Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the exact solution. Based on the local convergence of the collocation methods for VIEs, we present the convergence analysis for the numerical blow-up time. Numerical experiments illustrate the analysis

First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

The Vacuum System of HIRFL

AbstractThe vacuum system of Heavy Ion Research Facility in Lanzhou (HIRFL) is a large and complex system. HIRFL consists of two ECR ion sources, a sector focus cyclotron (SFC), a separate sector cyclotron (SSC) and a multi-purpose cooling storage ring system which has a main ring (CSRm) and an experiment ring (CSRe). Several beam lines connect these accelerators together and transfer various heavy ion beams to more than 10 experiment terminals. According to the requirements of the ion acceleration and ion lifetime, the working pressure in each accelerator is different. SFC is nearly 50 years old. After upgrade, the working pressure in SFC is improved from 10-6mbar to 10-8mbar. The pressure in SSC which was built in the 1980s reaches the same level. The cooling storage ring system with a length of 500m came into operation in 2007. The average pressures in CSRm and CSRe are 5×10-12mbar and 8×10-12mbar respectively. Different designs were adopt for vacuum system of a dozen beam lines to meet specific requirement of each experiment terminal. Along with the extensive development of the heavy ion researches and applications, new accelerators of HIRFL are under construction. The vacuum system of the new machines will be designed and constructed followed the overall schedule

Dwarfing gene Rht18 from tetraploid wheat responds to exogenous GA₃ in hexaploid wheat

Rht18, derived from Triticum durum (tetraploid) wheat, is classified as a gibberellic acid (GA)-responsive dwarfing gene. Prior to this study, the responses of Rht18 to exogenous GA on agronomic traits in hexaploid wheat were still unknown. The response of Rht18 to exogenous GA3 on coleoptile length, plant height, yield components and other agronomic traits were investigated using F4:5 and F5:6 hexaploid dwarf lines with Rht18 derived from two crosses between the tetraploid donor Icaro and tall Chinese winter wheat cultivars, Xifeng 20 and Jinmai 47. Applications of exogenous GA3 significantly increased coleoptile length in both lines and their tall parents. Plant height was significantly increased by 21.3 and 10.7% in the GA3-treated dwarf lines of Xifeng 20 and Jinmai 47, respectively. Compared to the untreated dwarf lines, the partitioning of dry matter to ears at anthesis was significantly decreased while the partitioning of dry matter to stems was significantly increased in the GA3-treated dwarf lines. There were no obvious changes in plant height and dry matter partitioning in the GA3-treated tall parents. Exogenous GA3 significantly decreased grain number spike–1 while it increased 1000-kernel weight in both the dwarf lines and tall parents. Thus, applications of exogenous GA3 restored plant height and other agronomic traits of Rht18 dwarf lines to the levels of the tall parents. This study indicated that Rht18 dwarf mutants are GA-deficient lines with impaired GA biosynthesis

Effects of Mn and Ti doping on superconductivity and charge ordering in NaxCoO2 system

The superconductivity in Na0.3Co1-xMxO2.1.3H2O and the charge ordering in Na0.5Co1-xMxO2 have been investigated for M = Mn and Ti substituting for Co. We have first successfully synthesized the single-phase Na0.7Co1-xMxO2(M= Mn and Ti) materials with 0 < = x < = 0.1, then we obtained Na0.5Co1-xMxO2 (0 < = x < = 0.1, M = Mn and Ti) by Na deintercalation and Na0.3Co1-xMxO2.1.3H2O (0 < = x < = 0.1, M = Mn and Ti) by an additional water intercalations. X-ray diffraction measurements revealed that all samples are single-phase materials, their lattice parameters depend systematically on the Ti and Mn contents. Measurements of physical properties indicate that the superconductivity in Na0.3Co1-xMxO2.1.3H2O is suppressed evidently by Co-site doping and killed at x = 0.02 for Mn doping and x = 0.01 for Ti doping. Charge ordering and magnetic properties in Na0.5Co1-xMxO2 were also influenced by M-atom doping.Comment: 22 pages, 3 tables, and 6 figure

