Lump wave

There are three different definitions of current waveforms as shown in Figure 2.37. The first definition is the lump wave, which is expressed by two linear lines. The second is the double exponential wave, expressed by... 

The pressure-time variation in the driver section can be approximated by a quasi-steady model consisting of a single lumped-mass system with choked outflow at the minimum throat area when the ratio of the driver volume to the throat area is equal to 20 ft3/ft2 (6.1 m3/m2) or more. For smaller values of the ratio, the representation by a quasi-steady model becomes less accurate, and the numerical wave analysis approach is more suitable. 

Given a geochemical variable y, m measurements at times tu t2,..., tm produce the unevenly spaced time series yl5 y2,..., ym, which we lump together as the vector y. In order to find out eventual periodicities, Lomb (1976) suggests fitting the data by a sine wave using a least-square criterion. For any arbitrary frequency /, the fitting function is written... 

Consider first the series junction of N waveguides containing transverse force and velocity waves. At a series junction, there is a common velocity while the forces sum. For definiteness, we may think of A ideal strings intersecting at a single point, and the intersection point can be attached to a lumped load impedance Rj (s), as depicted in Fig. 10.11 for TV= 4. The presence of the lumped load means we need to look at the wave variables in the frequency domain, i.e., V(s) = C v for velocity waves and F(s) = C / for force waves, where jC denotes the Laplace transform. In the discrete-time case, we use the z transform instead, but otherwise the story is identical. 

Figure 10.11 Four ideal strings intersecting at a point to which a lumped impedance is attached. This is a series junction for transverse waves.

In this equation the wave length has been lumped into the constant K Using this equation for spherical particles, Drinker and Hatch (1936) have shown that a concentration of 350 particles per cc having a uniform diameter of 2 p. would require a distance, l, of 47 meters to reduce the intensity of the light 5 percent, that is, from 100 to 95 percent,... 

Since the transverse shear wave may penetrate the damping surface layer and the viscous liquid, additivity of the equivalent electrical elements in the BVD circuit is only valid under certain particular conditions. Martin and Frye [53] studied the impedance near resonance of polymer film coated resonators in air with a lumped-element BVD model, modified to account for the viscoelastic properties of the film. In addition to the elements shown in Fig. 12.3 to describe the quartz crystal and the liquid, L/ and Rf were added to describe the viscoelastic film overlayer. For a small... 

At high frequencies the electromagnetic wavelength inevitably becomes comparable with sample dimensions, and lumped-circuit methods must be abandoned in favour of distributed-circuit methods in which the sample becomes the medium for propagation of electromagnetic waves. Relative permittivity and loss must then be obtained from the observed wavelength and attenuation characteristics. 

The speed of electro-optic devices is greatly determined by the dielectric properties of the electro-optic material. For instance, the bandwidth per modulating power (A//P) of a guided-wave lumped-element modulator is given by ... 

Fig. 6. Lumped equivalent circuit for a transmission mode spectrometer near a resonance. Kj is the output voltage of the millimeter wave source, Rj is the source resistance, and Cf are the equivalent inductance and capacitance of the resonator, is the resonator resistance, and the load resistance of the detector. The mutual inductances M, and M2 model the coupling into and out of the resonator.

In patients lumped in this group, there is impaiiment in secretion of granule contents during platelet activaticHi and they demonstrate absence of the second wave of aggregation during stimulation of platelet-rich plasma with ADP and epinephrine. 

The PT model is frequently used as a minimalistic approximation for more complex models. For instance, it is the mean-field version of the Frenkel Kontorova (FK) model as stressed by D. S. Fisher [29,83] in the context of the motion of charge-density waves. The (mean-field) description of driven, coupled Josephson junctions is also mathematically equivalent to the PT model. This equivalence has been exploited by Baumberger and Carol for a model that, however, was termed the lumped junction model [84] and that attempts to... 

Haim et al. aim at a description of waves that were observed during the electrodissolution of an Ni wire in sulfuric acid. ° Their starting point is a lumped system, the behavior of which they had previously treated in order to simulate the global dynamics of Ni dissolution. This model falls into the category of HNDR oscillators, with the variables being the double-layer potential and the degree of surface modification. The latter is assumed to be local, and migration currents provide the only communication channel. The potential distribution in the electrolyte is presumed to obey Laplace s equation. Haim et al., however, missed... 

V. Zykov, G. Bordiougov, H. Brandtstadter, I. Gerdes, and H. Engel. Periodic forcing and feedback control of nonlinear lumped oscillators and meandering spiral waves. Phys. Rev. E, 68 1-11, 2003. 

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