Chaos in the thermal regime for pinned manifolds via functional RG

The statistical correlations of two copies of a d-dimensional elastic manifold embedded in slightly different frozen disorder are studied using the Functional Renormalization Group to one-loop accuracy, order O(eps = 4-d). Determining the initial (short scale) growth of mutual correlations, i.e. chaos exponents, requires control of a system of coupled differential (FRG) equations (for the renormalized mutual and self disorder correlators) in a very delicate boundary layer regime. Some progress is achieved at non-zero temperature, where linear analysis can be used. A growth exponent a is defined from center of mass fluctuations in a quadratic potential. In the case where temperature is marginal, e.g. a periodic manifold in d=2, we demonstrate analytically and numerically that a = eps (1/3 - 1/(2 log(1/T)) with interesting and unexpected logarithmic corrections at low T. For short range (random bond) disorder our analysis indicates that a = 0.083346(6) eps, with large finite size corrections.Comment: 14 pages, 3 figure

Critical exponents of the driven elastic string in a disordered medium

We analyze the harmonic elastic string driven through a continuous random potential above the depinning threshold. The velocity exponent beta = 0.33(2) is calculated. We observe a crossover in the roughness exponent zeta from the critical value 1.26 to the asymptotic (large force) value of 0.5. We calculate directly the velocity correlation function and the corresponding correlation length exponent nu = 1.29(5), which obeys the scaling relation nu = 1/(2-zeta), and agrees with the finite-size-scaling exponent of fluctuations in the critical force. The velocity correlation function is non-universal at short distances.Comment: 4 pages, 3 figures. corrected references and typo

On the Self-Affine Roughness of a Crack Front in Heterogeneous Media

The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front dynamics, are not changing the scaling exponent which characterizes the roughness of the front. The scaling exponent thus predicted by the model is much smaller than the one observed experimentally. The inevitable conclusion is that the gap between the results of experiments and the model that is supposed to describe them is too large, and some new physics has to be invoked for another model.Comment: 4 pages, 4 figure

Depinning exponents of the driven long-range elastic string

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure

Roughness and multiscaling of planar crack fronts

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $\xi$. The problem is shown to have two important length scales, $\xi$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $\xi$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $\zeta \approx 0.39$ is recovered for scales larger than both $\xi$ and $L_c$. If $L_c > \xi$, these regimes are separated by a third regime characterized by the Larkin exponent $\zeta_L \approx 0.5$. We discuss the experimental implications of our results.Comment: 8 pages, two figure

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

DOE-EM privatization and the 2006 Plan: Principles for procurement policies and risk management

The Department of Energy`s Office of Environmental Remediation and Waste Management (EM) has recently set in place programs to restructure the strategic planning mechanism that will drive its clean-up schedule, The 2006 Plan, and to create a new set of business relationships with private contractors that will reduce costs--privatization. Taken together, the 2006 Plan and privatization will challenge EM to create new business practices to recast its risk management policies to support these initiatives while ensuring that its responsibilities toward the environment, human health, and worker safety (ES and H) are maintained. This paper argues that the 2006 Plan has transformed EM`s traditional, bottoms-up approach based on technical dictates to a top-down approach based on management goals--a transformation from an engineering problem to an economic problem. The 2006 Plan evolved from EM`s Ten-Year Plan, and seeks to convert the largely open-ended planning approach previously undertaken by EM to a plan bounded by time and dollars. The plan emphasizes making tradeoffs and choosing activities that deliver the most clean-up for the dollar. It also recognizes that each major player--stakeholders, DOE, OMB and Congress--has distinct interests that must be resolved if the process is to succeed. This, in turn, has created the need for a corresponding transformation in risk management practices from compliance-driven to benefit/cost-driven

Risk reduction and the privatization option: First principles

The Department of Energy`s Office of Environmental Restoration and Waste Management (EM) faces a challenging mission. To increase efficiency, EM is undertaking a number of highly innovative initiatives--two of which are of particular importance to the present study. One is the 2006 Plan, a planning and budgeting process that seeks to convert the clean-up program from a temporally and fiscally open-ended endeavor to a strictly bounded one, with firm commitments over a decade-long horizon. The second is a major overhauling of the management and contracting practices that define the relationship between the Department and the private sector, aimed at cost reduction by increasing firms` responsibilities and profit opportunities and reducing DOE`s direct participation in management practices and decisions. The goal of this paper is to provide an independent perspective on how EM should create new management practices to deal with private sector partners that are motivated by financial incentives. It seeks to ground this perspective in real world concerns--the background of the clean-up effort, the very difficult technical challenges it faces, the very real threats to environment, health and safety that have now been juxtaposed with financial drivers, and the constraints imposed by government`s unique business practices and public responsibilities. The approach is to raise issues through application of first principles. The paper is targeted at the EM policy officer who must implement the joint visions of the 2006 plan and privatization within the context of the tradeoff between terminal risk reduction and interim risk management

Tangent algorithm for photogravitropic balance in plants and Phycomyces blakesleeanus: Roles for EHB1 and NPH3 of Arabidopsis thaliana

Plant organs that are exposed to continuous unilateral light reach in the steady-state a photogravitropic bending angle that results from the mutual antagonism between the photo- and gravitropic responses. To characterize the interaction between the two tropisms and their quantitative relationship we irradiated seedlings of Arabidopsis thaliana that were inclined at various angles and determined the fluence rates of unilateral blue light required to compensate the gravitropism of the inclined hypocotyls. We found the compensating fluence rates to increase with the tangent of the inclination angles (0? lt ? lt 90? or max. 120?) and decrease with the cotangent (90? lt ? lt 180? or max. 120?of the inclination angles. The tangent dependence became also evident from analysis of previous data obtained with Avena sativa and the phycomycete fungus, Phycomyces blakesleeanus. By using loss-of function mutant lines of Arabidopsis, we identified EHB1 (enhanced bending 1) as an essential element for the generation of the tangent and cotangent relationships. Because EHB1 possesses a C2-domain with two putative calcium binding sites, we propose that the ubiquitous calcium dependence of gravi- and phototropism is in part mediated by Ca2+-bound EHB1. Based on a yeast-two-hybrid analysis we found evidence that EHB1 does physically interact with the ARF-GAP protein AGD12. Both proteins were reported to affect gravi- and phototropism antagonistically. We further showed that only AGD12, but not EHB1, interacts with its corresponding ARF-protein. Evidence is provided that AGD12 is able to form homodimers as well as heterodimers with EHB1. On the basis of these data we present a model for a mechanism of early tropism events, in which Ca2+-activated EHB1 emerges as the central processor-like element that links the gravi- and phototropic transduction chains and that generates in coordination with NPH3 and AGD12 the tangent / cotangent algorithm governing photogravitropic equilibrium

Veraenderung der Grundwasserqualitaet bei der Wassergewinnung im Einflussbereich von Oberflaechengewaessern in einer intensiv genutzten Region. Bd. 1. Hauptbericht

TIB Hannover: RN 8422 (1985,37) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman