The constructive approach on existence of time optimal controls of system governed by nonlinear equations on Banach spaces

In this paper, a new approach to the existence of time optimal controls of system governed by nonlinear equations on Banach spaces is provided. A sequence of Meyer problems is constructed to approach a class of time optimal control problems. A deep relationship between time optimal control problems and Meyer problems is presented. The method is much different from standard methods

Molecular Dynamics Simulation of Macromolecules Using Graphics Processing Unit

Molecular dynamics (MD) simulation is a powerful computational tool to study the behavior of macromolecular systems. But many simulations of this field are limited in spatial or temporal scale by the available computational resource. In recent years, graphics processing unit (GPU) provides unprecedented computational power for scientific applications. Many MD algorithms suit with the multithread nature of GPU. In this paper, MD algorithms for macromolecular systems that run entirely on GPU are presented. Compared to the MD simulation with free software GROMACS on a single CPU core, our codes achieve about 10 times speed-up on a single GPU. For validation, we have performed MD simulations of polymer crystallization on GPU, and the results observed perfectly agree with computations on CPU. Therefore, our single GPU codes have already provided an inexpensive alternative for macromolecular simulations on traditional CPU clusters and they can also be used as a basis to develop parallel GPU programs to further speedup the computations.Comment: 21 pages, 16 figure

Transition threshold in Ge x Sb 10 Se 90-x glasses

GexSb10Se90-x glasses with Ge content from 7.5 to 32.5at.% have been prepared by melt-quench technique, and the physical parameters including glass transition temperature (Tg), density (ρ), compactness (C), shear elastic moduli (Cs), compression elasti

Spin-Orbit Coupling and Ion Displacements in Multiferroic TbMnO3

The electronic and magnetic properties of TbMnO3 leading to its ferroelectric (FE) polarization were investigated on the basis of relativistic density functional theory (DFT) calculations. In agreement with experiment, we show that the spin-spiral plane of TbMnO3 can be either the bc- or ab-plane, but not the ac-plane. As for the mechanism of FE polarization, our work reveals that the "pure electronic" model by Katsura, Nagaosa and Balatsky (KNB) is inadequate in predicting the absolute direction of FE polarization. For the ab-plane spin-spiral state of TbMnO3, the direction of FE polarization predicted by the KNB model is opposite to that predicted by DFT calculations. In determining the magnitude and the absolute direction of FE polarization in spin-spiral states, it is found crucial to consider the displacements of the ions from their ecntrosymmetric positions

Renormalization of tensor-network states

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network states/models in two dimensions. A second renormalization scheme is introduced to take into account the environment contribution in the calculation of the partition function of classical tensor network models or the expectation values of quantum tensor network states. It improves significantly the accuracy of the coarse grained tensor renormalization group method. In the study of the quantum tensor-network states, we point out that the renormalization effect of the environment can be efficiently and accurately described by the bond vector. This, combined with the imaginary time evolution of the wavefunction, provides an accurate projection method to determine the tensor-network wavfunction. It reduces significantly the truncation error and enable a tensor-network state with a large bond dimension, which is difficult to be accessed by other methods, to be accurately determined.Comment: 18 pages 23 figures, minor changes, references adde

The Tensor Current Divergence Equation in U(1) Gauge Theories is Free of Anomalies

The possible anomaly of the tensor current divergence equation in U(1) gauge theories is calculated by means of perturbative method. It is found that the tensor current divergence equation is free of anomalies.Comment: Revtex4, 7 pages, 2 figure

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

Discrete Singular Convolution for the Prediction of High Frequency Vibration of Plates

10.1016/S0020-7683(01)00183-4International Journal of Solids and Structures39165-8