Simple Oscillatory Field

FIGURE 1. Spin rate of yeast (Saccharomyces cerevisiae) in a four-pole rotating electric field as a function of the square of the applied voltage on electrodes with a l-mm gap. The frequency of the applied field was 60 kHz. Measurements of the spin rate ) for cells in various concentrations of sucrose in water. (Squares, circles, triangles, and diamonds designate data for 0, 100, 200, and 300 g sucrose per liter, respectively). The resistivity of the solutions was adjusted to 133 k 2cm. The cells examined were from 10-day-old culture, and were classified as 98% viable by methylene blue stain test. 

What are the possible explanations for lone cell rotation in a simple oscillating field The most compelling reason seems to be that of an internal dipolar oscillation within the cell. This oscillation would be present only with live cells since upon the death of the cell spinning ceases. This seems to be supported by the fact that the cells spin at a much lower rate than that being applied by the external field. The cell rotates at somewhere between 0.1 and 30.0 Hz, while the external field oscillates at, say, 600 kHz. The presence of an internal dipolar field oscillation would interact with the externally applied field to provide a rotational torque and thus induce the spinning. 

The cellular oscillations are not necessarily dipolar, but may oscillate as linear quadrupoles or higher multipoles. In view of the relatively weak character of the cellular oscillations it would also be expected that the externally applied oscillatory fields would serve to pull or change the frequency into resonance with that of the applied field. This would cause the CSR spectrum to be broadened by the external frequency pulling. 

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Let us begin with the one-mode electron-transfer system. Model IVa, which still exhibits relatively simple oscillatory population dynamics [205]. SimUar to what is found in Fig. 5 for the mean-field description, the SH results shown in Fig. 13 are seen to qualitatively reproduce both diabatic and adiabatic populations, at least for short times. A closer inspection shows that the SH results underestimate the back transfer of the adiabatic population at t 50 and 80 fs. This is because the back reaction would require energetically forbidden electronic transitions which are not possible in the SH algorithm. Figure 13 also shows the SH results for the electronic coherence which are found to... 

A simple model that illustrated the behavior of the polarization when the water molecules are organized in water layers between perfectly flat surfaces was previously suggested.13 That model took into account the nearest-neighbor dipole interactions, but ignored the surface charges and the electrolyte ions. The model is extended here to cases in which an electrolyte as well as surface charges are also present. It will be shown that a treatment of all electrostatic interactions, in the assumption of an icelike structuring of water near interfaces, can predict an oscillatory behavior for both the polarization and the electric potential as well as a nonproportionality between the polarization and the electric fields. 

Although the theory of the SdH effect [256], which deals with the detailed problem of electron scattering in a magnetic field, is quite complicated a qualitative explanation is possible by virtue of a simple argument [257]. The probability for an electron to scatter is proportional to the number of states into which it can be scattered. As discussed above, for a metal in a magnetic field the density of states at the Fermi level N ep) will oscillate with the field and, therefore, the scattering probability and the electronic relaxation time r will oscillate, too. It can be shown that the oscillatory part of the density of states, Niep), has essentially the same analytic form as (3.6) with the... 

The main problem in the solution of non-linear ordinary and partial differential equations in combustion is the calculation of their trajectories at long times. By long times we mean reaction times greater than the time-scales of intermediate species. This problem is especially difficult for partial differential equations (pdes) since they involve solving many dimensional sets of equations. However, for dissipative systems, which include most applications in combustion, the long-time behaviour can be described by a finite dimensional attractor of lower dimension than the full composition space. All trajectories eventually tend to such an attractor which could be a simple equilibrium point, a limit cycle for oscillatory systems or even a chaotic attractor. The attractor need not be smooth (e.g., a fractal attractor in a chaotic system) and is in some cases difficult to compute. However, the attractor is contained in a low-dimensional, invariant, smooth manifold called the inertial manifold M which locally attracts all trajectories exponentially and is easier to find [134,135]. It is this manifold that we wish to investigate since the dynamics of the original system, when restricted to the manifold, reduce to a lower dimensional set of equations (the inertial form). The inertial manifold is, therefore, a useful notion in the field of mechanism reduction. 

Simple periodic behaviour is far from being the only mode of oscillation observed in chemical and, even more, biological systems. For many nerve cells, indeed, particularly in molluscs, oscillations take the form of bursts of action potentials, recurring at regular intervals representing a phase of quiescence. The best-characterized example of this mode of oscillatory behaviour known as bursting is provided by the R15 neuron of Aplysia (Alving, 1968 Adams Benson, 1985). Neurons of the central nervous system of mammals (Johnston Brown, 1984) also present this type of oscillations. In addition, complex oscillations have been observed and modelled in chemical systems (see, for example, Janz, Vanacek Field, 1980 Rinzel Troy, 1982, 1983 Petrov, Scott Sho waiter, 1992). 

The compliance relates the time dependence of the mechanical displacement of a polymer to the applied force and is a particular example of a transfer function %(transfer function converts an input function (force, electric field, polarisation etc.) to the observed signal or response function. In many case the response function is a displacement or like property. Consider a simple harmonic oscillator of mass m and natural frequency, too, which is subjected to an oscillatory force, Fexp(—i[Pg.364]

If the surface anchoring Is assumed to be elastic, one Immediately finds that surface reorientation Is Instantaneous and violently oscillatory when fields are suddenly applied unless a viscosity Independent of the five bulk parameters Is Introduced. Since the surface Is assumed to rotate but not to flow, a simple viscosity that resists surface rotation, Ys, may be Introduced. 

Small-amplitude oscillatory flow is often referred to as dynamic shear flow. Fluid deformation under d)mamic simple shear flow can be described by considering ttie fluid wiflun a small gap dX2 between two large parallel plates of which the upper one undergoes small amplitude oscillations in its own plane with a frequency velocity field within the gap can be given by d , = ydxj but y is not a constant as in steady simple shear. Instead it varies sinusoidally and is given by... 

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