非局域Lai-Das Sarma-Villain方程动力学标度性质的研究

使用动力学重整化群和直接标度分析的方法研究了非局域Lai-Das Sarma-Villain方程的动力学标度性质.动力学重整化群分析表明非局域非线性项的存在能够导致新的固定点和连续变化的动力学标度指数的产生.使用直接标度分析方法则分别得到了在弱耦合和强耦合区内的标度指数值.在弱耦合区域内得到的标度指数与动力学重整化方法得到的标度指数值能很好地吻合. 关键词： 表面生长 动力学重整化群分析 标度分析     

非线性漂移的Fokker-Planck方程的非定态解

本文用格林函数方法讨论Fokker-Planck方程的非定态问题,将标度理论的“标度区”和“最终时区”统一考虑。在标度理论的头两个时区,所得结果与标度理论的解一致。当t→∞时,所得的非定态解趋于Fokker-Planck方程的定态解,解决了标度区分布函数在稳定点发散的问题,避免了“标度区”和“最终时区”对接的困难。 关键词：     

非平衡相变的临界标度理论及普适性

综述了作者近年来在非平衡相变临界（ Ｎ Ｐ Ｃ） 标度理论及普适性研究的进展。主要包括一般 Ｎ Ｐ Ｃ 系统规格化模型,局域序参量的概率分布,广义势的临界渐近形式,空时有关函数及其临界奇异行为。论证了 Ｎ Ｐ Ｃ 系统的临界可标度性,导出了一组普适的 Ｎ Ｐ Ｃ 标度关系,由之计算出的４ 种 Ｎ Ｐ Ｃ 普适类的临界指数与目前已知的实验及理论结果吻合得非常好。此外,还讨论了非平衡相变临界标度理论的普适性,将平衡相变临界标度理论作为一种特殊极限情况含于同一理论体系中。     

非平衡相变的临界标度理论及普适性

综述了作者近年来在非平衡相变临界（ Ｎ Ｐ Ｃ） 标度理论及普适性研究的进展。主要包括一般 Ｎ Ｐ Ｃ 系统规格化模型,局域序参量的概率分布,广义势的临界渐近形式,空时有关函数及其临界奇异行为。论证了 Ｎ Ｐ Ｃ 系统的临界可标度性,导出了一组普适的 Ｎ Ｐ Ｃ 标度关系,由之计算出的４ 种 Ｎ Ｐ Ｃ 普适类的临界指数与目前已知的实验及理论结果吻合得非常好。此外,还讨论了非平衡相变临界标度理论的普适性,将平衡相变临界标度理论作为一种特殊极限情况含于同一理论体系中。     

非局域Sun-Guo-Grant方程的自洽模耦合理论

通过选取具有正确渐近行为的标度函数形式，将自洽的模耦合理论推广应用到对非局域的Sun-Guo-Grant方程的动力学标度性质的研究中.通过分析得到，在强耦合区基底维数d=1,2的情况下，动力学指数z随非局域参数ρ的变化关系.将这一结果与动力学重正化群理论和直接标度分析得到的结果进行了对比. 关键词： 表面粗糙生长动力学 动力学标度 自洽模耦合理论     

增长及非增长无标度网络的成因解析

分析两类无标度网络的形成原因,提出一个无标度网络演化模型并进行一系列数值实验.基于分析和实验得到推论:只要保持足够低的网络密度,通过基于度的偏好连接就可形成长期稳定的无标度网络.规模增长和点边增删既是客观存在,又起到了控制网络密度的作用,足够低的网络密度和基于度的偏好连接是所有无标度网络共同的必要条件.推论可同时解释增长和非增长无标度网络的形成原因.研究结果有助于理解各种真实无标度网络和建立相应的模型.     

含时空关联噪声的非局域及各向异性Kardar-Parisi -Zhang方程的直接标度分析

将直接标度分析方法推广应用到含时间空间关联噪声的非局域及各向异性KardarParisiZhang方程的动力学标度分析中,分别得到了方程在强耦合区和弱耦合区的标度指数值.在弱耦合区得到的标度指数能与使用动力学重整化方法得到的结果相吻合 关键词： 表面生长 标度分析 KPZ方程     

类矢标准模型中规范相互作用与引力的统一

提出在无轻子的超对称类矢标准模型中,在规范作用双圈修正和引力单圈弦修正下,研究规范耦合和引力之间的统一问题.结果表明,需要两个中间质量标度.其中低质量标度在未来实验室可到达的范围内,高的质量标度约为10¹⁶GeV.     

