Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Quasi-chemical treatment of intermediate phases appearing in nonstoichiometric compounds

A quasi-chemical treatment of the superlattice formation model is applied to intermediate phases appearing in nonstoichiometric compounds. Two kinds of interaction energy are introduced and both the intermediate phase and two-phase separation are described in a single formula. The order parameter and the free energy are obtained as a function of temperature and composition. The boundaries of phases are determined by the common-tangent method.     

Synthesis and properties of novel crown ether-annelated 4′,5′-diaza-9′-(1,3-dithiole-2-ylidene)-fluorenes and their ruthenium(II) complexes

Two novel redox-active 1,3-dithiole (DT) ring-fused 4,5-diazafluorene ligands with crown ether moieties (L1 and L2) were synthesized and characterized. The crystal structure of L1 was studied. The electrochemical and spectroscopic properties of these new ligands, as well as the corresponding bis(bipyridine)ruthenium(II) complexes [4: Ru L1(bpy)₂ and 5: Ru L2(bpy)₂], were also been investigated.     

Intermediate phase appearing in nonstoichiometric compounds

Intermediate phases appearing in nonstoichiometric compounds are treated statistically using the model of superlattice formation. The condition for occurrence of the phase, relation between the concentration of defects and order parameter, and width of the phase are obtained. Decreasing of fluctuations of the distributed particles is accompanied characteristically with occurrence of the intermediate phase.     

Random dynamics of the Morris-Lecar neural model

Determining the response characteristics of neurons to fluctuating noise-like inputs similar to realistic stimuli is essential for understanding neuronal coding. This study addresses this issue by providing a random dynamical system analysis of the Morris-Lecar neural model driven by a white Gaussian noise current. Depending on parameter selections, the deterministic Morris-Lecar model can be considered as a canonical prototype for widely encountered classes of neuronal membranes, referred to as class I and class II membranes. In both the transitions from excitable to oscillating regimes are associated with different bifurcation scenarios. This work examines how random perturbations affect these two bifurcation scenarios. It is first numerically shown that the Morris-Lecar model driven by white Gaussian noise current tends to have a unique stationary distribution in the phase space. Numerical evaluations also reveal quantitative and qualitative changes in this distribution in the vicinity of the bifurcations of the deterministic system. However, these changes notwithstanding, our numerical simulations show that the Lyapunov exponents of the system remain negative in these parameter regions, indicating that no dynamical stochastic bifurcations take place. Moreover, our numerical simulations confirm that, regardless of the asymptotic dynamics of the deterministic system, the random Morris-Lecar model stabilizes at a unique stationary stochastic process. In terms of random dynamical system theory, our analysis shows that additive noise destroys the above-mentioned bifurcation sequences that characterize class I and class II regimes in the Morris-Lecar model. The interpretation of this result in terms of neuronal coding is that, despite the differences in the deterministic dynamics of class I and class II membranes, their responses to noise-like stimuli present a reliable feature.     

Comparative Study of the Determination of Parabens in Shampoos by Liquid Chromatography with Amperometric and Coulometric Detection

The simultaneous determination of four para‐hydroxybenzoic acid esters (parabens) in shampoos was studied by liquid chromatography (LC) with amperometric (LC‐AD) and coulometric (LC‐CD) detection. The parabens were separated on an ODS C18 reversed column by isocratic elution with a mobile phase based on methanol‐0.1 M acetic acid (60 : 40%, v/v) with 0.02 M NaClO₄ at a flow rate of 0.8 mL min^?1. The limit of detection (S/N>3) for the analytes was in the 15–25 pg (injected mass) range at an applied potential of 1.20 V vs. Ag/AgCl using the LC‐AD and in the 2–3 pg range at a potential of 0.790 V vs. Pd using the LC‐CD. The peak ratio of the internal standard peak (IS: 4‐hydroxybenzoic acid sec‐butyl ester) versus the analyte peak was found to be related to the amount injected from 0.1 ng to 100ng (r=0.996–0.999) with the LC‐AD and from 0.050 ng to 100 ng range (r=0.999–1.000) with the LC‐CD. The relative standard deviation (RSD, n=10) was comprised between 1.8 to 3.5% by LC‐AD ( 5 ng injected) and between 2.0 to 2.4% by LC‐CD (0.5 ng injected). The determination of four most used parabens in ten different shampoos was successfully realized.     

Biradical character of linear π-conjugated oligomer dications composed of thiophene, pyrrole, and methylthio end-capping units

Combined DFT calculations and UV-vis-NIR, ESR, and SQUID measurements revealed that the ground-state electronic structure of a linear π-conjugated oligomer dication composed of two pyrrole and six or seven thiophene rings and methylthio end-capping units is dominated by a singlet biradical character.     

New Criteria for Self-Adjointness and its Application to Dirac–Maxwell Hamiltonian

We present a new theorem concerning a sufficient condition for a symmetric operator acting in a complex Hilbert space to be essentially self-adjoint. By applying the theorem, we prove that the Dirac–Maxwell Hamiltonian, which describes a quantum system of a Dirac particle and a radiation field minimally interacting with each other, is essentially self-adjoint. Our theorem covers the case where the Dirac particle is in the Coulomb-type potential.     

A note on stochastic phase lockings in a relaxation oscillator forced by a sine input with additive noise

Summary Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. Using the probability density functions of the first-passage time, the operator which governs a transition of an input phase density after one cycle of the oscillator is defined. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.