[en] Several methods developed in different fields have been applied to reactor noise analysis; the probability distribution method in the probability theory, the Langevin technique in the statistical physics, the time series analysis in the statistics, and the Kalman filter in the control theory. For reactor diagnosis or reactor safety, it is important to understand relations among them and their merits. To make full use of signals included in reactor noise, the above mentioned methods and techniques are discussed systematically from the physical viewpoint of the contraction of information and coarse-graining in time and space. Properties of noise sources and spatial dependence of model are also discussed. (author)

[en] In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection.

[en] We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the entropy production rate, the entropy flux rate and the three components of the entropy production. All equations are cast in a way suitable for large-scale analysis of linear Langevin systems. Our results are also applied to different types of electrical circuits, which suitably illustrate the most relevant aspects of the problem. (paper)

[en] Time dependent anisotropic small angle neutron scattering patterns of rodlike micelles in a time dependent shear gradient are presented. The real time experiments have a resolution of 100 ms. The value of the rotational diffusion coefficient D turned out to be approximately 1 s^-1. (author) 6 refs., 4 figs

[en] The multi-dimensional Langevin approach is among the most powerful approach for understanding nuclear dynamics, in general, and fission, in particular. This work is devoted to a meticulous study of some limitations of current Langevin models. Evidence for the occurrence of potential spurious features is demonstrated. These are the results of a puzzling interplay involving the transport coefficients which govern the dynamics, on the one hand, and the modelling of nuclear shapes and scission, on the other hand. We reveal the conditions under which, and the mechanism by which, the result can be biased by practical aspects of the implementation of the theory. The implications of this study for the interpretation of experimental data are also discussed. As critical and cautious analysis of the predictions is recommended, and we comment on a strategy for identifying possible bias. (paper)

[en] The problem of effective equations is reviewed and discussed. Starting from the classical Langevin equation, we show how it can be generalized to Hamiltonian systems with non-standard kinetic terms. A numerical method for inferring effective equations from data is discussed; this protocol allows to check the validity of our results. In addition we show that, with a suitable treatment of time series, such protocol can be used to infer effective models from experimental data. We briefly discuss the practical and conceptual difficulties of a pure data-driven approach in the building of models. (statphys 27)

[en] The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

[en] The possibility of using the complex Langevin equation for simulating complex effective actions is described. 17 refs.; 6 figs

[en] Langevin equations with external non-white noise are considered. A Fokker Planck equation valid in general in first order of the correlation time tau of the noise is derived. In some cases its validity can be extended to any value of tau. The effect of a finite tau in the nonequilibrium phase transitions induced by the noise is analyzed, by means of such Fokker Planck equation, in general, for the Verhulst equation under two different kind of fluctuations, and for a genetic model. It is shown that new transitions can appear and that the threshold value of the parameter can be changed. (orig.)

[en] The fluctuation-dissipation theorem is not expected to hold for systems that either violate detailed balance of have time-dependent or nonpotential forces. Therefore, the relation between response and correlation functions should have contributions due to the nonequilibrium nature. An explicit formula for such a contribution is calculated, which in the present derivation appears as a history-dependent term. These relations are the Ward-Takahashi identifies of a supersymmetric formulation of the Langevin models, and the new term results from a broken supersymmetry. 29 refs