Linear and non linear response in the aging regime of the 1D trap model

We investigate the behaviour of the response function in the one dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time tw+t given that a small bias h is applied at time tw. Several scaling regimes are found, depending on the relative values of t, tw and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation dissipation relation is, in this case, valid even in the aging regime.Comment: 5 pages, 3 figures, 3 references adde

Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting time $t_w$, in the linear as well as in the non-linear response regime. Using a real-space renormalization procedure that becomes exact in the limit of strong disorder $\mu \to 0$, we obtain explicit results for many observables, such as the diffusion front, the mean position, the thermal width, the localization parameters and the two-particle correlation function. In particular, the scaling functions for these observables give access to the complete interpolation between the unbiased case and the directed case. Finally, we discuss in details the various regimes that exist for the averaged position in terms of the two times and the external field.Comment: 27 pages, 1 eps figur

Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature

We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two delta peaks, which are completely out of equilibrium with each other. The statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit $T \to 0$. We first compute disorder averages of one-time observables, such as the diffusion front, the thermal width, the localization parameters, the two-particle correlation function, and the generating function of thermal cumulants of the position. We then study aging and sub-aging effects : our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two-time correlations. We also extend the RSRG method to include systematic corrections to the previous zero temperature procedure via a series expansion in $T$. We then consider the generalized trap model with parameter $\alpha \in [0,1]$ and obtain that the large scale effective model at low temperature does not depend on $\alpha$ in any dimension, so that the only observables sensitive to $\alpha$ are those that measure the `local persistence', such as the probability to remain exactly in the same trap during a time interval. Finally, we extend our approach at a scaling level for the trap model in $d=2$ and obtain the two relevant time scales for aging properties.Comment: 33 pages, 3 eps figure

Localization properties of the anomalous diffusion phase x tμx ~ t^{\mu} in the directed trap model and in the Sinai diffusion with bias

We study the anomalous diffusion phase $x ~ t^{\mu}$ with $0<\mu<1$ which exists both in the Sinai diffusion at small bias, and in the related directed trap model presenting a large distribution of trapping time $p(\tau) \sim 1/\tau^{1+\mu}$. Our starting point is the Real Space Renormalization method in which the whole thermal packet is considered to be in the same renormalized valley at large time : this assumption is exact only in the limit $\mu \to 0$ and corresponds to the Golosov localization. For finite $\mu$, we thus generalize the usual RSRG method to allow for the spreading of the thermal packet over many renormalized valleys. Our construction allows to compute exact series expansions in $\mu$ of all observables : at order $\mu^n$, it is sufficient to consider a spreading of the thermal packet onto at most $(1+n)$ traps in each sample, and to average with the appropriate measure over the samples. For the directed trap model, we show explicitly up to order $\mu^2$ how to recover the diffusion front, the thermal width, and the localization parameter $Y_2$. We moreover compute the localization parameters $Y_k$ for arbitrary $k$, the correlation function of two particles, and the generating function of thermal cumulants. We then explain how these results apply to the Sinai diffusion with bias, by deriving the quantitative mapping between the large-scale renormalized descriptions of the two models.Comment: 33 pages, 3 eps figure

Is prnt a pseudogene? identification of ram prt in testis and ejaculated spermatozoa

A hallmark of prion diseases or transmissible spongiform encephalopaties is the conversion of the cellular prion protein (PrPC), expressed by the prion gene (prnp), into an abnormally folded isoform (PrPSc) with amyloid-like features that causes scrapie in sheep among other diseases. prnp together with prnd (which encodes a prion-like protein designated as Doppel), and prnt (that encodes the prion protein testis specific - Prt) with sprn (shadow of prion protein gene, that encodes Shadoo or Sho) genes, constitute the "prion gene complex". Whereas a role for prnd in the proper functioning of male reproductive system has been confirmed, the function of prnt, a recently discovered prion family gene, comprises a conundrum leading to the assumption that ruminant prnt is a pseudogene with no protein expression. The main objective of the present study was to identify Prt localization in the ram reproductive system and simultaneously to elucidate if ovine prnt gene is transcribed into protein-coding RNA. Moreover, as Prt is a prnp-related protein, the amyloid propensity was also tested for ovine and caprine Prt. Recombinant Prt was used to immunize BALB/c mice, and the anti-Prt polyclonal antibody (APPA) immune response was evaluated by ELISA and Western Blot. When tested by indirect immunofluorescence, APPA showed high avidity to the ram sperm head apical ridge subdomain, before and after induced capacitation, but did not show the same behavior against goat spermatozoa, suggesting high antibody specificity against ovine-Prt. Prt was also found in the testis when assayed by immunohistochemistry during ram spermatogenesis, where spermatogonia, spermatocytes, spermatids and spermatozoa, stained positive. These observations strongly suggest ovine prnt to be a translated protein-coding gene, pointing to a role for Prt protein in the ram reproductive physiology. Besides, caprine Prt appears to exhibit a higher amyloid propensity than ovine Prt, mostly associated with its phenylalanine residue.publishersversionpublishe

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Clay mineralogy and magnetic susceptibility of Oxisols in geomorphic surfaces

Studies analyzing the variability of clay minerals and magnetic susceptibility provide data for the delineation of site-specific management areas since many of their attributes are important to agronomy and the environment. This study aimed to evaluate the spatial variability of clay minerals, magnetic susceptibility, adsorbed phosphorus and physical attributes in Oxisols of sandstones in different geomorphic surfaces. For that purpose, soil samples were collected every 25 m along a transect located within the area where the geomorphic surfaces were identified and mapped. The transect occupied the central portion of 500 ha, where it was also sampled for density purposes with one sample per six hectares. Soil samples were collected at a depth of 0.0-0.2 m. The results of the physical, chemical, mineralogical and magnetic susceptibility analyses were subjected to statistical and geostatistical analyses. The nature of the clay minerals and magnetic susceptibility was dependent on the variation of the soil parent material. High values of magnetic susceptibility were associated with the presence of maghemite and magnetite of coarse size. The spatial variability of crystallinity and the content of Fe oxides, as well as magnetic susceptibility, were dependent on the age of the geomorphic surfaces. The youngest surface had greater spatial variability of these attributes. The iron (goethite and hematite) and aluminum (gibbsite) oxides in the youngest geomorphic surface influenced the low values of soil density and high values of total pore volume, micropores and P adsorption. The characterization of the spatial variability of Fe oxides and susceptibility allowed for the delineation of homogeneous areas