Analysis of Spontaneous Electrochemical Oscillations by the Wavelet Transformation Method

A new way of analyzing current oscillations that accompany anodic metal dissolution is presented. A wavelet transformation is used for separation and spectral analysis of singular courses—elementary components of electrochemical oscillation recordings. A method of obtaining oscillation energy distribution analogous to the spectral power density function is presented. It is shown that the chaotic component (Shil'nikov chaos) can be separated from the deterministic component of the described process.     

Quantum chaos and magnetotransport in lateral superlattices: The transition from weak to strong modulation potential

Magnetotransport in lateral superlattices covers a variety of apparently different physics dependent on the amplitude of the modulation potential relative to the Fermi energy ranging from the weakly modulated 2DEG to the antidot lattice. Here we investigate the transition between weak modulation and antidots within the quantum-mechanical theory by studying (i) the single-particle spectrum with respect to quantum signatures of classical chaos and (ii) the change of characteristic features in the magnetoresistance starting from the Kubo formula.     

Working group report: Astroparticle and neutrino physics

The working group on astroparticle and neutrino physics at WHEPP-9 covered a wide range of topics. The main topics were neutrino physics at INO, neutrino astronomy and recent constraints on dark energy coming from cosmological observations of large scale structure and CMB anisotropy.     

Oscillations of the magnetoresistance of a two-dimensional electron gas under microwave irradiation: Influence of the irradiation frequency

We present measurements of the magnetoresistance of a two-dimensional electron gas (2DEG) under continuous microwave as a function of the irradiation frequency. In a previous work by Simovič et al. [Phys. Rev. B 71 (2005) 233303], the magnetoresistance under microwave was shown to be modulated by oscillations of large amplitude that are periodic with magnetic field, their period and phase depending strongly on the electron density. Here we show that the phase and the amplitude of the microwave-induced oscillations also depend on the frequency of irradiation and the sign of the magnetic field.     

A numerical method for acoustic oscillations in tubes

A numerical method to obtain the neutral curve for the onset of acoustic oscillations in a helium-filled tube is described. Such oscillations can cause a serious heat loss in the plumbing associated with liquid helium dewars. The problem is modelled by a second-order, ordinary differential eigenvalue problem for the pressure perturbation. The numerical method to find the eigenvalues and track the resulting points along the neutral curve is tailored to this problem. The results show that a tube with a uniform temperature gradient along it is much more stable than one where the temperature suddenly jumps from the cold to the hot value in the middle of the tube.     

Weak-field magnetoresistance anomaly and Shubnikov–de Haas oscillations in Sn-doped InSb thin films on GaAs (100) substrates

Distinctive magnetoresistance (MR) effects in weak magnetic fields before the appearance of Shubnikov–de Haas (SdH) oscillations at low temperatures in Sn-doped (7×10¹⁶ cm⁻³) InSb films grown on GaAs(100) substrates by MBE have been investigated with decreasing film thickness d from 1 μm. The negative MR found in weak magnetic fields for d0.5 μm can be broadly divided into two regimes: T-sensitive negative MR below B_c observed with anisotropy between parallel and perpendicular magnetic field and a T-insensitive parabolic one above B_c observable only under in-plane magnetic fields. The latter is ascribable to the skipping orbit effect due to surface boundary scattering. In vanishing magnetic fields far below B_c, the negative MR reduces with decreasing d and the different positive MR overlaps with it below 0.5 μm, eventually dominating the positive MR at d0.2 μm. These results have been analyzed using a two-layer model for the films, where the composition of the upper layer under the surface and the lower one adjacent to the InSb/GaAs interface is assumed. The MR data in the extremely weak magnetic fields below 100 G for each layer have been successfully fitted to the two-dimensional (2D) weak localization (WL) theory. These results explain that the crossover from the 2D WL to the weak anti-localization (WAL) occurs when the interface is approached with the increase of SO interaction in the layers caused by the increased influence of the asymmetric potential at the hetero interface (Rashba term) and the SO rate in the intrinsic InSb film due to the crystal field of the zinc-blende structure (Dresselhaus term) is as small as τ_so⁻¹3×10⁸ s⁻¹.     

A regularization method for evolutionary problems in mechanics of visco-plastic media

We study a regularization method for solving the Cauchy problem for parabolic inclusions that arise in the mechanics of visco-plastic media. We also consider some applications of the regularization method to the problem of forced oscillations and prove that the set of solutions to the Cauchy problem is acyclic for the parabolic inclusions under consideration. Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 483–493, October, 1997. Translated by M. A. Shishkova     

On the Chaotic Behavior of a Third-Order Log-Domain Filter

Operation of log-domain filters revolves around the large-signal forward-active mode exponential current-voltage relationship of the bipolar junction transistor, which is used to map the input currents to the logarithmic domain, where the analog processing takes place, and to convert the filtered voltage waveforms back to the linear domain. Sometimes, the inherent internal nonlinearity of such circuits is the cause of unwanted externally-nonlinear effects. In this paper a differential third-order log-domain Chebyshev low-pass filter is designed by applying the method of operational simulation of doubly-terminated LC ladders. When the six grounded shunt capacitors of this filter are properly replaced with three half-sized floating capacitors, as is common practice in internally-linear fully-differential capacitively-loaded circuits, under particular conditions the resulting system exhibits limit-cycle oscillations, period-doubling bifurcations and chaotic behavior for zero-input. The presence of chaos is confirmed by extracting the spectrum of Lyapunov exponents of the system from the time series of the output voltage.     

Boundedness in nonlinear oscillations

In this paper, the boundedness of all solutions of the nonlinear differential equation (φ_p(x′))′ + αφ_p(x⁺) – βφ_p(x^–) + f(x) = e(t) is studied, where φ_p(u) = |u|^p–2 u, p ≥ 2, α, β are positive constants such that = 2w^–1 with w ∈ ?⁺\?, f is a bounded C⁵ function, e(t) ∈ C⁶ is 2π_p‐periodic, x⁺ = max{x, 0}, x^– = max{–x, 0}. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)