A vicinal surface model for epitaxial growth with logarithmic free energy

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+\alpha u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ converging to a constant that only depends on the initial data is also investigated both analytically and numerically.Comment: 18 pages, 7 figure

Optimal control-based inverse determination of electrode distribution for electroosmotic micromixer

This paper presents an optimal control-based inverse method used to determine the distribution of the electrodes for the electroosmotic micromixers with external driven flow from the inlet. Based on the optimal control method, one Dirichlet boundary control problem is constructed to inversely find the optimal distribution of the electrodes on the sidewalls of electroosmotic micromixers and achieve the acceptable mixing performance. After solving the boundary control problem, the step-shaped distribution of the external electric potential imposed on the sidewalls can be obtained and the distribution of electrodes can be inversely determined according to the obtained external electric potential. Numerical results are also provided to demonstrate the effectivity of the proposed method

Growth, Properties and Applications of Bi0.5Na0.5TiO3 Ferroelectric Nanomaterials.

The emerging demands for miniaturization of electronics has driven the research into various nanomaterials. Lead-free Bi0.5Na0.5TiO3 (BNT) ferroelectric nanomaterials have drawn great interest owing to their superiorities of large remanent polarization, high pyroelectric and piezoelectric coefficients, unique photovoltaic performance and excellent dielectric properties. As attractive multifunctional ferroelectrics, BNT nanomaterials are widely utilized in various fields, such as energy harvest, energy storage, catalysis as well as sensing. The growing desire for precisely controlling the properties of BNT nanomaterials has led to significant advancements in material design and preparation approaches. BNT ferroelectric nanomaterials exhibit significant potential in fabrication of electronic devices and degradation of waste water, which pushes forward the advancement of the Internet of things and sustainable human development. This article presents an overview of research progresses of BNT ferroelectric nanomaterials, including growth, properties and applications. In addition, future prospects are discussed