Search

A simple and instantaneous phase definition is proposed for the study of discrete maps by taking the change of chaotic signal at each iteration time as a vector. With such a definition, an exact phase can be calculated at any iteration time for any scalar signal or two-dimensional vector of interest. As examples, the phase synchronization behavior is discussed for a two-dimensional globally coupled map lattice and a one-way coupled map lattice.

We show that two identical fully connected chaotic neural networks can always achieve a stochastic synchronization state when linked with a sufficiently large common noise. This is the case for both low-dimensional hyperchaos and high-dimensional spatiotemporal chaos. When the parameters of the two driven systems possess a tiny difference, weakly noise-induced synchronization is obtained. Unstable finite-precision synchronization of chaos with positive conditional Lyapunov exponent is also observed. It is caused by the on-off synchronizing intermittent dynamics.

In this study, effects of microstructure on the viscous permeability and Forchheimer coefficient of monodispersed fibers are investigated. The porous material is represented by a unit cell which is assumed to be repeated throughout the medium. Based on the orientation of the fibers in the space, fibrous media are divided into three categories: one-, two-, and three-directional (1D, 2D, and 3D) structures. Parallel and transverse flow through square arrangements of 1D fibers, simple 2D mats, and 3D simple cubic structures are solved numerically over a wide range of porosity (0.35ε0.95) and Reynolds number (0.01Re200). The results are used to calculate the permeability and the inertial coefficient of the considered geometries. An experimental study is performed; the flow coefficients of three different ordered tube banks in the moderate range of Reynolds number (0.001Re15) are determined. The numerical results are successfully compared with the present and the existing experimental data in the literature. The results suggest that the permeability and Forchheimer coefficient are functions of porosity and fiber orientation. A comparison of the experimental and numerical results with the Ergun equation reveals that this equation is not suitable for highly porous materials. As such, accurate correlations are proposed for determining the Forchheimer coefficient in fibrous porous media.

The temperature dependence of the thermoelectric power of the high-temperature superconductor ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ is reported. The contribution of holes from the valence band satisfying a Fermi-liquid model gives the major part of the measured thermoelectric power. The results show that the conduction-band electrons also contribute to the total output of the thermoelectric power and the portion of the electron's contribution increases with temperature. An explicit expression for the thermolectric power of the 2:2:2:3 phase was derived based on a two-band model and the experimental data, which is given as S(\ensuremath{\mu}V)=0.121T-(280-0.2T)${\mathit{e}}^{\mathrm{\ensuremath{-}}550/\mathit{T}}$. A general formula, S=AT+(B\ensuremath{\lambda}+CT)exp(-\ensuremath{\lambda}/T), is found to give a close description of the thermoelectric power of various cuprate high-${\mathit{T}}_{\mathit{c}}$ superconductors.

In a previous work [K. W. Wong, P. C. W. Fung, H. Y. Yeung, and W. Y.Kwok, Phys. Rev. B 45, 13017 (1992)] we carried out a detailed numerical analysis of the oxygen isotope effect on the La-doped Y-Ba-Cu-O system using the excitonic-enhancement model (EEM). Following up such work, we present here another numerical analysis of the effects of oxygen deficiency on the superconductivity of the YBa 2 Cu 3 O 7-δ ceramic based on experimental data and the EEM

The excitonic-enhancement model (EEM) is based on the simultaneous excitonic and «generalized» Cooper-pair condensation of a charge-unbalanced system that is described by a two-band model consisting of a valence and a conduction band separated by a band gap G. A detailed numerical analysis of the consequences of the EEM with respect to shift of T c due to the oxygen isotope erect on the La-doped Y-Ba-Cu-O system is carried out

Results of site-specific and orbital-resolved partial density of states of YBa{sub 2}Cu{sub 3}O{sub 7} obtained from a first-principles self-consistent calculation using the orthogonalized linear combination of atomic orbitals method are presented. Special features in the bonding of the apical oxygen, O(4) are emphasized. The usefulness of these results in the interpretation of some experimental data is discussed.

The two-dimensional hydrogen problem is solved analytically. In the nonrelativistic case, exact formulas for energy eigenvalues and eigenfunctions for both the discrete and continuous parts of the spectrum, dipole matrix elements, dc Stark effect, single- and two-photon transition rates, and fine and hyperfine structures are obtained. Comparison is made between the two- and the three-dimensional cases. Some interesting aspects of the solution unique to the two-dimensional case are discussed.

We have recently proposed a simple method to create a strange nonchaotic attractor with any chaotic system @Phys. Rev. E 59, 5338 ~1999!#. Such a system is controlled to switch periodically between a chaotic and a quasiperiodic attractor, each with an appropriate time duration. A topological condition for this approach is pointed out in the preceding Comment by Neumann and Pikovsky @Phys. Rev. E 64, 058201 ~2001!#. We show that this condition is not necessary if the durations are sufficiently long. Our approach is a general method to construct a strange nonchaotic attractor in any chaotic system.

We have studied phase synchronization between two identical Rössler oscillators connected in the drive-response configuration by a single phase signal. Before the transition to phase synchronization, the distribution of the time interval between consecutive 2pi jumps shows several sharp peaks. With a strong phase signal coupling, the n:m phase synchronization between the oscillators can be achieved. For the n (not equal) m phase synchronizing state, some values of coupling strength result in a phenomenon characterized by a reduction in the mean amplitude of the response termed amplitude reduction. In these regions, the mean rotation speed of the response remains approximately constant while the locking ratio n:m varies.

