Distributions of Fragments

From this it can be concluded that the wide distribution of fragment sizes from milhng is inherent in the breakage process itself and that attempts to improve grinding efficiency by weakening the particles will result in coarser fragments which may reqiiire a further break to reach the desired size. 

The cumulative probability distribution of fragments larger than length / is obtained from... 

Figure 8.20. Cumulative number distribution of fragments from four expanding ring experiments (10 fragments each) and comparison with one-dimensional theoretical distribution based on Poisson statistics.

The more common approach is the actual positioning of random lines on a surface to create a statistical distribution of fragment sizes. One example of this, suggested by Mott and Linfoot (1943), is a construction of randomly positioned and oriented infinite lines as illustrated in Fig. 8.23. If the random lines are restricted to horizontal or vertical orientation an analytic solution can be obtained for the cumulative fragment number (Mott and Linfoot,... 

In Baker (1978b), an analysis was made of 25 accidental vessel explosions to determine the mass and range distributions of fragments. Most of these results are presented here. Because data were limited, it was necessary to cluster like events into six groups in order to yield an adequate base for useful statistical analysis. Information on each group is presented in Table 9.9. The original table incorporated... 

Fig. 30. Schematic view of rupture and erosion of particles and the typical size distribution of fragments obtained.

Size distributions of fragments produced in a single rupture event are self-similar... 

Although the size distribution of fragments from heparinase (and hep-aranase) digests reflects the relative content of regular sequences 5 in different heparin preparations and fractions, these sequences may be quantitated only when the enzyme efficiency is high, and products are... 

After this first step, where some samples are eliminated because they are not suited to the protocol, the positive ion mode is used to investigate haem, an iron porphyrin which is a blood marker. Spectra taken of the haem reference show that it can be detected due to [M]+ and [M+H]+ ions (respectively, at m/z 616.2 and 617.2), and also due to a large distribution of fragment peaks between m/z 350 and m/z 550 (Figure 15.12a). The same spectrum has also been obtained for haemoglobin leading to the conclusion that the presence of protein does not disturb the detection of haem. 

Fragmentation Characteristics. As a manifestation of expl output fragmentation is characterized by velocity and size distribution of fragments. For some purposes, die size and shape of.fragments are predetermined either by preforming or by modifications of the case or chge design which predisposes it to break as desired... 

E. Low Panel Test. This test is similar to a certain extent to that described as item C. Here, four cylindrical quadrants of wooden panels surround the bomb at distances from it of 10, 20, 30 40 meters. Each panel is 7/8 thick, 12 wide and 5.57 ft high to simulate the size of a man. A bomb is detonated statically and the number of fragments passing thru the panels at different distances is counted and the distribution of fragments is recorded (Ref 1, p213)... 

F. Silhouette Test. In this test a bomb is dropped into the center of a series of wooden boards or panels arranged in open rectangular formation, 15 by 45 ft, and the number of fragments passing thru the panels is detd. The panels are of the same size as in the previous test. The number and distribution of fragments are recorded (Ref 1, p213)... 

In this chapter we present an analysis of recent advances in quantum and semiclasslcal theory concerned with the prediction of energy distributions of fragments formed by singlephoton photodissociation. Advances in experimental technique have resulted in significant progress in this field see Jackson and Okabe, this volume, and references (5-7). Hence, a theoretical state-to-state description of polyatomic photodissociation is of considerable interest. 

Figure 1. Schematic view of dynamical processes, associated time scales (see text), and observables. The first bottom panel displays a typical ionization cross-section, the second one a typical optical spectrum associated to Mie plasmon and the third one sketches a possible distribution of fragments. From [6].

When the efflux rate and the cleavage rate have a similar time scale we observe three peaks in the distribution of fragments (see Fig. 14.11b). Similar to what is observed experimentally [23], the third peak is much smaller than the other two, and the second peak is larger than the first peak. In our model, the first peak corresponding to the small fragments reflects an efficient cleavage mechanism where fragments are repeatedly cleaved before they are released from the CP. These rest ... 

In the present chapter, we describe how molecules respond to an ultra-short intense laser held by referring to our recent series of studies. In Sect. 1.2, we describe the experimental techniques - such as mass-resolved momentum imaging (MRMI) and coincidence momentum imaging (CMI) - that have been developed in order to measure the momentum distributions of fragment ions generated by the Coulomb explosions of molecules in intense laser helds. In Sect. 1.3, we show how the dynamics induced within CS2 by ultra-short intense laser helds is elucidated by the CMI method from momentum... 

As introduced in the previous section, we can extract the essential features of nuclear dynamics of molecules in intense laser fields from the momentum distributions of the respective fragment ion species. On the other hand, due to the presence of a number of different explosion pathways contributing simultaneously to the momentum distribution of fragment ions, the information for the respective fragmentation pathways can only be obtained after the simultaneous analysis of all of the observed MRMI maps of the fragment ions involved in the pathway, and a number of assumptions need to be introduced into the analysis. 

Since the covariance map is constructed based on one-dimensional TOF mass spectra, the angular distribution of fragment ions with respect to the laser polarization direction is only indirectly incorporated into the map through the momentum distribution along the TOF axis (see [19] for the extension to two-dimensional measurements). In order to derive three-dimensional momentum vector distributions of the fragment ions together... 

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