Sinusoidal length changes

Bagni, M. A., Colombini, B., Amenitsch, H., Bernstorff, S., Ashley, C. C., Rapp, G., and Griffiths, P. J. (2001). Frequency-dependent distortion of meridional intensity changes during sinusoidal length oscillations of activated skeletal muscle. Biophys. J. 80, 2809-2822. 

The inlet monomer concentration was varied sinusoidally to determine the effect of these changes on Dp, the time-averaged polydispersity, when compared with the steady-state case. For the unsteady state CSTR, the pseudo steady-state assumption for active centres was used to simplify computations. In both of the mechanisms considered, D increases with respect to the steady-state value (for constant conversion and number average chain length y ) as the frequency of the oscillation in the monomer feed concentration is decreased. The maximum deviation in D thus occurs as lo 0. However, it was predicted that the value of D could only be increased by 10-325S with respect to the steady state depending on reaction mechanism and the amplitude of the oscillating feed. Laurence and Vasudevan (12) considered a reaction with combination termination and no chain transfer. 

When a chemical or biochemical reaction takes place in the sensor area, only the light that travels through this arm will experience a change in its effective refractive index. At the sensor output, the intensity (I) of the light coming from both arms will interfere, showing a sinusoidal variation that depends on the difference of the effective refractive indexes of the sensor (Neff,s) and reference arms (Neff,R) and on the interaction length (L) ... 

The motion given by this solution is called uniform harmonic motion. It is a sinusoidal oscillation in time with a fixed frequency of oscillation. Figure 8.1 shows the position and the velocity of the suspended mass as a function of time. The motion is periodic, repeating itself over and over. During one period, the argument of the sine changes by In, so that if r is the period (the length of time required for one cycle of the motion). 

The instantaneous value of the current I or voltage V varies sinusoidally with time (Fig. 5.21b) and is represented by the projection in Fig. 5.21c onto the horizontal axis of a vector V or I of length corresponding to the current of voltage amplitude. The vector rotates counterclockwise with a change of angular frequency with time. Because both vectors I and V are in phase, their phasors rotate together. 

The power P(z) of the fundamental mode distance z along the sinusoid in Fig. 22-2 attenuates because of the radiation loss. If we subdivide the deformity into lengths dz which are short compared with L, but long enough for the above analysis to be valid, the change in modal power over distance dz is given by... 

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