New types of 3-D systems of quadratic differential equations with chaotic dynamics based on Ricker discrete population model

The wide class of 3-D autonomous systems of quadratic differential equations, in each of which either there is a couple of coexisting limit cycles or there is a couple of coexisting chaotic attractors, is found. In the second case the couple consists of either Lorentz-type attractor and another attractor of a new type or two Lorentz-type attractors. It is shown that the chaotic behavior of any system of the indicated class can be described by the Ricker discrete population model: z_i+1 = z_i exp(r − z_i), r > 0, z_i > 0, i = 0, 1, … . The values of parameters, at which in the 3-D system appears either the couple of limit cycles or the couple of chaotic attractors, or only one limit cycle, or only one sphere-shaped chaotic attractor, are indicated. Examples are given.     

Shape Coexistence and the N=28 Shell Closure Far from Stability

A mass measurement experiment by a time of flight method with the SPEG spectrometer at GANIL has been performed to investigate the N=20 and N=28 shell closures far from stability. The masses of 31 neutron-rich nuclei in the range A=29–47 have been measured. The precision of 19 masses has been significantly improved and 12 masses were measured for the first time. The neutron-rich Cl, S and P isotopes are seen to exhibit a change in shell structure around N=28. Comparison with shell model and relativistic mean field calculations demonstrate that the observed effects arise from deformed prolate ground state configurations associated with shape coexistence. The evidence of an isomeric state in the ⁴³S and its interpretation by a shell model calculation confirm the analysis of the masses and constitutes the first evidence of the predicted shape coexistence around N=28. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electrical transport and magnetic ordering in R 2Ti3Ge4 (R=Dy, Ho and Er) compounds

New R ₂Ti₃Ge₄ (R=Dy, Ho and Er) intermetallic compounds have been synthesized and characterized by X-ray diffraction and low temperature ac magnetic susceptibility, electrical resistivity and thermoelectric power measurements were carried out. The compounds crystallize in the parent, Sm₅Ge₄-type orthorhombic structure (space group Pnma) and lanthanide contraction is observed as one moves along the rare-earth series. The changeover from paramagnetic to antiferromagnetic phase happens at low temperatures and the ordering temperature scales with the de Gennes factor. The electrical resistivity is metallic with a negative curvature above 100 K. Thermopower displays a weak maximum at temperatures less than 50 K signifying the possible phonon and magnon drag effects.     

Shape coexistence and the N = 28 shell closure far from stability

The masses of 31 neutron-rich nuclei in the range A = 29-47 have been measured. The precision of 19 masses has been significantly improved and 12 masses were measured for the first time. The neutron-rich Cl, S, and P isotopes are seen to exhibit a change in shell structure around N = 28. Comparison with shell model and relativistic mean field calculations demonstrate that the observed effects arise from deformed prolate ground state configurations associated with shape coexistence. Evidence for shape coexistence is provided by the observation of an isomer in 43S.     

Elastic properties of the Ta–V system: bcc Ta0.33V0.67 and C15 TaV2

Resonant ultrasound spectroscopy was used to measure the elastic constants of bcc Ta_0.33V_0.67 over the temperature range 3.5–300?K; the results were compared to earlier measurements on C15 TaV₂. The temperature dependence of the polycrystalline shear modulus is completely different in the two phases; that of the bcc phase decreases with temperature whereas that of the C15 phases increases in an anomalous fashion. This difference is consistent with a model involving doubly-degenerate levels at the X point of the Brillouin zone in the C15 phase with the Fermi level lying near the doubly degenerate level. This model accounted for the unusual behaviour of the C15 phase. Debye temperatures were determined from the ultrasonic measurements: 295?K for the C15 phase and 315?K for the bcc phase.     

First observation of the neutron-rich nuclei42Si,45, 46P,48S,and51Cl from the interaction of 44 MeV/u48Ca +64Ni

Five new very neutron-rich isotopes,⁴²Si,^45,46P,⁴⁸S and⁵¹Cl, are identified from the interaction of a 44 MeV/u⁴⁸Ca beam with a⁶⁴Ni target.     

Shape coexistence and the N = 20 shell closure far from stability by inelastic scattering

Following mass measurements in the region N = 20 and N = 28, we have studied inelastic nuclear scattering for the nuclei ³⁴Si, ³³Al and ³²Mg. No evidence for a low-lying shape isomeric 0⁺ state was found in ³⁴Si, and an upper limit for the population cross-section could be established, rendering its existence very unlikely. A new transition was found in ³³Al, that is a good candidate for a 2p-2h state and therefore a determination of the 2p-2h gap at N = 20. Inelastic nuclear scattering strongly excites 3^- states, as seen in ³⁴Si. A strong transition was found in ³²Mg that should correspond to the first 3^- in this nucleus, lying very low as compared to theory and systematics in this region. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: mittig@ganil.fr     

On existence of homoclinic orbits for some types of autonomous quadratic systems of differential equations

The new existence conditions of homoclinic orbits for the system of ordinary quadratic differential equations are founded. Further, the realization of these conditions together with the Shilnikov Homoclinic Theorem guarantees the existence of a chaotic attractor at 3D autonomous quadratic system. Examples of the chaotic attractors are given.