Total destruction of invariant tori for the generalized Frenkel-Kontorova model

We consider generalized Frenkel-Kontorova models on higher dimensional lattices. We show that the invariant tori which are parameterized by continuous hull functions can be destroyed by small perturbations in the $C^r$ topology with $r<1$

Model anisotropic quantum Hall states

Model quantum Hall states including Laughlin, Moore-Read and Read-Rezayi states are generalized into appropriate anisotropic form. The generalized states are exact zero-energy eigenstates of corresponding anisotropic two- or multi-body Hamiltonians, and explicitly illustrate the existence of geometric degrees of in the fractional quantum Hall effect. These generalized model quantum Hall states can provide a good description of the quantum Hall system with anisotropic interactions. Some numeric results of these anisotropic quantum Hall states are also presented.Comment: 10 pages, 5 figure

Renormalization of the Sigma-Omega model within the framework of U(1) gauge symmetry

It is shown that the Sigma-Omega model which is widely used in the study of nuclear relativistic many-body problem can exactly be treated as an Abelian massive gauge field theory. The quantization of this theory can perfectly be performed by means of the general methods described in the quantum gauge field theory. Especially, the local U(1) gauge symmetry of the theory leads to a series of Ward-Takahashi identities satisfied by Green's functions and proper vertices. These identities form an uniquely correct basis for the renormalization of the theory. The renormalization is carried out in the mass-dependent momentum space subtraction scheme and by the renormalization group approach. With the aid of the renormalization boundary conditions, the solutions to the renormalization group equations are given in definite expressions without any ambiguity and renormalized S-matrix elememts are exactly formulated in forms as given in a series of tree diagrams provided that the physical parameters are replaced by the running ones. As an illustration of the renormalization procedure, the one-loop renormalization is concretely carried out and the results are given in rigorous forms which are suitable in the whole energy region. The effect of the one-loop renormalization is examined by the two-nucleon elastic scattering.Comment: 32 pages, 17 figure

Ammonia as a possible element in an energy infrastructure: catalysts for ammonia decomposition

The possible role of ammonia in a future energy infrastructure is discussed. The review is focused on the catalytic decomposition of ammonia as a key step. Other aspects, such as the catalytic removal of ammonia from gasification product gas or direct ammonia fuel cells, are highlighted as well. The more general question of the integration of ammonia in an infrastructure is also covered

Compositional redistribution during casting of Hg sub 0.8 Cd sub 0.2 Te alloys

A series of Hg(0.8)Cd(0.2)Te ingots was cast both vertically and horizontally under well-defined thermal conditions by using a two-zone furnace with isothermal heat-pipe liners. The main objective of the experiments was to establish correlations between casting parameters and compositional redistribution and to develop ground-based data for a proposed flight experiment of casting of Hg(1-x)Cd(x)Te alloys under reduced gravity conditions. The compositional variations along the axial and radial directions were determined by precision density measurements, infrared transmission spectra, and X-ray energy dispersion spectrometry. Comparison between the experimental results and a numerical simulation of the solidification process of Hg(0.8)Cd(0.2)Te is described

Exploiting Cognitive Structure for Adaptive Learning

Adaptive learning, also known as adaptive teaching, relies on learning path recommendation, which sequentially recommends personalized learning items (e.g., lectures, exercises) to satisfy the unique needs of each learner. Although it is well known that modeling the cognitive structure including knowledge level of learners and knowledge structure (e.g., the prerequisite relations) of learning items is important for learning path recommendation, existing methods for adaptive learning often separately focus on either knowledge levels of learners or knowledge structure of learning items. To fully exploit the multifaceted cognitive structure for learning path recommendation, we propose a Cognitive Structure Enhanced framework for Adaptive Learning, named CSEAL. By viewing path recommendation as a Markov Decision Process and applying an actor-critic algorithm, CSEAL can sequentially identify the right learning items to different learners. Specifically, we first utilize a recurrent neural network to trace the evolving knowledge levels of learners at each learning step. Then, we design a navigation algorithm on the knowledge structure to ensure the logicality of learning paths, which reduces the search space in the decision process. Finally, the actor-critic algorithm is used to determine what to learn next and whose parameters are dynamically updated along the learning path. Extensive experiments on real-world data demonstrate the effectiveness and robustness of CSEAL.Comment: Accepted by KDD 2019 Research Track. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining (KDD'19

Understanding the Clean Interface between Covalent Si and Ionic Al2O3

The atomic and electronic structures of the (001)-Si/(001)-gamma-Al2O3 heterointerface are investigated by first principles total energy calculations combined with a newly developed "modified basin-hopping" method. It is found that all interface Si atoms are fourfold coordinated due to the formation of Si-O and unexpected covalent Si-Al bonds in the new abrupt interface model. And the interface has perfect electronic properties in that the unpassivated interface has a large LDA band gap and no gap levels. These results show that it is possible to have clean semiconductor-oxide interfaces