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.     

1+1维抛射沉积模型内部结构动力学行为的数值研究

采用Kinetic Monte Carlo方法对1+1维抛射沉积(BD)模型内部结构的动力学行为进行了大量的数值模拟研究.分别分析了空洞密度和内部界面的动力学行为.研究表明,空洞密度呈高斯型分布,其平均值首先随生长时间快速增长,然后达到一个与基底尺寸无关的饱和值.除表面宽度,还引入了新的极值统计方法来分析该模型内部界面的动力学行为,分析结果显示,1+1维BD模型内部界面的演化满足标准的Family-Vicsek标度规律,并且属Kardar-Parisi-Zhang方程所描述的普适类.最后对表面宽度和极值统计两种理论方法的有限尺寸效应进行了比较.     

科赫分形基底上受限固-固模型动力学标度行为的数值研究

为分析基底结构对离散生长模型动力学性质的影响, 本文在随机游走指数十分接近而分形维数和谱维数均不相同的科赫格子和科赫曲线分形基底上对受限固-固(restricted solid-on-solid)模型的生长过程进行数值模拟研究. 通过分析表面宽度和饱和表面极值高度的统计行为发现: 随机游走的动力学指数能够对饱和粗化表面的动力学行为起主要贡献. 尽管分形基底具有不同的分形维数和谱维数, 但是在两种分形基底上得到了在误差范围内相同的粗造度指数. 两种分形基底上饱和表面相对生长高度极大(小)值分布分别可以很好的塌缩在一起, 且很好的满足Asym2Sig函数分布.     

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.     

C20与Si(100)-(2×1)重构表面相互作用的计算机模拟研究

用分子动力学的方法模拟研究了低能C20与Si(100)-(2×1)重构表面的相互作用过程.将描述C、Si结构的Tersoff势和描述原子间短程排斥的KrC势相结合,建立了一个混合势作为原子间的相互作用模型.荷能C20垂直轰击到Si(100)-(2×1)表面后,由于在<110>方向受到非对称力场的作用而产生横向的集体运动,改变的入射能量导致C20与Si(100)-(2×1)表面最接近的垂直距离不同,从而受到不同的横向力场的作用而产生不同的表面运动特性.C20能量耗尽后稳定吸附在Si(100)-(2×1)表面,且只有两个稳定吸附位置,即二聚体(dimer)和"峡谷"(trough)位,这两个吸附位置的存在可用C20与Si(100)-(2×1)表面之间非对称的表面力场分布来定性解释.最终C20与Si(100)-(2×1)表面有强烈的化学键形成.模拟结果与STM的实验观察结果进行了比较.     

β-SiC(001)-(2×1)表面结构的第一性原理研究

利用缀加平面波加局域轨道(APW+LO)的第一性原理方法计算了β-SiC(001)-(2×1)表面的原子及电子结构. 原子结构的计算结果表明，与Si(001)-(2×1) 表面的非对称性Si二聚体模型不同，β-SiC(001)-(2×1)表面为对称性的Si二聚体模型，其二聚体的Si原子间键长也较大，为0.269nm. 电子结构的计算结果表明，在费米能级处有明显的态密度，因此β-SiC(001)-(2×1)表面呈金属性. 在带隙附近存在四个表面态带,其中的两个占有表面态带已由价带的同步辐射光电子能谱实验得到证实. 关键词： 碳化硅 缀加平面波加局域轨道方法 原子结构 电子结构     

噪声信号特征量分布函数相似特性的研究

应用高速数据采集卡,记录悬浮颗粒计数光电传感器本底噪声信号序列值,研究噪声信号独立特征量, 如信号幅度极值、上升沿幅值、下降沿幅值、极值时序间隔,以及特征量乘积值等统计分布规律. 结果表明,上述独立特征量均能够与以自然数l为自变量的对数正态分布函数高度符合, 噪声信号特征量统计分布呈现出高度相似特征.基于这种统计相似性,还可推出噪声信号不同特征量对应的统计自变量之间的幂函数变换关系.噪声信号特征量统计分布函数相似性可理解为噪声信号集合统计分形特性的一种表现.     

