38 research outputs found
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 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