A mechanical model of normal and anomalous diffusion

The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are presented. These show that above a threshold value of the field normal diffusion is superimposed to ballistic motion. The diffusion constant can be given explicitly. At the threshold field the transition between conduction and localization is accompanied by an anomalous diffusion. Our results exemplify that, even in the absence of time-dependent stochastic forces, a purely mechanical model equipped with a quenched disorder can exhibit normal as well as anomalous diffusion, the latter emerging as a critical property.Comment: 16 pages, no figure

PATTERN RECOGNITION IN MAINTAINING RELIABILITY

In the paper a feedback control scheme for running and maintenance of industrial equipments is developed, where only input and output signals of the control loop are observable, the actual state of the system will be estimated from the output signals using pattern recognition. Technical and statistical expertise in the control loop are separated, therefore appropriate statistical tools and problems (classification, feature extraction, life statistics) can be individually accessed. The phenomenon of aging is modelled by random transitions among parameter classes with different failure rates. Optimization is reduced to a Markovian decision process. Concrete technical examples illustrate the relevance of the model

RELIABILITY OF INTEGRATED MATERIAL AND DATA PROCESSING SYSTEMS (IMDP)

The reliability estimation of Integrated and Data Processing Systems because of their complexity and costs requires special methods. In this paper the possibilities to increase reliability, optimum maintenance strategies, real-time monitoring problems are discussed. The general principle of a reliability prediction procedure using mathematical pattern recognition methods is given

Weak integrability breaking and level spacing distribution

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular, for the gapless case we find that the crossover coupling as a function of the volume $L$ scales with a $1/L^2$ law for weak breaking as opposed to the $1/L^3$ law previously found for the strong case.Comment: 15 pages, 12 figures. v2: references added. v3: text thoroughly revised, presentation clarified and improved, main results and conclusions unchange