Effective single-band Hamiltonian for electron-phonon coupling in cuprate superconductors

We derive an effective single-band Hubbard type Hamiltonian for CuO₂ planes. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. We start with first-principles density functional theory parameters and then map onto a single-band model. Unlike previous mappings to a single-band Hamiltonian, ours explicitly preserves the Fermi surface shape and matrix elements of the many-band Hamiltonian. We consider both in-plane oxygen breathing modes as well as out-of-plane tilting modes. The latter modes have a quadratic electron-phonon coupling, and are also highly anharmonic in La₂CuO₄ based superconductors. The coupling to breathing modes is too small to account for highT _c, while the coupling to quadratic modes is much stronger even though they would be neglected in a standard Migdal-Eliashberg approach to superconductivity.     

一族Liouville可积系及其双约束流的Hamilton系统

构造了Loop代数 A2的一个子代数,由此建立了一个3×3等谱问题,由屠规彰格式得到了一族Liouville意义下的可积Hamilton方程族。通过建立双对称约束,得到了该方程族的两组约束流,并将其化为广义Hamilton系统。     

Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method

The satellite image deconvolution problem is ill-posed and must be regularized. Herein, we use an edge-preserving regularization model using a ? function, involving two hyperparameters. Our goal is to estimate the optimal parameters in order to automatically reconstruct images. We propose to use the maximum-likelihood estimator (MLE), applied to the observed image. We need sampling from prior and posterior distributions. Since the convolution prevents use of standard samplers, we have developed a modified Geman-Yang algorithm, using an auxiliary variable and a cosine transform. We present a Markov chain Monte Carlo maximum-likelihood (MCMCML) technique which is able to simultaneously achieve the estimation and the reconstruction.     

Bayesian Model Uncertainty In Smooth Transition Autoregressions

Abstract. In this paper, we propose a fully Bayesian approach to the special class of nonlinear time‐series models called the logistic smooth transition autoregressive (LSTAR) model. Initially, a Gibbs sampler is proposed for the LSTAR where the lag length, k, is kept fixed. Then, uncertainty about k is taken into account and a novel reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is proposed. We compared our RJMCMC algorithm with well‐known information criteria, such as the Akaikes? information criteria, the Bayesian information criteria (BIC) and the deviance information criteria. Our methodology is extensively studied against simulated and real‐time series.     

基于能量整型方法的永磁同步直线电机位置控制

针对永磁同步直线电机(PMLSM)的位置控制问题,从能量整型控制的角度进行了研究。基于哈密顿反馈耗散控制方法,结合系统的物理能量特性,在dq旋转坐标系下建立了包含电能和动能的永磁同步直线电机闭环系统哈密顿函数,通过反馈耗散方法对永磁同步直线电机进行速度控制器设计,保证了系统在稳态运行点达到输入/输出能量的动态平衡。为了提高系统响应性能,提出了阻尼参数PID自整定方法实现阻尼参数的自调节,并通过设计位置控制外环构成了包含位置、速度的双环控制系统,实现了PMLSM位置控制。实验结果表明,所设计的控制器具有良好的稳定性、快速的位置跟踪性和抗干扰能力。     

Voltage dependence of the tunnelling current: an exact expression

An exact expression for the tunnelling current measured with a scanning tunnelling microscope (STM) is obtained. It clarifies the information deducible from the ‘spectroscopic mode’ of the STM and raises the question of the observability of surface states. The connection with the Transfer Hamiltonian approach is made, and the conditions of validity of the latter are analysed.     

基于哈密顿解法的矩形厚板分析

建立了分析Reissner-Mindlin厚板问题的哈密顿解法。首先,以x坐标模拟时间坐标,选用互为对偶的混合变量作为基本变量,建立哈密顿正则微分方程组。然后,采用分离变量法和特征函数展开法在相应的边界条件下求出级数解。最后,给出矩形厚板典型例题的解答,分析了级数解的收敛性质。与常用的半逆解法相比,Hamilton解法有其优点:一是求解方法严密合理、有规可循;二是应用范围广,可用于求解系列问题。     

The globally Bi-3-connected property of the honeycomb rectangular torus

The honeycomb rectangular torus is an attractive alternative to existing networks such as mesh-connected networks in parallel and distributed applications because of its low network cost and well-structured connectivity. Assume that m and n are positive even integers with n ? 4. It is known that every honeycomb rectangular torus HReT(m,n) is a 3-regular bipartite graph. We prove that in any HReT(m,n), there exist three internally-disjoint spanning paths joining x and y whenever x and y belong to different partite sets. Moreover, for any pair of vertices x and y in the same partite set, there exists a vertex z in the partite set not containing x and y, such that there exist three internally-disjoint spanning paths of G-{z} joining x and y. Furthermore, for any three vertices x, y, and z of the same partite set there exist three internally-disjoint spanning paths of G-{z} joining x and y if and only if n ? 6 or m = 2.     

An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

新哈密顿振幅方程的行波孤子解

本文给出了新哈密顿振幅方程的行波解法，并得到了一种新的严格解析孤波解，同时简要讨论了该解析解的频率啁啾特性和相位调制特性。