相关论文: Asymptotic analysis for a second order curved thin…
We carry out the asymptotic analysis as $n \to \infty$ of a class of orthogonal polynomials $p_{n}(z)$ of degree $n$, defined with respect to the planar measure \begin{equation*} d\mu(z) = (1-|z|^{2})^{\alpha-1}|z-x|^{\gamma}\mathbf{1}_{|z|…
We propose a theoretical study for Si thin film thickness measurement that is based on incident low energy electron beam on the film and counting the transmitted/incident electron fraction. It estimates the thin film thickness distribution…
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for…
Organisms in nature can alter the short-range order of an amorphous precursor phase, thereby controlling the resulting crystalline structure. This phenomenon inspired an investigation of the effect of modifying the short-range order within…
We rigorously derive from first principles the generic Landau amplitude equation that describes the primary bifurcation in electrically driven convection. Our model accurately represents the experimental system: a weakly conducting,…
This paper deals with a nonlinear degenerate parabolic equation of order $\alpha$ between 2 and 4 which is a kind of fractional version of the Thin Film Equation. Actually, this one corresponds to the limit value $\alpha=4$ while the Porous…
Phase fluctuations in finite thickness layered superconducting films are studied theoretically. The model consists of a set of layers, coupled to each other via a gradient-like term in the phase-only action. It is shown that the effective…
We study a class of lubrication-type equations modeling the spread of thin poroelastic biofilms at air/agar interfaces. Starting from a biofilm slab model, we perform a formal multi-scale asymptotic expansion to derive a reduced nonlinear…
We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based…
We present results from molecular dynamics simulations of strictly two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of thickness of the order of the radius of gyration. We find that the dynamics of the 2D melt is…
The comprehensive understanding of superconductivity is a multi-scale task that involves several levels, starting from the electronic scale determining the microscopic mechanism, going to the phenomenological scale describing vortices and…
Experiments have investigated shape changes of polymer films induced by asymmetric swelling by a chemical vapor. Inspired by recent work on the shaping of elastic sheets by non-Euclidean metrics [Y. Klein, E. Efrati, and E. Sharon, Science…
We consider a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths. We construct a weak solution of the flow by means of an implicit variational scheme. We show long-time existence…
Due to the wide range of applications, theoretical models of Fe3O4 films are found to be important. Ultra thin Fe3O4 films with ferrite structure have been theoretically investigated using second order perturbed modified Heisenberg…
The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that…
Thin films are usually obtained by depositing atoms with a continuous flux. We show that using a chopped flux changes the growth and the morphology of the film. A simple scaling analysis predicts how the island densities change as a…
A hydrostatically stressed soft elastic film circumvents the imposed constraint by undergoing a morphological instability, the wavelength of which is dictated by the minimization of the surface and the elastic strain energies of the film.…
Classical molecular-dynamics simulations have been carried out to investigate densification mechanisms in silicon dioxide thin films deposited on an amorphous silica surface, according to a simplified ion-beam assisted deposition (IBAD)…
We have used density functional theory to study the nonlinear screening properties of a two-dimensional (2D) electron gas. In particular, we consider the screening of an external static point charge of magnitude Z as a function of the…
Harmonic analysis of the temperature dependence of the nonlinear ac susceptibility of Nb thin film gives excellent agreement with the susceptibility calculated on basis of model of the hysteretic critical state in 2D disk.