Multifractal analysis of stress time series during ultrathin lubricant film melting

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is we studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of $stick-slip$ friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.Comment: 22 pages, 10 figures, 41 reference

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001

The molecular function and clinical phenotype of partial deletions of the IGF2/H19 imprinting control region depends on the spatial arrangement of the remaining CTCF binding sites

At chromosome 11p15.5, the imprinting centre 1 (IC1) controls the parent of origin-specific expression of the IGF2 and H19 genes. The 5 kb IC1 region contains multiple target sites (CTS) for the zinc-finger protein CTCF, whose binding on the maternal chromosome prevents the activation of IGF2 and allows that of H19 by common enhancers. CTCF binding helps maintaining the maternal IC1 methylation-free, whereas on the paternal chromosome gamete-inherited DNA methylation inhibits CTCF interaction and enhancer-blocking activity resulting in IGF2 activation and H19 silencing. Maternally inherited 1.4-2.2 kb deletions are associated with methylation of the residual CTSs and Beckwith-Wiedemann syndrome, although with different penetrance and expressivity. We explored the relationship between IC1 microdeletions and phenotype by analysing a number of previously described and novel mutant alleles. We used a highly quantitative assay based on next generation sequencing to measure DNA methylation in affected families and analysed enhancer-blocking activity and CTCF binding in cultured cells. We demonstrate that the microdeletions mostly affect IC1 function and CTCF binding by changing CTS spacing. Thus, the extent of IC1 inactivation and the clinical phenotype are influenced by the arrangement of the residual CTSs. A CTS spacing similar to the wild-type allele results in moderate IC1 inactivation and is associated with stochastic DNA methylation of the maternal IC1 and incomplete penetrance. Microdeletions with different CTS spacing display severe IC1 inactivation and are associated with IC1 hypermethylation and complete penetrance. Careful characterization of the IC1 microdeletions is therefore needed to predict recurrence risks and phenotypical outcomes. © The Author 2012. Published by Oxford University Press