International Journal of Modern Physics B

Hysteresis is a common phenomenon in a type of nonlinear waves. Corresponding to the negative tangential branch of a hysteretic curve the steady wave solutions are unstable due to saddle instability; such a saddle steady wave (SSW) is a moving saddle point in the system. In a model system based on a nonintegrable equation derived in fluid and plasma physics, a clear connection is found between turbulent solutions and the appearance of hystereses. A physical cause underlying this phenomenon is the embedded saddle point. In this review paper we focus on a senario of strong turbulent motion that is related to the saddle point. It is shown that in the reference frame moving with the SSW the nonlinear wave can be transformed into a set of coupled oscillators for which the SSW provides a potential; when the orbit of the oscillators collides with the saddle point a crisis onsets; subsequently occurs another critical event during which the master oscillator gets free from the trapping of the potential, inducing a transition to spatiotemporal chaos. The turbulent state after the transition is actually a special kind of self-organized motion characteristic by on-off imperfect phase synchronization among these oscillators.

We revisit the problem of the electronic properties of a single strand of DNA, formulating the Hückel approximation for π-electrons in both the sugar-phosphate backbone chain and the π-stacking of nitrogenous bases in a single strand of DNA where the nitrogenous bases are adenine (A), guanine (G), cytosine (C) and thymine (T), respectively. We calculate the electronic band structure of π-electrons: (i) in the single nitrogenous base molecules such as A, G, C and T, (ii) in the single sugar-phosphate molecule, (iii) in the single nucleotide systems such as A, G, C, T with the single sugar-phosphate group, and (iv) in the system of a single strand of DNA with an infinite repetition of a nucleotide such as A, G, C and T, respectively. We find the following: In the case of (i), there is an energy gap between the energy levels for the HOMO and LUMO in the nitrogenous base. This guarantees the semiconducting character of the bases as a mother material. In the case of (ii), there are the HOMO localized at the oxygen site with a double bond and the LUMO localized around the phosphorus atom, which have a quite large energy gap. In the case of (iii), the energy levels for the HOMO and LUMO of the nitrogenous base remain almost the same as those of the nucleotide, while those of the sugar-phosphate group remain the same as well. The HOMO of the sugar-phosphate group exists right below the HOMO of the nitrogenous base. Therefore, comparing the energy levels for the HOMOs of the nitrogenous base group with those of the sugar-phosphate group, the nitrogenous base group behaves as a donor while the sugar-phosphate group behaves as an acceptor. In the case of (iv), there are energy bands and band gaps for the extended states in the nitrogenous base group and the sugar-phosphate group as well as the discrete levels for the localized states at the phosphate site in the spectrum. There is a transition from semiconductor to semimetal as the π-electron hopping between the nitrogenous bases of nucleotide is increased. The details of the above will be discussed in the present paper. Thus, we show the powerfulness of the Hückel theory in the study of DNA as well, although this theory is, at the first glance, oversimplified and purely phenomenological.

We investigate inverse retarded synchronization between two uni-directionally linearly coupled chaotic non-identical Ikeda models and show that parameter mismatches are of crucial importance to achieve synchronization. We establish that independent of the relation between the delay time in the coupled systems and the coupling delay time, only inverse retarded synchronization with the coupling delay time is obtained. We derive existence and stability conditions for the inverse retarded synchronization manifold. We show that with parameter mismatch or without it neither inverse complete nor inverse anticipating synchronization occurs. Numerical simulations fully support the analytical approach.

We propose the use of a self-oscillating dynamical system — the pre-Galileian clock equation — for modeling the laryngeal tone. The parameters are shown to be the minimal control needed for generating the prosody of the human speech. Based on this model, we outline a peak delay detection algorithm for extracting the prosody of the real speech.

Temperature dependence of the critical current density j_c(T) for the superconducting magnesium diboride MgB₂ is studied in the vicinity of T_c by using a two-band Ginzburg–Landau (G–L) theory. The result is in good agreement with experimental data for a bulk MgB₂. Comparision of obtained results with single-band GL theory are presented.

We present a density functional theory (DFT) calculation in the generalized gradient approximation to study the possibility for the existence of Jahn–Teller (JT) or pseudo Jahn–Teller (PJT) type local distortions in the La–Ba–Cu–O superconducting system. We performed the calculation and correspondingly group theory classification of the electronic ground state of the CuO₆^-10 elongated octahedra cluster, immersed in a background simulating the superconductor. Part of the motivation to do this study is that the origin of the apical deformation of the CuO₆^-10 cluster is not due to a pure JT effect, having therefore a non a priori condition to remove the degeneracy of the electronic ground state of the parent regular octahedron. We present a comparative analysis of the symmetry classified electron spectrum with previously reported results using unrestricted Hartree–Fock calculations (UHF). Both the DFT and UHF calculations produced a non-degenerate electronic ground state, not having therefore the necessary condition for a pure JT effect. However, the appearance of a degenerate E_g state near to the highest occupied molecular orbital in the DFT calculation, suggests the possibility for a PJT effect responsible for a local distortion of the oxidized cluster.