Dependence of magnetic field generation by thermal convection on the rotation rate: A case study

Dependence of magnetic field generation on the rotation rate is explored by direct numerical simulation of magnetohydrodynamic convective attractors in a plane layer of conducting fluid with square periodicity cells for the Taylor number varied from zero to 2000, for which the convective fluid motion halts (other parameters of the system are fixed). We observe 5 types of hydrodynamic (amagnetic) attractors: two families of two-dimensional (i.e. depending on two spatial variables) rolls parallel to sides of periodicity boxes of different widths and parallel to the diagonal, travelling waves and three-dimensional “wavy” rolls. All types of attractors, except for one family of rolls, are capable of kinematic magnetic field generation. We have found 21 distinct nonlinear convective MHD attractors (13 steady states and 8 periodic regimes) and identified bifurcations in which they emerge. In addition, we have observed a family of periodic, two-frequency quasiperiodic and chaotic regimes, as well as an incomplete Feigenbaum period doubling sequence of bifurcations of a torus followed by a chaotic regime and subsequently by a torus with 1/3 of the cascade frequency. The system is highly symmetric. We have found two novel global bifurcations reminiscent of the SNIC bifurcation, which are only possible in the presence of symmetries. The universally accepted paradigm, whereby an increase of the rotation rate below a certain level is beneficial for magnetic field generation, while a further increase inhibits it (and halts the motion of fluid on continuing the increase), remains unaltered, but we demonstrate that this “large-scale” picture lacks many significant details.     

Coexistence of attractors in autonomous Van der Pol–Duffing jerk oscillator: Analysis,chaos control and synchronisation in its fractional-order form

Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in \(R^3\), the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic, quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for \(a>0\), and a chaotic attractor coexisting with a quasiperiodic attractor for \(a=0\). Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions.     

Photoemission spectra of deuterated silicon clusters: experiment and theory

We compare experimentally measured and ab initio computed photoelectron spectra of negatively charged deuterated silicon clusters ( , 4m10, 0n2) produced in a plasma environment. Based on this comparison, we discuss the kinetics and thermodynamics of the cluster formation and the effect of deuterium on the geometrical and electronic structure of the clusters.     

Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤ q < ∞, or the -norm of the gradient of the vorticity with 3/p + 2/q ≤ 4, 1 ≤ q, 1 ≤ p, is sufficiently small near z.     

Improvement of the intergranular pinning energy in uniaxially compacting (Bi-Pb)<Subscript>2</Subscript>Sr<Subscript>2</Subscript>Ca<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>10+δ</Subscript> ceramic samples

Measurements of the electrical resistivity as a function of temperature, ρ(T), for different values of applied magnetic field, B_a (0 ≤ B_a ≤ 50 mT), were performed in polycrystalline samples of Bi_1.65Pb_0.35Sr₂Ca₂ Cu₃O_10+δ subjected to different uniaxial compacting pressure (UCP). We have found appreciable differences in the grain orientation between samples by using X-ray diffractometry. From the X-ray diffraction patterns performed, in powder and pellet samples, we have estimated the Lotgering factor along the (00l) direction, F_(00l). The results indicate that F_(00l) increases ~23% with increasing UCP suggesting that grains of these samples are preferentially aligned along the c-axis, which is parallel to the compacting direction. The resistive transition of the samples have been interpreted in terms of the thermally activated flux-creep model. In addition, the effective intergranular pinning energy, U₀, have been determined for different applied magnetic field. The magnetic field dependence of U₀, for B_a > 8 mT, was found to follow a H^{- α} dependence with α = 0.5 for all samples. The analysis of the experimental data strongly suggested that increasing UCP results in appreciable changes in both the grain alignment and the grain connectivity of the samples. We have successfully interpreted the data by considering the existence of three different superconducting levels within the samples: the superconducting grains, the weak-links, and the superconducting clusters.     