HCOOH在Pd-Fe(111)(nPd∶nFe=1∶1)表面吸附的密度泛函理论研究简

采用密度泛函理论与周期性平板模型相结合的方法,对HCOOH在Pd(111)表面top,fcc,hcp,bridge四个吸附位和Pd-Fe(111)表面Pd-top,Fe-top,PdPd-bridge,PdFe-bridge,FeFe-bridge,Pd2Fehcp,PdFe2-hcp,Pd2Fe-fcc,PdFe2-fcc等9个吸附位的13种吸附模型进行了能量计算、构型优化,得到了HCOOH较有利的吸附位;并对清洁表面进行能带分析.结果表明:掺杂Fe后,Pd催化剂对HCOOH催化活性增强;HCOOH在Pd(111)表面的最稳定吸附位fcc的吸附能是-41.8kJ·mol-1,在Pd-Fe(111)表面的最稳定吸附位Pd2Fe-hcp的吸附能是-126.5kJ·mol-1,而且HCOOH在金属表面属于化学吸附.     

激光溅射沉积制备的ZnO:Ga薄膜表面形貌分析

薄膜表面形貌定量研究有助于薄膜生长机理的认识.研究的薄膜是用激光脉冲沉积法(PLD)制备的ZnO:Ga(GZO)透明导电薄膜.由于GZO薄膜的生长是在远离平衡态情况下实现的,具备自仿射分形特征,可以用高度-高度相关函数进行描述.通过对用原子力显微镜(AFM)获得的表面高度数据进行相关运算,定量地分析了PLD制备的GZO...     

多量子比特WV纠缠态在Lipkin-Meshkov-Glick模型下的量子Fisher信息

量子Fisher信息在参数估计理论和量子精密测量领域扮演着非常重要的角色,不仅可以用来标定量子系统的测量精度极限,还可用于有益量子计量的纠缠态判定.本文从量子测量的角度出发,对多比特WV态(α|W_N>+(1-α²)^1/2|00...0>)进行研究,通过计算其在局域操作下和Lipkin-Meshkov-Glick (LMG)非局域操作模型下的量子Fisher信息,分析其在精密测量方面的表现.研究发现:在局域操作下,随着参数α由0到1的变化,多比特WV态的量子Fisher信息逐渐变大,表明其量子纠缠程度在不断增加,也体现出更强的量子测量能力.在LMG非局域操作下,随着相互作用强度γ的增大,N=3量子比特WV态的量子Fisher信息值趋于稳定,几乎不受参数α的影响,而当体系量子比特数N> 3时,量子Fisher信息值会随参数α的变大而变大;当参数α固定时,多比特WV态的量子Fisher信息会随着相互作用强度γ的增强而变大,呈现出相互作用强度越大,WV态的量子测量能力越强.     

Conformal Invariance of Isoheight Lines of the (2+1)-Dimensional Wolf-Villain Surfaces

In order to learn more about the statistical properties of the surface fluctuations of the Wolf-Villain (WV) model and confirm the applicability of the Schramm-Loewner evolution theory (SLEκ) to WV surfaces, the contour lines of the (2+1)-dimensional saturated surfaces of the WV model are investigated numerically. The results obtained show that the isoheight lines of the WV surfaces are conformally invariant and can also be described in the frame of the SLEκ theory with the diffusivity κ=4. The calculated fractal dimension of the contours is d _f =1.31±0.02.     

Effects of the Ehrlich-Schwoebel potential barrier on the Wolf-Villain model simulations for thin film growth

Wolf-Villain (WV) model is a simple model used to study ideal molecular beam epitaxy (MBE) growth by using computer simulations. In this model, an adatom diffuses instantaneously within a finite diffusion length to maximize its coordination number. We study statistical properties of thin films grown by this model. The morphology of the WV model is found to be kinetically rough with a downhill particle diffusion current. In real MBE growth, however, there are additional factors such as the existence of a potential barrier that is known as the Ehrlich-Schwoebel (ES) barrier. The ES barrier is an additional barrier for an adatom that diffuses over a step edge from the upper to a lower terrace which is known to induce an uphill particle current. We found that with the addition of the ES barrier, the WV-ES model morphology is rough with mound formation on the surface when the barrier is strong enough. To confirm these results, the correlation function is also studied. We find no oscillation in the correlation function in the WV model. For the WV-ES model, the correlation function oscillates. These results confirm that a strong enough ES barrier can cause mound formation on the WV surface in our study.     

