Fundamentals of Detecting Motion

A much simpler and more flexible approach, however, extends the scheme of pulsed magnetic field gradients discussed above to include more complex time dependences. To see how this can be done, we write down the general dependence of the phase shift accumulated at time t subject to a space-dependent Larmor frequency  

If we expand the position of a spin into a Taylor series  

Terms of higher order than acceleration are usually not considered in NMR experiments. We can thus identify three integrals that are the respective Fourier conjugates to position r0, velocity v0 and acceleration a0. 

In this section, we will focus on the different types of motion and their experimental determination, and will not consider imaging itself Section 1.5 will then combine the two encodings of position and motion into velocity imaging sequences. 

Let us first have a doser look at the dependence of the signal on the application of a pair of gradients with equal duration and intensity but opposite direction. This pair represents a two-fold encoding of position into the phase of the spins the total phase can be written as 

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The natural diffusion of those aromatic compounds and essential oils quickly is detected. What is not observed is the diffusion phenomenon of Brownian motion. The ability to be able to determine which brand of cologne or perfume fragrance is in the immediate environment and how widely it is spread is not easy to be achieved. When a device is able to respond to these fundamental events of change, and is able to signa-turize them, the information retrieved is what basically constitutes a sensor response. 

Experimental observations, such as the coincidence of onset of function with onset of protein motion and long-range connectivity, lead one to infer that correlated fluctuations are among the fundamental principles of enzyme activity. The proof of this inference, through the detection of cross-correlations, remains an open and difficult problem. There is a substantial body of evidence, however, that bears on the correlation of solvent and protein motions, and understanding of the details of this coupling is likely to come soon. 

Today, a technique called transition state spectroscopy that uses lasers with pulse widths around 10 fsec facilitates the detection of transient species with extronely short lifetimes. In this time interval, a bond in its fundamental vibration covers a distance of only 2X10" m. As such, this technique enables one to obtain a sequence of images of vibrational motion of a chemical bond in the act of breaking. However, it is worth remembering that owing to the Heisenberg uncertainty principle ... 

In 1887 two American scientists, physicist Albert Michelson and physical chemist Edward Morley, performed an experiment that was designed to detect the motion of Earth through a hypothetical medium known as the luminiferous ether, which was thought to be present throughout space. They made their measurements with a very sensitive optical instrument now called a Michelson interferometer. Their observations showed no indication of movement through the predicted ether. This outcome was unexpected and has become one of the fundamental experimental results in support of the theory of special relativity, developed by Albert Einstein in 1905. 

In the dynamic resonance experimental technique, a body is forced to vibrate and the constants are determined from the resonant frequencies. The types of vibration utilized are usually the longitudinal, flexural or torsional modes. The first two allow E to be determined and the last gives the shear modulus. It is usually easier to excite flexural waves than longitudinal ones, thus the use of flexural and torsional waves will be emphasized in this discussion. To use the dynamic resonance approach, the solution to the differential equations of motion must be known and this has been accomplished for several specimen shapes. In particular, it is common to use specimens of rectangular or circular cross-section, as solutions are readily available. Vibrations in the fundamental mode usually give the largest amplitude and are, therefore, the easiest to detect. 

In the 1960s, the development of high-energy accelerators and more sophisticated detection systems ied to the discovery of many new and exotic particles. They were all unstable and existed for only small fractions of a second nevertheless they set into motion a search for a theoretical description that could account for them all. The large number of these apparently fundamental particles suj ested strongly that they do not, in fact, represent the most fundamental level of the structure ofmatter. Physicists found themselves in a position similar to Mendeleev when the periodic table was being developed. Mendeleev realized that there had to be a level of structure below the elements themselves, which explained the chemical properties and the interrelations between elements. 

When the space-filling protein component is removed, it becomes possible to view the located water molecules within the myosin motor. As shown in Figure 1.5B, an impressive number and distribution of the detected water molecules appear. It can also be expected that there are many more water molecules relevant to function of the myosin motor that are too mobile to be seen by X-ray diffraction, just as is apparent in the crevices and recesses of the surface. By the consilient mechanism these water molecules (seen in Fig. 1.5B and the additional unseen water molecules) are essential to motor function. These water molecules, which in our view are essential for Life, we choose to call the waters of Thales. Thus, as required for this protein motor to function by the consilient mechanism, internal water molecules do exist. Accordingly, in our view, this fundamental protein motor that produces motion contains ample water as part of the structure in order to function in the competition for water between oil-like and vinegar-like groups, which competition expresses as a repulsion between these groups. 

Flow visualization is a branch of fluid mechanics that provides visual perception of the dynamic behavior of fluids flows. The fundamental principle of any flow visualization technique lies in the detection of fluid transport by altering the fluid properties while leaving the fluid motion unaltered. Microscale flow visualization focuses on imaging microfluidic flows, with the most common techniques broadly classified into particle-based and scalar-based methods. 

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