On logarithmic extensions of local scale-invariance

Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena.     

Laser-induced ablation and crater formation at high laser flux

Laser ablation and crater formation have been studied on a copper target using a 10 Hz Nd:YAG laser system delivering pulses up to 100 mJ in 40 ps with a flux on target F?≤?5000 J/cm². Crater dimensions were measured using optical microscope or scanning electron microscope. In order to understand the process of crater formation, we considered various theoretical models present in the literature and revised them taking into account the occurrence of plasma phenomena, which are important at the intensities used in this experiment. We also compared our experimental results with other results obtained at the PALS laboratory, using a 0.44 μm wavelength laser and much higher laser intensities. Finally, we explore the possibility of extending the information derived from laser-produced craters to other types of craters.     

Fluctuation scaling in complex systems: Taylor's law and beyond1

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form ‘fluctuations ≈ constant × average^α’, where the exponent α is predominantly in the range [1/2, 1]. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names Taylor's law or fluctuation scaling. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.     

Hagena团簇尺度定律中锥形喷嘴的等效孔径

本文首先详细重演了锥形喷嘴的等效孔径d_eq, 并根据d_eq的定义给出了它与气体团簇喷流的径向宽度之间的依赖关系. 然后以高背压氩气团簇喷流为例, 通过成像喷流的Rayleigh 散射光的空间分布研究了不同背压下喷流的径向宽度, 并与Hagena 团簇尺度定律中直线流模型假设的喷流径向宽度进行了比较. 结果表明, Hagena 直线流模型假设的喷流径向宽度小于实际的径向宽度, 且实际宽度与气体背压有关. 进一步的研究表明, 直线流模型对喷流宽度的估计偏差导致对锥形喷嘴等效孔径的估计偏差, 这为Hagena 尺度定律估计团簇平均尺寸的偏差给出了一种可能的解释. 关键词： 气体团簇 Hagena尺寸定律 锥形喷嘴的等效孔径     

Minor hysteresis loops model based on exponential parameters scaling of the modified Jiles–Atherton model

In this present work, the minor hysteresis loops model based on parameters scaling of the modified Jiles–Atherton model is evaluated by using judicious expressions. These expressions give the minor hysteresis loops parameters as a function of the major hysteresis loop ones. They have exponential form and are obtained by parameters identification using the stochastic optimization method “simulated annealing”. The main parameters influencing the data fitting are three parameters, the pinning parameter k, the mean filed parameter α and the parameter which characterizes the shape of anhysteretic magnetization curve a. To validate this model, calculated minor hysteresis loops are compared with measured ones and good agreements are obtained.     

矩阵值函数空间中尺度空间的稠密性

多分辨分析的概念在小波基构造中起着非常重要的作用,并经历了从经典多分辨分析到多重多分辨分析,再到矩阵值多分辨分析的研究历程.本文基于矩阵值多分辨分析,研究并给出了矩阵值函数空间中尺度空间稠密性的两个充要条件,并在此基础之上得到了稠密性的两个充分条件.     

Hydrogen storage in different carbon materials: Influence of the porosity development by chemical activation

The hydrogen adsorption capacity of different types of carbon nanofibers (platelet, fishbone and ribbon) and amorphous carbon have been measured as a function of pressure and temperature. The results showed that the more graphitic carbon materials adsorbed less hydrogen than more amorphous materials. After a chemical activation process, the hydrogen storage capacities of the carbon materials increased markedly in comparison with the non-activated ones.BET surface area of amorphous carbon increased by a factor of 3.5 and the ultramicropore volume doubled, thus increasing the hydrogen adsorption by a factor of 2. However, BET surface area in platelet CNFs increased by a factor of 3 and the ultramicropore volume by a factor of 6, thus increasing the hydrogen storage by a factor of 4.5. The dependency of hydrogen storage capacity of carbon materials on the BET surface area was evaluated using both a condensation model and experimental results. Comparison of data suggests that the hydrogen adsorption capacity clearly depends on the pore structure and so, on the accessibility to the internal surface.     

逐段非趋势波动分析方法及我国证券市场的实证研究

为了研究金融时间序列在不同时段波动的持久性特征,本文提出了一种逐段非趋势波动分析方法。该方法首先建立多阶段分割动态规划模型对时间序列进行分割,随后对各子序列逐段进行非趋势波动分析。对我国证券市场的七个主要指数的实证研究结果表明,本文提出的逐段非趋势波动分析方法能够有效揭示股票指数持久性特征随时间变化的现象,也有助于更深入的比较不同指数间持久性特征的相似程度。     

Estimations of Hölder Regularities and Direction of Singularity by Hart Smith and Curvelet Transforms

Using Hart Smith’s and curvelet transforms, new necessary and new sufficient conditions for an L ²(?²) function to possess Hölder regularity, uniform and pointwise, with exponent α>0 are given. Similar to the characterization of Hölder regularity by the continuous wavelet transform, the conditions here are in terms of bounds of the transforms across fine scales. However, due to the parabolic scaling, the sufficient and necessary conditions differ in both the uniform and pointwise cases. We also investigate square-integrable functions with sufficiently smooth background. Specifically, sufficient and necessary conditions, which include the special case with 1-dimensional singularity line, are derived for pointwise Hölder exponent. Inside their “cones” of influence, these conditions are practically the same, giving near-characterization of direction of singularity.     

On stability at the Hamiltonian Hopf Bifurcation

For a 2 d.o.f. Hamiltonian system we prove the Lyapunov stability of its equilibrium with two double pure imaginary eigenvalues and non-semisimple Jordan form for the linearization matrix, when some coefficient in the 4th order normal form is positive (the equilibrium is known to be unstable, if this coefficient is negative). Such the degenerate equilibrium is met generically in one-parameter unfoldings, the related bifurcation is called to be the Hamiltonian Hopf Bifurcation. Though the stability is known since 1977, proofs that were published are either incorrect or not complete. Our proof is based on the KAM theory and a work with the Weierstrass elliptic functions, estimates of power series and scaling.