相关论文: Asymptotic analysis for a second order curved thin…

In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by…

Consider the three-dimensional flow of a viscous Newtonian fluid upon an abitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a model of the dynamics of the film, the…

Short review on the different models for the electro-thermal 3-omega method. We present the deduction of the fundamental relation between the 3-omega voltage with the temperature rise to determine the thermal conductivity. The usage of the…

This article is concerned with the asymptotic behavior of the two-dimensional inviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time-decay rates of the smooth solutions to that system. The…

A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are…

Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…

In soft matter, the phase of nematic liquid crystals can be made from anisotropic molecules in single component materials, or as a suspension of mesoscopic nematogens. The later offers more versatility in the experimental design of complex…

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and…

Understanding the growth of organic semi-conducting molecules with shape anisotropy is of high relevance to the processing of optoelectronic devices. This work provides insight into the growth of thin films of the prototypical rodlike…

The thickness evolution of in-plane magnetization reversal in ultrathin films is studied with a theoretical model that takes account of surface roughness typical of epitaxial growth. Guided by N\'{e}el's model, step edge sites of…

When a flexible plate is peeled off a thin and soft elastic film bonded to a rigid support, uniformly spaced fingering patterns develop along their line of contact. While, the wavelength of these patterns depends only on the thickness of…

We consider a heterogeneous elastic structure which is stratified in some direction. We derive the limit problem under the assumption that the Lam\'e coefficients and their inverses weakly* converge to Radon measures. Our method applies…

Ordering of mobile defects in functional materials can give rise to fundamentally new phases possessing ferroic and multiferroic functionalities. Here we develop the Landau theory for strain induced ordering of defects (e.g. oxygen…

The study of atomically thin two-dimensional materials is a young and rapidly growing field. In the past years, a great advance in the study of the remarkable electrical and optical properties of 2D materials fabricated by exfoliation of…

We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic…

We study the electronic structure of WTe$_2$ thin film fakes with different thickness down to 11 nm. Angle-dependent quantum oscillations reveal a crossover from a three-dimensional (3D) to a two-dimensional (2D) electronic system when the…

The effect of fluctuation induced weakly first order phase transition known for three dimensional (3D) type I superconductors appears in a modified and strongly enhanced variant in thin (quasi-2D) superconducting films. The unusual…

Strain engineering is widely used in material science to tune the (opto-)electronic properties of materials and enhance the performance of devices. Two-dimensional atomic crystals are a versatile playground to study the influence of strain,…

The three-dimensional shapes of thin lamina such as leaves, flowers, feathers, wings etc, are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric, given on the…

For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…