Modulator undulator

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

In equation 1, bmin is the minimum feature size transferable, A is the wavelength of light, s is the separation between the mask and the substrate, and d is the thickness of the resist layer. In projection printing, a series of undulating maxima and minima are produced. Because of mutual interference, the dark region is never completely dark, and the maximum brightness does not correspond to 100% transmission. The quality of transfer can be conveniently indicated by the modulation index, M, which is defined as follows ... 

The modulations of S in the linear analysis are maximum at the boundaries and in phase with the layer displacement u. The sign of the amplitude depends on the coupling to the velocity field (only the anisotropic part — /) [< is relevant) and on the coupling to the director undulations (via M , only for the nematic... 

Using amplitude or frequency modulation of a carrier at frequency tog, we can achieve exact frequency division if we make sidebands of the carrier to such low frequency that we can force the condition wg-nQ = (n+2) 2-a>g = 2 so that tog/ 2 = n+1. For example, if we examine Fig. 2, we can achieve exact frequency division by any means which locks the phase of the carrier to the phase of the amplitude modulation that is, the undulations of the carrier do not "slip" under the envelope of the amplitude modulation. A divider based on these principles would be quite useful if 2 is in the microwave region (or below) where precise frequency synthesis is possible. Since 2 and n could be freely chosen, any value of uig could be measured in a single device. 

Qi and Wang also observed a transient undulated HEX state during the melting of the HEX phase to the disordered state. This is consistent with the experimental observation in the shear cessation experiments of Bates and co-workers (Bates et al., 1994a Almdal et al., 1996). In these experiments, an initially disordered phase of the asymmetric poly(ethylenepropylene-b-ethylethylene) (PEP-PEE) diblock copolymer close to the order-disorder boundary is subjected to a steady shear which induces a transition to the HEX phase. The shear is then suddenly stopped and a transient modulated state is observed as the system relaxes back to the DIS. Insofar as a HEX... 

A steady concentration of the reactant is not observed when the confluent reagent stream is not properly added. Pronounced differences in matrix composition (e.g., colour and suspended matter), flow rates and viscosity of the carrier and confluent streams may result in a pulsed addition of the confluent stream. The effect is random, but if the fluid-propelling device is a peristaltic pump, it is characterised by a typical frequency, dictated by the rotation speed of the peristaltic pump. A pulsating flow is then established, leading to undulations in the recorded peak. The effect is reduced if the involved streams converge with similar mean linear velocities. As the effect is characterised by a constant frequency, the modulated signal (ripple) is easily filtered out. 

The structures were originally described in terms of undulating chains of MO7 pentagonal bipyramids, with a composition of M Os- The cation coordination was described as a mixture of octahedral and pentagonal bipyramidal. Interstitial metal atoms situated in sites between sheets of pentagonal bipyramids were invoked to achieve the correct composition. It is now clear that the cations are in a hexagonal planar array and that the anion array is continuously modulated, and expands or contracts to fit the anion to cation ratio. In some places, the cation coordination is well represented by a pentagonal bipyramid, and in other places by an octahedron. Elsewhere the coordination polyhedra can be described as distorted variants of these. 

We need to explain why we only observe the 102 diffuse spot. We could have expected that the 101 diffuse spot should be stronger than the 102 . This can be explained by considering that the undulations only affect a part of the layer so that the structure factor governing this modulation will be different from that governing the smectic reflection intensities. For simplicity, the electron density profile of the smectic layer may here be represented by step functions (Fig. 16). 

Experiments have been carried out on p-(nitrobenzyloxy)-biphenyl [30] and typical patterns in the conductive range at onset are shown in Fig. 6. At low frequencies disordered rolls without point defects have been observed with a strong zig-zag (ZZ) modulation (see Fig. 6a) which can be interpreted as the isotropic version of oblique rolls. Above a critical frequency, a square pattern is observed which retains the ZZ character because the lines making up the squares are undulated. At onset the structure is disordered however, after a transient period defects are pushed out and the structure relaxes into a nearly defect-free, long-wave modulated, quasi-periodic square pattern (see Fig. 6b). 

Figure 6. Snapshots of EC patterns slightly above onset for case B. a ZZ modulated disordered rolls, b undulated (soft) squares.

Figure 19 (a) [001] HREM image of YBa2Cu306.66 characterized by strains and contrast modulations, (b) Enlargement showing variations in the spacing of the rows and their undulation. 

The focus of this review is an experimental analysis of the factors that modulate the range and magnitude of the undulation pressure between bilayers composed of... 

Polar Columnar (ColP) Phases In calamitic rod-shaped LCs, the frustration occurring in the layer organization of molecules due to steric and/or polar effects leads to form a variety of 2D density structures such as undulated layers, modulated layers (ribbons), and Cols. The situation for bent-core molecules with an ability to form macroscopic polar order is much more complex, and different types of modulated smectic and Col phases form. Since their 2D X-ray patterns, structural models, and nomenclature have been in great detail described in the two previous reviews [29, 32], in this section, the field-induced switching properties of polar columnar (ColP) phases are focused on. 

---