Weak solutions of the convective Cahn-Hilliard equation with degenerate mobility

In this paper, the existence of weak solutions of a convective Cahn-Hilliard equation with degenerate mobility is studied. We first define a notion of weak solutions and establish a regularized problems. The existence of such solutions is obtained by considered the limits of the regularized problems.Comment: 16 page

Fourier spectral approximation for the convective Cahn-Hilliard equation in 2D cas

In this paper, we consider the Fourier spectral method for numerically solving the 2D convective Cahn-Hilliard equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error bound are also considered

On the Cauchy problem of 3D incompressible Navier-Stokes-Cahn-Hilliard system

In this paper, we are concerned with the well-posedness and large time behavior of Cauchy problem for 3D incompressible Navier-Stokes-Cahn-Hilliard equations. First, using Banach fixed point theorem, we establish the local well-posedness of solutions. Second, assuming $\|(u_0,\nabla\phi_0)\|_{\dot{H}^\frac12}$ is sufficiently small, we obtain the global well-posedness of solutions. Moreover, the optimal decay rates of the higher-order spatial derivatives of the solution are also obtained

Asymptotic behavior of solutions to 3D incompressible Navier-Stokes equations with damping

In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.Comment: 6 pages, 0 figur

NormalNet: Learning-based Normal Filtering for Mesh Denoising

Mesh denoising is a critical technology in geometry processing that aims to recover high-fidelity 3D mesh models of objects from their noise-corrupted versions. In this work, we propose a learning-based normal filtering scheme for mesh denoising called NormalNet, which maps the guided normal filtering (GNF) into a deep network. The scheme follows the iterative framework of filtering-based mesh denoising. During each iteration, first, the voxelization strategy is applied on each face in a mesh to transform the irregular local structure into the regular volumetric representation, therefore, both the structure and face normal information are preserved and the convolution operations in CNN(Convolutional Neural Network) can be easily performed. Second, instead of the guidance normal generation and the guided filtering in GNF, a deep CNN is designed, which takes the volumetric representation as input, and outputs the learned filtered normals. At last, the vertex positions are updated according to the filtered normals. Specifically, the iterative training framework is proposed, in which the generation of training data and the network training are alternately performed, whereas the ground truth normals are taken as the guidance normals in GNF to get the target normals. Compared to state-of-the-art works, NormalNet can effectively remove noise while preserving the original features and avoiding pseudo-features

Global existence of a generalized Cahn-Hilliard equation with biological applications

In this paper, on the basis of the Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for a generalized Cahn-Hilliard equation with biological applications.Comment: 8 page

Special uniform decay rate of local energy for the wave equation with variable coefficients on an exterior domain

We consider the wave equation with variable coefficients on an exterior domain in $\R^n$($n\ge 2$). We are interested in finding a special uniform decay rate of local energy different from the constant coefficient wave equation. More concretely, if the dimensional $n$ is even, whether the uniform decay rate of local energy for the wave equation with variable coefficients can break through the limit of polynomial and reach exponential; if the dimensional $n$ is odd, whether the uniform decay rate of local energy for the wave equation with variable coefficients can hold exponential as the constant coefficient wave equation . \quad \ \ We propose a cone and establish Morawetz's multipliers in a version of the Riemannian geometry to derive uniform decay of local energy for the wave equation with variable coefficients. We find that the cone with polynomial growth is closely related to the uniform decay rate of the local energy. More concretely, for radial solutions, when the cone has polynomial of degree $\frac{n}{2k-1}$ growth, the uniform decay rate of local energy is exponential; when the cone has polynomial of degree $\frac{n}{2k}$ growth, the uniform decay rate of local energy is polynomial at most. In addition, for general solutions, when the cone has polynomial of degree $n$ growth, we prove that the uniform decay rate of local energy is exponential under suitable Riemannian metric. It is worth pointing out that such results are independent of the parity of the dimension $n$, which is the main difference with the constant coefficient wave equation. Finally, for general solutions, when the cone has polynomial of degree $m$ growth, where $m$ is any positive constant, we prove that the uniform decay rate of the local energy is of primary polynomial under suitable Riemannian metric.Comment: 23 pages. arXiv admin note: text overlap with arXiv:1811.1266

Topological luminophor Y2O3:Eu3++Ag with high electroluminescence performance

Improving luminescent intensity is a significant technical requirement and scientific problem for the luminescent performance of fluorophor materials through the ages. The process control and luminescence performance still limit the developments of luminescent intensity even through it can be improved partly by covering or magnetron sputtering of precious metals on the surface of the fluorophore materials. On the basis of the improvement of luminescence center radiative transition rate by surface plasma resonance and Y2O3:Eu3+ microsheet phosphors, a fundamental model for topological luminophor Y2O3:Eu3++Ag was designed referencing the concepts of topological materials in order to enhance luminescent performance by composite-luminescence, which composed of Eu3+centric electroluminescence and surface plasma-enhanced photoluminescence by Ag. The topological luminophor Y2O3:Eu3++Ag was successfully synthesized with an asymmetric-discrete Ag nanocrystal topological structure on the surface just via illumination. Experiment results suggest that the luminescence performance of topological luminophor Y2O3:Eu3++Ag increased by about 300% compared with that of Y2O3: Eu3+ phosphors on the same conditions. The design of a topological luminophor provides a new approach to further improve the luminescent intensity of phosphors

Adaptive Switching Control of Wind Turbine Generators for Necessary Frequency Response

This letter proposes a new control strategy for wind turbine generators to decide the necessity of switches between the normal operation and frequency support modes. The idea is to accurately predict an unsafe frequency response using a differential transformation method right after power imbalance is detected so as to adaptively activate a frequency support mode only when necessary. This control strategy can effectively avoid unnecessary switches with a conventional use of deadband but still ensure adequate frequency response

Probing the Intra-Component Correlations within Fisher Vector for Material Classification

Fisher vector (FV) has become a popular image representation. One notable underlying assumption of the FV framework is that local descriptors are well decorrelated within each cluster so that the covariance matrix for each Gaussian can be simplified to be diagonal. Though the FV usually relies on the Principal Component Analysis (PCA) to decorrelate local features, the PCA is applied to the entire training data and hence it only diagonalizes the \textit{universal} covariance matrix, rather than those w.r.t. the local components. As a result, the local decorrelation assumption is usually not supported in practice. To relax this assumption, this paper proposes a completed model of the Fisher vector, which is termed as the Completed Fisher vector (CFV). The CFV is a more general framework of the FV, since it encodes not only the variances but also the correlations of the whitened local descriptors. The CFV thus leads to improved discriminative power. We take the task of material categorization as an example and experimentally show that: 1) the CFV outperforms the FV under all parameter settings; 2) the CFV is robust to the changes in the number of components in the mixture; 3) even with a relatively small visual vocabulary the CFV still works well on two challenging datasets.Comment: It is manuscript submitted to Neurocomputing on the end of April, 2015 (!). One year past but no review comments we received yet