Using the equation-of-motion method we derive, based on the pair approximation (Hartree-Fock (HF), BCS) of the hard-sphere model for superfluid He, the Bogoliubov equation for the superfluid phase. At the temperature T = T/sub lambda/ the off-diagonal pairing factor (BCS) has to vanish, and the excitation energy must become that of the HF solution. This condition yields a transition temperature T/sub lambda/ = 2.3 degreeK. The superfluid density rho/sub S/ as a function of temperature is also investigated. Furthermore assuming the net translational kinetic energy of the liquid to be E/sub T/ = (1/2) ..cap omega.. (rho/sub S/V/sub S//sup 2/ + rho/sub N/V/sub N//sup 2/) we investigate the response of our system to the corresponding perturbation H/sub I/. We calculate the persistent current components and which exhibits the right behavior for T ..-->.. 0 and T ..-->.. T/sub lambda/.

The band structures of cubic ${\mathrm{Cu}}_{2}$O and monoclinic CuO crystals have been calculated by means of the first-principles orthogonalized linear combination of atomic orbitals method. Using the wave functions obtained, the frequency-dependent interband optical conductivities are also evaluated. The results show ${\mathrm{Cu}}_{2}$O to be a direct-gap semiconductor, while CuO is semiconductorlike with an intrinsic hole population at the top of the valence band (VB). By comparing with a variety of existing data, we conclude that band theory works extremely well for ${\mathrm{Cu}}_{2}$O, but is less satisfactory for CuO. This could be due to strong correlation effects for states near the top of the VB in CuO. A careful reanalysis of optical data and excitonic spectra in ${\mathrm{Cu}}_{2}$O in conjunction with our calculations suggests a complete reinterpretation of these data. A clear distinction between the intrinsic gap and the optical gap is argued. We conclude that the intrinsic gap in ${\mathrm{Cu}}_{2}$O is of the order of 0.8 eV, while the optical gap is of the order 2.0--2.3 eV. The excitonic series in ${\mathrm{Cu}}_{2}$O is due to the Coulombic attraction of the hole at the top of the VB and the electron in the next-higher conduction band (CB), not the lowest CB, because of the forbidden symmetry associated with angular-momentum conservation. This reinterpretation of the excitonic data is also consistent with a calculated low value for the static dielectric constant ${\ensuremath{\epsilon}}_{0}$ of order of 4 for ${\mathrm{Cu}}_{2}$O.

The optical properties of orthorhombic Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ crystal are studied by a first-principles method. The interband optical conductivity shows strong directional anisotropy in the 0-3.0 eV range. A plasmon energy of 2.8 eV is predicted. Analysis of the static dielectric constant in the case of a semiconductorlike band structure supports the excitonic-enhanced superconducting mechanism in the Y-Ba-Cu-O system.

The basic goal of this paper is to present the theory which stands at the basis of the calculations of the /sup 4/He excitation spectrum reported by Wong and Huang. The exact N-particle hard-sphere pseudopotential is constructed through the method of non-local-field operators developed earlier. Keeping only the two-body interaction terms, this pseudopotential replaces the exact two-particle boundary conditions which is demonstrated here and thus has been proposed as a model potential for actual helium-helium interaction in the liquid state. A pair state of the Bogoliubov type is used to calculate the ground-state energy of such a system. An expansion-parameter scheme is presented which drastically simplifies the mathematics involved and justifies previous approximations employed by one of the authors. The expansion describes the dilute case by assuming a large portion of the particles in the zero-momentum state and the dense case by assuming only a negligible portion of the particles in the Bose-Einstein state.

The excitation spectrum of a Bose system of hard spheres is obtained in a high-density calculation including multiple scattering processes. The hard-sphere interaction is represented by a non-Hermitian pseudopotential constructed in a previous work, and the $T$-matrix method of Brueckner and Sawada is adopted with modifications to take into account the non-Hermitian property of the Hamiltonian. The inclusion of multiple scattering is found essentially to give a screening effect to the two-body interaction in a many-body medium. The screening factor is studied within certain approximations and is shown to play a very important role in determining the shape of the excitation spectrum. The effect of depletion of particles from the zero-momentum state due to particle interaction is also included in a self-consistent way and is found to be very small. The calculated spectrum is then applied to liquid helium and there is a good qualitative agreement with experiments. Especially, a roton-type dip exists in the spectrum.

A generalized pseudopotential for hard-sphere interaction is obtained, which is valid for all angular-momentum states. This pseudopotential is then used in the evaluation of both the ground-state energy and the excitation spectrum for a dilute Bose system of hard spheres. The calculated ground-state energy agrees with that obtained by other authors; the excitation spectrum obtained for liquid helium resembles the phonon-roton spectrum introduced by Landau.

Utilizing a roton-roton interaction derived from a hard-sphere model for superfluid helium we obtained a qualitatively correct temperature dependence to the correction of the transition temperature ${T}_{\ensuremath{\lambda}}$ due to roton-roton interaction as compared to that calculated without such roton-roton interaction.