Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

In the last decade the subordinated processes have become popular and have found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called normal tempered stable, is related to the tempered stable subordinator, while the second one–to the inverse tempered stable process. We compare the main properties (such as probability density functions, Laplace transforms, ensemble averaged mean squared displacements) of such two subordinated processes and propose the parameters’ estimation procedures. Moreover we calibrate the analyzed systems to real data related to indoor air quality.     

On finite truncation of infinite shot noise series representation of tempered stable laws

Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise series representation is the only exact simulation method for the tempered stable process and has recently attracted attention for simulation use with ever improved computational speed. In this paper, we derive series representations for the tempered stable laws of increasing practical interest through the thinning, rejection, and inverse Lévy measure methods. We make a rigorous comparison among those representations, including the existing one due to Imai and Kawai [29] and Rosiński (2007) [3], in terms of the tail mass of Lévy measures which can be simulated under a common finite truncation scheme. The tail mass are derived in closed form for some representations thanks to various structural properties of the tempered stable laws. We prove that the representation via the inverse Lévy measure method achieves a much faster convergence in truncation to the infinite sum than all the other representations. Numerical results are presented to support our theoretical analysis.     

A new method for stable numerical differentiation

In this paper, we proposed a new algorithm for stable numerical differentiation by optimizing node intervals. With the algorithm, noise-free differentiated values can be extracted within one-percent error. By overcoming noise problem due to numerical differentiation process, our algorithm can easily extract the differentiated values. Also, it can be extended to high order differentiation. To confirm the proposed algorithm, we applied it to the analysis of MOSFET electrical characteristics. It will provide us with a useful analysis tool in the field of parameter extraction from numerical data such as device characterization.     

Interactions of heavy stable hadronising particles

In this article, we study the interactions of stable, hadronising new states, arising in certain extensions of the standard model. A simple model, originally intended for stable gluino hadrons, is developed to describe the nuclear interactions of hadrons containing any new colour triplet or octet stable parton. Hadron mass spectra, nuclear scattering cross sections and interaction processes are discussed. Furthermore, an implementation of the interactions of heavy hadrons in GEANT 3 is presented, signatures are studied, and a few remarks about possible detection with the ATLAS experiment are given.Received: 2 April 2004, Published online: 6 August 2004     

Parameterization of meandering phenomenon in a stable atmospheric boundary layer

Accounting for the current knowledge of the stable atmospheric boundary layer (ABL) turbulence structure and characteristics, a new formulation for the meandering parameters to be used in a Lagrangian stochastic particle turbulent diffusion model has been derived. That is, expressions for the parameters controlling the meandering oscillation frequency in low wind speed stable conditions are proposed. The classical expression for the meandering autocorrelation function, the turbulent statistical diffusion theory and ABL similarity theory are employed to estimate these parameters. In addition, this new parameterization was introduced into a particular Lagrangian stochastic particle model, which is called Iterative Langevin solution for low wind, validated with the data of Idaho National Laboratory experiments, and compared with others diffusion models. The results of this new approach are shown to agree with the measurements of Idaho experiments and also with those of the other atmospheric diffusion models. The major advance shown in this study is the formulation of the meandering parameters expressed in terms of the characteristic scales (velocity and length scales) describing the physical structure of a turbulent stable boundary layer. These similarity formulas can be used to simulate meandering enhanced diffusion of passive scalars in a low wind speed stable ABL.     

基于2008年1月中国南方低温雨雪冰冻事件10-30天延伸期稳定分量的研究

对北半球1978-2007年1月6日-2月4日逐日500 hPa高度场资料带通滤波,得到10-30 d 时间尺度分量,结合经验正交函数分解方法(empirical orthogonal function, EOF)提取出气候态基底.同样滤波北半球2008年1月冰冻雨雪事件的逐日实况资料,并将其投影到气候态基底上,利用各贡献率作为考察该EOF分量对原场的影响指标. 从10-30 d延伸期预报的角度提取稳定分量进行诊断分析,探讨影响此次天气过程的主要因素.通过贡献率分析方法把10-30 d延伸期稳定分量划分为气候态稳定分量和异常型稳定分量两个部分.结果表明:气候态稳定分量在我国南方2008年1月冰冻雨雪事件中占主体地位,异常型稳定分量相当于在气候态稳定分量的基础上叠加的扰动值, 但异常型稳定分量在本次过程中的作用不能忽视,甚至起到关键性的作用, 并且与实况距平在太平洋地区整体环流形势有较好的对应.这些结论加深了对10-30 d 时间尺度可预报性的认识,为10-30 d延伸期预报提供了一种新的思路和解决问题的途径.     

Generation of stable bright pulse and the dark soliton interaction in nonlinear left-handed materials

In homogeneous and isotropic nonlinear left-handed materials (LHMs), using the split step Fourier transform method, we demonstrate that two dark electromagnetic solitons which are the solutions of coupled nonlinear Schrödinger equations (CNLS) move along a line toward each other, when the distance between them down to a certain value, the interaction of the two dark solitons can produce a stable bright electromagnetic pulse that behaves like a bright soliton. Although our mathematical analysis shows that the new generated stable bright pulse is not an exact solution of the CNLS, it can propagate steadily in the nonlinear LHMs. And this unusual phenomenon can also be observed in our numerical simulation results by another method.