Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets

We present comprehensive numerical results for domain growth in the two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber kinetics. We characterize the evolution via the {\it domain growth law}, and two-time quantities like the {\it autocorrelation function} and {\it autoresponse function}. Our results clearly establish that the growth law shows a crossover from a pre-asymptotic regime with "power-law growth with a disorder-dependent exponent" to an asymptotic regime with "logarithmic growth". We compare this behavior with previous results on one-dimensional disordered systems and we propose a unifying picture in a renormalization group framework. We also study the corresponding crossover in the scaling functions for the two-time quantities. Super-universality is found not to hold. Clear evidence supporting the dimensionality dependence of the scaling exponent of the autoresponse function is obtained.Comment: Thoroughly revised manuscript. The Introduction, Section 2 and Section 4 have been largely rewritten. References added. Final version accepted for publication on Journal of Statistical Mechanics: Theory and Experimen

Nonlinear susceptibilities and the measurement of a cooperative length

We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure

EDITORIAL: Intraoperative Quality Control of Carotid Endarterectomy

Von Dr. J. Utsc

Scaling and universality in the aging kinetics of the two-dimensional clock model

We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_\chi}f(t/s)$, we find $a_\chi$ consistent with the value $a_\chi =0.28$ found in the two-dimensional Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures

Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model

We study the nonconserved phase ordering dynamics of the d = 2, 3 random field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three di- mensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, the exponent in the preasymptotic power law is disorder-dependent, rather than being the one of the pure system. Furthermore, we find that the autocorre- lation function does not display superuniversal behavior. This restores consistency with previous results for the d = 1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond Ising model.Comment: To be published in Physical Review

Scaling Behavior of Response Functions in the Coarsening Dynamics of Disordered Ferromagnets

We study coarsening dynamics in the ferromagnetic random bond Ising model in d = 1; 2. We focus on the validity of super-universality and the scaling properties of the response functions. In the d = 1 case, we obtain a complete understanding of the evolution, from pre- asymptotic to asymptotic behavior. The corresponding response function shows a clear violation of super-universality. Further, our results for d = 1; 2 settle the controversy regarding the decay exponent which characterizes the response function

Nonlinear response and fluctuation dissipation relations

A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR.Comment: 24 pages, 6 figure

Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems

The relationship between statics and dynamics proposed by Franz, Mezard, Parisi and Peliti (FMPP) for slowly relaxing systems [Phys.Rev.Lett. {\bf 81}, 1758 (1998)] is investigated in the framework of non disordered coarsening systems. Separating the bulk from interface response we find that for statics to be retrievable from dynamics the interface contribution must be asymptotically negligible. How fast this happens depends on dimensionality. There exists a critical dimensionality above which the interface response vanishes like the interface density and below which it vanishes more slowly. At $d=1$ the interface response does not vanish leading to the violation of the FMPP scheme. This behavior is explained in terms of the competition between curvature driven and field driven interface motion.Comment: 11 pages, 3 figures. Significantly improved version of the paper with new results, new numerical simulations and new figure

Does the Presence of an Iliac Aneurysm Affect Outcome of Endoluminal AAA Repair? An Analysis of 336 Cases

AbstractObjective: to determine whether the presence of an iliac aneurysm compromises outcome of endovascular exclusion of AAA and to ascertain the fate of the iliac aneurysmal sac.Patients and methods: between April 1997 and March 2001, data on 336 consecutive patients undergoing endovascular repair for AAA were entered in a prospective database. Suitability for endovascular repair was assessed by preoperative contrast-enhanced computed tomography. A maximum common iliac artery (CIA) diameter ≥20mm was defined as iliac aneurysm. Patients with and without iliac aneurysms were compared to early (immediate conversion or perioperative death) and late failure (increase in aneurysm diameter or persisting graft-related endoleak, or late AAA rupture or conversion).Results: fifty-nine patients (18%) had iliac aneurysms, 19 were bilateral, for a total of 78 aneurysmal iliac arteries (median diameter 23mm; range 20–50mm). A distal seal was achieved by landing in 33 external iliac arteries, in 20 ectatic CIAs, and in 25 normal CIAs. Operating time differed significantly between patients with and without CIA aneurysms (153±71 vs 123±55min,p =0.0001), whereas no statistically significant differences were found with respect to early and late failure (2% vs 3%, p=0.5 and 14% vs 8%, p=0.11, respectively). There were no cases of buttock or colon necrosis. At a median follow-up of 14 months (range 0–46; i.q.r. 7–27 months) common iliac diameter decreased ≥2mm in 49 cases, remained stable in 25, and increased ≥2mm in 3.Conclusion: the presence of iliac aneurysm rendered endoluminal AAA repair more complex but did not affect feasibility and long-term outcome of the procedure. In our experience internal iliac exclusion was never associated with significant morbidity. These data may be useful when considering endovascular repair in high-risk patients with challenging anatomy

Role of Duplex Scan in Endoleak Detection After Endoluminal Abdominal Aortic Aneurysm Repair

AbstractObjective: to validate the role of duplex scan in endoleak detection in postoperative surveillance of endoluminal abdominal aneurysm repair (EAAR). Patients and methods between April 1997 and March 1999, 103 patients were eligible for duplex and computed tomography (CT) scan after EAAR. Mean follow-up was 8 months (range 1–24 months). The study protocol comprised concurrent examination with colour-duplex and CT scan at 1, 6, and 12 months after EAAR, for a total of 198 concurrent examinations. All duplex scan examinations were performed by two vascular surgeons with the same machine (ATL HDI 3000). Interobserver agreement in endoleak detection (κ=1) and in type of endoleak (κ=0.7) was evaluated in 50 random duplex examinations. Endoleak detection was examined comparatively in duplex and CT scan, the latter being the gold standard. Sensitivity and specificity tests together with negative- and positive-predictive values (NPV and PPV) were calculated. Results duplex scan was not feasible in one patient. On CT scan the endoleak rate was 4% at one month, 3% at 6 months, and 4% at one year. Overall, CT scan detected 12 endoleaks. With respect to endoleak detection, duplex scan revealed a great ability in ruling out false-negative results (sensitivity 91.7%, NPV 99.4%), but overestimated the presence of endoleak (specificity 98.4%, PPV 78.6%). Regarding type of endoleak, the ability of duplex scan to identify the source of endoleak was low (sensitivity 66.7%). Conclusions duplex scan, if validated, appears to be a reliable means for excluding the presence of endoleak after EAAR