Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160

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简立方格点自避行走所模拟的高分子链吸附和塌缩

采用复合Markov链法,针对简立方格点上的自避行走模型,研究了同时具有对壁的吸附作用ε1和最近邻相互作用ε2的高分子链的热力学性质.相互作用能量参数ε1和ε2分别联系于参数α和β.令链长N=100,由这种Monte Carlo方法可得出链的自由能FN (α ,β),热容2FN(α,β)/2α和2FN(α,β)/2β,吸附点平均数〈m〉/N,最近邻相互作用对平均数〈n〉/N和均方末端距对壁的垂直分量RZ2.除已有方法由热容数据可绘出α-β相图外,建议由结构参数〈m〉/N ,〈n〉/N和RZ2绘制相图,并发现二者基本一致.所得相图表明,存在4个相区,分别是解吸-膨胀相(DE),吸附-膨胀相(AE),解吸-紧密相(DC)和吸附 -紧密相(AC).在伸展区和塌缩区,随着吸附作用的增强,会出现吸附相转变.在解吸区和吸附区,随着自相互作用的增大,也将出现塌缩相转变.相图出现了两个三相点,即AE-AC-DC三相点和AE-DE-D C三相点.     

基于多通道时间分辨光学层析成像系统的差分图像重建

报道了基于32通道时间分辨光学层析成像系统的差分图像重建结果,实验采用两个光参数与生物组织体大致相同的圆柱型模拟体,分别用于模拟新生儿头部和成人手臂,重建结果表明;采用差分测量的方法很好地重建出异质体的位置．尺寸及吸收系数相对于背景的变化;模拟和实验重建验证了所发展的二维,半三维重建算法的可行性;使用平均飞行时间作为数据类型,32个探测通道测量,比用强度作为数据类型或16通道测量更为准确地分出了两个相距20mm的异质体。结果表明目前的系统可以定性地重建出异质体的位置,尺寸,吸收系数的变化,展示该光学层析成像技术将在监测诸如血液含氧量变化,组织体涉氧新陈代谢等生理过程中具有良好应用前景,也对该种成像方法存在的问题及进一步改进的措施进行了讨论。     

Minimax Bounds in Nonparametric Estimation of Multidimensional Deterministic Dynamical Systems

We consider the problem of estimating a multidimensional discrete deterministic dynamical system from the first n + 1 observations. We exhibit the optimal rate function r _n and show that the nearest neighbor estimator achieves this optimal rate, extending a recent study carried out by Guerre and Maës [18] in the univariate case. Previous results strongly rely on the natural order structure of the set of real numbers. Here the optimal rate function is defined from multidimensional spacings which are edge lengths of simplices associated with a triangulation of the Voronoi cells built from the observations. A simulated example illustrates the theory.     

基于希尔伯特-黄变换的近红外脑功能成像信号分析

近红外光谱技术(Near-infrared spectroscopy,NIRS)已被广泛应用于无损大脑功能检测,然而传统时频分析方法并不适用于非稳态、非线性的血氧信号。在视觉刺激实验中,采集被试前额叶的血氧信号,分别比较了傅里叶谱分析法、小波谱分析法和希尔伯特黄变换(Hilbert-Huang transform,HHT)方法在近红外脑功能成像信号分析中应用的结果。实验表明基于希尔伯特黄变换的谱分析方法优于其它两种方法,并且使近红外光谱研究可以采用事件相关设计的实验,为形成近红外光谱信号分析的标准方法开辟了新的途径。     

超表面上表面等离激元波的光栅衍射行为研究

本文利用严格数值仿真研究了550~700 nm波段的可见光通过金属光栅耦合方式激发的表面等离激元(SPP)波在金属表面的光栅衍射行为与现象。研究结果表明:SPP波在金属表面的衍射行为与自由空间光相比有极大不同,由于SPP波的近场属性,经金属光栅衍射后在近场可表现出明显的光栅分光现象,但经过一段传输距离后则分光现象消失而表现为不同级次的光合为同一束光;在近场衍射情况下,其情况与自由空间光衍射行为类似,对SPP亚波长金属光栅来说同样只有零级透射光;而当金属光栅周期大于SPP波长时,高级衍射级次则开始出现。研究结果对下一步在金属表面上实现微米级片光谱仪器具有重要借鉴意义。     

L_2-Cross-Validation最近邻中位数估计的相合性:m-相依情形

给出了m-相依情形的L     

Determining bottom price-levels after a speculative peak

During a stock market peak the price of a given stock (i) jumps from an initial level p ₁(i) to a peak level p ₂(i) before falling back to a bottom level p ₃(i). The ratios A(i) = p ₂(i)/p ₁(i) and B(i)= p ₃(i)/p ₁(i) are referred to as the peak- and bottom-amplitude respectively. The paper shows that for a sample of stocks there is a linear relationship between A(i) and B(i) of the form: B=0.4A+b. In words, this means that the higher the price of a stock climbs during a bull market the better it resists during the subsequent bear market. That rule, which we call the resilience pattern, also applies to other speculative markets. It provides a useful guiding line for Monte Carlo simulations. Received 9 June 2000     

Scaling relationship between effective critical exponents throughout the crossover region in thin Ising films

The Monte Carlo (MC) approach is used to check the validity of the scaling relationship for the effective critical exponents in thin Ising films. We investigate this relationship not just in the critical region but throughout the crossover to the expected two-dimensional behavior. Our results indicate that this scaling relationship is very well-fulfilled throughout the entire crossover temperature region, as predicted by a previous renormalization group analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for plates with increasing L, up to L=100. The evolution of the maximum value of the effective critical exponents with film thickness is discussed. Received 22 April 1999