1,245 research outputs found

    Convolution of multifractals and the local magnetization in a random field Ising chain

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    The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two multifractals. In this paper we prove relations between the multifractal properties of two measures and the multifractal properties of their convolution. The pointwise dimension at the boundary of the support of the convolution is the sum of the pointwise dimensions at the boundary of the support of the convoluted measures and the generalized box dimensions of the convolution are bounded from above by the sum of the generalized box dimensions of the convoluted measures. The generalized box dimensions of the convolution of Cantor sets with weights can be calculated analytically for certain parameter ranges and illustrate effects we also encounter in the case of the measure of the local magnetization. Returning to the study of this measure we apply the general inequalities and present numerical approximations of the D_q-spectrum. For the first time we are able to obtain results on multifractal properties of a physical quantity in the one-dimensional random-field Ising model which in principle could be measured experimentally. The numerically generated probability densities for the local magnetization show impressively the gradual transition from a monomodal to a bimodal distribution for growing random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the introduction and the conclusions, some typos were corrected, 24 pages, LaTeX2e, 9 figure

    Orbits and phase transitions in the multifractal spectrum

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    We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective field exhibits a sharp drop of all D_q with q < 0 at some critical strength of the random field. We introduce the concept of orbits which naturally group the points of the support of the invariant measure. We then show that the pointwise dimension at all points of an orbit has the same value and calculate it for a class of periodic orbits and their so-called offshoots as well as for generic orbits in the non-overlapping case. The sharp drop in the D_q-spectrum is analytically explained by a drastic change of the scaling properties of the measure near the points of a certain periodic orbit at a critical strength of the random field which is explicitly given. A similar drastic change near the points of a special family of periodic orbits explains a second, hitherto unnoticed transition in the D_q-spectrum. As it turns out, a decisive role in this mechanism is played by a specific offshoot. We furthermore give rigorous upper and/or lower bounds on all D_q in a wide parameter range. In most cases the numerically obtained D_q coincide with either the upper or the lower bound. The results in this paper are relevant for the understanding of random iterated function systems in the case of moderate overlap in which periodic orbits with weak singularity can play a decisive role.Comment: The article has been completely rewritten; the title has changed; a section about the typical pointwise dimension as well as several references and remarks about more general systems have been added; to appear in J. Phys. A; 25 pages, 11 figures, LaTeX2

    Managing Backlash: The Evolving Investment Treaty Arbitrator?

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    The Revolving Door in International Investment Arbitration

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    Abstract It is often claimed that international investment arbitration is marked by a revolving door: individuals act sequentially and even simultaneously as arbitrator, legal counsel, expert witness, or tribunal secretary. If this claim is correct, it has implications for our understanding of which individuals possess power and influence within this community; and ethical debates over conflicts of interests and transparency concerning ‘double hatting’—when individuals simultaneously perform different roles across cases. In this article, we offer the first comprehensive empirical analysis of the individuals that make up the entire investment arbitration community. Drawing on our database of 1039 investment arbitration cases (including ICSID annulments) and the relationships between the 3910 known individuals that form this community, we offer the first use of social network analysis to describe the full investment arbitration community and address key sociological and normative questions in the literature. Our results partly contradict recent empirical scholarship as we identify a different configuration of central ‘power brokers’. Moreover, the normative concerns with double hatting are partly substantiated. A select but significant group of individuals score highly and continually on our double hatting index.</jats:p

    Backlash and State Strategies in International Investment Law

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    This book provides an important corrective to existing theories of international law by focusing on how states respond to increased legalisation and rely on legal expertise to manoeuvre within and against international law

    Nonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit

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    A finite array of NN globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling there is a clear separation of time scales of center of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the center of mass coordinate. We compute analytically the stationary probability and the moments of the center of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter ac(N)a_c(N) is determined. We identify a crossover from linear to square root scaling with increasing distance from aca_c. The crossover point approaches aca_c in the limit N→∞N \to \infty which reproduces previous results for infinite arrays. The results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on NN and is determined by the scaling behaviour near a fixed point of the stochastic flow

    The randomly driven Ising ferromagnet, Part I: General formalism and mean field theory

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    We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field theory. A novel type of first order phase transition related to spontaneous symmetry breaking and dynamic freezing is found. The non-equilibrium stationary state has a complex structure, which changes as a function of parameters from a singular-continuous distribution with Euclidean or fractal support to an absolutely continuous one.Comment: 12 pages REVTeX/LaTeX format, 12 eps/ps figures. Submitted to Journal of Physics

    Using short-term postseismic displacements to infer the ambient deformation conditions of the upper mantle

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    Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophyscial Research 117 (2012): B01409, doi:10.1029/2011JB008562.To interpret short-term postseismic surface displacements in the context of key ambient conditions (e.g., temperature, pressure, background strain rate, water content, creep mechanism), we combined steady state and transient flow into a single constitutive relation that can explain the response of a viscoelastic material to a change in stress. The flow law is then used to investigate mantle deformation beneath the Eastern California Shear Zone following the 1999 M7.1 Hector Mine earthquake. The flow law parameters are determined using finite element models of relaxation processes, constrained by surface displacement time series recorded by 55 continuous GPS stations for 7 years following the earthquake. Results suggest that postseismic flow following the Hector Mine earthquake occurs below a depth of ~50 km and is controlled by dislocation creep of wet olivine. Diffusion creep models can also explain the data, but require a grain size (3.5 mm) that is smaller than the inferred grain size (10–20 mm) based on the mantle conditions at these depths. In addition, laboratory flow laws predict dislocation creep would dominate at the stress/grain size conditions that provide the best fit to diffusion creep models. Model results suggest a transient creep phase that lasts ~1 year and has a viscosity ~10 times lower than subsequent steady state flow, in general agreement with laboratory observations. The postseismic response is best explained as occurring within a relatively hot upper mantle (e.g., 1200–1300°C at 50 km depth) with a long-term background mantle strain rate of 0.1–0.2 μstrain/yr, consistent with the observed surface strain rate. Long-term background shear stresses at the top of the mantle are ~4 MPa, then decrease with depth to a minimum of 0.1–0.2 MPa at 70 km depth before increasing slowly with depth due to the pressure dependence of viscosity. These conditions correspond to a background viscosity of 1021 Pa s within a thin mantle lid that decreases to ~5 × 1019 Pa s within the underlying asthenosphere. This study shows the utility of using short-term postseismic observations to infer long-term mantle conditions that are not readily observable by other means.This work was supported by the National Science Foundation grants EAR-0952234 (A.M.F.), EAR-0810188 (G.H.), and EAR-0854673 (M.D.B.).2012-07-3
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