Resonant drift

As mentioned in the introduction, meandering and resonant drift of spiral waves in the photosensitive BZ reaction can be achieved experimentally by a periodically changing light intensity [9, 90]. The Doppler effect imposes superspiral structures in the case of spiral wave dynamics other than rigid rotation. These superspiral structures have been observed in experiments see for example [11, 41, 55, 56, 89]. See [70] for a mathematical analysis based on linearized analysis and eigenfunctions. 

Resonant drift of a spiral wave under periodic parameter modulation. 250... 

The control methods we have in mind base on the resonant drift of spiral waves in response to a periodic change in the excitability of the whole... 

In this paper we demonstrate that all known feedback-mediated control methods based on the phenomenon of resonant drift can be considered in the framework of a unified theoretical approach. This approach allows to analyze existing methods of discrete and continuous control, and helps to elaborate novel control algorithms. The theoretical predictions are confirmed by numerical computations and experimental studies. 

Resonant drift of a spiral wave is a displacement of the spiral wave center induced by a periodic modulation of the medium excitability. This phenomenon has been predicted for a kinematical model of weakly excitable media [14], confirmed experimentally as well as in numerous numerical simulations [16, 19, 20, 45], and explained as a generic property of excitable media [15, 17]. 

The phenomenon of resonant drift is induced under modulation with frequency ojm = w- In this case, from Eq. (9.11) follows fe = fe-i =. .. = 0. All particular displacements occur in the same direction and the total shift of the spiral location after k perturbations is given by... 

Thus, the velocity of the resonant drift induced by the periodic modulation is determined by the ratio h/Tm- Under resonant forcing, ujm = the drift is along a straight line whose direction depends on the initial orientation of the spiral wave o and on the constant ip. More generally, if the parameter modulation is given by... 

Application of one-channel feedback control to spiral waves in the light-sensitive BZ system allows to observe the discrete set of stable resonant attractors experimentally [21, 30, 43, 46]. Note, that Eq. (9.23) for the radius of the resonance attractor contains only one medium dependent parameter (p, which specifies the direction of the resonance drift. To avoid a rather complicated experimental procedure to determine this value, the obtained experimental data were fitted to the theoretically predicted linear dependence (9.23) using p = —0.31. The results are shown in Fig. 9.3 by dashed lines. Then, the boundaries of the basin of attraction were specified in accordance with Eq. (9.24) (solid lines in Fig. 9.3). 

The theoretically predicted destruction of the resonance attractor in response to deviations from the circular shape of the integration domain has been confirmed experimentally within the light-sensitive BZ medium. A spiral wave was exposed to uniform illumination proportional to the total gray level obtained in an elliptical integration domain. Fig. 9.13(b) shows the resonant drift mediated during global feedback control. The spiral wave drifts towards a stable node of the drift velocity field. Close to this fixed point the drift velocity becomes very slow. Thus, the experimentally observed termination of the spiral drift at certain positions in a uniform medium is explained in the framework of the developed theory of feedback-mediated resonant drift. 

We have shown that all existing methods of spiral wave control can be considered in the framework of a unified theoretical approach. This approach is based on the well established phenomenon of resonant drift induced by a periodic parametric modulation at the rotation frequency of a spiral wave [14-20]. The direction of resonant drift depends on the initial orientation of the spiral and on the phase of the first Fourier component of the periodic modulation. To specify the spiral orientation we propose to... 

It was extremely important to demonstrate that because the phase of the feedback signal depends on the spiral orientation, the direction of feedback-induced resonant drift is determined only by the spiral location and does not depend on its initial orientation. Thus, under feedback control the dynamics of spiral waves can be described by a drift velocity field [47, 53]. 

To find explosives Gas analyzers, chromatography instruments, drift-spectrometers, neutron defectosopes, nuclear-magnetic and nuclear-quadrupole resonant instruments... 

In LN, the bonded interactions are treated by the approximate linearization, and the local nonbonded interactions, as well as the nonlocal interactions, are treated by constant extrapolation over longer intervals Atm and At, respectively). We define the integers fci,fc2 > 1 by their relation to the different timesteps as Atm — At and At = 2 Atm- This extrapolation as used in LN contrasts the modern impulse MTS methods which only add the contribution of the slow forces at the time of their evaluation. The impulse treatment makes the methods symplectic, but limits the outermost timestep due to resonance (see figures comparing LN to impulse-MTS behavior as the outer timestep is increased in [88]). In fact, the early versions of MTS methods for MD relied on extrapolation and were abandoned because of a notable energy drift. This drift is avoided by the phenomenological, stochastic terms in LN. 

The heightened appreciation of resonance problems, in particular, has been quite recent [63, 62], and contrasts the more systematic error associated with numerical stability that grows systematically with the discretization size. Ironically, resonance artifacts are worse in the modern impulse multiple-timestep methods, formulated to be symplectic and reversible the earlier extrapolative variants were abandoned due to energy drifts. 

