Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

Experimentally tracking unstable steady states by large periodic modulation

Experimental suppression of chaos has been achieved in an optically pumped far-infrared (NH3)-N-15 laser which displays Lorenz-like chaos. The method of control involves the application of a large amplitude slow (i.e., nonresonant) modulation of the pump power. This may be related to a delayed bifurcation to chaos observed when the pump power is ramped at a constant late.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Periodic orbit resonances in layered metals in tilted magnetic fields

The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field that is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur when the frequency is a harmonic of the frequency at which the magnetic field causes the electrons to oscillate on the Fermi surface within the layers. The intensity of the different harmonic resonances varies significantly with the direction of the field. The resonances occur for both coherent and weakly incoherent interlayer transport and so their observation does not imply the existence of a three-dimensional Fermi surface. [S0163-1829(99)51240-X].

Periodic electric field enhanced transport through membranes

We examine the mean flux across a homogeneous membrane of a charged tracer subject to an alternating, symmetric voltage waveform. The analysis is based on the Nernst-Planck flux equation, with electric field subject to time dependence only. For low frequency electric fields the quasi steady-state flux can be approximated using the Goldman model, which has exact analytical solutions for tracer concentration and flux. No such closed form solutions can be found for arbitrary frequencies, however we find approximations for high frequency. An approximation formula for the average flux at all frequencies is also obtained from the two limiting approximations. Numerical integration of the governing equation is accomplished by use of the numerical method of lines and is performed for four different voltage waveforms. For the different voltage profiles, comparisons are made with the approximate analytical solutions which demonstrates their applicability. (c) 2005 Elsevier B.V. All rights reserved.

A continuum model for periodic two-dimensional block structures

A continuum model for regular block structures is derived by replacing the difference quotients of the discrete equations by corresponding differential quotients. The homogenization procedure leads to an anisotropic Cosserat Continuum. For elastic block interactions the dispersion relations of the discrete and the continuous models are derived and compared. Yield criteria for block tilting and sliding are formulated. An extension of the theory for large deformation is proposed. (C) 1997 by John Wiley & Sons, Ltd.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high T-c cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu3O8+delta, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high T-c cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high T-c cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.

Recent advances in processing and characterization of periodic mesoporous MCM-41 silicate molecular sieves

The discovery of periodic mesoporous MCM-41 and related molecular sieves has attracted significant attention from a fundamental as well as applied perspective. They possess well-defined cylindrical/hexagonal mesopores with a simple geometry, tailored pore size, and reproducible surface properties. Hence, there is an ever-growing scientific interest in the challenges posed by their processing and characterization and by the refinement of various sorption models. Further, MCM-41-based materials are currently under intense investigation with respect to their utility as adsorbents, catalysts, supports, ion-exchangers, and molecular hosts. In this article, we provide a critical review of the developments in these areas with particular emphasis on adsorption characteristics, progress in controlling the pore sizes, and a comparison of pore size distributions using traditional and newer models. The model proposed by the authors for adsorption isotherms and criticalities in capillary condensation and hysteresis is found to explain unusual adsorption behavior in these materials while providing a convenient characterization tool.

Transforming chaos to periodic oscillations

We demonstrate that the dynamics of an autonomous chaotic class C laser can be controlled to a periodic state via external modulation of the pump. In the absence of modulation, above the chaos threshold, the laser exhibits Lorenz-like chaotic pulsations. The average amplitude and frequency of these pulsations depend on the pump power. We find that there exist parameter windows where modulation of the pump power extinguishes the chaos in favor of simpler periodic behavior. Moreover we find a number of locking ratios between the pump and laser output follow the Farey sequence.

Dynamics of a mesoscopic charge quantum bit under continuous quantum measurement

We present the conditional quantum dynamics of an electron tunneling between two quantum dots subject to a measurement using a low transparency point contact or tunnel junction. The double dot system forms a single qubit and the measurement corresponds to a continuous in time readout of the occupancy of the quantum dot. We illustrate the difference between conditional and unconditional dynamics of the qubit. The conditional dynamics is discussed in two regimes depending on the rate of tunneling through the point contact: quantum jumps, in which individual electron tunneling current events can be distinguished, and a diffusive dynamics in which individual events are ignored, and the time-averaged current is considered as a continuous diffusive variable. We include the effect of inefficient measurement and the influence of the relative phase between the two tunneling amplitudes of the double dot/point contact system.

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

Suitability of acoustic perturbation measures in analysing periodic and nearly periodic voice signals

In recent years, acoustic perturbation measurement has gained clinical and research popularity due to the ease of availability of commercial acoustic analysing software packages in the market. However, because the measurement itself depends critically on the accuracy of frequency tracking from the voice signal, researchers argue that perturbation measures are not suitable for analysing dysphonic voice samples, which are aperiodic in nature. This study compares the fundamental frequency, relative amplitude perturbation, shimmer percent and noise-to-harmonic ratio between a group of dysphonic and non-dysphonic subjects. One hundred and twelve dysphonic subjects ( 93 females and 19 males) and 41 non-dysphonic subjects ( 35 females and 6 males) participated in the study. All the 153 voice samples were categorized into type I ( periodic or nearly periodic), type II ( signals with subharmonic frequencies that approach the fundamental frequency) and type III ( aperiodic) signals. Only the type I ( periodic and nearly periodic) voice signals were acoustically analysed for perturbation measures. Results revealed that the dysphonic female group presented significantly lower fundamental frequency, significantly higher relative amplitude perturbation and shimmer percent values than the non-dysphonic female group. However, none of these three perturbation measures were able to differentiate between male dysphonic and male non-dysphonic subjects. The noise-to-harmonic ratio failed to differentiate between the dysphonic and non-dysphonic voices for both gender groups. These results question the sensitivity of acoustic perturbation measures in detecting dysphonia and suggest that contemporary acoustic perturbation measures are not suitable for analysing dysphonic voice signals, which are even nearly periodic. Copyright (C) 2005 S. Karger AG, Basel.