe$_2$ offers significant advantages, including the production of high-qualityfilms, possible long range in-plane ordering and precise control over layer thicknesses. However,the mean island size of WTe$_2$ grown by…

Intrinsic magnetic topological insulators have emerged as a promising platform to study the interplay between topological surface states and ferromagnetism. This unique interplay can give rise to a variety of exotic quantum phenomena,…

Using molecular beam epitaxy (MBE) to grow multi-elemental oxides (MEO) is generally challenging, partly due to difficulty in stoichiometry control. Occasionally, if one of the elements is volatile at the growth temperature, stoichiometry…

SrMoO$_3$ is a promising material for its excellent electrical conductivity, but growing high-quality thin films remains a challenge. Here we synthesized epitaxial films of SrMoO$_3$ using the molecular beam epitaxy (MBE) technique under a…

Taking into account the occurrence of a zero of the surface diffusion current and the requirement of the Ehrlich-Schwoebel effect, Siegert et al \cite{Siegert94} formulate a model of Langevin type that describes the growth of pyramidlike…

Immense interests in thin-film fabrication for industrial applications have driven both theoretical and computational aspects of modeling its growth with an aim to design and control film's surface morphology. Oftentimes, smooth surface is…

We report on the growth of epitaxial ZnO thin films and ZnO based heterostructures on sapphire substrates by laser molecular beam epitaxy (MBE). We first discuss some recent developments in laser-MBE such as flexible ultra-violet laser beam…

We present models of surfaces of crystals in an environment where molecular beam epitaxy (MBE) and related methods of crystal growth like atomic layer epitaxy (ALE) can be performed. Besides detailed models of reconstructed (001) surfaces…

In this study, high-quality thin films of the topological semimetal phase NiTe$_2$ were prepared using molecular beam epitaxy (MBE) technique, confirmed through X-ray diffraction with pronounced Laue oscillations. Electrical transport…

This paper is concerned with the Cauchy problem for the relativistic membrane equation (RME) embedded in $\mathbb R^{1+(1+n)}$ with $n=2,3$. We show that the RME with a class of large (in energy norm) initial data admits a global, smooth…

We study the Cauchy problem for generalized electron magnetohydrodynamics (EMHD). We establish the local existence and uniqueness of solutions in critical Sobolev spaces, as well as global existence and uniqueness for small initial data. In…

This paper is concerned with the Cauchy problem of the two-dimensional MHD system with magnetic diffusion. It was proved that the MHD equations have a unique global strong solution around the equilibrium state $(0, e_1)$. Furthermore, the…

Variational level set method has become a powerful tool in image segmentation due to its ability to handle complex topological changes and maintain continuity and smoothness in the process of evolution. However its evolution process can be…

Materials informatics exploiting machine learning techniques, e.g., Bayesian optimization (BO), has the potential to offer high-throughput optimization of thin-film growth conditions through incremental updates of machine learning models in…