Effect of step permeability on step instabilities due to alternation of kinetic coefficients on a growing vicinal face

We study the effect of step permeability on step instabilities on a growing vicinal face. When alternation of kinetic coefficients is taken into account, pairing of steps occurs on the vicinal face. Irrespective of the step permeability, the step pairs are stable for a wandering instability. The bunching of step pairs occurs if the steps are impermeable. The bunch size increases with time as t^β with β=1/2, which does not depend on the form of the repulsive interaction potential between steps. The repulsion influences the relation between the step distance in a bunch and the bunch size. When the repulsive potential ζ with the step distance l is given by ζ∼l^-ν, the average step distance in a bunch decreases as with α=1/(ν+1). The exponents, β and α are the same as those in the bunching induced by the Ehrlich-Schowebel effect in growth.     

On the scaling of probability density functions with apparent power-law exponents less than unity

We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent of a probability density is less than 1, the associated finite-size scaling ansatz has a scaling exponent τ equal to 1, provided that the fraction of events in the universal scaling part of the probability density function is non-vanishing in the thermodynamic limit. We find the general result that τ≥1 and . Moreover, we show that if the scaling function approaches a non-zero constant for small arguments, , then . However, if the scaling function vanishes for small arguments, , then τ= 1, again assuming a non-vanishing fraction of universal events. Finally, we apply the formalism developed to examples from the literature, including some where misunderstandings of the theory of scaling have led to erroneous conclusions.     

Two-step laser excitation of the highly excited even-parity states of atomic mercury

We report term energies and quantum defects of highly excited even-parity states of mercury in the 83 876–84 140 cm^-1 energy range, employing a two-step laser excitation scheme via the S₀↦6s6p³P₁ inter-combination transition. Two dye lasers, pumped by a common Nd:YAG laser, were frequency doubled by BBO crystals and used to record the spectra in conjunction with a thermionic diode ion detector. Our new observations include the much extended D₂ (22 ≤n ≤52) series and a few members of the S₁ (24 ≤n ≤30) Rydberg series. Members of the D₂ Rydberg series with such a high n value are reported for the first time. The relative intensities of the D₂ and S₁ transitions (m = 4, 5 and 6) of group II-B elements excited from the P₁ inter-combination states are also discussed.     

Synthesis and physical properties of LaO1-xFxFeAs

We have prepared the newly discovered Fe-based superconducting material LaO_1-xF_xFeAs (0 ≤ x ≤ 0.2) in polycrystalline form and have investigated the samples by means of structural, thermodynamic and transport measurements. Our investigations reveal a non superconducting phase at 0 ≤ x 0.04 which for x = 0 is characterized by a structural transition towards an orthorhombic distortion at T_s ≈ 160 K and antiferromagnetic spin order at T_N ≈ 138 K. Both transitions lead to strong anomalies in various transport properties as well as in magnetization and in specific heat. Remarkably, the transition temperatures are only weakly doping dependent up to x ≈ 0.04. However, the transitions are abruptly suppressed at x ≥ 0.05 in favour of a superconducting phase with a critical temperature T_c 20 K. Upon further increasing the F-doping T_c increases up to a maximum of T_c = 26.8 K at x = 0.1 which is followed by a decrease down to T_c ≈ 10 K at x ≥ 0.15.     

Quintom cosmologies admitting either tracking or phantom attractors

In this Letter we investigate the evolution of a class of cosmologies fueled by quintom dark energy and dark matter. Quintom dark energy is a hybrid of quintessence and phantom which involves the participation of two real scalar fields playing the roles of those two types of dark energy. In that framework we examine, from a dynamical systems perspective, the possibility that those fields are coupled among them by considering an exponential potential with an interesting functional dependence similar but not identical to others studied before. The model we consider represents a counterexample to the typical behavior of quintom models with exponential potentials because it admits either tracking attractors (w=0$w=0$), or phantom attractors (w<−1$w<-1$).     

Mo6S6 nanowires: structural, mechanical and electronic properties

The properties of nanowires were investigated with ab initio calculations based on the density-functional theory. The molecules build weakly coupled one-dimensional chains, like and Mo₆S_9-xI_x, and the crystals are strongly uniaxial in their mechanical and electronic properties. The calculated moduli of elasticity and resilience along the chain axis are c₁₁ = 320 GPa and E_R = 0.53 GPa, respectively. The electronic band structure and optical conductivity indicate that the crystals are good quasi-one-dimensional conductors. The frequency-dependent complex dielectric tensor ε, calculated in the random-phase approximation, shows a strong Drude peak in ε_∥, i.e., for the electric field polarised parallel to the chain axis, and several peaks related to interband transitions. The electron energy loss spectrum is weakly anisotropic and has a strong peak at the plasma frequency ħω_p ≈20 eV. The stability analysis shows that is metastable against the formation of the layered .     

