Related papers: Well-posedness for a molecular beam epitaxy model
We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that…
Constitutive equations are derived for a 1-D micropolar Timoshenko beam made of a web-core lattice material. First, a web-core unit cell is modeled by discrete classical constituents, i.e., the Euler-Bernoulli beam finite elements (FE). A…
We prove the global existence of the unique mild solution for the Cauchy problem of the cut-off Boltzmann equation for soft potential model $\gamma=2-N$ with initial data small in $L^N_{x,v}$ where $N=2,3$ is the dimension. The proof relies…
We report on the growth of epitaxial Sr2RuO4 films using a hybrid molecular beam epitaxy approach in which a volatile precursor containing RuO4 is used to supply ruthenium and oxygen. The use of the precursor overcomes a number of issues…
Atomically thin transition metal dichalcogenide films with distorted trigonal (1T$^\prime$) phase have been predicted to be candidates for realizing quantum spin Hall effect. Growth of 1T$^\prime$ film and experimental investigation of its…
We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. We first prove the global existence of evolution variational inequality solution with a general initial data using the gradient…
We study the Cauchy problem for a weighted porous medium equation on $\R$ associated with a Gibbs probability measure $\pi=e^{-V}$. Under a Poincar\'e inequality for $\pi$ and the convexity assumption on $V$, we prove well-posedness and…
Chromium selenide thin films were grown epitaxially on Al${_2}$O${_3}$(0001) and Si(111)-(7${\times}$7) substrates using molecular beam epitaxy (MBE). Sharp streaks in reflection high-energy electron diffraction and triangular structures in…
In this paper we mainly investigate the Cauchy problem of the finite extensible nonlinear elastic (FENE) dumbbell model with dimension $d\geq2$. We first proved the local well-posedness for the FENE model in Besov spaces by using the…
We consider very weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds, that are assumed to satisfy general curvature bounds and to be stochastically complete. We identify a class of initial data…
Consider the Cauchy problem of one dimensional porous medium equation (PME) with reactions. We first prove a general convergence result, that is, any bounded global solution starting at a nonnegative compactly supported initial data…
We report on the epitaxial growth and surface structure of infinite-layer cuprate Sr1-xNdxCuO2 films on SrTiO3(001) substrates by combining ozone-assisted molecular beam epitaxy and in situ scanning tunneling microscopy. Careful substrate…
This paper deals with stability and the large-time decay to any given global smooth solutions of the 3D density-dependent incompressible Boussinesq system. The decay rate for solutions of the corresponding Cauchy problem is obtained in this…
We establish the existence and uniqueness of mild solutions for the polyatomic ellipsoidal BGK model, which is a relaxation type kinetic model describing the evolution of polyatomic gaseous system at the mesoscopic level.
A three-step process was developed for growing high-quality, optically uniform WSe2 monolayers by molecular beam epitaxy (MBE) with advantage of using hexagonal boron nitride (hBN). The process was optimized to maximize the efficiency of…
We prove the global well-posedness of the one-dimensional Navier-Stokes-Korteweg equations driven by a stochastic multiplicative noise. The analysis is performed for the general case of capillarity and viscosity coefficients $k(\rho)=…
We study the mathematical properties of a model of cell division structured by two variables, the size and the size increment, in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct…
We have investigated the growth of BaTiO3 thin films deposited on pure and 1% Nb-doped SrTiO3(001) single crystals using atomic oxygen assisted molecular beam epitaxy (AO-MBE) and dedicated Ba and Ti Knudsen cells. Thicknesses up to 30 nm…
In this article we study a model from epitaxial thin-film growth. It was originally introduced as a phenomenological model of growth in the presence of a Schwoebbel barrier, where diffusing particles on a terrace are not allowed to jump…
We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening…