Domain Wave Research Articles

BIFURCATIONS OF SOLITARY WAVES AND DOMAIN WALL WAVES FOR KdV-LIKE EQUATION WITH HIGHER ORDER NONLINEARITY

Bifurcations of solitary waves and domain wall waves for a KdV-like equation with higher order nonlinearity are studied, by using bifurcation theory of planar dynamical systems. Bifurcation parameter sets are shown. Numbers of solitary waves and domain wall waves are given. Under some parameter conditions, a lot of explicit formulas of solitary wave solutions and domain wall solutions are obtained.

Solar Origin of a Series of Well‐collimated Electron Events

We investigate the solar origin and propagation of a series of well-collimated energetic electron events on 1997 November 28, measured in situ by the Electron, Proton, and Alpha Monitor (EPAM) experiment on the Advanced Composition Explorer (ACE) spacecraft. EPAM measures electrons in the energy range from 40 to 300 keV over a wide range of look directions and with better than 1 minute time resolution. During the events in our study, the particles are strongly collimated along the magnetic field. As such, these near-relativistic (beta = 0.4-0.7) particles tend to be scatter free; their observed arrival at ACE provides a good estimate of the release time back to the Sun. EPAM results are extended to 20 keV using energetic electron data from the Three-Dimensional Plasma Analyzer (3DP) experiment on the Wind spacecraft. We combine these observations with fast imaging of the solar corona in the meter wave domain, provided by the Nancay radioheliograph, and dynamic spectral information from the WAVES experiment on the Wind spacecraft. Together, this complement of observations of solar energetic particle events provides insight into the onset times and sites of particle acceleration in the low corona. The imaging observations at metric radio frequencies show three series of similar events off the west limb of the Sun that extend into interplanetary type III bursts. The third event corresponds only to a strong in situ particle event. During this time period, the coronagraphic observations from the Large Angle and Spectrometric Coronagraph experiment on the Solar and Heliospheric Observatory reveal a dimming and some morphological changes in the vicinity of the injection site, suggesting the opening of the magnetic field. We find that for the strongest event, the onset times for the energetic particles measured at the spacecraft reveal a dispersion in the inferred release times back at the Sun versus energy. The onset times measured for electrons with energies above 60 keV are not compatible with the release time back at the Sun inferred from particles of lower energies. This dispersion can be successfully explained by the radio data: the radio observations reveal two successive energetic electron injections separated by a few minutes. The observations thus show that there is a later release of the particles detected in situ at higher energies and that the origin of the phenomenon is in the low corona.

Origin of single Q charge-density wave domains in chromium

Q-domain configurations in chromium are investigated measuring X-ray diffraction due to charge-density wave satellites at (0 0 1) and (1 1 1) crystal faces. Scanning the reciprocal space around satellites at samples with and without preparation of single Q and making a reflection topography of CDW satellite (0, 0, 2±2 δ) it was possible to show that a (0 0 1) face induces a single- Q state, even without any external anisotropy.

Towards a limited XANES refinement in strongly correlated systems.

Three components of O1 atom displacements have been derived from the direct fit of the polarized Ellab Cu K-edge XANES spectrum of Nd(1.85)Ce(0.15)CUO(4-delta) superconductor. The best fit is achieved for a 60 to 40% mixture of 2x2 undistorted antiferromagnetic and modified charge density wave (MCDW) domains. The local structure of the MSDW is characterized by correlated displacements of deltaO1 parallel = 0.12 +/- 0.04, deltaO1 perpendicular = 0.25 +/- 0.08, and deltaO1z = 0.12 +/- 0.1 A. An agreement factor over the range of 8980-9040 eV is 2-3 times smaller than it may be obtained from single-electron MS calculations. This improvement comes from accounting for many-body excitations and the relationship between electronic and local structure in the CuO2 planes.

Charge-Density Waves in Self-Assembled Halogen-Bridged Metal Chains

Self-assembled growth of an ordered layer of Pt-Br-Pt chains on a Pt(110) surface is demonstrated. Upon slight doping with excess bromine, charge-density wave (CDW) domains separated by well-localized solutions are observed in the Br/Pt layer by scanning tunneling microscopy. Depending on annealing and adatom concentration, a global, long-range-ordered CDW ground state can be established. Angle-resolved UV photoemission data reveal the corresponding Fermi surface and its removal upon the Peierls transition. The CDW phase is stable to well above room temperature.

Paired Hall states versus unidirectional CDW in a tilted field forν=52

We formulate the composite fermions in the presence of an in-plane magnetic field. As the in-plane field increases, if we assume the state at $\nu=5/2$ turns into the mixed state between the unidirectional charge density wave domains and paired Hall state, we can phenomenologically fit the theoretically defined gap to the experimental measured results. We explain the destruction of the paired Hall states and then a phase transition from the paired Hall state to the unidirectional charge density wave from a symmetry point of view.

Observation of charge-density wave domains on the Cr(110) surface by low-temperature scanning tunneling microscopy

We have studied the Cr(110) surface with low-temperature scanning tunneling microscopy at 6 to 145 K. For tunneling voltages below +/-150 mV we observe a surface charge-density wave (CDW) with a wavelength of 42 A and wave fronts aligned with the [001] in-plane direction. The observed wave pattern is identified as the surface projection of the bulk CDW's arising from the spin-density wave ground state of Cr with the Q vector parallel to [100] and [010], respectively. The bulk CDW with Q parallel to the [001] in-plane direction appears, however, to be strongly suppressed at the Cr(110) surface.

Seismic waveform modeling and surface wave tomography in a three-dimensional Earth: asymptotic and non-asymptotic approaches

We investigate the impact of the theoretical limitations brought by asymptotic methods on upper-mantle tomographic models deduced from long-period surface wave data (period >80 s), by performing a synthetic test using a non-asymptotic formalism. This methodology incorporates the effects of back and multiple forward scattering on the wave field by summing normal modes computed to third order of perturbations directly in the 3D Earth, and models the sensitivity to scatterers away from the great-circle path. We first compare the methods we used for the forward problem, both theoretically and numerically. Then we present results from the computation of 7849 synthetic Love waveforms in an upper mantle model consisting of two heterogeneities with power up to spherical harmonic degree 12. The waveforms are subsequently inverted using a 0th order asymptotic formalism (equivalent to a path-average approximation in the surface waves domain). We show that the main structures are retrieved, but that the theoretical noise on the output model is of the same order as the noise due to the path-coverage and a priori constraints.

Forced convective structures in a differential-flow reactor

A model of an autocatalytic reaction in a differential-flow reactor is considered in which the reactant is immobilized and the autocatalyst allowed to flow (with uniform velocity) and to diffuse. Consideration is given to the influence that a periodic external signal (fluctuations in the inflow concentration of the autocatalyst) can have upon the convective structures which exist in this model. It is shown that, depending on the frequency of the signal, there are two parameter regions giving distinct spatio-temporal responses. There is a region of high excitation waves (convected forced waves) which appear for a finite range of frequencies. Outside this range there are two domains of natural response waves. Close to the boundary of these regions there are irregular responses suggestive of an excitable system: packets of travelling waves of complex form develop which appear at non-regular intervals surrounded by small amplitude periodic waves.

Resonance wave interactions in a weakly viscous liquid

A study is made of non-linear wave interactions in a weakly viscous liquid. Using the averaged variational method, new interaction equations are derived. It is shown that results of this paper reduce to those obtained earlier for weak second-order resonant interactions in the limit as viscosity ν→0. The Lax–Wendroff method having second-order accuracy with respect to space and time is chosen for numerical calculations because the method does not depend on the direction of wave propagation or domains of dependence. The non-linear resonant evolution of amplitude triads has been investigated for different values of viscosity. Numerical results with graphical representations are presented in some detail.

