Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities

The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability conditions, one of them is the Rota-Baxter identity. The theory is illustrated by means of the algebra of Laurent series, the related hierarchies are classified and examples, also new, of Manakov-Santini type systems are constructed, including those that are related to the dispersionless modified Kadomtsev-Petviashvili equation and so called dispersionless r-th systems

Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems

We introduce the cotangent universal hierarchy that extends the so-called universal hierarchy (as for the latter, see e.g. arXiv:nlin/0202008, arXiv:nlin/0312043 and arXiv:nlin/0310036). Then we construct a (2+1)-dimensional double central extension of the cotangent universal hierarchy and show that this extension is bi-Hamiltonian. This yields, as a byproduct, the central extension of the original universal hierarchy.Comment: 12 pages, LaTeX 2e, minor changes (typos fixed, English improved, etc.

On deformations of standard R-matrices for integrable infinite-dimensional systems

Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are presented as well as new integrable evolution equations are constructed.Comment: 14 page

Novikov algebras and a classification of multicomponent Camassa-Holm equations

A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by Bai and Meng. These multi-component bi-Hamiltonian systems obtained by this construction may be interpreted as Euler equations on the centrally extended Lie algebras associated to the Novikov algebras. The related bilinear forms generating cocycles of first, second and third order are classified. Several examples, including known integrable equations, are presented.Comment: V2: some comments and references are adde

Construction and separability of nonlinear soliton integrable couplings

A very natural construction of integrable extensions of soliton systems is presented. The extension is made on the level of evolution equations by a modification of the algebra of dynamical fields. The paper is motivated by recent works of Wen-Xiu Ma et al. (Comp. Math. Appl. 60 (2010) 2601, Appl. Math. Comp. 217 (2011) 7238), where new class of soliton systems, being nonlinear integrable couplings, was introduced. The general form of solutions of the considered class of coupled systems is described. Moreover, the decoupling procedure is derived, which is also applicable to several other coupling systems from the literature.Comment: letter, 10 page

Thermo-mechanical Analysis of Cold Helium Injection into Gas Storage Tanks made of Carbon Steel Following Resistive Transition of the LHC Magnets

A resistive transition (quench) of the LHC sector magnets will be followed by cold helium venting to a quench buffer volume of 2000 m3 at ambient temperature. The volume will be composed of eight medi um-pressure (2 MPa) gas storage tanks made of carbon steel, which constrains the temperature of the wall to be higher than -50oC (223 K). The aim of the analysis is the assessment of a possible spot c ooling intensity and thermo-mechanical stresses in the tank wall following helium injection

Sliding-window analysis tracks fluctuations in amygdala functional connectivity associated with physiological arousal and vigilance during fear conditioning

We evaluated whether sliding-window analysis can reveal functionally relevant brain network dynamics during a well-established fear conditioning paradigm. To this end, we tested if fMRI fluctuations in amygdala functional connectivity (FC) can be related to task-induced changes in physiological arousal and vigilance, as reflected in the skin conductance level (SCL). Thirty-two healthy individuals participated in the study. For the sliding-window analysis we used windows that were shifted by one volume at a time. Amygdala FC was calculated for each of these windows. Simultaneously acquired SCL time series were averaged over time frames that corresponded to the sliding-window FC analysis, which were subsequently associated with the whole-brain seed-based amygdala sliding-window FC using the GLM. Surrogate time series were generated to test whether connectivity dynamics could have occurred by chance. In addition, results were contrasted against static amygdala FC and sliding-window FC of the primary visual cortex, which was chosen as a control seed, while a physio-physiological interaction (PPI) was performed as cross-validation. During periods of increased SCL, the left amygdala became more strongly coupled with the bilateral insula and medial prefrontal cortex, core areas of the salience network. The sliding-window analysis yielded a connectivity pattern that was unlikely to have occurred by chance, was spatially distinct from static amygdala FC and from sliding-window FC of the primary visual cortex, but was highly comparable to that of the PPI analysis. We conclude that sliding-window analysis can reveal functionally relevant fluctuations in connectivity in the context of an externally cued task