Phase structure of two-dimensional spin models and percolation

For a class of classical spin models in 2D satisfying a certain continuity constraint it is proven that some of their correlations do not decay exponentially. The class contains discrete and continuous spin systems with Abelian and non-Abelian symmetry groups. For the discrete models our results imply that they show either long-range order or are in a soft phase characterized by powerlike decay of correlations; for the continuous models only the second possibility exists. The continuous models include a version of the plane rotator [O(2)] model; for this model we rederive, modulo two conjectures, the Fröhlich-Spencer result on the existence of the Kosterlitz-Thouless phase in a very simple way. The proof is based on percolation-theoretic and topological arguments.     

在局部区域上的奇摄动反应扩散方程初始边值问题

本文是讨论一类在局部区域上的奇摄动反应扩散初始边值问题.利用算子理论和 不动点原理,得到了相应问题解的存在性和唯一性.     

Diffusion via splitting and remeshing via merging in vortex methods

The technique of splitting a fat vortex element (with a core width larger than some threshold) into some thin ones in order to fix the convergence problem of the core‐spreading vortex methods is convenient and efficient. In particular, it keeps the method purely Lagrangian. In the present investigation, the splitting process is further viewed as part of the physical diffusion process. A new splitting method in which several weaker child vortices surround a thinned but still strong parent vortex is proposed. It is found that because of the survival of the parent vortex, the error arising from the splitting events can be largely reduced. The computational amount on the other hand is kept reasonably large by merging similar and close‐by vortices. The merging scheme designed herein not only involves fewer restrictions but also allows merging vortices of opposite rotations through the viewpoint of remeshing. The validity and accuracy of these techniques, proposed particularly for simulations undergoing lots of splitting and merging events, are verified by successfully simulating the interactions between two Burgers vortices under an external straining field. Copyright © 2005 John Wiley & Sons, Ltd.     

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH3 on Pt(1 0 0) coupled by diffusion

The Lombardo–Imbihl–Fink (LFI) ODE model of the NO+NH₃ reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH₃ and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH₃ and H.     

AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk)<∞is proved.     

广义非简谐振子的多尺度微扰理论

应用多尺度微扰理论到广义非简谐振子, 得到了一阶经典和量子微扰解. 特别是 我们的量子解在极限条件下能方便地转变为经典解, 并且坐标和动量算符的对易 关系的简化十分自然. 与Taylor级数解相比较, 无论是在经典还是在量子解 中频率移动都出现在各阶振动表达式中, 所以多尺度微扰解是弱耦合非简谐振动的较好解法.     

Copper diffusion in Ti-Si-N layers formed by inductively coupled plasma implantation

Ternary Ti-Si-N refractory barrier films of 15 nm thick was prepared by low frequency, high density, inductively coupled plasma implantation of N into Ti_xSi_y substrate. This leads to the formation of Ti-N and Si-N compounds in the ternary film. Diffusion of copper in the barrier layer after annealing treatment at various temperatures was investigated using time-of-flight secondary ion mass spectrometer (ToF-SIMS) depth profiling, X-ray diffractometer (XRD), field emission scanning electron microscopy (FESEM), energy dispersive X-ray (EDX) and sheet resistance measurement. The current study found that barrier failure did not occur until 650 °C annealing for 30 min. The failure occurs by the diffusion of copper into the Ti-Si-N film to form Cu-Ti and Cu-N compounds. FESEM surface morphology and EDX show that copper compounds were formed on the ridge areas of the Ti-Si-N film. The sheet resistance verifies the diffusion of Cu into the Ti-Si-N film; there is a sudden drop in the resistance with Cu compound formation. This finding provides a simple and effective method of monitoring Cu diffusion in TiN-based diffusion barriers.     

Moisture sorption, transport, and hydrolytic degradation in polylactide

Management of moisture penetration and hydrolytic degradation of polylactide (PLA) is extremely important during the manufacturing, shipping, storage, and end-use of PLA products. Moisture transport, crystallization, and degradation, in PLA have been measured through a variety of experimental techniques including size-exclusion chromatography, differential scanning calorimetry, and X-ray diffraction. Quartz crystal microbalance and dynamic vapor sorption experiments have also been used to measure moisture sorption isotherms in PLA films with varying crystallinity. A surprising result is that, within the accuracy of the experiments, crystalline and amorphous PLA films exhibit identical sorption isotherms.     

频率受随机过程调制的体系中的光谱扩散

通过在Bloch方程中增加描述对频率微扰的随机过程项{ω(t)},我们讨论了系统在窄谱带的光激发后的光谱扩散。特别是以下两种情况:1)如果ω以相同的概率变化为系综中的任一ω’,光谱是一个指数式衰减的定域峰和指数式增长的动态非均匀背底的叠加。2)如果ω'到ω的概率仅与|ω’-ω|有关,非定域峰随时间变宽。作为一个例子,我们讨论了频率受多个独立随机电报过程调制的系统中的光谱扩散。