An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematic

AdS Black Hole with Phantom Scalar Field

In this paper, we present an AdS black hole solution with Ricci flat horizon in Einstein-phantom scalar theory. The phantom scalar fields just depend on the transverse coordinates $x$ and $y$, and which are parameterized by the parameter $\alpha$. We study the thermodynamics of the AdS phantom black hole. Although its horizon is a Ricci flat Euclidean space, we find that the thermodynamical properties of the black hole solution are qualitatively same as those of AdS Schwarzschild black hole. Namely there exists a minimal temperature, the large black hole is thermodynamically stable , while the smaller one is unstable, so there is a so-called Hawking-Page phase transition between the large black hole and the thermal gas solution in the AdS spacetime in Poincare coordinates. We also calculate the entanglement entropy for a strip geometry dual to the AdS phantom black holes and find that the behavior of the entanglement entropy is qualitatively the same as that of the black hole thermodynamical entropy.Comment: 6 pages, 8 figure

Learning Social Image Embedding with Deep Multimodal Attention Networks

Learning social media data embedding by deep models has attracted extensive research interest as well as boomed a lot of applications, such as link prediction, classification, and cross-modal search. However, for social images which contain both link information and multimodal contents (e.g., text description, and visual content), simply employing the embedding learnt from network structure or data content results in sub-optimal social image representation. In this paper, we propose a novel social image embedding approach called Deep Multimodal Attention Networks (DMAN), which employs a deep model to jointly embed multimodal contents and link information. Specifically, to effectively capture the correlations between multimodal contents, we propose a multimodal attention network to encode the fine-granularity relation between image regions and textual words. To leverage the network structure for embedding learning, a novel Siamese-Triplet neural network is proposed to model the links among images. With the joint deep model, the learnt embedding can capture both the multimodal contents and the nonlinear network information. Extensive experiments are conducted to investigate the effectiveness of our approach in the applications of multi-label classification and cross-modal search. Compared to state-of-the-art image embeddings, our proposed DMAN achieves significant improvement in the tasks of multi-label classification and cross-modal search

A Study on Project-Driven Practice and Innovation Abilities of IT Students’ Club

IT students’ clubs play an irreplaceable role in training students’ innovation and practical abilities. Through questionnaires and interviews, the paper analyzes students’ participation in IT clubs, the training of students’ innovation and practical abilities and the problems existing in the organization management of clubs. By referring to the successful experience of Wuhan University of Science and Technology in the practice teaching reform, a “project-driven” system for training practice and innovation abilities, which focused on training students’ innovation spirit and practical abilities, was established and achieved remarkable success