A closed formulation of sound fields in front of periodical absorbents

Periodic resonant absorbers are known to give excessive back scattering for frequencies above a limit which is governed by the geometric proportions of the periodicity. One way to model this phenomenon is to transform the geometry into the wave number domain and solve the corresponding equation with respect to the pressure field. A drawback is that the equation matrix consists of an infinite (but relatively fast converging) set of harmonic components and therefore has to be truncated in order to be solved. However, it is possible to make use of the Poisson sum formula and obtain a closed formulation which can be solved in the wave domain without truncation. Furthermore, it is possible to transform the exact solution back to the spatial domain. This will yield an infinite series consisting of components which can be designated a physical interpretation. These components, i.e., partial pressures related to corresponding geometry, which constitute an exact solution, can then be truncated in a controlled and physical way.

Toward controllable photonic crystals for centimeter- and millimeter-wave devices

In this paper, we present several experimental and theoretical studies showing the feasibility of active photonic crystal controlled either by electrical elements or by light. The controllability of photonic crystals at centimeter wavelengths is proposed with the periodic insertion of diodes along the wires of a two-dimensional (2-D) metallic structure. For only three crystal periods with commercially available devices, more than 30 dB variations of the crystal transmission are predicted over a multigigahertz range by switching the diodes. From calculation models, a tight analogy is shown between these crystals and those consisting of discontinuous metallic rods with dielectric inserts. The numerical models as well as the proposed technology are validated by experimental measurements on 2-D crystals with either continuous or discontinuous metallic rods. The partial control of a 3-D layer-by-layer dielectric structure at millimeter wavelengths is also demonstrated in the second part of the work. A laser light is used to modulate the transmission level of defect modes by photo-induced free carrier absorption. The overall results are expected to contribute to further developments of switchable electromagnetic windows as well as to tunable waveguide structures in the microwave and millimeter wave domains.

Quantitative characterization of 2D traveling-wave patterns

Two-dimensional traveling-wave convection patterns in ethanol-water mixtures with negative separation ratio are discussed. A review is given for several numerical techniques that have been developed to characterize traveling-wave patterns. The basic properties of the patterns are determined using the spatiotemporal Fourier transform. Temporal demodulation of each pixel is used to calculate the complex order parameter of the pattern. The kinematics of the large domains of waves are derived from the complex order parameter using the assumption that the pattern consists of a single deformed wave component. The interactions of waves at the domain boundaries is measured by performing a rigorous spatiotemporal demodulation of the pattern. Finally, the topological structure of the complex order parameter is investigated, and spatiotemporal disorder in the pattern is described in terms of the statistics and dynamics of phase defects.

Plasma Heating: NBI & RF, an Introduction

The additional heating and non-inductive current-drive methods are reviewed. First, the limitations of ohmic heating in tokamaks are examined and the motivations for using additional heating in tokamaks or other machines are discussed. Next we sketch the principles of heating by injection of fast neutrals - or Neutral Beam Injection (NBI). The principle of the injector is briefly outlined. Positive and negative ion based concepts are discussed. The remainder of the lecture focuses on the processes by which the beam transfers energy to the plasma: the ionisation and slowing-down processes. Next, I make a review of the different heating schemes based on the transfer of electromagnetic energy to the plasma. The different wave heating frequency ranges are listed and the propagation and damping peculiarities are sketched in each domain. Heating in the Alfvén and lower hybrid wave domains are described in some more details.

Thermodynamic limit to light trapping in thin planar structures

We calculate the degree to which absorption can be enhanced by light trapping in a material whose thickness is on the order of a wavelength of light. The calculation makes use of an extension of the radiance theorem in the wave domain and represents the ultimate upper limit as determined by the laws of thermodynamics. It is a general upper limit, based solely on considerations of the modal structure of the device and independent of the technique used to couple light into the material. We assume only that the coupling mechanism is isotropic. An important parameter in our result is the density of guided modes within the planar structure, which we calculate. We find that even for structures supporting only a small number of guided modes, significant enhancements in absorption are possible.

A Theory for Reduced Order Control Design of Plate Systems

This paper describes the theory of wave domain control for the reduced control design of plate systems. A transformation, which changes the original system into an image system in which the control force is designed in wave domain control and wave control, is proposed such that the number of degrees-of-freedom of the undisturbed state in its image system is reduced. The control design in the original system is then derived by an inverse transformation. This work focuses on, first, proposing a new wave control theory and, second, applying the theory for structural control design.

