Monotonicity and logarithmic convexity relating to the volume of the unit ball

Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence $\frac{\Omega_{n}^{1/(n\ln n)}}{\Omega_{n+1}^{1/[(n+1)\ln(n+1)]}}$ is strictly decreasing for $n\ge2$. In addition, some monotonic and concave properties of several functions relating to $\Omega_{n}$ are extended and generalized.Comment: 12 page

Differential Transverse Flow in Central C-Ne and C-Cu Collisions at 3.7 GeV/nucleon

Differential transverse flow of protons and pions in central C-Ne and C-Cu collisions at a beam energy of 3.7 GeV/nucleon was measured as a function of transverse momentum at the SKM-200-GIBS setup of JINR. In agreement with predictions of a transversely moving thermal model, the strength of proton differential transverse flow is found to first increase gradually and then saturate with the increasing transverse momentum in both systems. While pions are preferentially emitted in the same direction of the proton transverse flow in the reaction of C-Ne, they exhibit an anti-flow to the opposote direction of the proton transverse flow in the reaction of C-Cu due to stronger shadowing effects of the heavier target in thr whole range of transverse momentum.Comment: 15 pages, 5 figure

Modular Equations and Distortion Functions

Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds for singular values of complete elliptic integrals.Comment: 23 page

Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.Comment: Accepted in EPJ

Preparation and ferroelectric properties of (124)-oriented SrBi4Ti4O15 ferroelectric thin film on (110)-oriented LaNiO3 electrode

A (124)-oriented SrBi4Ti4O15 (SBTi) ferroelectric thin film with high volume fraction of {\alpha}SBTi(124)=97% was obtained using a metal organic decomposition process on SiO2/Si substrate coated by (110)-oriented LaNiO3 (LNO) thin film. The remanent polarization and coercive field for (124)-oriented SBTi film are 12.1 {\mu}C/cm2 and 74 kV/cm, respectively. No evident fatigue of (124)-oriented SBTi thin film can be observed after 1{\times}10e9 switching cycles. Besides, the (124)-oriented SBTi film can be uniformly polarized over large areas using a piezoelectric-mode atomic force microscope. Considering that the annealing temperature was 650{\deg}C and the thickness of each deposited layer was merely 30 nm, a long-range epitaxial relationship between SBTi(124) and LNO(110) facets was proposed. The epitaxial relationship was demonstrated based on the crystal structures of SBTi and LNO.Comment: 11 pages, 4 figures, published in Journal of Materials Science: Materials in Electronics (JMSE), 19 (2008), 1031-103

Proton Differential Elliptic Flow and the Isospin-Dependence of the Nuclear Equation of State

Within an isospin-dependent transport model for nuclear reactions involving neutron-rich nuclei, we study the first-order direct transverse flow of protons and their second-order differential elliptic flow as a function of transverse momentum. It is found that the differential elliptic flow of mid-rapidity protons, especially at high transverse momenta, is much more sensitive to the isospin dependence of the nuclear equation of state than the direct flow. Origins of these different sensitivities and their implications to the experimental determination of the isospin dependence of the nuclear equation of state by using neutron-rich heavy-ion collisions at intermediate energies are discussed.Comment: 15 pages, 6 figures. Phys. Rev. C (2001) in pres

Electron-Phonon Interacation in Quantum Dots: A Solvable Model

The relaxation of electrons in quantum dots via phonon emission is hindered by the discrete nature of the dot levels (phonon bottleneck). In order to clarify the issue theoretically we consider a system of $N$ discrete fermionic states (dot levels) coupled to an unlimited number of bosonic modes with the same energy (dispersionless phonons). In analogy to the Gram-Schmidt orthogonalization procedure, we perform a unitary transformation into new bosonic modes. Since only $N(N+1)/2$ of them couple to the fermions, a numerically exact treatment is possible. The formalism is applied to a GaAs quantum dot with only two electronic levels. If close to resonance with the phonon energy, the electronic transition shows a splitting due to quantum mechanical level repulsion. This is driven mainly by one bosonic mode, whereas the other two provide further polaronic renormalizations. The numerically exact results for the electron spectral function compare favourably with an analytic solution based on degenerate perturbation theory in the basis of shifted oscillator states. In contrast, the widely used selfconsistent first-order Born approximation proves insufficient in describing the rich spectral features.Comment: 8 pages, 4 figure

The magnetic field topology associated to two M flares

On 27 October, 2003, two GOES M-class flares occurred in the lapse of three hours in active region NOAA 10486. The two flares were confined and their associated brightenings appeared at the same location, displaying a very similar shape both at the chromospheric and coronal levels. We focus on the analysis of magnetic field (SOHO/MDI), chromospheric (HASTA, Kanzelhoehe Solar Observatory, TRACE) and coronal (TRACE) observations. By combining our data analysis with a model of the coronal magnetic field, we compute the magnetic field topology associated to the two M flares. We find that both events can be explained in terms of a localized magnetic reconnection process occurring at a coronal magnetic null point. This null point is also present at the same location one day later, on 28 October, 2003. Magnetic energy release at this null point was proposed as the origin of a localized event that occurred independently with a large X17 flare on 28 October, 2003, at 11:01 UT. The three events, those on 27 October and the one on 28 October, are homologous. Our results show that coronal null points can be stable topological structures where energy release via magnetic reconnection can happen, as proposed by classical magnetic reconnection models.Comment: 14 pages, 7 figure

Modelling of Nb influence on phase transformation behaviours from austenite to ferrite in low carbon steels

In this paper, a new model has been developed to predict the phase transformation behaviours from austenite to ferrite in Nb-containing low carbon steels. The new model is based on some previous work and incorporates the effects of Nb on phase transformation behaviours, in order to make it applicable for Nb-containing steels. Dissolved Nb atoms segregated at prior austenite grain boundaries increase the critical energy for ferrite nucleation, and thus the ferrite nucleation rate is decreased. Dissolved Nb atoms also apply a solute drag effect to the moving transformation interface, and the ferrite grain growth rate is also decreased. The overall transformation kinetics is then calculated according to the classic Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory. The new model predictions are quite consistent with experimental results for various steels during isothermal transformations or continuous cooling