平行电磁场中里德堡氢原子的自相似结构研究

利用半经典方法研究了平行电磁场中里德堡氢原子的分形自相似现象. 通过研究平行电磁场中里德堡氢原子的逃逸时间和初始出射角间的关系, 发现了逃逸时间图的自相似结构, 并通过研究与图中冰柱对应的逃逸轨道, 得到了自相似结构和逃逸轨道之间的关系, 发现了该类自相似逃逸轨道满足的规律. 进一步研究了标度能量和标度磁场对体系动力学的影响, 表明标度能量和标度磁场均控制体系的分形自相似结构. 当标度能量或标度磁场比较小时, 没有自相似现象, 随着标度能量或标度磁场的增大, 自相似出现, 体系变复杂.     

二维随机蜂巢网格熔断动力学过程和熔断面标度性质的数值模拟

石墨烯等材料具有典型的二维蜂巢结构,而随机电阻丝模型则是研究非均匀材料断裂十分有效的统计物理学模型.本文尝试对二维蜂巢结构随机电阻丝网络熔断的动力学过程及熔断面性质进行数值模拟分析,以此来研究二维非均质蜂窝材料熔断的动力学性质和熔断面的动力学标度性质.模拟研究表明,二维随机蜂窝网格的熔断动力学过程和熔断面具有明显的标度性质,得到的熔断面整体和局域粗糙度指数分别为α=0.911±0.005和α_(loc)=0.808 ± 0.003,这两者之间的明显差异表明熔断面具有奇异标度性.通过对熔断面极值高度的分析发现,熔断面高度的极值统计分布能很好地满足Asym2sig型分布,而不是最常见的三种极值统计分布.本文的研究表明,随机电阻丝模型在模拟非均匀材料的电流熔断过程和熔断表面标度性的分析中同样适用和有效.     

Distributions and moments of structural properties for percolation clusters

We study numerically and by scaling methods the distributions and moments of several structural properties of percolation clusters in two and three dimensions. The clusters are generated at criticality and properties such as the distribution of the mass as a function of linear size or chemical distance are studied. Our results suggest that the hierarchy of moments can be represented by a single gap exponent. Using a scaling approach, we obtain analytical forms for the different distribution functions which agree very well with the numerical data.     

Dynamical and spatial aspects of sandpile cellular automata

The Bak, Tang, and Wiesenfeld cellular automaton is simulated in 1, 2, 3, 4, and 5 dimensions. We define a (new) set of scaling exponents by introducing the concept of conditional expectation values. Scaling relations are derived and checked numerically and the critical dimension is discussed. We address the problem of the mass dimension of the avalanches and find that the avalanches are noncompact for dimensions larger than 2. The scaling of the power spectrum derives from the assumption that the instantaneous dissipation rate of the individual avalanches obeys a simple scaling relation. Primarily, the results of our work show that the flow of sand down the slope does not have a 1/f power spectrum in any dimension, although the model does show clear critical behavior with scaling exponents depending on the dimension. The power spectrum behaves as 1/f ² in all the dimensions considered.     

分形基底上受限固-固模型动力学性质的数值模拟研究

为了探讨非完整基底结构对生长表面动力学行为的影响,本文在具有相同分形维数而不同谱维数的谢尔宾斯基箭头和蟹状分形基底上对受限固-固(restricted solid-on-solid,RSOS)模型的生长过程进行了大量的数值模拟研究.通过计算表面宽度和饱和表面极值高度的统计行为对生长表面的动力学行为进行了分析.结果表明,分形基底结构对生长表面的动力学行为具有显著的影响.尽管在两种基底上受限固-固模型的表面宽度均表现出很好的动力学标度行为,仍然满足Family-Vicsek标度规律,但由此计算得到的动力学标度指数并不相同.饱和生长表面的极值高度并不能满足三种常用的极值统计分布,即Weibull,Gumbel和Frechet分布,而是能很好地符合Asym2Sig分布.     

