Stabilization of avalanche processes on dynamical networks

The stabilization of avalanches on dynamical networks has been studied. Dynamical networks are networks where the structure of links varies in time owing to the presence of the individual “activity” of each site, which determines the probability of establishing links with other sites per unit time. An interesting case where the times of existence of links in a network are equal to the avalanche development times has been examined. A new mathematical model of a system with the avalanche dynamics has been constructed including changes in the network on which avalanches are developed. A square lattice with a variable structure of links has been considered as a dynamical network within this model. Avalanche processes on it have been simulated using the modified Abelian sandpile model and fixed-energy sandpile model. It has been shown that avalanche processes on the dynamical lattice under study are more stable than a static lattice with respect to the appearance of catastrophic events. In particular, this is manifested in a decrease in the maximum size of an avalanche in the Abelian sandpile model on the dynamical lattice as compared to that on the static lattice. For the fixed-energy sandpile model, it has been shown that, in contrast to the static lattice, where an avalanche process becomes infinite in time, the existence of avalanches finite in time is always possible.     

Molecular orientation effects in gas-surface dynamical processes

We report studies of chemical reactions on single crystalline Si surfaces induced by oriented molecular beams. We discuss the obtained steric effects on Si from the viewpoint of the strength of the gas-surface interaction, in comparison with the steric effects appearing on the graphite surface. Oriented molecular beams demonstrate the possibility for controlling surface chemical reactions by varying the orientation of the incident molecules. The steric effects found on Si surfaces hint at new ways of material fabrication on Si surfaces.     

Communities and dynamical processes in a complex software network

Complex technological networks represent a growing challenge to support and maintain as their number of elements become higher and their interdependencies more involved. On the other hand, for networks that grow in a decentralized manner, it is possible to observe certain patterns in their overall structure that may be taken into account for a more tractable analysis. An example of such a pattern is the spontaneous formation of communities or modules. An important question regarding the detection of communities is if these are really representative of any internal network feature. In this work, we explore the community structure of a real complex software network, and correlate this modularity information with the internal dynamical processes that the network is designed to support. Our results show that the dependence between community structure and internal dynamical processes is remarkable, supporting the fact that a community division of this complex network is helpful in the assessment of the underlying dynamical structure, and thus is a useful tool to achieve a simpler representation of the complexity of the network.     

Multivariate analysis of PECVD data

Basic research in PECVD aims at disclosing relations between quantities determining the plasma performance and solid-state properties of deposited thin films. Linear concepts of multivariate analysis provide a simple and very useful first approach to this goal. In this paper we apply the techniques of principal component analysis, canonical correlation and group analysis to recently published PECVD data. We also touch upon experimental strategy.     

Modelling of dynamical processes in a molecular crystal by NMR

In this contribution we report on the plastic crystal 1-chloroadamantane dynamics via conventional frequency dependent (¹H and ¹³C) and field cycling NMR measurements. A suitable microscopic dynamical model, worked out from from X-ray analysis is developed and the molecular motions are interpreted in terms of: self diffusion and dipolar molecular axis combined with uniaxial rotation. In the rotator phase the molecules execute a bimodal reorientation process whereas the uniaxial rotation solely persists in the low temperature phase. In both phases, the residence times exhibit an Arrhenius temperature dependence. The results confirm the existence of a dynamic crossover transition predicted by molecular dynamics simulation.     

Fourier analysis of multi-frequency dynamical systems

The Fourier spectrum of a multiply periodic system appears complex due to resonances at integer combinations of the fundamental frequencies. We show how to “reorder” the peaks in the Fourier spectrum to yield a simpler structure which reveals important aspects of the time series which are not clearly seen in the ordinary Fourier transform. As examples, we study time series from circle and torus maps, and from experimental data by Gollub and Benson.     

Multivariate analysis methods in physics

In this article, a review of multivariate methods based on statistical learning is given. Several popular multivariate methods useful in high-energy physics analysis are discussed. Selected examples from current research in particle physics are discussed, both from online trigger selection and from off-line analysis. In addition, statistical learning methods, not yet applied in particle physics, are presented and some new applications are suggested. The text was submitted by the author in English.     

