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].

Movement-related potentials in Huntington's disease: movement preparation and execution

Movement-related potentials (MRPs) reflect increasing cortical activity related to the preparation and execution of voluntary movement. Execution and preparatory components may be separated by comparing MRPs recorded from actual and imagined movement. Imagined movement initiates preparatory processes, but not motor execution activity. MRPs are maximal over the supplementary motor area (SMA), an area of the cortex involved in the planning and preparation of movement. The SMA receives input from the basal ganglia, which are affected in Huntington's disease (HD), a hyperkinetic movement disorder. In order to further elucidate the effects of the disorder upon the cortical activity relating to movement, MRPs were recorded from ten HD patients, and ten age-matched controls, whilst they performed and imagined performing a sequential button-pressing task. HD patients produced MRPs of significantly reduced size both for performed and imagined movement. The component relating to movement execution was obtained by subtracting the MRP for imagined movement from the MRP for performed movement, and was found to be normal in HD. The movement preparation component was found by subtracting the MRP found for a control condition of watching the visual cues from the MRP for imagined movement. This preparation component in HD was reduced in early slope, peak amplitude, and post-peak slope. This study therefore reported abnormal MRPs in HD. particularly in terms of the components relating to movement preparation, and this finding may further explain the movement deficits reported in the disease.

The preparation and execution of self-initiated and externally-triggered movement: A study of event-related fMRI

Studies of functional brain imaging in humans and single cell recordings in monkeys have generally shown preferential involvement of the medially located supplementary motor area (SMA) in self-initiated movement and the lateral premotor cortex in externally cued movement. Studies of event-related cortical potentials recorded during movement preparation, however, generally show increased cortical activity prior to self-initiated movements but little activity at early stages prior to movements that are externally cued at unpredictable times. In this study, the spatial location and relative timing of activation for self-initiated and externally triggered movements were examined using rapid event-related functional MRI. Twelve healthy right-handed subjects were imaged while performing a brief finger sequence movement (three rapid alternating button presses: index-middle-index finger) made either in response to an unpredictably timed auditory cue (between 8 to 24 s after the previous movement) or at self-paced irregular intervals. Both movement conditions involved similar strong activation of medial motor areas including the pre-SMA, SMA proper, and rostral cingulate cortex, as well as activation within contralateral primary motor, superior parietal, and insula cortex. Activation within the basal ganglia was found for self-initiated movements only, while externally triggered movements involved additional bilateral activation of primary auditory cortex. Although the level of SMA and cingulate cortex activation did not differ significantly between movement conditions, the timing of the hemodynamic response within the pre-SMA was significantly earlier for self-initiated compared with externally triggered movements. This clearly reflects involvement of the pre-SMA in early processes associated with the preparation for voluntary movement. (C) 2002 Elsevier Science.

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.