Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

Mutual heavy ion dissociation in peripheral collisions at ultrarelativistic energies

We study mutual dissociation of heavy nuclei in peripheral collisions at ultrarelativistic energies. Earlier this process was proposed for beam luminosity monitoring via simultaneous registration of forward and backward neutrons in zero degree calorimeters at Relativistic Heavy Ion Collider. Electromagnetic dissociation of heavy ions is considered in the framework of the Weizsacker-Williams method and simulated by the RELDIS code. Photoneutron cross sections measured in different experiments and calculated by the GNASH code are used as input for the calculations of dissociation cross sections. The difference in results obtained with different inputs provides a realistic estimation for the systematic uncertainty of the luminosity monitoring method. Contribution to simultaneous neutron emission due to grazing nuclear interactions is calculated within the abrasion model. Good description of CERN SPS experimental data on Au and Pb dissociation gives confidence in predictive power of the model for AuAu and PbPb collisions at RHIC and LHC.Comment: 46 pages with 7 tables and 13 figures, numerical integration accuracy improved, next-to-leading-order corrections include

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Exploring Species Limits in Two Closely Related Chinese Oaks

Background. The species status of two closely related Chinese oaks, Quercus liaotungensis and Q. mongolica, has been called into question. The objective of this study was to investigate the species status and to estimate the degree of introgression between the two taxa using different approaches. [br/] Methodology/Principal Findings. Using SSR (simple sequence repeat) and AFLP (amplified fragment length polymorphism) markers, we found that interspecific genetic differentiation is significant and higher than the differentiation among populations within taxa. Bayesian clusters, principal coordinate analysis and population genetic distance trees all classified the oaks into two main groups consistent with the morphological differentiation of the two taxa rather than with geographic locations using both types of markers. Nevertheless, a few individuals in Northeast China and many individuals in North China have hybrid ancestry according to Bayesian assignment. One SSR locus and five AFLPs are significant outliers against neutral expectations in the interspecific FST simulation analysis, suggesting a role for divergent selection in differentiating species.[br/] Main Conclusions/Significance. All results based on SSRs and AFLPs reached the same conclusion: Q. liaotungensis and Q. mongolica maintain distinct gene pools in most areas of sympatry. They should therefore be considered as discrete taxonomic units. Yet, the degree of introgression varies between the two species in different contact zones, which might be caused by different population history or by local environmental factors