Invaded cluster simulations of the XY model in two and three dimensions

The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 2000^2 and 120^3 respectively. A soft spin O(2) model, in the same universality class as the 3D XY model, is also studied. The static critical properties of the model and the dynamical properties of the algorithm are reported. The results are K_c=0.45412(2) for the 3D XY model and eta=0.037(2) for the 3D XY universality class. For the 2D XY model the results are K_c=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show any critical slowing for the magnetization or critical temperature estimator for the 2D or 3D XY models.Comment: 30 pages, 11 figures, problem viewing figures corrected in v

Self-avoiding walks and connective constants in small-world networks

Long-distance characteristics of small-world networks have been studied by means of self-avoiding walks (SAW's). We consider networks generated by rewiring links in one- and two-dimensional regular lattices. The number of SAW's $u_n$ was obtained from numerical simulations as a function of the number of steps $n$ on the considered networks. The so-called connective constant, $\mu = \lim_{n \to \infty} u_n/u_{n-1}$, which characterizes the long-distance behavior of the walks, increases continuously with disorder strength (or rewiring probability, $p$). For small $p$, one has a linear relation $\mu = \mu_0 + a p$, $\mu_0$ and $a$ being constants dependent on the underlying lattice. Close to $p = 1$ one finds the behavior expected for random graphs. An analytical approach is given to account for the results derived from numerical simulations. Both methods yield results agreeing with each other for small $p$, and differ for $p$ close to 1, because of the different connectivity distributions resulting in both cases.Comment: 7 pages, 5 figure

Practitioner’s Section: Integrated Resource Efficiency Analysis for Reducing Climate Impacts in the Chemical Industry

Reducing greenhouse gas emissions of the material-intensive chemical industry requires an integrated analysis and optimization of the complex production systems including raw material and energy use, resulting costs and environmental and climate impacts. To meet this challenge, the research project InReff (Integrated Resource Efficiency Analysis for Reducing Climate Impacts in the Chemical Industry) has been established. It aims at the development of an IT-supported modeling and evaluation framework which is able to comprehensively address issues of resource efficiency and climate change within the chemical industry, e.g. the minimization of material and energy intensity and consequently greenhouse gas emissions, without compromising on production performance. The paper presents background information on resource efficiency and the research project, an ideal-typical decision model for resource efficiency analysis, the conceptual approach for an IT-based integration platform as well as the case study design at the industrial project partners’ sites. These first results are linked to future activities and further research questions are highlighted in the concluding section

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.Comment: 61 pages, 3 figures, RevTe

Amino-acid PET versus MRI guided re-irradiation in patients with recurrent glioblastoma multiforme (GLIAA) – protocol of a randomized phase II trial (NOA 10/ARO 2013-1)

Background: The higher specificity of amino-acid positron emission tomography (AA-PET) in the diagnosis of gliomas, as well as in the differentiation between recurrence and treatment-related alterations, in comparison to contrast enhancement in T1-weighted MRI was demonstrated in many studies and is the rationale for their implementation into radiation oncology treatment planning. Several clinical trials have demonstrated the significant differences between AA-PET and standard MRI concerning the definition of the gross tumor volume (GTV). A small single-center non-randomized prospective study in patients with recurrent high grade gliomas treated with stereotactic fractionated radiotherapy (SFRT) showed a significant improvement in survival when AA-PET was integrated in target volume delineation, in comparison to patients treated based on CT/MRI alone. Methods: This protocol describes a prospective, open label, randomized, multi-center phase II trial designed to test if radiotherapy target volume delineation based on FET-PET leads to improvement in progression free survival (PFS) in patients with recurrent glioblastoma (GBM) treated with re-irradiation, compared to target volume delineation based on T1Gd-MRI. The target sample size is 200 randomized patients with a 1:1 allocation ratio to both arms. The primary endpoint (PFS) is determined by serial MRI scans, supplemented by AA-PET-scans and/or biopsy/surgery if suspicious of progression. Secondary endpoints include overall survival (OS), locally controlled survival (time to local progression or death), volumetric assessment of GTV delineated by either method, topography of progression in relation to MRIor PET-derived target volumes, rate of long term survivors (> 1 year), localization of necrosis after re-irradiation, quality of life (QoL) assessed by the EORTC QLQ-C15 PAL questionnaire, evaluation of safety of FET-application in AA-PET imaging and toxicity of re-irradiation. Discussion: This is a protocol of a randomized phase II trial designed to test a new strategy of radiotherapy target volume delineation for improving the outcome of patients with recurrent GBM. Moreover, the trial will help to develop a standardized methodology for the integration of AA-PET and other imaging biomarkers in radiation treatment planning. Trial registration: The GLIAA trial is registered with ClinicalTrials.gov (NCT01252459, registration date 02.12.2010), German Clinical Trials Registry (DRKS00000634, registration date 10.10.2014), and European Clinical Trials Database (EudraCT-No. 2012-001121-27, registration date 27.02.2012)