Global AMI.5 sun illumination of intensity 100 mW/cm ). The DOS (or defect) is found to be low with a dangling bond (DB) density, as measured by electron spin resonance (esr) of - 10 cm . The inherent disorder possessed by these materials manifests itself as band tails which emanate from the conduction and valence bands and are characterized by exponential tails with an energy of 25 and 45 meV, respectively the broader tail from the valence band provides for dispersive transport (shallow defect controlled) for holes with alow drift mobiUty of 10 cm /(s-V), whereas electrons exhibit nondispersive transport behavior with a higher mobiUty of - 1 cm /(s-V). Hence the material exhibits poor minority (hole) carrier transport with a diffusion length <0.5 //m, which puts a design limitation on electronic devices such as solar cells. 

The deuterium line of the deuterated solvent is used for this purpose, and, as stated earlier, the intensity of this lock signal is also employed to monitor the shimming process. The deuterium lock prevents any change in the static field or radiofrequency by maintaining a constant ratio between the two. This is achieved via a lock feedback loop (Fig. 1.10), which keeps a constant frequency of the deuterium signal. The deuterium line has a dispersion-mode shape i.e., its amplitude is zero at resonance (at its center), but it is positive and negative on either side (Fig. 1.11). If the receiver reference phase is adjusted correcdy, then the signal will be exactly on resonance. If, however, the field drifts in either direction, the detector will... 

In obtaining experimental information about the isomeric forms of ions, a variety of techniques have been used. These include ion cyclotron resonance (ICR),31 flow tube techniques, notably the selected ion flow tube (SIFT),32 and the selected ion flow drift tube (SIFDT)32 (and its simpler variant33), collision induced dissociation (CID),10,11 and the decomposition of metastable ions in mass spectrometers.13 All of these techniques are mentioned in the text of Section in whore they have provided data relevant to the present review. 

The price to pay for getting the higher intermediate frequency in such a convenient way would be the less clock-jitter tolerance, so that the apparent resolution of the resonance line can be degraded compared with that obtained in the conventional detection scheme. For this reason, we demonstrated the high-resolution liquid-state NMR experiment, in which the resonance line width was on the order of Hz. In fact, we observed a drift of the peak position when we used a less stable clock... 

DGE a AC AMS APCI API AP-MALDI APPI ASAP BIRD c CAD CE CF CF-FAB Cl CID cw CZE Da DAPCI DART DC DE DESI DIOS DTIMS EC ECD El ELDI EM ESI ETD eV f FAB FAIMS FD FI FT FTICR two-dimensional gel electrophoresis atto, 10 18 alternating current accelerator mass spectrometry atmospheric pressure chemical ionization atmospheric pressure ionization atmospheric pressure matrix-assisted laser desorption/ionization atmospheric pressure photoionization atmospheric-pressure solids analysis probe blackbody infrared radiative dissociation centi, 10-2 collision-activated dissociation capillary electrophoresis continuous flow continuous flow fast atom bombardment chemical ionization collision-induced dissociation continuous wave capillary zone electrophoresis dalton desorption atmospheric pressure chemical ionization direct analysis in real time direct current delayed extraction desorption electrospray ionization desorption/ionization on silicon drift tube ion mobility spectrometry electrochromatography electron capture dissociation electron ionization electrospray-assisted laser desorption/ionization electron multiplier electrospray ionization electron transfer dissociation electron volt femto, 1CT15 fast atom bombardment field asymmetric waveform ion mobility spectrometry field desorption field ionization Fourier transform Fourier transform ion cyclotron resonance... 

Photoionization, where electrons are released by molecules following the absorption of energy from photons, has long been viewed as a non-radioactive means to ionize explosives in the vapor phase [39]. In recent years, two teams have sought to employ laser ionization with IMS for explosive determinations. A team at Implant Sciences Corporation has utilized a laser (or flash lamp) for sampling surfaces and for ionization of sample vapors in an IMS analyzer [40, 41]. In their approach, the sample is removed from a surface with an increased temperature from laser exposure. Gases (and presumably particulate matter) from over the surface are drawn into an IMS drift tube using a wall-free inlet vida supra). In the IMS drift tube, resonance multi-photon ionization by a laser is used to produce ions from the explosives. Their... 

The frequency of a single-mode laser inside the spectral gain profile of its active medium is mainly determined by the eigenfrequency of the active laser cavity mode. Therefore any instability of resonator parameters, such as variation of cavity length, mirror vibrations or thermal drifts of the refractive index will show up as frequency fluctuations and drifts of the laser line. 

A disadvantage of the LR-CPMG detection method is its total insensitivity to field/frequency offset which must be adjusted before a profile measurement and cannot be corrected by means of a simple procedure during an automatic profile measurement. This requires a higher degree of longterm field stability (including any thermal effects) than the other methods. Despite the insensitivity of the technique, in fact, the field may not be allowed to drift too far from resonance where the RF pulses would lose their efficiency (excursions up to about 5 kHz are, however, quite tolerable). 

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