Sampling regions

Precisely controllable rf pulse generation is another essential component of the spectrometer. A short, high power radio frequency pulse, referred to as the B field, is used to simultaneously excite all nuclei at the T,arm or frequencies. The B field should ideally be uniform throughout the sample region and be on the order of 10 ]ls or less for the 90° pulse. The width, in Hertz, of the irradiated spectral window is equal to the reciprocal of the 360° pulse duration. This can be used to determine the limitations of the sweep width (SW) irradiated. For example, with a 90° hard pulse of 5 ]ls, one can observe a 50-kHz window a soft pulse of 50 ms irradiates a 5-Hz window. The primary requirements for rf transmitters are high power, fast switching, sharp pulses, variable power output, and accurate control of the phase. 

Fig. 5. Diffraction profile from (a) a single sHt and (c) many sHts. (b) The sampling region from many sHts.

The niobium-zirconium wire used remains superconducting at 4° K. even in the strong field of the solenoid itself. The unique feature of the new apparatus is the very high field homogeneity in the sample region (2 cm. diameter sphere) kept at room temperature (34). 

In addition to the effects discussed above, two further possible sources of discrimination peculiar to ion-molecule reactions must be considered. First, although it is known that most primary ions are formed without kinetic energy, such may not be the case for ions produced by ion molecule reactions. Secondary ions formed in exothermic ion-molecule reactions could retain a considerable fraction of the exo-thermicity as kinetic energy and diffuse from the sampling region at a rate considerably greater than predicted from the ambient temperature. The limited evidence to date (40) indicates that the kinetic energy of the product ions is small, but this may not be true for all types of reactions. 

Is it possible to stratify the sampling region in such a way as to reduce the spatial variations within strata ... 

It is only natural to consider ways that would allow us to use our knowledge of the whole distribution P0(AU), rather than its lew-AU tail only. The simplest strategy is to represent the probability distribution as an analytical function or a power-series expansion. This would necessarily involve adjustable parameters that could be determined primarily from our knowledge of the function in the well-sampled region. Once these parameters are known, we can evaluate the function over the whole domain of interest. In a way, this approach to modeling P0(AU) constitutes an extrapolation strategy. 

The sample size in a real simulation is always finite, and usually relatively small. Thus, understanding the error behavior in the finite-size sampling region is critical for free energy calculations based on molecular simulation. Despite the importance of finite sampling bias, it has received little attention from the community of molecular simulators. Consequently, we would like to emphasize the importance of finite sampling bias (accuracy) in this chapter. 

Joyner and Roberts (28) have gone further by constructing a sample cell, differentially pumped, within the spectrometer. Gas is leaked at a constant rate into the sample region. There is a small hole about 2 mm above the surface of the sample through which the electrons excited from the sample pass into the spectrometer. X-rays are directed at the surface through an aluminum window a second small opening is provided if exitation is by UV radiation. In this way the system pressure can be kept at 10-3 Pa while there is a steady pressure of 100 Pa above the sample. 

Recall that the image resolution, down and Across, is inversely proportional to the size of the region of Fourier space sampled, as given by 2, where An and Av are the sizes of the sides of the sampled region. The unambiguous scene size is inversely proportional to the Fourier space sampling frequency. 

When this procednre is followed, a different probability fnnction 7r (g) will be obtained over the sampled region. The correct PMF (i.e., for the biased potential) is related to the new probability fnnction according to... 

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