Steady states in the twin-well potential oscillator: Computer simulations and approximate analytical studies

The paper is focused on the phenomena of various steady-state oscillations exhibited by the twin-well potential system. Regions of existence of different attractors in the system parameter domain are examined and a picture book of different steady states for fixed damping and forcing is presented: 20 different combinations of single or coexisting, small orbit or large orbit, periodic and chaotic attractors are displayed. Computer simulations are followed by an approximate analytical analysis: A study of various forms of instability of periodic solutions gives close form approximate criteria for occurrence of T-periodic small orbit and large orbit oscillations, and for cross-well chaos.     

Structural properties of transparent Ti-V oxide semiconductor thin films

Transparent oxide semiconducting thin films based on mixed Ti-V oxides were prepared using a modified reactive magnetron sputtering method. Based on structural investigations performed with the help of x-ray diffraction and transmission electron microscopy analysis, two distinct regions in the prepared thin film have been observed: a nanocrystalline TiO₂-V₂O₃-V₂O₅ mixed composition, and a thin layer consisting of amorphous phase and nanocystalline TiO₂ phase deposited directly at the substrate. Optical measurements show excellent transmission in the visible spectral range of 73%, on average. Resistivity of the thin film was found at the order of 10⁵ Ω cm at room temperature. The preparation of mixed Ti-V oxides provides a combination of high transparency and semiconducting properties.     

An analysis of mean life and lifetime of unstable elementary particles

A theoretical analysis of the concept of lifetime and mean life of unstable elementary particles is presented. New analytic formulas for lifetime and mean life as a function of decay width and the mass of unstable particle are derived for Breit-Wigner and Matthews-Salam energy distributions. It is demonstrated that, for unstable particles with a larger width or decay energy threshold, the deviation from the generally accepted mean life ^m = ^–1 is significant. The behavior of the decay law P(t) for small times is analyzed, and it is shown that the Breit-Wigner distribution violates the condition P(t = 0) = 0, whereas the Matthews-Salam distribution satisfies it.     

The Weierstrass–Mandelbrot Process Revisited

We derive a functional central limit theorem for quasi-Gaussian processes. In particular, we prove that the limit of the Mandelbrot–Weierstrass process is a complex fractional Brownian motion.     

De Sitter Quasigroups

The Cayley–Klein parameters for the de Sitter groups SO(4, 1) and SO(3, 2) are introduced, and in an extension of the earlier investigation of quasigroups connected with Clifford groups, quasigroups connected with the SO(4, 1) and SO(3, 2) groups are determined. It is shown that these quasigroups have eight-dimensional, double-valued irreducible cracovian representations. The covariance of a five-dimensional form of the Dirac equation with respect to the quasi-rotations forming quasigroups connected with the groups SO(4, 1) and SO(3, 2) is demonstrated. An analogy is drawn between Weyl's hidden symmetry group and a quasigroup.     

Optical and microstructural properties of self-assembled InAs quantum structures in silicon

The InAs quantum structures were formed in silicon by sequential ion implantation and subsequent thermal annealing. Two kinds of crystalline InAs nanostructures were successfully synthesized: nanodots (NDs) and nanopyramids (NPs). The peaks at 215 and 235 cm^?1, corresponding to the transverse optical (TO) and longitudinal optical (LO) InAs single-phonon modes, respectively, are clearly visible in the Raman spectra. Moreover, the PL band at around 1.3 µm, due to light emission from InAs NDs with an average diameter 7±2 nm, was observed. The InAs NPs were found only in samples annealed for 20 ms at temperatures ranging from 1000 up to 1200°C. The crystallinity and pyramidal shape of InAs quantum structures were confirmed by HRTEM and XRD techniques. The average size of the NPs is 50 nm base and 50 nm height, and they are oriented parallel to the Si (001) planes. The lattice parameter of the NPs increases from 6.051 to 6.055 Å with the annealing temperature increasing from 1100 to 1200°C, due to lattice relaxation. Energy dispersive spectroscopy (EDS) shows almost stoichiometric composition of the InAs NPs.     

Oxidation of nickel studied by UV and X-ray photoelectron spectroscopy

The nature of argon-ion bombarded nickel surfaces (polycrystalline, and (111), (110) and (100) single crystals) and their subsequent interaction with oxygen at ordinary temperatures have been studied using X-ray and UV photoelectron spectroscopy, including angular variation measurements and the determination of work function changes, in combination in the same apparatus. Variations between the HeI spectra of the four clean substrates were taken to confirm the presence of substantial order within the depth sampled by UPS. The four surfaces exhibited similar but not identical behaviour during oxidation, resembling that reported by other workers from studies of both annealed single crystals and evaporated polycrystalline films. The initial process was deduced to be essentially dissociative chemisorption: no evidence supporting a previous suggestion of associative adsorption at low coverages was found. Oxygen commenced to penetrate below the surface of all samples before oxygen equivalent to a monolayer had been taken up (~10 L exposure) and further substantial uptake followed resulting in the formation of a stable film (~18 Å) of nickel oxide by ~100 L exposure. This oxide layer was not stoichiometric nickel(II) oxide: it was characterized by the presence of two distinct O 1s signals, the relative intensities of which depended on the crystallographic nature of the surface. It is tentatively suggested that the oxygen signal with the higher BE be associated with Ni^III. Comparison of the X-ray and UV spectra suggests that the oxide film is very non-uniform in thickness, some Ni metal remaining very close to the surface.     

High-spin levels in138Ce and140Nd Observed in the (α, 4n γ) reactions

Levels of¹³⁸Ce and¹⁴⁰Nd have been studied using the¹³⁸Ba(α,4nγ)¹³⁸Ce and¹⁴⁰Ce(α, 4nγ)¹⁴⁰Nd reactions. Singleγ-ray spectra,γ-γ coincidence spectra, angular and time distributions with respect to the beam bursts have been measured. A number of higher excited states with excitation energies up to about 5 MeV and with spin value up to 12 are populated in both nuclei. The lower states with spins and parities 7^?, 5^?, 6^? and 10⁺ can be explained by two-quasiparticle neutron configurations of the types (h _11/2 ^?1 ,d _3/2 ^?1 ) 7^? , (h _11/2 ^?1 ,S _1/2 ^?1 ) 5^?, 6^? and (h _11/2 ^?2 ) 10⁺. Several high-spin states observed in¹³⁸Ce and¹⁴⁰Nd can be explained qualitatively as four-quasiparticle states with two-proton-two-neutron configurations. The 3^? state at an energy of 2,137.4 keV is observed in¹³⁸Ce. The evidence for the existence of the low-lying 3^? states in¹⁴⁰Nd at 2,124.0 keV is discussed. Beside the known 9.6 ms (7^?) isomeric state in¹³⁸Ce another state at 3,538.5keV (10⁺) with a half life of about 200 ns has been observed. The observed levels in the¹³⁸Ce and¹⁴⁰Nd nuclei are compared with theoretical predictions using delta force interaction.     

Local convergence of quasi-Newton methods for B-differentiable equations

We study local convergence of quasi-Newton methods for solving systems of nonlinear equations defined by B-differentiable functions. We extend the classical linear and superlinear convergence results for general quasi-Newton methods as well as for Broyden's method. We also show how Broyden's method may be applied to nonlinear complementarity problems and illustrate its computational performance on two small examples.