Extended sampling

The equations of transfer do not incorporate time explicitly, but all local variations can be transformed into temporal variations via dt = dr / c, where c is the mean velocity of light in the scattering medium. As a consequence of scattering, the incident as well as the emitted photons show TOF dispersion in spatially extended samples. On diffuse... 

In bioanalysis, High-Performance Liquid Chromatography (HPLC) is the analytical technique most frequently used. Often, extended sample preparation is required to make a biological sample (the matrix) suitable for HPLC-analysis. The compound of interest, the analyte, has to be isolated from the matrix as selective and quantitative as possible. The quality of the sample preparation largely determines the quality of the total analysis procedure. In a survey Majors [2] showed that approximately 30% of an error generated during sample analysis was due to sample preparation, which indicates the need for error reduction and quality improvement in sample preparation. 

Figure 2. Schematic of the extrusion behavior of the JANAF specimen. The extended sample ( = 1.57) on the right shows a displacement of the oval markings through the jaw area (11)...

The first of the set is chlordane (Figure 2). In this case chlordane was collected primarily on the mixed-cellulose ester filter with about 10% collected on the sorbent. If the sampling device was only tested over the proposed sampling period, one hour in this case, vapor collected on the sorbent may not have been detected. Hence, extended sampling periods are necessary to realistically test collection efficiency of the individual sampling media in the train. Also, at higher temperatures and lower chlordane concentration, the fraction collected on the sorbent may be substantially increased. 

The results for the S-isomer are shown in Figure 5. The S-isomer was primarily found on the filter with a small fraction on the XAD-2 sorbent. Figure 6 shows the 0-isomer results. The XAD-2 sorbent collected the majority of this isomer. It also appeared that the material collected on the filter may be vapor since the curve levels out as in the heptachlor test. Thus, Demeton-0 probably has a higher vapor pressure than Demeton-S and this result is consistent with GC retention time data. These results demonstrate the value of testing proposed sampling devices with test atmospheres in detail and over extended sampling periods. 

We should also mention an early work by Slonimsky and Askadsky 74 who were apparently the first to observe structural changes taking place in extension under condition s of constant force. Three characteristic sections (see Fig. 20) were identified on the curves of strain versus tension time at F = const. These sections correspond to polymer flow in the amorphous state, the process of molecular ordering and crystallization, and, finally, to polymer flow in the crystalline state. The presence of crystalline formations on the latter section was detected with the help of X-ray-structural and electron-microscopic investigation of extended samples. As the tensile stress was lifted, the sample amorphised again and contracted. The occurrence of a drastic increase in strain on the second section was accounted for 74) by exhaustion of the longevity of supramolecular structures. 

The next option (it seems to be the only one left after Fig. 2a and Fig. 2b but see Fig. 2d) is a route that negotiates the probability ravine (free-energy barrier) presented by the two-phase region (Fig. 2c). The extended sampling tools we discuss in the next section are essential here with their refinement in recent years, this route has become increasingly attractive. 

It would be hard to write a definitive account of the development of extended sampling methods we will not attempt to do so. The seminal ideas are probably correctly attributed to Torrie and Valleau [22], who coined the terminology umbrella sampling. The huge literature of subsequent advances and rediscoveries may be rationalized a little by dividing it into two, according to how the macrostates to be weighted are defined. 

Extended sampling strategies utilizing this kind of representation appear in the literature with a variety of titles expanded ensemble [23], simulated tempering [24], and temperature scaling [25]. 

Realizations of this formalism go under the names adaptive umbrella sampling [26] and the multicanonical ensemble introduced by Berg and Neuhaus [27]. It seems right to attribute the recent revival in interest in extended sampling to the latter work. 

In Sections IV.C and IV.D we shall see that extended sampling strategies provide a rich variety of ways of tackling the phase coexistence problem, including the distinctive problems arising when one (or both) of the phases is of solid form. 

Viewed from the perspectives of configuration space provided by the caricature in Fig. 2, the most direct approach to the phase-coexistence problem calls for a full frontal assault on the ergodic barrier that separates the two phases. The extended sampling strategies discussed in Section III.C make that possible. The framework we need is a synthesis of Eqs. (10) and (32). We will refer to it generically as Extended Sampling Interface Traverse (ESIT). 

In contrast to canonical sampling distributions whose form can be written down [Eq. (1)] the Extended Sampling (ES) distributions discussed in Section III.C... 

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