Influence of age, lead axis, frequency of arrhythmic episodes, and atrial dimensions on P wave triggered SAECG in patients with lone paroxysmal atrial fibrillation.

Signal-averaged P wave of 42 patients with lone paroxysmal atrial fibrillation (PAF) and 29 normal subjects (N) were recorded, using three orthogonal leads and analyzed in the time and frequency (entire P wave or a 100-ms segment ranging from 75 ms before to 25 ms after the end of P wave) domains. PAFs were divided into a group of 12 having > or = 2 attacks a month (HF) and a group of 30 having < or = 2 attacks a year (LF). Statistically significant differences were absent with regard to ages of PAF and N; ages of HF, LF, and N at the time of signal-averaged ECG; ages of HF and LF at the time of the first arrhythmic episode; and elapsed times from the first episode. Length of P wave and some frequency-domain parameters were found to be significantly correlated with age. PAF showed a significantly longer duration of P wave in the frontal plane using the time-domain analysis. Frequency analysis was found to be useful in evaluating the influence of attack frequency. HF showed significantly higher values of some frequency-domain parameters than LF and N, while the three groups did not differ for time-domain analysis. P wave duration and frequency content of the three orthogonal leads proved to be significantly different in PAF and N. Right and left atrial echocardiographic dimensions proved to be higher (even if within normal limits) in HF than in LF and N. Results suggest that frequency analysis should be performed on the entire P wave.

Dielectric Voltage Response in Spin-density Wave of (TMTSF)2AsF6 at Low Temperature

Voltage response to constant unipolar pulse current in the spin-density wave (SDW) state of (TMTSF) 2 AsF 6 was studied. Below 3 K, leading and tailing edges of the voltage response are rounded at low electric field. The time dependent charge density accumulated in the lattice was estimated from the voltage profiles. It can be fitted by a stretched exponential formula; q(t) q 0 (1 - exp(-(t/T 1 ) β )). With increasing field q 0 increases and shows a maximum at the threshold electric field for depinning. In the pinned state, the relaxation time T 1 increases with decreasing temperature and its activation energy is approximately equal to that of ohmic conductivity. The index β is a linearly decreasing function of temperature and it is extrapolated to one at 0 K. Screening by normal carriers becomes imperfect and coupling between density wave domains becomes stronger on cooling.

Structural properties of kinks and domain walls in nonlinear oscillatory lattices.

Structural properties of self-localized steady-state modes in damped parametrically driven lattices have been numerically observed. The states are kinks, which are localized regions between two standing wave domains of the same wave number with an offset in spatial phase; and domain walls, which are localized regions between two standing wave domains of different wave numbers. The properties include preferred definite symmetry, a wide variety of distinct states, and hysteretic transitions that occur along boundaries in the plane of the drive parameters (amplitude and frequency). The transitions of the localized states exhibit the spontaneous processes of symmetry reversal and ``complexification,'' as well as the onset of quasiperiodicity and chaos. Simple plausible models based upon few degrees of freedom fail to correctly describe the instabilities, which indicates that the behavior is a collective phenomenon.

Application of a wave transform to pressure transient testing in porous media

Solutions to the diffusion equation for nonuniform media are difficult to obtain in a form that can be easily evaluated. Often the solutions are written as the inverse Laplace transform of an inverse Fourier transform. In this paper, I show that the wave transform of Bragg and Dettman (1968) coupled with the Cagniard-de Hoop method for solving the wave propagation problem results in simplified solutions to the problem of pressure transient testing in linear composite reservoirs. The potential usefulness of an inverse wave transform, which would transform measured pressure data (smooth) into a wave signal propagating at the ‘velocity’ of the square root of the diffusivity, is demonstrated by a synthetic example. In the example, diffusivity of the source region is estimated from the ‘time’ of the direct wave arrival, while diffusivity of a second, higher diffusivity region is estimated from the ‘velocity’ of the head wave. In the wave domain the time-like variable has units of (time)1/2 which makes the units of ‘velocity’ equal to L T-(1/2). I also demonstrate, using synthetic data, that it is difficult, but perhaps possible, to invert the wave transform numerically.