Duality in Two Capacitively Coupled Layered Arrays of Ultrasmall Josephson Junctions

We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on its physical parameter values. The former case is dominated by a Cooper-pair superfluid, while the quantum case is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and mean-field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one is in the quantum-fluctuations-dominated regime, we derive a duality transformation between the charge and vortex-dominated arrays that involves a gauge vector field which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.     

Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations

The relation between the parameters of a differential equation and corresponding discrete maps is becoming increasingly important in the study of nonlinear dynamical systems. Maps are well adopted for numerical computation and several universal properties of them are known. Therefore some perturbation methods have been proposed to deduce them for physical systems, which can be modeled by an ordinary differential equation (ODE) with a small nonlinearity. An iterative, rigorous algebraic method for the calculation of the coefficients of a Taylor expansion of a stroboscopic map from ODEs with not necessarily small nonlinearities is presented. It is shown analytically that most of the coefficients are small for a small integration time and grow slowly in the course of time if the flow vector field of the ODE is a polynomial in the state variables and if the ODE has a fixed point at the origin. For several nonlinear systems approximations of different orders are investigated.     

Efficient solution-processed bulk heterojunction solar cells by antiparallel supramolecular arrangement of dipolar donor-acceptor dyes

A series of dipolar donor–acceptor (D –A) chromophores with aminothiophene donor and different heterocyclic acceptor units is reported. By modulation of the acceptor strength, absorption bands over the whole visible spectrum are accessible as well as adjustment of the frontier molecular orbital levels. The performance of the chromophores in blends with fullerene acceptors in solution‐processed bulk heterojunction solar cells was studied and related to the molecular properties of the dyes. In particular, the effect of the large ground‐state dipole moments of these dyes was investigated by single crystal X‐ray analysis, which revealed antiparallel dimers, resulting in an annihilation of the dipole moments. This specific feature of supramolecular organization explains the excellent performance of merocyanine dyes in organic solar cells. With blends of HB366 :PC₇₁BM, the most efficient solar cell with a V_OC of 1.0 V, a J_SC of 10.2 mA cm^?2, and a power‐conversion efficiency of 4.5 % was achieved under standard AM1.5, 100 mW cm^?2 conditions. Under reduced lighting conditions, even higher efficiencies up to 5.1 % was obtained.     

Electrochemical and optical characterization of triarylamine functionalized gold nanoparticles

This paper describes the synthesis, structural analysis, and investigations of the optical and electrochemical properties of some gold nanoparticles (AuNPs) which consist of a triarylamine ligand shell attached to small gold cores (Au-Tara). The triarylamine chromophores were attached to small 4-bromobenzenethiol covered gold nanoparticles (ca. 2 nm in diameter) by Sonogashira reaction. This procedure yields triarylamine redox centers attached via π-conjugated bridging units of different length to the gold core. The AuNPs were analyzed with (1)H NMR spectroscopy, diffusion ordered NMR spectroscopy (DOSY), thermogravimetric analysis (TGA), and scanning transmission electron microscopy (STEM). Cyclic voltammetry (CV) technique was used to determine the composition of the redox active particles via the Randles-Sevcik equation. The optical and electrochemical properties of the Au-Tara nanoparticles and of their corresponding unbound ligands (Ref) were investigated with UV/vis/NIR absorption spectroscopy, Osteryoung square wave voltammetry (OSWV), and spectroelectrochemistry (SEC). These data show that the assembling of triarylamines in the vicinity of a gold nanoparticle can change the optical and electrochemical properties of the triarylamine redox chromophores depending on the kind and length of the bridging unit. This is due to gold core-chromophore and chromophore-chromophore interactions.     

Quasi-stationary chaotic states in multi-dimensional Hamiltonian systems

We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-β) oscillator chains with different boundary conditions and numbers of particles and a microplasma of identical ions confined in a Penning trap and repelled by mutual Coulomb interactions. For the FPU systems we show that, when chaos is limited within “small size” phase space regions, statistical distributions of sums of chaotic variables are well approximated for surprisingly long times (typically up to t≈10⁶) by a q-Gaussian (1<q<3) distribution and tend to a Gaussian (q=1) for longer times, as the orbits eventually enter into “large size” chaotic domains. However, in agreement with other studies, we find in certain cases that the q-Gaussian is not the only possible distribution that can fit the data, as our sums may be better approximated by a different so-called “crossover” function attributed to finite-size effects. In the case of the microplasma Hamiltonian, we make use of these q-Gaussian distributions to identify two energy regimes of “weak chaos”—one where the system melts and one where it transforms from liquid to a gas state-by observing where the q-index of the distribution increases significantly above the q=1 value of strong chaos.     

Biaxial nematic phase in model bent-core systems

We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.     

Parameter dependence of stochastic resonance in the stochastic Hodgkin-Huxley neuron

Recently, the phenomena of stochastic resonance (SR) have attracted much attention in the studies of the excitable systems under inherent noise, in particular, nervous systems. We study SR in a stochastic Hodgkin-Huxley neuron under Ornstein-Uhlenbeck noise and periodic stimulus, focusing on the dependence of properties of SR on stimulus parameters. We find that the dependence of the critical forcing amplitude on the frequency of the periodic stimulus shows a bell-shaped structure with a minimum at the stimulus frequency, which is quite different from the monotonous dependence observed in the bistable system at a small frequency range. The frequency dependence of the critical forcing amplitude is explained in connection with the firing onset bifurcation curve of the Hodgkin-Huxley neuron in the deterministic situation. The optimal noise intensity for maximal amplification is also found to show a similar structure.