Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

Gaudin Models and Bending Flows: a Geometrical Point of View

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym

Implementation of an elasto-viscoplastic constitutive law in Abaqus/Standard for an improved characterization of rock materials

Subsidence modeling is an important activity in the oil and gas industry, for the environmental and operational implications associated to this phenomenon. Abaqus/Standard has been used for many years in Eni as the main numerical simulator for studying the geomechanical behavior of reservoirs. The results of a large campaign of acquisition of subsidence monitoring data in conjunction with the advanced analysis of laboratory experiments have shown that, in some cases, an improved mechanical characterization can be tailored to better capture the complex behavior of the reservoir rock under the effect of underground fluid withdrawal. In this work we first present an implementation in Abaqus/Standard of an elasto-viscoplastic model – namely the Vermeer and Neher model – as user defined material by means of the UMAT subroutine. Next, we provide the results of various simulations of laboratory tests that were performed to investigate its capability to identify the main features of the behavior of reservoir sands, also including time dependency. Finally, we show a preliminary application to a synthetic, nonetheless realistic, reservoir model that has been performed to assess the capabilities of the elasto-viscoplastic model in the simulation of subsidence evolution

Pharmacological fMRI: effects of subanesthetic ketamine on resting-state functional connectivity in the default mode network, salience network, dorsal attention network and executive control network

BACKGROUND: Subanesthetic dosages of the NMDAR antagonist, S-Ketamine, can cause changes in behavior in healthy subjects, which are similar to the state acute psychosis and are relevant in translational schizophrenia research. Functional magnetic resonance imaging (fMRI) can be used for non-hypothesis-driven analysis of brain connectivity. The correlation between clinical behavioral scores and neuroimaging can help to characterize ketamine effects on healthy brains in resting state. METHOD: Seventeen healthy, male subjects (mean: 27.42 years, SD: 4.42) were administered an infusion with S-Ketamine (initial bolus 1 mg/kg and continuous infusion of 0.015625 mg/kg/min with dosage reduction −10%/10 min) or saline in a randomized, double-blind, cross-over study. During infusion, resting state connectivity was measured and analyzed with a seed-to-voxel fMRI analysis approach. The seed regions were located in the posterior cingulate cortex, intraparietal sulcus, dorsolateral prefrontal cortex and fronto-insular cortex. Receiver operating characteristics (ROC) were calculated to assess the accuracy of the ketamine-induced functional connectivity changes. Bivariate Pearson correlation was used for correlation testing of functional connectivity changes with changes of clinical scores (PANSS, 5D-ASC). RESULTS: In the executive network (ECN), ketamine significantly increases the functional connectivity with parts of the anterior cingulum and superior frontal gyrus, but no significant correlations with clinical symptoms were found. Decreased connectivity between the salience network (SN) and the calcarine fissure was found, which is significantly correlated with negative symptoms (PANSS) (R2 > 0.4). CONCLUSION: Decreased ketamine-induced functional connectivity in the salience network may qualify as accurate and highly predictive biomarkers for ketamine induced negative symptoms