Multivariate analysis of multiple impedance spectra

A one-step method for evaluation of multiple impedance measurements in a multivariate analysis is presented. Usually two steps are necessary to extract model parameters like activation energy from impedance measurements at two or more temperatures. First, each measurement is analyzed with CNLS (complex nonlinear least squares) software using the same equivalent circuit. Second, activation energy is obtained in a NLS fit of conductivity data. This two-step procedure could lead to doubtful results as fit errors because of noise in the first step could prevent reliable results in the second step. Error estimates of model parameters are only based on the second step, ignoring the quality of the first step. Using a one-step method, model parameters are directly obtained from multiple impedance measurements, often resulting in more reliable results and meaningful error estimates than for the two-step procedure. Similar approaches to the one proposed have been reported in literature. Although some approaches are reported to be implemented in a software package, none of these are available to the community. The aim of this paper is to clearly point out the mathematics used and the benefits of a simultaneous analysis of impedance spectra.     

On the equivalence between Bernoulli dynamical systems and stochastic Markov processes

We extend to Bernoulli systems the explicit construction (elaborated previously for the baker transformation) of non-unitary, invertible transformations Λ, which associate Markovian processes admitting an $\text{H}$-theorem with the unitary dynamical group, through a similarity relation. We characterize the symmetries of the Bernoulli system as well as those of the associated Markov processes and provide examples of symmetry breaking under the passage, through a Λ transformation, from Bernoulli systems to stochastic Markov processes.     

Two-step dynamical picture and generalized thermodynamical model for multi-particle production processes

A general non-equilibrium formulation of quantum statistical mechanics allows for statistical as well as for dynamical features of a system. From our two-step dynamical model formulated in this frame we then discuss the diffractive production of a leading particle and secondaries deriving from the “evaporation” of a simultaneously produced fireball.     

Multivariate calibration in TXRF analysis of water

The aim of this paper is the application of multivariate linear calibration for quantitative determination of elements (K, Cd, Co, Hg, As, Pb, Ni, and Al) in water by using Total Reflection X‐ray Fluorescence Analysis with partial least squares (PLS) as a regression method to improve a result of common univariate method. In purpose of elimination of matrix effects in X‐ray fluorescence analysis, experimental design was applied. As a set of standard samples for multivariate calibration, a five‐level eight‐factor calibration design of 25 samples was chosen, ensuring mutual orthogonality of factors. For model's validation, the independent test set of 15 samples was examined. The collection of spectra and quantitative measurements was carried out on S2 PICOFOX. The PLS regression was performed by using software package STATISTICA. Quality indicators of multivariate calibration as slope (b) and intercept (a) of calibration, correlation coefficient (r), determination coefficient (R²), root mean square errors of calibration and of prediction, standard errors of calibration and of prediction, biases of calibration, and biases of prediction were calculated. These results were compared with the univariate model, and as a result, the multivariate calibration method exceeds the univariate one. The obtained results could be applied in a laboratory for an analysis of water solutions in the concentration range 0.05–2.00 mg/L. In many real situations, when analytical chemist deals with multi‐element mixtures, multivariate calibration approach combined with orthogonal design for multivariate calibration set could be successfully used to improve a conventional univariate calibration.     

Power spectral analysis of a dynamical system

Power spectra for chaotic transitions in three dimensions are presented for a dynamical system first proposed by Rössler. Relations between the spectra and the topology of the corresponding strange attractor are discussed.     

Time windows of various nuclear methods for the observation of spin dynamical processes

The applications of various hyperfine tools to the study of spin dynamical processes are reviewed. A few typical line shapes in the context of the Mössbauer effect and μSR derived from stochastic model calculations are discussed and the interplay of time scales associated with various processes in relation to the time window of a given probe is assessed.     

Multivariate data analysis for Raman spectroscopic imaging

This article reviews the analytic techniques for Raman spectroscopic imaging with emphasis on chemometrics. Key information included in Raman spectra is often distributed broadly throughout the dataset. It is possible to condense the information into a very compact matrix representation by a chemometric technique of factor analysis such as principal component analysis (PCA) or self‐modeling curve resolution (SMCR). PCA yields two matrices called scores and loadings which complementarily represent the entire features broadly distributed in the dataset. This concept can be further extended to other forms of data transformation schemes, including bilinear data decomposition based on SMCR analysis. SMCR offers a firmer model which is chemically or physically interpretable. The information derived from these techniques readily brings useful insight into building a mechanistic model for understanding complex phenomena studied by Raman spectroscopy. Illustrative examples are given for applications of both PCA and SMCR to Raman imaging of pharmaceutical tablets. Copyright © 2009 John Wiley & Sons, Ltd.