Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations

Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the Cahn-Hilliard equation and the thin film type equation. The up-to-date theoretical explanation of the numerical stability relies on the assumption that the deriva- tive of the nonlinear potential function satisfies a Lipschitz type condition, which in a rigorous sense, implies the boundedness of the numerical solution. In this work we remove the Lipschitz assumption on the nonlinearity and prove unconditional energy stability for the stabilized semi-implicit time-stepping methods. It is shown that the size of stabilization term depends on the initial energy and the perturba- tion parameter but is independent of the time step. The corresponding error analysis is also established under minimal nonlinearity and regularity assumptions

Gradient bounds for a thin film epitaxy equation

We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions $d\le 3$

Ontology-based data semantic management and application in IoT- and cloud-enabled smart homes

The application of emerging technologies of Internet of Things (IoT) and cloud computing have increasing the popularity of smart homes, along with which, large volumes of heterogeneous data have been generating by home entities. The representation, management and application of the continuously increasing amounts of heterogeneous data in the smart home data space have been critical challenges to the further development of smart home industry. To this end, a scheme for ontology-based data semantic management and application is proposed in this paper. Based on a smart home system model abstracted from the perspective of implementing users’ household operations, a general domain ontology model is designed by defining the correlative concepts, and a logical data semantic fusion model is designed accordingly. Subsequently, to achieve high-efficiency ontology data query and update in the implementation of the data semantic fusion model, a relational-database-based ontology data decomposition storage method is developed by thoroughly investigating existing storage modes, and the performance is demonstrated using a group of elaborated ontology data query and update operations. Comprehensively utilizing the stated achievements, ontology-based semantic reasoning with a specially designed semantic matching rule is studied as well in this work in an attempt to provide accurate and personalized home services, and the efficiency is demonstrated through experiments conducted on the developed testing system for user behavior reasoning

Test of CPT symmetry in cascade decays

Cascade mixing provides an elegant place to study the $B^0-\bar{B^0}$ mixing. We use this idea to study the CPT violation caused by $B^0-\bar{B^0}$ mixing. An approximation method is adopted to treat the two complex $B^0-\bar{B^0}$ mixing parameters $\theta$ and $\phi$. A procedure to extract the parameters $\theta$ and $\phi$ is suggested. The feasibility of exploring the CPT violation and determining of $\theta$ and $\phi$ in the future B-factories and LHC-B is discussed.Comment: Latex, 17 pages, some errors modifie