Raman spectroscopy study of NaxCoO2 and superconducting NaxCoO2.yH2O

The Raman spectra of the parent compound NaxCoO2 (x=0.75) and the superconducting oxyhydrates NaxCoO2.yH2O with different superconducting temperatures (Tc) have been measured. Five Raman active phonons around 195 cm-1 (E1g), 482 cm-1, 522 cm-1, 616 cm-1 (3E2g), 663 cm-1 (A1g) appear in all spectra. These spectra change systematically along with the intercalation of H2O and superconducting properties. In particular, the Raman active phonons (A1g and E1g) involving the oxygen motions within the Co-O layers show up monotonous decrease in frequency along with superconducting temperature Tc. The fundamental properties and alternations of other active Raman phonons in the superconducting materials have also been discussed.Comment: 16 pages, 4 figures, 2 table

Structural Phase Transitions and Sodium Ordering in Na0.5CoO2: a Combined Electron Diffraction and Raman Spectroscopy Study

The nonstoichiometric NaxCoO2 system exhibits extraordinary physical properties that correlate with temperature and Na concentration in its layered lattice without evident long-range structure modification when conventional crystallographic techniques are applied. For instance, Na0.7CoO2, a thermodynamically stable phase, shows large thermoelectric power; water-intercalated Na0.33CoO2.1.3H2O is a newly discovered superconductor with Tc ~ 4K, and Na0.5CoO2 exhibits an unexpected charge ordering transition at around Tco ~ 55 K. Recent studies suggest that the transport and magnetic properties in the NaxCoO2 system strongly depend on the charge carrier density and local structural properties. Here we report a combined variable temperature transmission electron microscopy and Raman scattering investigation on structural transformations in Na0.5CoO2 single crystals. A series of structural phase transitions in the temperature range from 80 K to 1000 K are directly identified and the observed superstructures and modulated phases can be interpreted by Na-ordering. The Raman scattering measurements reveal phase separation and a systematic evolution of active modes along with phase transitions. Our work demonstrates that the high mobility and ordering of sodium cations among the CoO2 layers are a key factor for the presence of complex structural properties in NaxCoO2 materials, and also demonstrate that the combination of electron diffraction and Raman spectroscopy measurements is an efficient way for studying the cation ordering and phase transitions in related systems.Comment: 22 pages, 5 figure

Charmless Bs→PP,PV,VVB_s\to PP, PV, VV Decays Based on the six-quark Effective Hamiltonian with Strong Phase Effects II

We provide a systematic study of charmless $B_s \to PP, PV, VV$ decays ($P$ and $V$ denote pseudoscalar and vector mesons, respectively) based on an approximate six-quark operator effective Hamiltonian from QCD. The calculation of the relevant hard-scattering kernels is carried out, the resulting transition form factors are consistent with the results of QCD sum rule calculations. By taking into account important classes of power corrections involving "chirally-enhanced" terms and the vertex corrections as well as weak annihilation contributions with non-trivial strong phase, we present predictions for the branching ratios and CP asymmetries of $B_s$ decays into PP, PV and VV final states, and also for the corresponding polarization observables in VV final states. It is found that the weak annihilation contributions with non-trivial strong phase have remarkable effects on the observables in the color-suppressed and penguin-dominated decay modes. In addition, we discuss the SU(3) flavor symmetry and show that the symmetry relations are generally respected

The energy spectrum of all-particle cosmic rays around the knee region observed with the Tibet-III air-shower array

We have already reported the first result on the all-particle spectrum around the knee region based on data from 2000 November to 2001 October observed by the Tibet-III air-shower array. In this paper, we present an updated result using data set collected in the period from 2000 November through 2004 October in a wide range over 3 decades between $10^{14}$ eV and $10^{17}$ eV, in which the position of the knee is clearly seen at around 4 PeV. The spectral index is -2.68 $\pm$ 0.02(stat.) below 1PeV, while it is -3.12 $\pm$ 0.01(stat.) above 4 PeV in the case of QGSJET+HD model, and various systematic errors are under study now.Comment: 12 pages, 7 figures, accepted by Advances in space researc