Magnetic-resonance-imaging-derived indices for the normalization of left ventricular morphology by body size

Scaling left ventricular (LV) mass and other cardiac dimensions to account for individual body size is important. The traditional method of simple ratio scaling using, for example, body surface area (BSA) assumes a linear and proportional relationship and accurate measurement of both LV mass and BSA. These assumptions can be questioned; hence, we examined the appropriateness of methods and different indices using highly accurate magnetic resonance imaging scans. Cardiac and whole-body scans were performed in 172 young, healthy, male subjects (age range, 17-28 years) to assess LV mass, volume, linear dimensions, lean body mass and fat mass. Height, body mass and BSA were determined anthropometrically. Relationships were examined for linearity and closeness of fit using log-log least-squares linear regression to determine the slope exponent b (where 1.0 indicates linearity). The relationship between LV mass and lean body mass (b=.90+/-.15; r(2)=.66) was linear and geometrically consistent. This was also the case for LV end-diastolic volume (b=.70), although the confidence intervals were broader (+/-0.32) and the r(2) (.31) smaller. The relationships between LV mass, volume and other variables were generally not linear or geometrically consistent. LV linear dimensions did not demonstrate any linear relationships, and in particular, those with BSA were extremely poor (r(2)=.02-.09). In summary, the traditional scaling of LV measurements to BSA does not remove the influence of body size and other techniques should be considered. Lean body mass was the most appropriate variable for simple indexing of LV mass. No body size variable had a linear and proportional relationship with LV linear dimensions, and the use of simple ratio scaling for these is seriously questioned.     

Scaling behavior of two-dimensional domain growth: Computer simulation of vertex models

Computer simulations are performed for vertex models which are coarse-grained models for dynamical cellular patterns in two dimensions. By simulating large systems, we obtain conclusive evidence of scaling behavior, that is, a power law for the growth of the average cell size and the scaling properties for the distribution functions of edge number and size of cells. Several versions of the vertex models are obtained by making some approximations for the equation of motion of a vertex, and we compare the statistical properties of the patterns in the scaling regime.     

Some Statistical Properties of the Burgers Equation with White-Noise Initial Velocity

We revisit the one-dimensional Burgers equation in the inviscid limit for white-noise initial velocity. We derive the probability distributions of velocity and Lagrangian increments, measured on intervals of any length x. This also gives the velocity structure functions. Next, for the case where the initial density is uniform, we obtain the distribution of the density, over any scale x, and we derive the density two-point correlation and power spectrum. Finally, we consider the Lagrangian displacement field and we derive the distribution of increments of the Lagrangian map. We check that this gives back the well-known mass function of shocks. For all distributions we describe the limiting scaling functions that are obtained in the large-scale and small-scale limits. We also discuss how these results generalize to other initial conditions, or to higher dimensions, and make the connection with a heuristic multifractal formalism. We note that the formation of point-like masses generically leads to a universal small-scale scaling for the density distribution, which is known as the “stable-clustering ansatz” in the cosmological context (where the Burgers dynamics is also known as the “adhesion model”).     

Linguistic and acoustic correlates of the perceptual structure found in an individual differences scaling study of vowels

Subjects judged the similarities among a set of American English vowels (See Text) presented in isolation or in a/dVd/ consonantal frame. Individual differences scaling was employed to analyze these similarities data for each of the conditions separately and for the two conditions combined. In all cases, perceptual dimensions corresponding to the advancement, height, and tenseness vowel features were recovered. Given the determinacy of individual differences scaling, this finding is taken to provide strong evidence for the perceptual significance of those features. The perceptual dimensions are considered in relation to various acoustic parameters of the stimuli employed in this study. They are also considered in relation to perceptual dimensions that have been observed in other vowel scaling studies.     

Mass gap of lattice O(3) non-linear σ-model with naive and improved actions

We evaluate the strong coupling expansion for the mass gap of the euclidean lattice O(3) non-linear σ-model in two dimensions with the naive action and with the tree level improved action. For the naive action the expansion series exhibits scaling behaviour in the weak coupling region. For the tree level improved action, our series is consistent with Monte Carlo data in the intermediate coupling region but is too short to reproduce the scaling.     

Scaling behavior in a stochastic self-gravitating system

A system of stochastic differential equations for the velocity and density of classical self-gravitating matter is investigated by means of the field theoretic renormalization group. The existence of two types of large-scale scaling behavior, associated with physically admissible fixed points of the renormalization-group equations, is established. Their regions of stability are identified and the corresponding scaling dimensions are calculated in the one-loop approximation (first order of the epsilon expansion). The velocity and density fields have independent scaling dimensions. Our analysis supports the importance of the rotational (nonpotential) components of the velocity field in the formation of those scaling laws.