Spatial distribution, mass spectra

If all uncertainties like initial spatial distribution of NSs, their kick velocity distribution, characteristics of emission (atmospheric effects etc.), mass spectrum of NSs are fixed, then Log N - Log S distribution of close-by NSs can be a powerful tool to put constraints on models of thermal evolution of NSs. 

For the last two methods, there is the assumption that extraneous material from the chromatogram does not unduly and adversely affect the quality of the mass spectrum recorded. The chromatogram is placed, intact, within a source housing and a spatially resolved map of organic or bio-organic compounds distributed across the surface is measured. 

In typical DESI imaging experiments, the collected tissue sample is flash frozen in liquid nitrogen and subsequently cut in micron thin sections using a cryostat-microtome the thin tissue slices are thaw mounted onto glass microscope slides for analysis the ions generated by the DESI (Chapter 2) are transported fi om surfaces to the gas phase for mass analysis as the surface is being moved in order to cover the entire sample area a mass spectrum is acquired for each pixel on the surface and finally, tissue images are constructed to display the spatial intensity distribution of individual selected lipid ion. 

FIGURE 2.4 Two ions formed in different locations with respect to the backing plate, and the effects of spatial distributions on the mass spectrum. 

Such a discrete frequency spectrum can be obtained from the diagonalization of the dynamic matrix. We shall not go into the details here except to mention that the dynamic matrix is a 3V x 3N matrix formed by the mass weighted position fluctuations along the three spatial coordinates of each individual atom. However, if the spectrum is continuous, then the addition can be replaced by integration and a function describing the probability distribution of the frequencies of the spectmm appears. This new function is called the density of state (DOS) and the integration of this function over the whole frequency range is the total number of modes of vibration, 3N 6. 

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