Thermally fluctuating superconductors in two dimensions

In many two-dimensional superconducting systems, such as Josephson-junction arrays, granular superconducting films, and the high-temperature superconductors, it appears that the electrons bind into Cooper pairs below a pairing temperature (T(P)) that is well above the Kosterlitz-Thouless temperature (T(KT)) the temperature below which there is long-range superconducting order). The electron dynamics at temperatures between T(KT) and T(P) involve a complex interplay of thermal and quantum fluctuations, for which no quantitative theory exists. Here we report numerical results for this region, by exploiting its proximity to a T = 0 superconductor-insulator quantum phase transition. This quantum critical point need not be experimentally accessible for our results to apply. We characterize the static, thermodynamic properties by a single dimensionless parameter, gamma(T). Quantitative and universal results are obtained for the frequency dependence of the conductivity, which are dependent only upon gamma(T) and fundamental constants of nature.     

一类二维交通流模型的周期态

Ｏ．Ｂｉｈａｍ，Ａ．Ａ．Ｍｉｄｄｌｅｔｏｎ和Ｄ．Ｌｅｖｉｎｅ利用元胞自动机模拟城市交通，发现有两种稳定的运动态，继这方面的研究，本文发现介于这两种稳定状态之间的其他状态也是稳定的，并且具有运动的周期性，从而使这方面研究的结论趋于完善。     

排斥型有效互作用下的超导电性

分析了电子间在有效排斥互作用下的超导电性．发现当能带宽度Ｗ＞Ｅｃ，ｏ（）时，存在电子对；当Ｗ＜Ｅｃ，ｏ时，电子对消失．从而认为在电子对消失的区域，描写超导电性的应该是某种准粒子对，而不是电子对．     

二维和三维的时间分数阶电报方程的解析解

提出分离变量法解决二维、三维的时间分数阶电报方程问题,利用该方法得到二维、三维的时间分数阶电报方程满足非齐次Dirichlet 边界条件下的解析解。     

产品设计中机械制图的革命--关于先三维后二维的制图体系

随着产品造型的多样化,仅用二维视图表达设计信息难度大,数据形式后续分析困难。本文基于新时代的信息高效优化与设计人员的人性化考虑,提出了计算机辅助先三维后二维的机械制图体系的革命     

Polarons and confinement of electronic motion to two dimensions in a layered manganite

A remarkable feature of layered transition--metal oxides-most famously, the high-temperature superconductors--is that they can display hugely anisotropic electrical and optical properties (for example, seeming to be insulating perpendicular to the layers and metallic within them), even when prepared as bulk three-dimensional single crystals. This is the phenomenon of 'confinement', a concept at odds with the conventional theory of solids, and recognized as due to magnetic and electron-lattice interactions within the layers that must be overcome at a substantial energy cost if electrons are to be transferred between layers. The associated energy gap, or 'pseudogap', is particularly obvious in experiments where charge is moved perpendicular to the planes, most notably scanning tunnelling microscopy and polarized infrared spectroscopy. Here, using the same experimental tools, we show that there is a second family of transition-metal oxides--the layered manganites La(2-2x)Sr(1+2x)Mn2O7--with even more extreme confinement and pseudogap effects. The data demonstrate quantitatively that because the charge carriers are attached to polarons (lattice- and spin-textures within the planes), it is as difficult to remove them from the planes through vacuum-tunnelling into a conventional metallic tip, as it is for them to move between Mn-rich layers within the material itself.     

二维区域Legendre-Galerkin谱方法的后验误差估计

讨论了二维区域Legendre-Galerkin谱方法的后验误差估计子,并分析其可靠性和有效性, 特别地,该估计子只包含模型方程右端项的信息,给出了该后验误差估计子的显式表达式,极大地方便了在工程计算中的应用。     

二维Kalman滤波及其在森林资源动态预测中的应用

报道了二维Kalman滤波在森林资源动态预测中的应用,并首次应用二维Kalman滤波研究森林蓄积。利用吉林省松江河局1975－1989年四次连续清查的30块样地资料建立了二维坐标系,应用二维Kalman滤波对森林蓄积动态作出估计与预测,经检验,效果良好。     

费米共振与溶剂效应

研究溶液中费米共振随压强的变化规律,通过与纯溶液进行比较,分析并讨论了溶剂效应的本质.并通过变换溶剂方法和变换溶液浓度方法中的溶剂效应变化研究费米共振规律.     

二维、三维空间Riesz分数阶扩散方程的基本解

讨论二维、三维空间Riesz分数阶扩散方程的解,用特征函数幂级数形式定义二维、三维分数阶拉普拉斯算子,并给出分数阶拉普拉斯算子与Riesz分数阶导数的关系。最后用谱表示法导出二维、三维空间Riesz分数阶扩散方程在齐次和非齐次情况下的在有界区间上满足一定初边值条件的基本解。     

二维麦克斯韦方程的分裂的高阶时域有限差分方法

本文将分裂算子的时域有限差分方法与高阶差分方法相结合,提出了二维麦克斯韦方程的分裂的高阶时域有限差分格式(SHO-FDTDⅠ)及其修正格式(SHO-FDTDⅡ),用Fourier方法证明了这两种格式是无条件稳定的,其中格式Ⅰ是损耗(dissipative)的,格式Ⅱ是非损耗(non-dissipative)的,然后推导出了它们的数值弥散关系式,最后用数值算例验证了理论分析,并给出了数值弥散误差的计算和增长因子模的计算.     

吸引-排斥情形下Keller-Segel模型的不稳定性

考虑源于趋化性的吸引 排斥情形下Keller Segel模型的稳态问题. 先将系统线性化, 研究仅含一个参数的有限维特征值问题; 再利用非负矩阵和图论的相关理论证明齐次定态解的存在性和不稳定性的充分条件.     

The existence of global solution and their weak limit of generalized Ginzburg-Landau equations in two dimensions

By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid limit to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the solution to the Ginzburg-Landau equations converges to the weak solution to the derivative nonlinear Schrödinger equations.     

平面弹性问题的高次有限元离散系统的局部多重网格法

自适应算法的每一次加密过程中,只需要在旧网格中增加少数加密节点,从而使得基于相邻网格的有限元函数空间,仅有少数高次有限元基函数需要发生改变.利用这一特性,本文针对平面弹性问题的自适应高次有限元离散系统,设计了一种基于局部松弛的多重网格法,即在每一次迭代过程中,先对高次有限元分层基函数中最高次齐次部分进行一次对称Gauss-Seidal 磨光,然后将残量方程投影到线性有限元空间,得到线性有限元离散系统,最后对该线性有限元离散系统进行一次局部磨光. 数值实验表明该方法对求解自适应网格下的高次有限元方程具有鲁棒性.