Subject sinusoidal

Identify the flow pattern of the prototype system by subjecting it to an impulse, step, or sinusoidal disturbance by injection of a tracer material as reviewed in Chapter 8. The result is classified as either complete mixing, plug flow, and an option between a dispersion, cascade, or combined model. 

If the material being subjected to the sinusoidal stress is elastic then there will be a sinusoidal variation of strain which is in phase with the stress, i.e. 

In dynamic mechanical analysis of plastics, the material is subjected to a sinusoidal variation of stress and the strain is recorded so that 1, 2 and S can be determined. The classical variation of these parameters is illustrated in Fig. 2.55. 

A uPVC rod of diameter 12 mm is subjected to an eccentric axial force at a distance of 3 ttun from the centre of the cross-section. If the force varies sinusoidally from — F to f at a frequency of 10 Hz, calculate the value of F so that fatigue failure will not occur in 10 cycles. Assume a safety factor of 2.5 and use the creep rupture and fatigue characteristics described in the previous question. Thermal softening effects may be ignored at the stress levels involved. 

An alternative method of studying the molecular motions of a polymeric chain is to measure the complex permitivity of the sample, mounted as dielectric of a capacitor and subjected to a sinusoidal voltage, which produces polarization of the sample macromolecules. The storage and loss factor of the complex permitivity are related to the dipolar orientations and the corresponding motional processes. The application of the dielectric thermal analysis (DETA) is obviously limited to macromolecules possessing heteroatomic dipoles but, on the other hand, it allows a range of frequency measurement much wider than DMTA and its theoretical foundations are better established. 

Figure 16. Schematic of the geometry of a section of liver before (top) and after (bottom) being subjected to slow freezing. During slow freezing, ice forms in the sinusoids and water flows osmotically from the cells into the sinusoids. (The upper drawing is slightly modified from Rubinsky and Pegg, 1988.)...

Experimentally DMTA is carried out on a small specimen of polymer held in a temperature-controlled chamber. The specimen is subjected to a sinusoidal mechanical loading (stress), which induces a corresponding extension (strain) in the material. The technique of DMTA essentially uses these measurements to evaluate a property known as the complex dynamic modulus, , which is resolved into two component parts, the storage modulus, E and the loss modulus, E . Mathematically these moduli are out of phase by an angle 5, the ratio of these moduli being defined as tan 5, Le. 

Figure 3.4 Schematic representation of the steps involved in obtaining a two-dimensional NMR spectrum. (A) Many FIDs are recorded with incremented values of the evolution time and stored. (B) Each of the FIDs is subjected to Fourier transformation to give a corresponding number of spectra. The data are transposed in such a manner that the spectra are arranged behind one another so that each peak is seen to undergo a sinusoidal modulation with A second series of Fourier transformations is carried out across these columns of peaks to produce the two-dimensional plot shown in (C).

Here A is the amplitude, cp the initial phase, and coo the frequency of free vibrations. Thus, in the absence of attenuation free vibrations are sinusoidal functions and this result can be easily predicted since mass is subjected to the action of the elastic force only. In other words, the sum of the kinetic and potential energy of the system remains the same at all times and the mass performs a periodic motion with respect to the origin that is accompanied by periodic expansion and compression of the spring. As follows from Equation (3.105) the period of free vibrations is... 

References 29-33 introduce the notion of coherence spectroscopy in the context of two-pathway excitation coherent control. Within the energy domain, two-pathway approach to coherent control [25, 34—36], a material system is simultaneously subjected to two laser fields of equal energy and controllable relative phase, to produce a degenerate continuum state in which the relative phase of the laser fields is imprinted. The probability of the continuum state to evolve into a given product, labeled S, is readily shown (vide infra) to vary sinusoidally with the relative phase of the two laser fields < ),... 

Theoretically, we are making the presumption that we can study and understand the dynamic behavior of a process or system by imposing a sinusoidal input and measuring the frequency response. With chemical systems that cannot be subject to frequency response experiments easily, it is very difficult for a beginner to appreciate what we will go through. So until then, take frequency response as a math problem. 

Fig. 5.3 Structures of two combined TxSI/TxRAs subject to high hepatic extraction by sinusoidal transport systems.

Dynamic melt viscosity studies on the star blocks and a similar triblock were carried out using a Rheometric Mechanical Spectrometer (RMS) (Rheometrics 800). Circular molded samples with -1.5 mm thickness and 2 cm diameter were subjected to forced sinusoidal oscillations (2% strain) between two parallel plates. The experiment was set in the frequency sweep mode. Data were collected at 180 and 210 °C. 

The dynamic melt viscosity measurements of select star blocks and a similar triblock were carried out on a rheometric mechanical spectrometer, RMS. Circular molded samples of 2 cm diameter and -1.5 mm thickness were subjected to forced sinusoidal oscillations. Dynamic viscosities were recorded in the frequency range of 0.01-100 rad/s at 180 °C. Figure 10 shows the complex viscosities of two select star blocks and a similar linear triblock. The plots showed characteristic behavior of thermoplastic elastomers, i.e., absence of Newtonian behavior even in the low frequency region. The complex viscosity of the star block... 

Cyclic voltammograms were also performed with platinum microelectrodes on skin surface at regular time intervals of about 7 h. Figure 8.10 shows the typical curve giving the evolution of the anodic current at 0.9V/SCE as a function of time. A sinusoidal evolution was observed for the nine volunteers. Current values as well as the amplitude and the period of the variations were different for each subject. It has been verified that the amplitude of the current variations was significantly higher than the accuracy of the amperometric response. Consequently, the variation of the anodic current was actually due to a variation of the oxido-reductive properties of the skin and was not an artifact of the measurements. 

The values of the piezoelectric properties of a material can be derived from the resonance behaviour of suitably shaped specimens subjected to a sinusoidally varying electric field. To a good approximation the behaviour of the piezoelectric... 

The most common dynamic method is oscillatory testing, in which the sample is subjected to a sinusoidal oscillatory strain, and the resulting oscillatory stress measured. The more sophisticated rotational viscometers have the additional capability of dynamically testing liquid-like materials using small angle oscillatory shear. A parallel disc viscometer can be set up for testing solid-like materials (e.g., butter), in oscillatory shear. Some UTM-type solids rheometers, in which the moving crosshead can be made to reciprocate sinusoidally, can be used to test solid-like materials in oscillatory deformation in compression, tension or shear. 

If a Maxwell element is subjected to a sinusoidal shear deformation that starts at time t = 0, Eq. (13.77) becomes... 

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