Value-at-risk estimation with wavelet-based extreme value theory: Evidence from emerging markets

This paper introduces wavelet-based extreme value theory (EVT) for univariate value-at-risk estimation. Wavelets and EVT are combined for volatility forecasting to estimate a hybrid model. In the first stage, wavelets are used as a threshold in generalized Pareto distribution, and in the second stage, EVT is applied with a wavelet-based threshold. This new model is applied to two major emerging stock markets: the Istanbul Stock Exchange (ISE) and the Budapest Stock Exchange (BUX). The relative performance of wavelet-based EVT is benchmarked against the Riskmetrics-EWMA, ARMA-GARCH, generalized Pareto distribution, and conditional generalized Pareto distribution models. The empirical results show that the wavelet-based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail-loss tests. The superior forecasting performance of the wavelet-based EVT model is also consistent with Basel II requirements, and this new model can be used by financial institutions as well.     

Automatic segmentation of white matter lesions on magnetic resonance images of the brain by using an outlier detection strategy

White matter lesions (WMLs) are commonly observed on the magnetic resonance (MR) images of normal elderly in association with vascular risk factors, such as hypertension or stroke. An accurate WML detection provides significant information for disease tracking, therapy evaluation, and normal aging research. In this article, we present an unsupervised WML segmentation method that uses Gaussian mixture model to describe the intensity distribution of the normal brain tissues and detects the WMLs as outliers to the normal brain tissue model based on extreme value theory. The detection of WMLs is performed by comparing the probability distribution function of a one-sided normal distribution and a Gumbel distribution, which is a specific extreme value distribution. The performance of the automatic segmentation is validated on synthetic and clinical MR images with regard to different imaging sequences and lesion loads. Results indicate that the segmentation method has a favorable accuracy competitive with other state-of-the-art WML segmentation methods.     

Baseline Methods for Bayesian Inference in Gumbel Distribution

Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.     

Are there “dragon-kings” events (i.e. genuine outliers) among extreme avalanches?

Predicting the occurrence and spatial extent of extreme avalanches is a longstanding issue. Using field data pooled from various sites within the same mountain range, authors showed that the avalanche size distribution can be described using either an extreme value distribution or a thick-tailed distribution, which implies that although they are much larger than common avalanches, extreme avalanches belong to the same population of events as “small” avalanches. Yet, when looking at historical records of catastrophic avalanches, archives reveal that a few avalanches had features that made them “extra-ordinary.” Applying avalanche-dynamics or statistical models to simulate these past events runs into considerable difficulty since the model parameters or the statical properties are very different from the values usually set to model extreme avalanches. Were these events genuine outliers (also called “dragon-kings”)? What were their distinctive features? This paper reviews some of the concepts in use to model extreme events, gives examples of processes that were at play in extreme avalanches, and shows that the concept of dragon-king avalanches is of particular relevance to describing some extreme avalanches.     

Measurements of WW and WZ production in W + jets final states in pp collisions

We study WW and WZ production with ?νqq (?=e,μ) final states using data collected by the D0 detector at the Fermilab Tevatron Collider corresponding to 4.3 fb(-1) of integrated luminosity from pp collisions at sqrt[s]=1.96 TeV. Assuming the ratio between the production cross sections σ(WW) and σ(WZ) as predicted by the standard model, we measure the total WV (V=W,Z) cross section to be σ(WV)=19.6(-3.0)(+3.2) pb and reject the background-only hypothesis at a level of 7.9 standard deviations. We also use b-jet discrimination to separate the WZ component from the dominant WW component. Simultaneously fitting WW and WZ contributions, we measure σ(WW)=15.9(-3.2)(+3.7) pb and σ(WZ)=3.3(-3.3)(+4.1) pb, which is consistent with the standard model predictions.     

Extreme value statistics distributions in spin glasses

We study the probability distribution of the pseudocritical temperature in a mean-field and in a short-range spin-glass model: the Sherrington-Kirkpatrick and the Edwards-Anderson (EA) model. In both cases, we put in evidence the underlying connection between the fluctuations of the pseudocritical point and the extreme value statistics of random variables. For the Sherrington-Kirkpatrick model, both with Gaussian and binary couplings, the distribution of the pseudocritical temperature is found to be the Tracy-Widom distribution. For the EA model, the distribution is found to be the Gumbel distribution. Being the EA model representative of uniaxial magnetic materials with quenched disorder like Fe(0.5)Mn)0.5)TiO(3) or Eu(0.5)Ba(0.5)MnO(3), its pseudocritical point distribution should be a priori experimentally accessible.     

Fracture strength of disordered media: universality, interactions, and tail asymptotics

We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the "weakest-link hypothesis" in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well-described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB-type asymptotic distributions and show that the universal extreme value forms may not be appropriate to describe the nonuniversal low-strength tail.