Observation of a new surface state on4He crystal interfaces

The equilibrium shape ofhcp ⁴He crystals has been studied at temperatures 0.05≤T≤0.7 K by means of a high precision optical interferometer. We find that the profile of the interfacial boundary, close to an almost horizontal c-facet, has a well-defined slope discontinuity separating two angular regions with different behavior of the surface stiffness. For surfaces tilted by an angle ϕ≤100 μrad with respect to the c-facet, we obtain, contrary to the linear angular dependence predicted by current theories.     

Experimental observation of strange nonchaotic attractors in a driven excitable system

We report the observation of strange nonchaotic attractors in an electrochemical cell. The system parameters were chosen such that the system observable (anodic current) exhibits fixed point behavior or period one oscillations. These autonomous dynamics were thereafter subjected to external quasiperiodic forcing. Systematically varying the characteristics (frequency and amplitude) of the superimposed external signal; quasiperiodic, chaotic and strange nonchaotic behaviors in the anodic current were generated. The inception of strange nonchaotic attractors was verified using standard diagnostic techniques.     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Kauffman Cellular Automata on Quasicrystal Topology

In this paper, we perform numerical simulations to study Kauffman cellular automata (KCA) on quasiperiod lattices. In particular, we investigate phase transition, magnetic entropy, and propagation speed of the damage on these lattices. Both the critical threshold parameter \(p_{c}\) and the critical exponents are estimated with good precision. In order to investigate the increase of statistical fluctuations and the onset of chaos in the critical region of the model, we have also defined a magnetic entropy to these systems. It is seen that the magnetic entropy behaves in a different way when one passes from the frozen regime (p < p_c) to the chaotic regime (p > p_c). For a further analysis, the robustness of the propagation of failures is checked by introducing a quenched site dilution probability q on the lattices. It is seen that the damage spreading is quite sensitive when a small fraction of the lattice sites are disconnected. A finite-size scaling analysis is employed to estimate the critical exponents. From these numerical estimates, we claim that on both pure (q =?0) and diluted (q =?0.05) quasiperiodic lattices, the KCA model belongs to the same universality class than on square lattices. Furthermore, with the aim of comparing the dynamical behavior between periodic and quasiperiodic systems, the propagation speed of the damage is also calculated for the square lattice assuming the same conditions. It is found that on square lattices the propagation speed of the damage obeys a power law as \(v\sim (p-p_{c})^{\alpha }\), whereas on quasiperiod lattices, it follows a logarithmic law as \(v \sim \ln (p-p_{c})^{\alpha }\).     

Escape of Brownian particles in an asymmetric bistable sawtooth potential driven by cross-correlated noises

The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change. Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: kmdcmei@public.km.yn.cn     

Future developments of INFN-LNL nuclear beam facilities

The accelerator group at INFN-LNL has been mostly engaged, recently, in completing and commissioning the higher current injector of the linac booster ALPI (named PIAVE) and in constructing and assembling the front-end part of a high current driver linac for the RNB facility SPES. PIAVE, designed to accelerate ions with A/Q = < 8.5 up to 1.2 MeV/u, is now completed. The injector has been commissioned with O, Ar, Ne and Xe beams. Neon and argon beams have been delivered to experiments for a total of about 400 hours. A consolidation program of PIAVE and ALPI is planned, so as to deliver a larger variety of beams with a current range  pnA and with an energy exceeding the Coulomb barrier in relevant nuclear reaction cases. The RNB facility SPES, allowing a frontier program in RNB physics, is being designed and prototyped: beams of neutron rich medium-to-heavy mass nuclei will be produced inducing ²³⁸U fission with a 40 MeV 200μA proton beam impinging onto a multi-slice direct target. A further development of ALPI will make it best suitable for the re-acceleration of radioactive nuclear species, after charge breeding and isotope selection.     

Quasiperiodic Solutions for Dissipative Boussinesq Systems

In this paper we analyze the behavior of the solution of the dissipative Boussinesq systems